Answers
Related Questions
Which of the following numbers is a factor of
63
6363?
Choose 1 answer:
Choose 1 answer:
(Choice A)
6
66
A
6
66
(Choice B)
3
33
B
3
33
(Choice C)
8
88
C
8
88
(Choice D)
2
22
D
2
2
Answers
The only number that is a factor of 63 and 6363 is option B: 3, while the other options are not factors
What is the scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
According to the given information:To determine which of the given numbers is a factor of 63 or 6363, we need to check if they divide the given numbers without leaving any remainder.
Option A: 6
63 ÷ 6 = 10 remainder 3
6363 ÷ 6 = 1060 remainder 3
Since both calculations leave a remainder of 3, 6 is not a factor of 63 or 6363.
Option B: 3
63 ÷ 3 = 21
6363 ÷ 3 = 2121
Since both calculations give a whole number without any remainder, 3 is a factor of 63 and 6363.
Option C: 8
63 ÷ 8 = 7 remainder 7
6363 ÷ 8 = 795 remainder 3
Since both calculations leave a remainder, 8 is not a factor of 63 or 6363.
Option D: 2
63 ÷ 2 = 31.5
6363 ÷ 2 = 3181.5
Since both calculations give a non-integer result, 2 is not a factor of 63 or 6363.
Therefore, the only number that is a factor of 63 and 6363 is option B: 3, while the other options are not factors
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Select THREE expressions that are equivalent
to 15x + 9y.
A. 15(x + 9y)
B. 3(5x + 3y)
C. 5(3x + 3y)
D. 9(15x + y)
E. 5x + 5x + 5x + 5y + 4y
F. x + 3x + 6x + 5x + y + 6y + y + y
Answers
ADF
Thats not the answer those are just my favorite letters
What is 6w-w to the cube root when w=288
Answers
6w - w = 6 * 288 - 288
Next, we simplify the expression inside the parentheses:
6 * 288 - 288 = 1728 - 288
Then, we subtract the two values to get the result:
1728 - 288 = 1440
Finally, we take the cube root of the result:
∛1440 ≈ 11.09 (rounded to two decimal places)
So, 6w - w to the cube root when w=288 is approximately equal to 11.09.
In 1995, 57. 5% of students at Gardiner university graduated in 4 or fewer years of study. In 2009, that number had fallen to 52. 8%. What was the rate of change for percent of students graduating within 4 years from 1995 to 2009.
Answers
The percent rate of change of students graduating within 4 years from 1995 to 2009 = 8.17%
Here, the percent of studenst graduated in 1995 = 57. 5%
and the percent of studenst graduated in 2009 = 52. 8%
First we find the relative change.
Let a represents the initial value and b represents the findal value
a = 57.5 and b = 52.8
so, the relative rate of change of students would be,
r = (b - a)/a
r = |(52.8 - 57.5)| / 57.5
r = 0.0817
And the percent rate of change of students graduating within 4 years from 1995 to 2009 would be,
p = r × 100
p = 0.0817 × 100
p = 8.17%
Therefore, the required percent is 8.17%
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Trapezoid ABCD undergoes the series of transformations listed to result in Trapezoid EFGH. Determine if Trapezoid EFGH is congruent to, an enlargement of, or a reduction of Trapezoid ABCD.
A
Translation down, followed by rotation of
90°
, followed by dilation by
a scale factor of 3.
congruent enlargement reduction B
Rotation of 45°
, followed by a reflection,
followed by a translation left.
congruent enlargement reduction C
Dilation by a scale factor of 12
,
followed by a translation up,
followed by a reflection.
congruent enlargement reduction D
Reflection, followed by a
dilation of a scale factor of 1,
followed by a rotation of 180°
.
congruent enlargement reduction
Answers
The correct answer is D. Trapezoid EFGH is congruent to Trapezoid ABCD after undergoing transformation D.
