By considering the reflection, the coordinates of the reflected square D'E'F'G' are:
D'(0,1) , E'(0,6), F'(5,6) and G'(5,1)
What is square?A square is a two-dimensional geometric shape that has four equal sides and four right angles. It is a type of rectangle, but with all sides equal. The opposite sides of a square are parallel and of equal length. A square can be defined by its side length or by the coordinates of its vertices.
What is reflection?Reflection is a type of transformation in geometry in which a shape is flipped over a given line, called the line of reflection. The image that is created is a mirror image of the original shape. The line of reflection can be a horizontal line, a vertical line, or any line that is not parallel to the axes. Reflecting a shape over a line involves taking the coordinates of each point of the shape and applying a specific rule (such as multiplying or adding a constant) to the x or y coordinate, depending on the line of reflection. This rule is often simple and easy to apply, such as reflecting over x = 1. The reflected shape will be in the same plane as the original shape but with a different orientation or position.
When a square is reflected in the line x=1, each of the points on the square will have their x-coordinate replaced by 1 subtracted from their original x-coordinate.
The coordinates of the reflected square D'E'F'G' can be found by applying this rule to the original coordinates of square DEFG:
D(1,1) => D'(1-1,1) => D'(0,1)
E(1,6) => E'(1-1,6) => E'(0,6)
F(6,6) => F'(6-1,6) => F'(5,6)
G(6,1) => G'(6-1,1) => G'(5,1)
So the coordinates of the reflected square D'E'F'G' are:
D'(0,1) , E'(0,6), F'(5,6) and G'(5,1)
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Please help quickly! Due in 2 hours! 20pts
A line which is perpendicular to this line would have a slope of ___.
Write your answer as a whole number or simplified fraction or improper fraction (not a decimal or mixed number). Use a / for a fraction bar.
Answer:
1/2
Step-by-step explanation:
A line that is perpendicular to another has an opposite reciprocal slope. In this case, we can see that the slope of the given line is -2, so the perpendicular line would have a slope of 1/2.
Answer:
1/2
Step-by-step explanation:
The slope of a line perpendicular to any given line is the negative reciprocal of the given line's slope:
[tex]m_\perp = \dfrac{1}{m}[/tex]
In this problem, the slope of the given line is [tex]\dfrac{-2}{1}[/tex] (rise over run).
So, to find the slope of a line that is perpendicular to it, we simply flip the given line's slope and change its sign.
[tex]m_\perp = \dfrac{1}{2}[/tex]
So, a line which is perpendicular to the given line would have a slope of 1/2.
Find the measure of MN
Answer:
The measure of arcMN is 60°
Step-by-step explanation:
All the way around the circle is 360°. Two marked arcs are 100° and 140°. AngleMON and AngleNOP are marked equal, which means that ArcMN and ArcNP are also equal. So we can write an equation:
100+140 + x+x =360
combine like terms.
240 + 2x = 360
subtract 240.
2x = 120
divide by 2
x = 60
ArcMN is 60°
32(43x−23) is equivalent to
Answer:
1376x-736
Step-by-step explanation:
Take 32 and multiply it by 43. By multiplying vertically, distribute the multiplication of 3 (from 43) times both the 2 and 3 of 32 (right to left)
3 x 2=6; 3 x 3=9:
32
x
43
--------
96
Then, distribute the multiplication of 4 (from 43) times both the 2 and 3 of 32 (right to left) and leave a zero under the last number of your previous answer while moving the distribution of numbers forward.
4 x 2=8; 4 x 3=12
32
x
43
--------
96
+
1280 <----(this is the zero you must leave under your previous set)
After distributing each number of 43 to each number of 32 while multiplying, add your answers together vertically from right to left and bring down the x:
96
+
1280
----------
1376x
Now do the same for 32 x -23 after learning vertical multiplication to get -736
Your final answer put together is 1376x-736
Which expression is equivalent to 2x² 4 3x² 2x 7?
Given Expression is equivalent to 5x^2 - 2x + 3 With the Same Variable and exponent we have added or subtracted their constant value.
First, try to learn what is an expression.
Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4x+ 15, for instance, the terms 4x and 15 are separated from the variable x by the arithmetic sign +.
