Answers
After the vertical stretch by factor 3 the function becomes g(x)=3x².
The given function is f(x)=x² is vertically stretched by the factor 3.
When we stretch a function vertically, we multiply the base function by its scale factor. Hence, we have g(x) = 3·f(x). Let’s make sure to distribute 3 to each of the term in f(x).
Here, g(x)=3×x²
g(x)=3x²
Therefore, after the vertical stretch by factor 3 the function becomes g(x)=3x².
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Related Questions
The ratio of the speeds of pulleys is inversely proportional to the ratio of their diameters. The speed reduction required on a pulley and belt drive is 4 to 1. If the drive is 4 inches in diameter, what size would be required for the driven pulley?
Answers
1 inch is the diameter of the driven pulley.
Let's use D to represent the driven pulley's diameter. The speed decrease needed, according to the issue description, is a 4 to 1 reduction.
This implies that the ratio of the diameters is also 4 to 1, as the speeds are inversely proportional to the diameters:
D/4 = 1/4
Multiplying both sides by 4 gives:
D = 1
Therefore, the diameter of the driven pulley should be 1 inch.
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If you were to graph 9x + 5y > 1 , where would you shade according to the slope of the line? The shading would occur above the solid line of the slope The shading would occur below the solid line of the slope. The shading would occur below the dashed line of the slope. The shading would occur above the dashed line of the slope.
Answers
The requried shading would occur above the solid line of the slope.
To graph the inequality 9x + 5y > 1, we first need to graph the equation 9x + 5y = 1, which is the equation of the line that separates the two regions determined by the inequality.
To graph this line, we can solve for y in terms of x:
9x + 5y = 1
y = (-9/5)x + 1/5
This is the equation of a line with slope -9/5 and y-intercept 1/5. We can plot this line on a coordinated plane. Since the slope of the line is negative, the shading should occur above the line, which means the correct answer is: The shading would occur above the solid line of the slope.
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_
5
Given f(x)=x+7, if f(x) = -13, find x.
2
Helpp
Answers
Answer: -20
Step-by-step explanation: I got negative twenty because if f(x) equals negative thirteen the we add negative seven because we need to flip the sign since it is negative and when you add you get negative twenty
To check, simply solve the eqation the way it first was, for example, f(x)=-20+7 which would be correct, equaling -13
Hopefully this helped, I' sorry if i am wrong
When graphing equations on paper we must show the x andy axis, numbers for these axis and the points for the
graph
True
False
Answers
Can someone help me please
Applying the Solution to a 3X3 System
At a family reunion, there only blood relatives, consisting of children, parents, and grandparents, in attendance. There were 400 people total. There were twice as many parents as grandparents, and 50 more children than parents. How many children, parents, and Grandparents were in attendance?
Show up all steps please
Answers
There are 70 grandparents, 140 parents, and 190 children in attendance at the family reunion
Given data ,
Let's denote the number of grandparents as "g", the number of parents as "p", and the number of children as "c".
Given that there were 400 people total at the family reunion, we can write the equation:
g + p + c = 400
Now , there were twice as many parents as grandparents, so we can write:
p = 2g
And we are given that there were 50 more children than parents, so we can write:
c = p + 50
Now we can use the equations (1), (2), and (3) to solve for the values of g, p, and c.
On simplifying the equation , we get
g + 2g + (2g + 50) = 400
5g + 50 = 400
5g = 400 - 50
5g = 350
g = 350 / 5
g = 70
Now we can substitute the value of g into (2) to find the value of p:
p = 2g = 2 x 70 = 140
And we can substitute the value of p into (3) to find the value of c:
c = p + 50 = 140 + 50 = 190
Hence , there were 70 grandparents, 140 parents, and 190 children in attendance at the family reunion
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In a factory, a sample of 40 light bulbs was selected from a box of 1,000 light bulbs. In the sample, 2 light bulbs would not work. Based on this sample, how many non-working light bulbs would be expected in the group of 1,000 light bulbs?
Answers
The number of non-working light bulbs that would be expected in the group of 1,000 light bulbs is: 50 bulbs
How to find the probability of selection?In survey sampling, the term probability of selection is one that refers to the chance (i.e. the probability from 0 to 1) that a member (element) of a population can be chosen for a given survey.
