The solution set of f(x) > 0 is x ∈ (-2, 8).
What is the set of the function?
To find the solution set of f(x) > 0, we need to first determine the critical values of x where f(x) changes sign.
Let's start by finding the domain of the function:
x² - 6x - 16 ≠ 0
We can solve for x by using the quadratic formula:
x = [6 ± √(6² + 4(16))]/2 = [6 ± √52]/2 = 3 ± √13
So the domain of f(x) is (-∞, 3 - √13) U (3 + √13, ∞).
Now let's factor the numerator and denominator of f(x):
f(x) = (x + 10)/[(x - 8)(x + 2)]
The critical points occur where the numerator or denominator of f(x) changes sign.
The numerator changes sign at x = -10, and the denominator changes sign at x = -2 and x = 8.
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Please hurry due today I will give you brainlest if correct
what are the steps for using a compass and straightedge to construct a line through point A that is parallel to line j? Drag the steps and drop them in order from start to finish.
1. place the point of the compass on point Q and open it to width QR
2. use the straightedge to draw AB-->.
3. Use the straightedge to draw a line k that passes through A and intersects line j. label the point A and draw an arc that intersects line k. Label the intersection as point S.
4. With the compass opening set to width QR, place the point of the compass on point S and draw an arc that intersects the arc that was drawn from point A. Lab the intersection of the arcs as point B. 5. Place the point of the compass on the point P and draw an arc that intersects lines j and k. label the intersections as points Q and R
Answer:
1. Place the point of the compass on point Q and open it to width QR.
2.Place the point of the compass on the point P and draw an arc that intersects lines j and k. Label the intersections as points Q and R.
3.Use the straightedge to draw a line k that passes through A and intersects line j. Label the point A and draw an arc that intersects line k. Label the intersection as point S.
4. With the compass opening set to width QR, place the point of the compass on point S and draw an arc that intersects the arc that was drawn from point A. Label the intersection of the arcs as point B.
5. Use the straightedge to draw AB -->.
Step-by-step explanation:
Select all the expressions that have the same value. a \large 3^3 b \large 3^4 c \large 6^2 d \large 6^3 e \large 9^2 f \large 9^3
The expressions that have the same value are: b) 3^4 = 81 and e) 9^2 = 81
Selecting all expressions that have the same value.To compare the expressions, we can simplify them using the rules of exponents:
a) 3^3 = 27
b) 3^4 = 81
c) 6^2 = 36
d) 6^3 = 216
e) 9^2 = 81
f) 9^3 = 729
Using the above as a guide, we have the following:
Therefore, the expressions that have the same value are: b) 3^4 = 81 and e) 9^2 = 81
So, options b and e have the same value.
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which diagram represents the expression |-5|
f(x) = - 2x ^ 2
g(x) = x - 3
h(x) = 2f(x) - g(x)
Find h (-1).
The indicated value h(-1) has a value of 0 when evaluated
Find the indicated value of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = - 2x ^ 2
g(x) = x - 3
h(x) = 2f(x) - g(x)
The indicated value of the function is
h(-1)
This means that
h(-1) = 2f(-1) - g(-1)
Calculate g(-1)
So, we have
g(-1) = -1 - 3
g(-1) = -4
Calculate f(-1)
So, we have
f(-1) = -2 * (-1)^2
f(-1) = -2
Recall that
h(-1) = 2f(-1) - g(-1)
Substitute the known values in the above equation, so, we have the following representation
h(-1) = 2 * -2 + 4
Evaluate
h(-1) = 0
Hence, the value is 0
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21) Kinzang is 1.49 m tall. He was 0.53 m at birth. How much did he grow?
Kinzang grew 0.96 meters.
We have,
To find how much Kinzang grew, we need to subtract his height at birth from his current height:
Height Kinzang grew = Current height - Height at birth
Height Kinzang grew = 1.49 m - 0.53 m = 0.96 m
Therefore,
Kinzang grew 0.96 meters.
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shayla is buying a birthday present for her mother. she decides to buy a bracelel for 20$. the sales tax is 6%. what is the total cost of the bracelet.
The total cost of the bracelet after tax cost addition would be = $21.2
How to calculate the total cost of bracelet?The initial cost of the bracelet = 20$
The percentage of tax = 6%
The cost of tax = 6/100 ×20/1 = $1.2
The total cost of the bracelet after the addition of tax would be = 20+1.2 = $21.2
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How many different words consisting of four different letters a,b,c,d,e,p that do not start with the letter p and do not end with the letter b and include the letters c,e
7(-6)+7(-1/8) answer
Answer:
[tex]\displaystyle -42 \;\frac{7}{8}[/tex]
Step-by-step explanation:
We will simplify this expression.