How to Determine if Trapezoid EFGH is congruent to, an enlargement of, or a reduction of Trapezoid ABCD.Let's first define the transformations:
A. Translation down, followed by rotation of 90°, followed by dilation by a scale factor of 3.
B. Rotation of 45°, followed by a reflection, followed by a translation left.
C. Dilation by a scale factor of 12, followed by a translation up, followed by a reflection.
D. Reflection, followed by a dilation of a scale factor of 1, followed by a rotation of 180°.
To determine if Trapezoid EFGH is congruent to, an enlargement of, or a reduction of Trapezoid ABCD, we need to analyze the effects of each transformation on the trapezoid.
A. Translation down, followed by rotation of 90°, followed by dilation by a scale factor of 3.
This transformation involves moving the trapezoid down, rotating it 90 degrees clockwise, and then increasing its size by a scale factor of 3. This transformation does not preserve angles or side lengths, so Trapezoid EFGH is not congruent to Trapezoid ABCD.
B. Rotation of 45°, followed by a reflection, followed by a translation left.
This transformation involves rotating the trapezoid 45 degrees clockwise, reflecting it across a line of reflection, and then moving it left. This transformation does not preserve angles or side lengths, so Trapezoid EFGH is not congruent to Trapezoid ABCD.
C. Dilation by a scale factor of 12, followed by a translation up, followed by a reflection.
This transformation involves increasing the size of the trapezoid by a scale factor of 12, moving it up, and then reflecting it across a line of reflection. This transformation does not preserve angles or side lengths, so Trapezoid EFGH is not congruent to Trapezoid ABCD.
D. Reflection, followed by a dilation of a scale factor of 1, followed by a rotation of 180°.
This transformation involves reflecting the trapezoid across a line of reflection, then increasing its size by a scale factor of 1 (i.e., not changing its size), and then rotating it 180 degrees. This transformation preserves angles and side lengths, so Trapezoid EFGH is congruent to Trapezoid ABCD.
Therefore, the correct answer is D. Trapezoid EFGH is congruent to Trapezoid ABCD after undergoing transformation D.
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A textbook store sold a combined total of 300 physics and biology textbooks in a week. The number of physics textbooks sold was 72 more than the number of biology textbooks sold. How many textbooks of each type were sold?
Answers
Hence, 186 physics textbooks and 114 biology textbooks were sold as it states that 300 textbooks were sold in total.
what is equation ?The formulas 2x + 3 and 7, for instance, are identical when written as 2x + 3 = 7, where x has been the variable. The x-value that fulfils the equality can be found by solving this equation. In this instance, we can take 3 out of both sides to get 2x = 4, and thereafter divide each sides by 2 to get x = 2. To describe relationships amongst quantities and to solve issues, equations are used widely in mathematics as well as in chemistry, chemistry, economics, and other sciences. They are also utilised in daily life, such as in financial computations and the solution of time, distance, and speed-related issues.
given
Assume that x biology textbooks were sold in total.
The issue states that there were 72 more physics textbooks sold than there were biology textbooks. Hence, x + 72 is the total number of physics textbooks sold.
It states that 300 textbooks were sold in total. Thus, we can create the following equation:
[tex]x + (x + 72) = 300[/tex]
When we simplify and find x, we obtain:
[tex]2x + 72 = 300\\2x = 300 - 72[/tex]
2x = 228
x = 114
Hence, 114 biology textbooks were sold.
The quantity of sold physics textbooks is given by x + 72, or 114 + 72 = 186.
Hence, 186 physics textbooks and 114 biology textbooks were sold as it states that 300 textbooks were sold in total.
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identify a syntax that sets the data type of the registerdate field to ""date"".
Answers
To set the data type of the registerdate field to "date", the syntax would depend on the programming language or database management system being used. However, here are some examples:
In SQL, the syntax would be:
ALTER TABLE tablename MODIFY COLUMN registerdate DATE;
This statement modifies the registerdate column in the tablename table to have a data type of DATE.
In PHP, the syntax for creating a table with a register date column of data type DATE would be:
CREATE TABLE tablename (
...,
registerdate DATE,
...
);
This creates a table called tablename with a column called registerdate of data type DATE.