We are told that a sample of 40 bulbs were picked from a box of 1000 bulbs and it was discovered that 2 of the bulbs were not working. Thus:
Fraction of bulbs not working = 2/40 = 0.05
Thus, number of bulbs not working in a sample of 1000 bulbs is:
0.05 * 1000 = 50 bulbs
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Which table represents the function? Pls help me
Answers
A linear equation is an equation in which each term has at max one degree. The table that represents a linear function is Table 1. Thus, the correct option is A.
We have,
A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c
Linear equation with two variables, when graphed on a cartesian plane with axes of those variables, give a straight line.
For the table to represent a linear function, the function must have a constant slope between any two points.
For the first table, the slope between the first two points is,
m = (7-3)/(2-1) = 4
The slope between the last two points is,
m = (15-11)/(4-3)
Hence, the table that represents a linear function is Table 1. Thus, the correct option is A.
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18 plus what equals 54
Answers
Answer:
Step-by-step explanation:
54 - 18 = 36
so...
18 + 36 = 54
i-Ready
Dilations and Similarity-Quiz-Level H
Rays are shown from point D, the center of dilation, through the vertices of AABC.
Dilate ABC by a scale factor of 3.
A
1
C
D
B
1
Answers
Based on the information provided dilate triangle ABC by a scale factor of 3, with point D as the center of dilation.
To perform a dilation, each point in the original figure is transformed by multiplying its coordinates by the scale factor and then translating the figure according to the center of dilation. In this case, each point in triangle ABC will be multiplied by a scale factor of 3, with point D as the center of dilation.
To dilate the triangle by a scale factor of 3, you can follow these steps
Draw rays from point D to the vertices of triangle ABC.Measure the distance between each vertex and point D. This distance will be the radius of the dilation.Multiply the x-coordinate and y-coordinate of each vertex by 3, since the scale factor is 3.Use the measured distances as a guide to draw the dilated triangle, with each vertex located at the end of a ray from point D.Hence, if the scale factor is greater than 1, the dilated figure will be larger than the original. If the scale factor is between 0 and 1, the dilated figure will be smaller than the original. If the scale factor is negative, the figure will be reflected across the center of dilation.
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Use the marks to identify the correct name for point T. The options are:
- Centroid
- Orthocenter
- Circumcenter
- Incenter
- None of the above
Answers
Point T is the orthocenter of this triangle because it is the point where all the three altitudes of the triangle are intersecting each other.
How to explain the triangleCircumcenter : The point of intersection of the three perpendicular bisectors.
Incenter : The point of intersection of the three angle bisectors.
Centroid : The point of intersection of the three medians.
Orthocenter : The point where all the three altitudes of the triangle meet or intersect each other.
In conclusion, based on the information, Point T is the orthocenter of this triangle because it is the point where all the three altitudes of the triangle are intersecting each other.
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arch
A group of students is given a 10 by 10 grid to cut into
individual unit squares. The challenge is to create two
squares using all of the unit squares. Their teacher
states that after the two new squares are formed, one
should have a side length two units greater than the
other.
Which equation represents x, the side length of the
greater square?
O x² + (x-2)2 = 10
O x² + 2x² = 10
O x² + (x-2)2 = 100
Ox²+2x² = 100
Answers
The equation that represents x, the side length of the greater square is this: x² + (x-2)²= 100.
Which equation represents x?The equation that represents x, the greater side length is x² + (x-2)²= 100. According to the instruction from the teacher, one of the squares should have a side that is two units greater than the first side.
So, if the first side was x, then the new side will be x2 and the same will be true of side, x -2 which now becomes (x-2)². Of course, multiplying a side 10 by 10 will also give 100. So, the correct equation will be C.
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The magnitude and direction of two forces acting on an object are 100 pounds, S80°E, and 90 pounds, N55°E,
respectively. Find the magnitude, to the nearest hundredth of a pound, and the direction angle, to the nearest tenth
of a degree, of the resultant force.
The magnitude is approximately ? pounds.
(Do not round until the final answer. Then round to the nearest hundredth as needed.)
Answers
The resultant force is gotten as 173.3780
What is a Resultant Force?A resultant force is described as the single force and associated torque obtained by combining a system of forces and torques acting on a rigid body via vector addition
we determine resultant force by following these steps:
Establish the magnitude and direction of each individual force acting on the object first.Next, we use Trigonometry to establish the x and y components for each one. For example, if a force comes at the object at 30 degrees from the x-axis with a strength of 10 N, then its x-component would be 8.66 N after calculating 10cos(30), while the y-component will be 5 N which is solved by applying 10sin(30).we then add all x components of the various forces together.See attached image for full working
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Select the correct answer.