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The following components make into a mathematical expression:
Constant, Variables, Terms, Operators.
Given expression is (2x^2-4) - (-3x^2+2x-7)
let's Multiply - sign inside the bracket.
2x^2 - 4 + 3x^2 - 2x + 7
With the Same Variable and exponent and their constant value, we can perform mathematical operations like addition, multiplication, and subtraction.
2x^2 + 3x^2 = 5x^2
5x^2 - 2x + 3.
Given Question is incomplete complete question here.
Which expression is equivalent to
[tex](2x^2-4)-(-3x^2+2x-7)[/tex]
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Ella stacks two boards under a table to make it level. One board is inch thick. The
other board is inch thick. Which equation most closely estimates the thickness of
the two boards?
"Thickness of two boards = Thickness of first board + Thickness of second board" would be the closely estimated equation.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, separated by the 'equal' sign.
Define quadratic equation.x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
The thickness of the two boards together can be represented by the sum of the thickness of each individual board. Therefore, the equation that most closely estimates the thickness of the two boards stacked together is:
Thickness of two boards = Thickness of first board + Thickness of second board
So in this case, the equation would be:
Thickness of two boards = inch + inch
This equation gives the total thickness of two boards stacked together and it's the closest estimation.
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How do you calculate F G and G of f?
You will be calculate the function F(G) = f(g(x)) and G(F) = g(f(x)).
What is function ?
A function is a kind of rule that, for one input, it gives you one output. Image source: by Alex Federspiel. An example of this would be y=x2. If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.
Have given ,
Two functions , f(x) and g(x)
The composition of two functions g and f is the new function we get by performing f first, and then performing g. For example, if we let f be the function given by f(x) = x2 and let g be the function given by g(x) = x + 3, then the composition of g with f is called gf and is worked out as gf(x) = g(f(x)) .
So , You will be calculate the function F(G) = f(g(x)) and G(F) = g(f(x)).
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In an examination, Kavita obtained 72%marks.If the maximum marks are 650, find the marks obtained by Kavita.
Answer:468
Step-by-step explanation:cause of the max mark is 650 /100=6.5 (1%)
then 6.5*72=468
What is equal function with example?
The given two functions are said to be equal functions if and only if both it's domain and range are equal.
In mathematics we use functions to show the relation between two objects.
They are used in various aspects of real life. The domain of a function is known as all the possible input values which can be given to the function.
The range of the function is the set of all the possible outputs which can be obtained from a function. We also have co-domain of a function which can be defined as the set of outputs for a relation or function , it can be equal to the range.
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At what ordered pair will the function
f ( x ) = √ x + 2 - 2
begin on the coordinate plane?
( ? , ?)
Answer:(-2,-2)
Step-by-step explanation:
The radical has a value of 0 when x = -2. At that point, the function value is ...
f(-2) = √(-(-2)-2) -2 = √(0) -2
f(-2) = -2
write a paragraph defending, refuting, or qualifying William Wordsworth's claim about the value of nature. Use a quote from one of his poems to support your claim OR present one of the quotes as a counterargument, if you are refuting his claim.
Answer: William Wordsworth, a prominent figure in the Romantic movement, believed that nature had an immense value and could have a profound impact on the human spirit. In his poem "I Wandered Lonely as a Cloud," he wrote, "Nature never did betray the heart that loved her," which is a claim that nature is a constant source of comfort and inspiration. In this poem he praises nature and its ability to be a source of beauty and joy.
One could argue that Wordsworth's claim is true based on the evidence that nature can have a positive impact on mental and physical health. Studies have shown that spending time in nature can reduce stress, improve mood, and boost overall well-being. Additionally, nature can be a source of inspiration for many artists and poets, including Wordsworth himself, who drew inspiration from the natural world for his poetry.
On the other hand, one could argue that Wordsworth's claim is idealistic and may not apply to everyone or every situation. Some people may not find nature as comforting or inspiring, especially those who live in urban areas with limited access to natural spaces. Additionally, there are negative impacts of human activities on nature, such as pollution and deforestation, which can make it harder for some people to find value in nature.