In Python using SQLAlchemy, the syntax for defining a registerdate column of data type Date in a declarative base would be:
from sqlalchemy import Column, Date
class MyTable(Base):
__tablename__ = 'mytable'
registerdate = Column(Date)
This creates a MyTable class with a column called registerdate of data type Date.
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To set the data type of the registerdate field to "date", the syntax would depend on the specific programming language or database system being used. However, a common syntax to set the data type to "date" is:
registerdate DATE;
This syntax would typically be used in the creation of a table or the declaration of a variable in a programming language that supports date data types.
To identify a syntax that sets the data type of the 'registerdate' field to "date", you can use the following SQL statement:
```sql
CREATE TABLE your_table_name (
registerdate DATE
);
```
Here's a step-by-step explanation of the syntax:
1. "CREATE TABLE" is the command to create a new table in the database.
2. "your_table_name" should be replaced with the desired name for your table.
3. Within the parentheses, you define the columns and their data types.
4. "registerdate" is the name of the field that you want to set the data type for.
5. "DATE" is the data type you are setting for the 'registerdate' field.
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Simplify the expression.
−7+11+ (−3) + 9 =
Answers
Answer:
10
Step-by-step explanation:
Answer: Simple. The answer is 10.
Can someone help with this question????
Answers
Answer:
besides this pic nothing else can be done
1) Consider the quadratic function: f (x) = (x + 3)2 – 2 and a function, g(x), which is created by translating
f (x) three units to the right, two units up, and reflected vertically over the x-axis. Complete the following tasks:
a) 15 points: Graph f (x) on the axes below and label it. Graph g(x) on the axes below and label it.
b) 10 points: Write the vertex form equation for g(x) below.
Answers
The graph of both functions are in the image at the end, and the vertex of g(x) are (0, 0).
How to graph the function g(x)?Here we know that the function f(x) is:
f(x)= (x + 3)² - 2
And g(x) is a translation of 3 units to the right, 2 units up, and reflected over the x-axis, then we have:
g(x) = -[ f(x - 3) + 2]
Replacing f(x) we get:
g(x) = -[ (x + 3 - 3)² -2 + 2]
g(x) = -x²
The graphs of both functions are the ones in the image at the end, there we can see that the vertex of g(x) is (0, 0).
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What are 2 questions that would require an interpretation of the table?
Answers
1. What is the relationship between education level and income in this population? 2. How does the popularity of different music genres vary across different age groups?
What do you mean by an interpretation?An interpretation is a way of understanding or explaining something. Interpretation often involves making connections between different elements or pieces of information to create a coherent understanding. It can also involve applying theories, frameworks, or methods to analyze or explain a particular subject. Ultimately, interpretations are subjective and may vary based on individual experiences and perspectives, making it important to consider multiple interpretations when analyzing a particular subject.
Here is two example questions:
1. What is the relationship between education level and income in this population?
Interpretation: To answer this question, you would need to examine a table that includes columns for education level and income, such as a cross-tabulation or a summary statistics table. You could look for patterns or trends in the data, such as higher incomes being associated with higher levels of education. You might also look for any outliers or anomalies in the data that could be affecting the overall relationship between education level and income.
2. How does the popularity of different music genres vary across different age groups?
Interpretation: To answer this question, you would need to examine a table that includes rows for different age groups and columns for different music genres, such as a frequency table or a bar chart. You could look for patterns or trends in the data, such as certain music genres being more popular among younger age groups or older age groups. You might also look for any outliers or anomalies in the data that could be affecting the overall relationship between age and music genre popularity.
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8. Katie surveyed people at a grocery store. She wanted to find out which animals were their
favorite pets. She asked the people she surveyed which animal they thought was the least
expensive to feed. The results are shown in the bar graph below.
Favorite Animal for a Pet
Number of Votes
1
8
6
N
O
Dog
Cat
Lizard
Bird
Animals
Which statement explains why Katie asked the wrong question?
OFewer people have lizards and birds for pets.
O The favorite animal for a pet is also the least expensive animal to feed.
O The least expensive animal to feed may not be the favorite animal for a pet.
An animal that is less expensive to buy could also be the favorite animal for a pet.
(1 point)
Answers
The statement "The least expensive animal to feed may not be the favorite animal for a pet" explains why Katie asked the wrong question.