Given:
7(-6)+7(-1/8)
Multiply:
[tex]\displaystyle -42- \frac{7}{8}[/tex]
Subtract:
[tex]\displaystyle -42 \;\frac{7}{8}[/tex]
Match the equation or expression to the number of terms, the coefficients and the constants.
Equation: [tex]6xt^4yz^3 + 10a = 1[/tex]. Number of terms: 2, Coefficients: 6, 10 and Constants: 1.
Equation: [tex]25abc^2ab + 3ac6bc + 25[/tex], Number of terms: 3. Coefficients: 25, 3, 6. Constants: 25
What is equation and an expression?
A random combination of integers, variables, functions, etc. can be described as an expression. An expression is, for instance, 3x - 2. An equation, on the other hand, is created when two independent expressions are joined by the equal to sign. An equation, for instance, is when 3x - 2 = 5 + x.
Equation/Expression: 6xt⁴yz³ + 10a = 1
Number of terms: 2
Coefficients: 6, 10
Constants: 1
Equation/Expression: 25abc²ab + 3ac6bc + 25
Number of terms: 3
Coefficients: 25, 3, 6
Constants: 25
Equation/Expression: 25y³xy + 5 = 100
Number of terms: 2
Coefficients: 25, 1
Constants: 5, 100
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In a survey 7 out of 8 people preferred cooking to washing dishes what percentage of the people surveyed preferred cooking
The percentage of the people that preferred cooking who where surveyed would be = 87.2%
How to calculate the percentage of people who preferred cooking?The total number of people surveyed = 8
The total number of people that preferred cooking = 7
The percentage of people that preferred cooking;
= 7/8×100/1
= 700/8
= 87.2%
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Find the surface area of the rectangular prism.
Answer:
40
Step-by-step explanation:
Hope this helps! =D
Brainliest! =D
What is the area of this quadrilateral?
4 cm
4 cm
3 cm
A. 20 square centimeters
B. 28 square centimeters
C. 22 square centimeters
D. 14 square centimeters
Answer:
28
Step-by-step explanation:
you first do the 4x4=16 then 4x3=12 then do 16+12=28
A right rectangular prism had a length 2 1/2yd, width 3 1/2yd, and height 1 1/2yd. You use cubes with fractional edge length 1/2yd to find the volume. How many cubes are there for each of the length, width, and height of the prism? Find the volume.
The volume of the rectangular prism is 13.125 cubic yards.
Calculating the number of cubes and the volumeTo find the number of cubes that fit along the length, width, and height of the rectangular prism, we need to divide the length, width, and height by the edge length of each cube, which is 1/2yd.
Along the length: (2 1/2 yd) / (1/2 yd) = 5 cubes
Along the width: (3 1/2 yd) / (1/2 yd) = 7 cubes
Along the height: (1 1/2 yd) / (1/2 yd) = 3 cubes
Therefore, there are 5 cubes along the length, 7 cubes along the width, and 3 cubes along the height of the rectangular prism.
To find the volume of the rectangular prism, we can multiply the length, width, and height:
Volume = (2 1/2 yd) x (3 1/2 yd) x (1 1/2 yd)
Volume = (5/2 yd) x (7/2 yd) x (3/2 yd)
Volume = (13.125 yd^3)
Therefore, the volume of the rectangular prism is 13.125 cubic yards.
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what is 5.25 in fraction form?
Answer:
To convert 5.25 to a fraction, we can first note that the decimal represents the number 5 units and 25 hundredths. We can write this as:
5.25 = 5 + 0.25
Next, we can convert the decimal 0.25 to a fraction by recognizing that it is equivalent to 25/100 or 1/4. Therefore:
5.25 = 5 + 1/4
We can then combine the whole number 5 with the fraction 1/4 by finding a common denominator:
5 + 1/4 = 20/4 + 1/4 = 21/4
Therefore, 5.25 as a fraction in simplest form is 21/4.
Answer:
i believe it should be
5 1/4
i apologize if wrong, it depends on the ratio (you didnt include it)
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Using the following set of data, calculate the lower quartile, the upper quartile, and the interquartile range.
20, 22, 25, 28, 29, 30, 32, 33, 34
Be sure to show your work for finding:
the lower quartile
the upper quartile
the interquartile range
Answer:
To find the lower and upper quartiles and the interquartile range, we first need to order the data from smallest to largest:
20, 22, 25, 28, 29, 30, 32, 33, 34
Next, we find the median (middle value) of the entire dataset:
Median = (29 + 30) / 2 = 29.5
This median value divides the data into two halves. We then find the median of the lower half of the data, which includes all values less than or equal to 29.5:
Lower half: 20, 22, 25, 28, 29
Median of lower half = (25 + 28) / 2 = 26.5
This value, 26.5, is the lower quartile (Q1).