Overall, while Wordsworth's claim that "Nature never did betray the heart that loved her" is a strong statement, and it holds true for many people, but it's a personal perspective that may not apply to everyone. Each individual has their own relationship with nature and it's not always a constant source of comfort, however, it's a treasure that we should take care of, respect and appreciate in order to achieve a better quality of life.
Step-by-step explanation:
The magnolia trees purchased for planting at the school are 3 feel tall. Research shows that these types of trees grow at a average of 3/4 per year.
I made a equation y=3/4x+3
Please help me determine the hight of the tree in 3 years!
Using the linear function given, the tree will have a height of 5.25 feet in 3 years
What is Linear FunctionLinear functions are mathematical functions where the output values are in direct proportion to the input values. A linear function has the form
y = mx + c, where m is the slope of the line and c is the y-intercept.
In this problem, the function given already models y = mx + c
Since y = 3/4x + 3;
The height of the tree in 3 years can be solved as;
y = 3/4(3) + 3
y = 9/4 + 3
y = 5.25
The height of the tree in 3 years is 5.25 feet
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can someone please help with this question i’ve been stuck on it for an hour thanks
Answer:
110° and 215°
Step-by-step explanation:
to measure the bearing from one point to another
the bearing is measured clockwise from a north line.
(a)
clockwise from the north line N at C to D is 110°
(b)
clockwise from the north line N at C to D is 215°
Last year there
were 620 7th grade
students. This year
enrollment has
increased by 105%.
How many 7th
grade students are
there this year?
Answer: 1271
Step-by-step explanation:
620 + (105% × 620) =
620 + 105% × 620 =
(1 + 105%) × 620 =
(100% + 105%) × 620 =
205% × 620 =
205 ÷ 100 × 620 =
205 × 620 ÷ 100 =
127,100 ÷ 100 =
1,271
Which system of equations is represented by the graph?
one parabola opening upwards and one parabola opening downwards intersecting at points (3, 9) and (-3, 9)
y = x2 + 3x
y = –x2 + x + 18
y = x2
y = –x2 +18
y = x2
y = x2 + 18
y = x2
y = –x2 – x – 18
Answer:
Blue: y = x²
Red: y = -x² + 18
Step-by-step explanation:
The blue parabola opens upwards, therefore the term in x² is positive.
The red parabola opens downwards, therefore the term in x² is negative.
The x-value of the vertices of both parabolas is x = 0.
Therefore, the equations of both parabolas will not have a term in x.
The y-intercept of the blue parabola is also the y-value its vertex: y = 0.
The y-intercept of the red parabola is also the y-value its vertex: y = 18.
Therefore, the equation for each parabola is:
Blue: y = x²Red: y = -x² + 18To check, substitute x = ±3 into both equations:
Blue
[tex]x=3 \implies y=(3)^2=9[/tex]
[tex]x=-3 \implies y=(-3)^2=9[/tex]
Red
[tex]x=3 \implies y=-(3)^2+18=9[/tex]
[tex]x=-3 \implies y=-(-3)^2+18=9[/tex]
Answer:
y = x2
y = –x2 +18
Step-by-step explanation:
I got it right on the test.
Mike has $21 to spend at the mall. He spends all of his money on bracelets for his sisters. Bracelets cost $3 each. How many bracelets dose he buy?
Answer:
7
Step-by-step explanation:
HELP!!! I WILL GIVE YOU 24 POINTS!!!THINK SMaRTER| Sense or Nonsense? . Emilio and Julia used different ways to find ‡ + 4. Emilio used a rodel to find the quotient. Julia used a related multiplication equation to find the quotient. Whose answer makes sense? Whose answer is nonsense? Explain your reasoning.
Answer:
24
Step-by-step explanation:
24 it's could be ok. I think 24 is good.
Answer: I think it's nonsense??? Not quite sure...
Step-by-step explanation:
(Car Sales) Of the cars sold during the month of July, 85 had air conditioning, 102 had automatic transmission, and 54 had power steering. 8 cars had all three of these extras. 24 cars had none of these extras. 25 cars had only air conditioning, 56 cars had only automatic transmissions, and 26 cars had only power steering. 11 cars had both automatic transmission and power steering. How many cars had exactly two of the given options
24 cars lacked power steering but did have air conditioning and an automatic gearbox.