What is graphs?
Graphs are used by mathematicians to logically express or chart facts and values visually. A graph point typically depicts the relationship between several things.
While the cost of feeding an animal may be an important consideration for some people when choosing a pet, it is not necessarily the only or even the most important factor. Many people choose pets based on factors such as their personality, behavior, and the amount of attention and care they require.
Therefore, the animal that is least expensive to feed may not necessarily be the animal that people consider to be their favorite pet.
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Draw a dot plot (line plot) to show how many movies Shane watched in a four week period. (from weeks 1-4 he watched 2, 4, 0, and 5)
Answers
Answer:
The analysis is given below :
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Animal Pens
The animal shelter is building new animal playpens. They
use fencing to enclose an area shaped like a rectangle.
The design for one of the playpens is shown below. What
other playpens could be made with the same amount of
fencing?
8 ft
10 ft
80
10 ft
2. Be Efficient How much fencing is used for
the playpen design shown above? How do
you know? 20.2.2. MAI
Ion
3. Explain Leah says that a square playpen with sides that are 9 feet uses
the same amount of fencing. Is Leah's statement correct? Explain your thinking. 2022
4. Make Sense Describe one other playpen that could be made.
Answers
The total fencing used is 36 ft and the playpen would look like a square rather than a rectangle.
1) The given design uses 36 feet of fencing. Other playpens that could be made with the same amount of fencing are:
A square playpen with sides of length 9 feet (since 4 x 9 = 36)
A rectangular playpen with length 12 feet and width 6 feet (since 2 x (12 + 6) = 36)
2) The fencing used for the given design is the sum of the lengths of all four sides. From the diagram, we can see that the two shorter sides have a length of 8 feet each, and the two longer sides have a length of 10 feet each. Therefore, the total fencing used is:
2(8 ft) + 2(10 ft) = 16 ft + 20 ft = 36 ft
3) Leah's statement is not correct. A square playpen with sides of length 9 feet would require a perimeter of 4 x 9 = 36 feet, which is the same amount of fencing used for the given design. However, the shape of the playpen would be different, since the sides would all be equal in length. The playpen would look like a square rather than a rectangle.
4) Another playpen that could be made with the same amount of fencing is a rectangular playpen with length 18 feet and width 0 feet (i.e., a straight line). The perimeter would be:
2(18 ft) + 2(0 ft) = 36 ft
This playpen may not be practical for animals, but it satisfies the requirement of using 36 feet of fencing.
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Carol was packing up some of her old stuff into a box. A box can hold 2 pounds, but she only filled it up 1/2 full How much weight was in the box?
Answers
Answer:
1 pound
Step-by-step explanation:
If a box can hold 2 pounds but is only filled up 1/2 full, then there is only 1 pound of weight in the box.
To see why, consider that if the box was completely full, it would hold 2 pounds. But if it is only half full, it can only hold half of that amount, or 1 pound. Thus, the weight in the box is 1 pound.
Rewrite the expression as a product of four linear factors:
(12x² – 19x)² – 13(12x² – 19x) – 90
Answers
Answer:
(4x - 9)(3x + 2)(4x - 5)(3x - 1).
Step-by-step explanation:
Let's substitute y = (12x² - 19x):
So we have y² - 13y - 90, which can be factored as:
y² - 13y - 90 = (y - 18)(y + 5)
Substituting y back:
(12x² - 19x)² - 13(12x² - 19x) - 90 = [(12x² - 19x) - 18][(12x² - 19x) + 5]
= (12x² - 19x - 18)(12x² - 19x + 5)
= (4x - 9)(3x + 2)(4x - 5)(3x - 1)
Simplify. (3/4)^2= ?
Answers
Answer:
9/16.
Step-by-step explanation:
To simplify (3/4)^2, we simply need to square the numerator (3) and the denominator (4) separately, and then simplify the result:
(3/4)^2 = (3^2)/(4^2) = 9/16
Therefore, (3/4)^2 simplifies to 9/16.