Similarly, we find the median of the upper half of the data, which includes all values greater than or equal to 29.5:
Upper half: 30, 32, 33, 34
Median of upper half = (32 + 33) / 2 = 32.5
This value, 32.5, is the upper quartile (Q3).
Finally, we can calculate the interquartile range (IQR) as the difference between the upper and lower quartiles:
IQR = Q3 - Q1 = 32.5 - 26.5 = 6
Therefore, the lower quartile is 26.5, the upper quartile is 32.5, and the interquartile range is 6.
Write an equation of the form y = mx for the line shown below.
Answer:
y = (5/3)x + 2/3
Step-by-step explanation:
find slope
rise/run
(4--1)/(2--1)
(5)/(3)
M = 5/3
then plug in a point to get the y-intercept
4 = (5/3) * 2 + b
4 = 10/3 + b
subtract 10/3 on both sides
2/3 = b
in y =mx +b the equation is
y = (5/3)x + 2/3
What is the result when the number 59 is decreased by 3.9%? 59
Answer:
Step-by-step explanation:
To find the result when the number 59 is decreased by 3.9%, we need to first calculate what 3.9% of 59 is.
To do this, we can multiply 59 by 3.9% (or 0.039), which gives us:
59 x 0.039 = 2.301
This tells us that 3.9% of 59 is 2.301.
Next, we need to subtract 2.301 from 59 to get the final result:
59 - 2.301 = 56.699
Therefore, the result when the number 59 is decreased by 3.9% is 56.699. we could say that if you take 3.9% of 59 and subtract that amount from 59, the answer is 56.699.
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Question # 6 Multiple Choice Which of the following minerals is made of more than one element? Responses copper silver gold hornblende
Out of the following minerals hornblende is made up of more than one element. Therefore, option D is the correct answer.
What are minerals?Solid, naturally occurring materials known as minerals have a particular chemical makeup and crystal structure. They can be discovered in rocks, soil, and water and are primarily created by geological processes. Minerals are crucial for our bodies' nutritional needs as well as for the construction of structures and the manufacture of electronics, among other facets of our daily life.
Hornblende is a mineral made up of multiple elements, including calcium, magnesium, iron, aluminum, silicon, and sometimes sodium and potassium. The other minerals listed, copper, silver, and gold, are each made up of a single element.
Therefore, the correct option is d. Hornblende
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Solve the systems of equations shown below.
2x- 6y = -12
X + 2y = 14
Many fences in a rectangular area for his dog to play in the backyard. The area measures 35 yards by 45 yards .What is the length of fence that Manny uses a) 1,575 yards b) 160 yards c) 80 yards d) 35 yards
On solving the provided question we can say that Manny would thus require 160 yards of fencing to surround the rectangular plot.
What is perimeter?A boundary is a closed route that embraces, encircles, or delimits a two-dimensional form or length in one dimension. The perimeter of a circle or an ellipse is its outermost section. The perimeter calculation is used in a variety of real-world situations. The perimeter of a form is the radius of its edge. Discover how to calculate the perimeter by adding the lengths of the sides of various shapes. The perimeter of a shape may always be calculated by multiplying the lengths of its sides. The perimeter of a thing is the region that surrounds it. At your house, one example is an enclosed garden. The distance around anything is referred to as its perimeter. A 200-foot fence will be required for a 50-foot-by-50-foot yard.
P = 2(l + w), where l is the length and w is the width, gives the perimeter of a rectangle.
The length in this example is 35 yards, while the breadth is 45 yards. So,
[tex]P = 2(35 + 45)\\= 2(80)\\= 160 yards\\[/tex]
Manny would thus require 160 yards of fencing to surround the rectangular plot.
As a result, option (b) 160 yards is the right answer.
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15 POINTS!!!! PLEASE, I'M BEGGING. 15 POINTS!!!!
Which investment choice has the potential for the greatest rate of return?
Corporate bonds
Government bonds
Common stocks
Preferred stocks
Answer:
mark me as brainliest
Step-by-step explanation:
common stocks
find the values of variables, then find the lengths of the sides of each quadrilateral
or
Last night, Clara and her brother, Stefan, made personal pizzas for dinner. Clara put 4 pepperoni pieces and 6 ham pieces on her pizza. Stefan put 6 pepperoni pieces and 10 ham pieces on his pizza. Did Clara's and Stefan's pizzas have the same ratio of pepperoni pieces to ham pieces?
Clara's and Stefan's pizzas did not have the same ratio of pepperoni pieces to ham pieces.
How to calculate the ratios of two different pizza?For Clara,
The number of pepperoni pieces = 4
The number of ham pieces = 6
The ratio = 4:6 = 2:3
For Stefan,
The number of pepperoni piece = 6
The number of ham piece = 10
The ratio = 6:10 = 3:5
Therefore the ratio of Clara's and Stefan's pizzas is not the same.