According to the question,
No. of cars with Air conditioning = 88
No. of cars with Automatic transmission = 96
No. of cars with power steering = 76
All three = 4
None of these extras = 19
Only air conditioning = 23
Only automatic transmissions = 61
Only power steering = 28
Power steering and automatic transmission both = 11
The calculation for missing values:
11 - 4 = 7
96-61-4-7 = 24
88-24-4-23=37
It is obvious that 24 cars lacked power steering but did have air conditioning and an automatic gearbox.
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What is the smallest positive integer that is both a multiple of $7$ and a multiple of $4$?
The smallest positive integer that is both a multiple of 7 and a multiple of 4, is 28 .
How to find the smallest positive integer ?To find the smallest positive integer that is both a multiple of 7 and a multiple of 4, first find the multiples of both 4 and 7 to see which multiples are common between them and which are the lowest.
The multiples of 4 and 7 are:
Multiples of 4 :
4, 8, 12, 26, 20, 24, 28, 32, 36, 40,
Multiples of 7 :
7 , 14 , 21 , 28 , 35 , 42 , 49
The smallest positive integer that is both a multiple of 7 and a multiple of 4 is therefore 28.
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Select the correct answer. A figure shows a pyramid of height 3 h and a rectangular prism of height h. This pyramid has the same base as the prism, and its height is three times the height of the prism. What is the ratio of the volume of the pyramid to the volume of the prism? A. volume of pyramid volume of prism = 1 B. volume of pyramid volume of prism = 1 9 C. volume of pyramid volume of prism = 3 D. volume of pyramid volume of prism = 2 3 Reset Next
Answer:
Step-by-step explanation:
The ratio of the volume of the pyramid to the volume of the prism is 1.so, the option A. is correct.
Let the base of the base of a prism is b and the height of the prism is h.
so, the volume of the prism-
V= [tex]b^{2}[/tex] h
also, given that base of the given pyramid is also b and the height of the pyramid is three times the height of the prism.
h'=3h
so, the volume of the square pyramid-
V'=[tex]\frac{1}{3}[/tex][tex]b^{2}[/tex]h'
V'=[tex]\frac{1}{3}[/tex][tex]b^{2}[/tex](3h)
V'=[tex]b^{2}[/tex]h
so, now-
[tex]\frac{V'}{V}[/tex]=[tex]\frac{b^{2}h }{b^{2}h }[/tex]
[tex]\frac{V'}{V}[/tex]= 1
so. the ratio of the volume of the pyramid to the volume of the prism is 1.
Match each trig function with its corresponding trigonometric ratio.
Find Sin A, Sin B, Cos A, Cos B, Tan A, Tan B
The trigonometric ratios for the triangle in this problem are given as follows:
sin(A) = a/c.cos(A) = b/c.tan(A) = a/b.sin(B) = b/c.cos(B) = a/c.tan(B) = b/a.What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.The sides are connect by the right angle, of 90 degrees, while the hypotenuse is the straight line segment that connects the endpoints of each of the sides.
Then the trigonometric ratios presented on the bullet points are used for angles A and B in this problem.
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Evaluating Linear Functions
The value of linear equations are f(x) = -17 and f(x) = -73 .
What is linear equation ?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).
Equation with two variables of degree one is referred to as a linear equation with two variables. Formal expression: ax+by+c=0, where a, b, c R & a, b 0.
A)
f(x) = -2x + 7 when x = -12f (x) = -2*12 + 7
= -24 + 7
= -17
f(x) = 5x - 13 when x = -14f(x) = 5*-14 - 13
= -60 -13
= -73
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What should be added in the polynomial x³ 6x² 11x 8 so that it is completely divisible by X² 3x 2?
The number that should be added in the polynomial [tex]x^{3}-6x^{2} +11x+8[/tex] , so that it is completely divisible by [tex]x^{2} -3x+2[/tex] is -14 .
What are Polynomials ?
A polynomial is defined as a type of algebraic expression where the exponents of all the variables is a whole number.