Answer:
0.5625
Step-by-step explanation:
(3/4)²
9/16
0.5625
since critical values of t vary by sample size, before using the t table we must first calculate
Answers
Critical values of t, which are used for hypothesis testing and confidence interval calculations, vary depending on the sample size and the degrees of freedom.
b) degrees of freedom.
Degrees of freedom (df) are calculated based on the sample size and represent the number of independent pieces of information available in the data. It is an important parameter in determining the appropriate critical value to use from the t-distribution table. Therefore, before using the t-table, it is essential to calculate the degrees of freedom of the data set in question.
Options a, c, and d are not correct answers as they do not pertain to the calculation needed before using the t-table.
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Complete Question
Since critical values of t vary by sample size, before using the t table we must first calculate:
a) the Z score.
b) degrees of freedom.
c) the population standard deviation.
d) the sample size.
The degrees of freedom will then determine the critical values of t that should be used in calculating confidence intervals or conducting hypothesis tests. Therefore, it is important to consider the sample size when working with t statistics and using the t table.
To answer your question, before using the t-table, you must first calculate the degrees of freedom. The degrees of freedom are important as they determine the critical values of t based on your sample size. Here's a step-by-step explanation:
1. Obtain your sample data.
2. Determine the sample size (n) by counting the number of data points in your sample.
3. Calculate the degrees of freedom (df) by subtracting 1 from the sample size: df = n - 1.
4. Refer to the t-table with the calculated degrees of freedom to find the critical values of t for your desired level of confidence or significance.
By following these steps, you'll be able to find the appropriate critical values of t based on your sample size before using the t-table.
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If a sphere has a volume of 36π cubic inches, what is its radius?
radius = ___ inches
Answers
The radius of the sphere is approximately 3.634 inches.
We have,
The formula for the volume of a sphere is:
V = (4/3)πr³
where V is the volume of the sphere and r is its radius.
We know that the volume of the sphere is 36π cubic inches.
Substituting this value into the formula, we get:
36π = (4/3)πr³
Multiplying both sides by 3/4π, we get:
r³ = (36π)/(3/4π) = 48
Taking the cube root of both sides.
r = (48)^(1/3)
r = 3.634 inches (rounded to three decimal places)
Therefore,
The radius of the sphere is approximately 3.634 inches.
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SOMEONE PLS HELP ASAP
Answers
Answer:
10.12
Step-by-step explanation:
440=(x)(4x+3)
=10.11979...
Players A and B have a normal form game where each player chooses High or Low. If A and B both pick L, then they each get 3. If A picks Land B picks H, then A gets 9 and B gets 4. If they both pick H, then A gets 0 and B gets 6. If A picks Hand B picks L then they both get 5. In this game, A's best response to B choosing Lis while B's best response to A choosing Lis____ a. Н; Н b. H;L c. L;H
d. L;L
Answers
To find A's best response to B choosing L in normal form game, we can compare the payoffs for A choosing H and L when B chooses L.
If A chooses H and B chooses L, then A's payoff is 0 and B's payoff is 6.
If A chooses L and B chooses L, then A's payoff is 3 and B's payoff is 3.
Comparing the payoffs, we see that A gets a higher payoff if he chooses H when B chooses L. Therefore, A's best response to B choosing L is H.
To find B's best response to A choosing L, we can compare the payoffs for B choosing H and L when A chooses L.
If A chooses L and B chooses H, then A's payoff is 9 and B's payoff is 4.
If A chooses L and B chooses L, then A's payoff is 3 and B's payoff is 3.
Comparing the payoffs, we see that B gets a higher payoff if he chooses L when A chooses L. Therefore, B's best response to A choosing L is L.
So, the answer is (c) L;H. A's best response to B choosing L is H, and B's best response to A choosing L is L.
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3x - 24 > 54 solve the inequality?
Answers
1. Add 24 to both sides to isolate the variable term: 3x > 78
2. Divide both sides by 3 to solve for x: x > 26
Therefore, the solution to the inequality is x > 26.
There are 56 people at the party. Only 14
of them are wearing red. What percent of
people are NOT wearing red?
Answers
Answer: 75%
have a good day/night and crush that homework/class!! you are loved
brainliest??