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What is the greatest common factor of the polynomial below?
12x²9x
OA. 4x
OB. 3x
OC. 4x²
OD. 3x²
The greatest common factor (GCF) of the polynomial 12x²9x is 3x, therefore option B is correct.
How to Find the Greatest Common Factor of a Polynomial?The Greatest Common Factor (GCF) of a polynomial is the largest factor that all of the terms in the polynomial have in common.
To find the GCF, we need to find the largest factor that both terms have in common. Both terms have a factor of 3x, so that is the greatest common factor. Factoring out 3x from each term gives:
12x²9x = 3x(4x)3(3x) = 3x(4x3)
So the GCF of 12x²9x is 3x.
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Help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The calculated value of the perimeter of triangle ABD is 48 units.
Calculating the perimeter of the triangle ABDGiven that
A(1, 1), B(17, 1) and D(17, 13)
To find the perimeter of triangle ABD, we need to find the lengths of its three sides and add them up.
We can use the distance formula to find the lengths of the sides.
The distance between points A and B is:
AB = √((17 - 1)^2 + (1 - 1)^2) = √(256) = 16
The distance between points B and D is:
BD = √((17 - 17)^2 + (13 - 1)^2) = √(144) = 12
The distance between points D and A is:
DA = √((1 - 17)^2 + (1 - 13)^2) = √(256 + 144) = √(400) = 20
Therefore, the perimeter of triangle ABD is:
AB + BD + DA = 16 + 12 + 20 = 48
So, the perimeter of triangle ABD is 48 units.
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It is equally probable that the pointer on the spinner
shown will land on any one of the eight regions,
numbered 1 through 8. If the pointer lands on
a borderline, spin again. Find the probability that the
pointer will stop on an even number or a number less
than six
Answer: the answer is 4
Step-by-step explanation: good luck
Carole surveyed the class for a math project. Below are the results of her survey. What type of graph is best for Carole to display her data? A. bar graph B. line graph C. histogram D. circle graph
Answer:
A
Step-by-step explanation:
it is a bar graph because it involves class interval
Richard is saving money for a down payment on a car. He opens a savings account at his local bank and deposits $500. He models his savings plan with the equation y = 200x + 500 based on his current monthly savings rate.
Here the correct statements can be
The y-intercept represents D) the starting amount in his savings account.
The slope represents C) the change in the dependent variable with respect to the independent variable.
What is meant by y-intercept?
The y-intercept is the point where a line intersects the y-axis on a graph. It represents the value of the dependent variable when the independent variable is zero.
What is meant by the term slope?
The slope is a measure of the steepness of a line on a graph. It is calculated by dividing the change in the y-coordinate by the change in the x-coordinate between two points on the line.
According to the information
The y-intercept of the linear model y = 200x + 500 represents the starting amount in Richard's savings account.
The slope of the linear model y = 200x + 500 represents the change in the dependent variable (y, the savings amount) with respect to the independent variable (x, the number of months). Specifically, the slope of 200 means that for every additional month, Richard's savings will increase by $200.
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Find the mean of the data set:
87,79,92,71,88,70,91,82,85
Round your answer to the nearest tenth.
Provide your answer below:
The mean of the data set is 82.77
How to calculate the mean of the data set?If we want to find the mean, we would have to put it at the back of our minds that the mean is the same as the average. As such, we would have to take the sum of all the values that have been listed in the data set and divide by the total number of the data.
The first step is to arrange the data set orderly from smallest to largest;
70, 71,79, 82,88,85,87,91,92
We have nine values in the data set thus the mean is;
70+71+79+82+88+85+87+91+92/9= 745/9= 82.77
Hence the mean of the data set is 82.77
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Question in attachment...................
Answer:
12.5ft tall.
Step-by-step explanation:
The volume of a rectangular box is V = L x W x H
We are given volume, length, and width, allowing us to solve for height.
3000 ft^3 = 96 ft x 2.5 ft x H ft
Divide both sides by 96 x 2.5 to isolate H
3000 / (96 x 2.5) = H
H = 12.5 ft.
Answer:
12.5 feetStep-by-step explanation:
It's given that One of the first electronic computer was in the shape of a huge box. It was 96 m long and 2.5 m wide.
Length of the box = 96 feet
Breadth of the box = 2.5 feet
Also The amount of space inside was approximately 3,000 cubic feet i.e volume of the box is 3000 ft³.
We know that volume of cuboid is calculated by,
Volume = l × b × h96 × 2.5 × h = 3000
240 × h = 3000
h = 3000/240
h = 12.5 feet
Therefore, Height of the computer is 12.5 feet