The exponents of the variables in any polynomial is a non-negative integer. A polynomial consists of constants and variables.
the polynomial expression is ⇒ [tex]x^{2} -3x+2[/tex], which can be written in factor form as : [tex](x-1)(x-2)[/tex] ,
that means the polynomial is divisible by both x = 1 and x = 2 ;
So , on substituting [tex]x=1[/tex] in the polynomial [tex]x^{3}-6x^{2} +11x+8[/tex] ,
we get , [tex]1^{3}-6\times1^{2} +11\times 1+8[/tex] = 14 ;
on substituting [tex]x=2[/tex] in the polynomial [tex]x^{3}-6x^{2} +11x+8[/tex] ,
we get , [tex]2^{3}-6\times2^{2} +11\times 2+8[/tex] = 14 ;
So , the remainder is 14 .
Therefore , -14 should be added in the given polynomial .
The given question is incomplete , the complete question is
What should be added in the polynomial x³ -6x² +11x +8 so that it is completely divisible by x² -3x +2 ?
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Carl deposited $1220 in a bank that pays 9% interest, compounded monthly. Find the amount he will have at the end of 3 years.
a.
$3431.45
c.
$1549.40
b.
$1596.55
d.
$1334.44
The amount he will have at the end of 3 years is $1596.55.
Option B is the correct answer.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
P = $1220
r = 9%
n = 12
t = 3 years
Amount = P [tex](1 + r/n)^{nt}[/tex]
A = 1220 [tex](1 + 9/12)^{36}[/tex]
A = 1220 [tex](1 + 0.75)^{36}[/tex]
A = 1220 x [tex]1.75^{36}[/tex]
A = $1,596.55
Thus,
The amount after 3 years is $1596.55.
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Wenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows:
# of movies Frequency
0 4
1 9
2 5
3 6
4 1
a) Find the sample standard deviation, s. (Round your answer to two decimal places. )
b) Find the sample mean x^-
Answer: 35
Step-by-step explanation:
: i took this quiz before :)
PLS HELP!!!! Will give brainliest (multiple answers) 40PTS
Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weekly salary is $900. The following table shows the number of sales each salesman had during the first three weeks of this month.
Week 1 Week 2 Week 3
Salesman A 11 14 16
Salesman B 14 15 13
Salesman C 16 12 11
In which week(s), did Salesman C have a larger paycheck than both of the other salesmen? Select all that apply.
Week 3
None of the weeks.
Week 2
Week 1
Salesman C have a larger paycheck than both of the other salesmen in
None of the weeks.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Here, we have,
Salesman A works earns $65 per sale, with a maximum weekly commission of $1,300
Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale.
Salesman C does not earn any commission. His weekly salary is $900. Now we have that, A is getting $1300 commission,
and, salary of C is $900, he has no commission.
i.e. C can't earn more than A
Hence, Salesman C have a larger paycheck than both of the other salesmen in None of the weeks.
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The solution is Option D.
The week 1 is when Salesman C have a larger paycheck than both of the other salesmen and is given by the equation C = $ 900
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of sales be represented as x
Let the maximum weekly salary of Salesman C be = $ 900
Now , the weekly salary of Salesman A = $ 65x
where x is the number of sales
And , the weekly salary of Salesman B = $ 300 + $ 40x
Now , on week 1,
Salesman A made 11 sales
Substitute the value of x = 11 in the equation , we get
So , the salary of Salesman A on week 1 = 65 ( 11 )
On simplifying the equation , we get
The salary of Salesman A on week 1 = $ 715
And , Salesman B made 14 sales
Substitute the value of x = 14 in the equation , we get
The salary of Salesman B on week 1 = 300 + 40 ( 14 )
On simplifying the equation , we get
The salary of Salesman B on week 1 = 300 + 560
The salary of Salesman B on week 1 = $ 860
So , Salary of Salesman C on week 1 > salary of Salesman B on week 1 > salary of Salesman A on week 1
And , $ 900 > $ 860 > $ 715
Hence , the solution to the equation is week 1
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becky is doing research in which she needs 28 g of a substance that is 30% protein how many grams of each two ingredients one that is 50% protein in the other 25% protein should she mix together
Therefore, Becky must combine 25.6 grams of the second ingredient (25 percentage protein) with 2.4 grams of the first ingredient (50 percent protein) to create 28 grams of
Define percentage.A percentage (%) is a number that can alternatively be written as a decimal or fraction and represents a quantity as a proportion of 100. You can change a percentage to a fraction by putting 100 in the numerator and also the percentage number in the numerator.