Answer: 75%
Step-by-step explanation: 56 - 14 = 42. So, 42 people are not wearing red. 42/56 is .75, which is the decimal form for 75%. Also, if you simplify 42/56, you get 3/4 which is also 75%
(I NEED THIS ASAP)
5. A cylinder has radius 3 inches and height 5 inches. A cone has the same radius and height. (Lesson 5-13)
b. Find the volume of the cone.
c. What fraction of the cylinder's volume is the cone's volume?
Answers
Answer:
Step-by-step explanation:
V=15
fraction of cylinder volume is=22
When eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication. true or false
Answers
The statement "When eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication" is true because eliminating a loop-carried dependency that adds a constant simplifies the equation, but to obtain a closed-form direct solution, we need to express the result as a function of the current iteration's variables only
When eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication. This is because the loop-carried dependency adds a constant to the result of the previous iteration, which means that the current iteration's result is a function of both the current iteration's variables and the previous iteration's result.
By eliminating this dependency, we remove the need to use the previous iteration's result, which simplifies the equation. However, to obtain a closed-form direct solution, we need to express the result as a function of the current iteration's variables only, which often involves a multiplication. This is because multiplication is a fundamental mathematical operation that allows us to combine variables in a way that preserves their individual values.
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True. When eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication. This is because the loop-carried dependency is typically expressed as an addition, and removing it would result in a product of the loop index and the constant.
when eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication. This is because the process often involves applying mathematical transformations that result in multiplications to simplify the loop and eliminate dependencies.
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Find the surface area of the composite solid.
Answers
The surface area of the figure is derived to be equal to 656.4 square meters.
How to evaluate the surface area of a cylinderThe top of the figure is a triangular prism, the bottom is a triangle, and the sides are 3 same size rectangles, so the surface area is calculated as follows:
area of one top triangle face = 1/2 × 12 m × 5 m = 30 m²
area of top triangular prism = 3 × 30 m² = 90 m².
area of bottom triangle = 1/2 × 12 m × 10.4 m = 62.4 m²
area of one rectangle side = 14 m × 12 m = 168 m²
area of the three rectangle sides = 3 × 168 m² = 504 m²
surface area of the figure = 90 m² + 62.4 m² + 504 m²
surface area of the figure = 656.4 m².
Therefore, the surface area of the figure is derived to be equal to 656.4 square meters.
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URGENT! Will give brainliest :)
A line of best fit was drawn for 16 data points. What is the maximum number of these data points that mav not actually be on the line?
O A. 15
O B. 16
O C. 14
O D. 13
Answers
Answer:
The maximum number of data points that may not actually be on the line of best fit for 16 data points is 15 (Option A). This is because a line of best fit is an approximation of the relationship between the variables being studied, and it is unlikely that all data points will fall exactly on the line.
Step-by-step explanation:
To determine the line of best fit, a regression analysis can be performed. This involves finding the equation of the line that best represents the relationship between the variables. The line of best fit minimizes the distance between each data point and the line.
However, even with a perfect line of best fit, there may still be some data points that do not fall exactly on the line. This is due to natural variability in the data and measurement error.
Therefore, it is possible for all 16 data points to fall on the line of best fit, but it is more likely that some points will deviate slightly from the line. The maximum number of data points that may not actually be on the line is 15.
Listen
The length of a rectangle is given by the function 1(x) = 2x + 1, and the width of the rectangle is given by
function w(x) = x +4.
Which function defines the area of the rectangle?
Hint: A = 1- w
O a(z)=2x² + 9x +4
O a(z)=2x² + 5x +4
O a(z)=2-3
O a(z) = 3r+5
Answers
The correct function that defines the area of the rectangle is:
A(z) = 2[tex]x^{2}[/tex]+ 9x + 4 (option A).
HOW TO CALCULATE AREA OF THE RECTANGLE?The area of a rectangle is given by the product of its length and width. So, the function that defines the area of the rectangle would be:
A(x) = l(x) * w(x)
where l(x) is the length of the rectangle given by the function 1(x) = 2x + 1, and w(x) is the width of the rectangle given by the function w(x) = x + 4.