Here,
Becky will need to blend several substances to obtain the necessary level of protein in order to generate 28 grams of a material that is 30% protein.
Let's name the first ingredient's percentage of protein (50%) "x" and the second ingredient's percentage of protein (25%) "y".
That which we are aware of is
28 grams of the combination are present in total.
It has 30% protein.
50% of the first component is protein.
25% protein makes up the second component.
To express the issue, we can build up the following equations:
x + y = 28 (the total amount of the mixture is 28 grams) (the total amount of the mixture is 28 grams)
(0.50)x + (0.25)y = 0.30(28) (the mixture is 30% protein)
Now we can use the first equation to solve for one variable in terms of the other. If we solve for y, we get:
y = 28 - x
We can substitute this into the second equation:
(0.50)x + (0.25)y = 0.30(28) (28) (30% of the mixture is protein)
We may now solve for one variable in terms of the other using the first equation. If we figure out y, we obtain:
y = 28 - x
This can be used as a substitution in the second equation:
(0.50)x + (0.25)(28-x) = 0.30(28) (28)
which results in:
0.50x + 7 - 0.25x = 8.4
And simplifying even more
0.25x = 0.6
x = 2.4
We now know that 2.4 grams of the combination are made up of the first component, which is 50% protein. Using this knowledge, we can calculate the quantity of the second ingredient:
y=28 - x=28 - 2.4=25.6 grams
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The sum of three consecutive integers is 27. Find the value of the greatest of the three.
Answer: The greatest of the three is 10.
Step-by-step explanation:
27/3=9 so the numbers will be around nine.
8+9+10=27
Answer:
Let x represent the value of the smallest of the three consecutive integers.
Then, the value of the middle integer is x+1, and the value of the greatest integer is x+2.
Since the sum of the three integers is 27, we have:
x + (x+1) + (x+2) = 27
Combining like terms, we have:
3x + 3 = 27
Subtracting 3 from both sides, we have:
3x = 24
Dividing both sides by 3, we have:
x = 8
Therefore, the value of the smallest integer is 8, the value of the middle integer is 8+1 = 9, and the value of the greatest integer is 8+2 = 10.
Thus, the value of the greatest integer is 10.
Step-by-step explanation:
What is the discriminant of the quadratic equation 2x 5x^2 1?
The discriminant of the quadratic equation 2x + 5x² = 1 is 24.
The discriminant of a quadratic equation is the value calculated from the coefficients of the quadratic equation and it gives information about the nature of the roots of the equation. The discriminant can be used to determine the number and type of solutions/roots of the equation.
-If the discriminant is greater than zero, the equation has two distinct, real solutions (or roots).
-If the discriminant is equal to zero, the equation has one real solution (or root).
-If the discriminant is less than zero, the equation has no real solutions (or roots), only complex solutions.
The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac.
Plug in the values and solve for the discriminant of the quadratic equation 2x + 5x² = 1.
b² - 4ac = (2)² - 4(5)(-1) = 24
Hence, the discriminant is 24.
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At what point does the graph of the linear equation 2x 3y =- 15?
The graph of the linear equation 2x - 3y = -15 is a line that passes through the point (-5, 5), and has a slope of 2/3.
The linear equation
2x - 3y = -15
can be written in the form
y = mx + b,
where m is the slope and b is the y-intercept. To find the slope of this equation, we can rearrange the equation to be in the form y = mx + b, which gives us
y = (2/3)x - 5.
This means that the slope of the line is 2/3. To find the y-intercept, we can plug in 0 for x and solve for y. This gives us
y = -5.
Therefore, the graph of this equation is a line that passes through the point (-5, 5) and has a slope of 2/3.
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the question in the picture below
Answer:
answer is option A
Step-by-step explanation:
2x+6≤10or2x+8>20
2x≤10-6 or 2x>12
x≤4/2 or x>2/12
x≤2 or x>6