Substituting the given functions for length and width, we get:
A(x) = (2x + 1) * (x + 4)
Now, we can expand and simplify the expression:
A(x) = [tex]2x^2 + 8x + x + 4[/tex]
A(x) = [tex]2x^2 + 9x + 4[/tex]
So, the correct function that defines the area of the rectangle is:
A(z) =[tex]2x^2 + 9x + 4 ([/tex]option A).
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Katte is buying plants and soil for her garden. The soil cost $4
per bag, and the plants cost $10 each. She wants to buy at least
5 plants. She cannot spend more than $100. Write and graph a
system of linear inequalities to model all possible solutions to the situation.
Answers
Answer: Hi! Read the explanation below:
Brainliest?
Step-by-step explanation:
Let's use the variables x and y to represent the number of bags of soil and plants, respectively, that Katte will buy.
The cost of x bags of soil is $4x, and the cost of y plants is $10y. Therefore, the total cost of Katte's purchases is:
$4x + $10y
We want to make sure that she doesn't spend more than $100, so we can write:
$4x + $10y ≤ $100
We also want to make sure that she buys at least 5 plants, so we can write:
y ≥ 5
Finally, we want to make sure that both x and y are non-negative, since you can't buy negative bags of soil or plants. Therefore, we can write:
x ≥ 0
y ≥ 0
Putting it all together, the system of linear inequalities is:
4x + 10y ≤ 100
y ≥ 5
x ≥ 0
y ≥ 0
To graph this system, we can start by graphing the boundary lines for each inequality. The boundary for 4x + 10y ≤ 100 is the line 4x + 10y = 100, which we can graph by finding two points on the line:
When x = 0, we have 10y = 100, so y = 10. Therefore, one point on the line is (0, 10).
When y = 0, we have 4x = 100, so x = 25. Therefore, another point on the line is (25, 0).
Plotting these two points and connecting them with a line gives us the boundary for 4x + 10y ≤ 100:
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11 | o
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10 | o
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9 | o
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8 | o
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7 | o
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6 | o
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5 | o
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--------|-----------------------------
0 25
The boundary for y ≥ 5 is the horizontal line y = 5. We can graph this line by plotting two points on the line:
When x = 0, we have y = 5, so one point on the line is (0, 5).
When x = 100/4 = 25, we still have y = 5, so another point on the line is (25, 5).
Plotting these two points and connecting them with a line gives us the boundary for y ≥ 5:
lua
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5 |-----------------------
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--------|-----------------------------
0 25
Finally, the boundaries x ≥ 0 and y ≥ 0 are simply the x and y axes, respectively. We can graph them as:
diff
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0 25
Putting it all together, the graph of the system of linear inequalities looks like:
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11 | o
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10 | o
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9 | o
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8 | o
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7 | o
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6 | o
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5 | o----------------------
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Use the X method to find the solutions of
6x2 + 2x – 20 = 0.
x =
-5
-2
1
2
x =
-10/3
-4/3
2/3
5/3
Answers
The values of x using the X method are x = -2 and x = 5/3, or in decimal form: x = -2, x = -1.33, and x = 0.83.
PolynomialsUsing the X method:
Step 1: Multiply the coefficients of the first and last terms: 6 × (-20) = -120.Step 2: Find two factors of -120 that add up to the coefficient of the middle term, which is 2. The factors are 12 and -10.Step 3: Rewrite the middle term using the two factors: 6x^2 + 12x - 10x - 20 = 0.Step 4: Group the first two terms and the last two terms: (6x^2 + 12x) + (-10x - 20) = 0.Step 5: Factor out the GCF of each group: 6x(x + 2) - 10(x + 2) = 0.Step 6: Factor out the common binomial factor (x + 2): (x + 2)(6x - 10) = 0.Step 7: Solve for x:x + 2 = 0 or 6x - 10 = 0
x = -2 or x = 10/6 = 5/3
Therefore, the solutions are x = -2 and x = 5/3, or in decimal form: x = -2, x = -1.33, and x = 0.83.
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