A number is selected at random from the set (2, 3, 4,... 10). Which event, by definition, covers the entire sample space of this experiment?
O A.
O B.
O C.
OD.
The number is even or less than 12.
The number is not divisible by 5.
The number is neither prime nor composite.
The number is greater than 2.
Reset
Next
Answers
The event that covers the entire sample space is option D, "The number is greater than 2." This is because every number in the sample space is greater than 2.
Option A, "The number is even or less than 12," does not cover the entire sample space because 9 and 10 are not even and 10 is greater than 12.
Option B, "The number is not divisible by 5," does not cover the entire sample space because 5 and 10 are both divisible by 5.
Option C, "The number is neither prime nor composite," does not cover the entire sample space because 2 and 3 are prime numbers.
Therefore, the correct answer is D.
The radius of Circle A is 8 mm. The radius of Circle B is 5 mm greater than the radius of Circle A. The radius of Circle C is 4 mm greater than the radius of Circle B. The radius of Circle D is 3 mm less than the radius of Circle C. What is the area of each circle? How many times greater than the area of Circle A is the area of Circle D?
Answers
Area of Circle A = π(8 mm)^2 ≈ 201.06 mm^2
Moving on to Circle B, we know that its radius is 5 mm greater than the radius of Circle A, which means:
Radius of Circle B = 8 mm + 5 mm = 13 mm
Using the same formula, we can find the area of Circle B:
Area of Circle B = π(13 mm)^2 ≈ 530.93 mm^2
Proceeding to Circle C, we know that its radius is 4 mm greater than the radius of Circle B, which means:
Radius of Circle C = 13 mm + 4 mm = 17 mm
Using the same formula, we can find the area of Circle C:
Area of Circle C = π(17 mm)^2 ≈ 907.92 mm^2
Finally, for Circle D, we know that its radius is 3 mm less than the radius of Circle C, which means:
Radius of Circle D = 17 mm - 3 mm = 14 mm
Using the same formula, we can find the area of Circle D:
Area of Circle D = π(14 mm)^2 ≈ 615.75 mm^2
To find how many times greater the area of Circle D is compared to the area of Circle A, we can divide the area of Circle D by the area of Circle A:
Area of Circle D / Area of Circle A ≈ 3.06
Therefore, the area of Circle D is approximately 3.06 times greater than the area of Circle A.
Answer:
Down There
Step-by-step explanation:
Radii:
Circle A - 8
Circle B - 13
Circle C - 17
Circle D - 14
Circle A Area:
(pi)(r)^2, where r = 8
64pi or about 201.06
Circle B Area:
(pi)(r)^2, where r = 13
169pi or about 530.93
Circle C Area:
(pi)(r)^2, where r = 17
289pi or about 907.92
Circle D Area:
(pi)(r)^2, where r = 14
196pi or about 615.75
Circle D is greater than Circle A's area by 132pi or about 414.69.
HELP ASAP ASAP PLS PLS I NEED DONE NOW AND BRAINLIEST
Mr. Harris graded papers at the end of the school day. The table below shows how many papers he graded in minutes.
Minutes Number of papers graded
6 4
12 8
24 16
45 30
At this rate, how many papers will Mr. Harris grade in 60 minutes?
34 papers
40 papers
44 papers
75 papers Mr. Harris graded papers at the end of the school day. The table below shows how many papers he graded in minutes.
Minutes Number of papers graded
6 4
12 8
24 16
45 30
At this rate, how many papers will Mr. Harris grade in 60 minutes?
34 papers
40 papers
44 papers
75 papers
Answers
Answer:
40
Step-by-step explanation:
6:4 = 1,5 which means he grades 1 paper per 1,5 minute. 60:1,5 = 40 papers
Given the function g(x) = -x² − 9x + 27, determine the average rate of change
of the function over the interval -9 ≤x≤-1.
Answers
The rate of change of the function g(x) in the interval -9 ≤ x ≤ -1 is 1
How to determine the rate of change?The rate of change of a function y = f(x) on the interval [a, b] is given by the formula below:
R = (f(b) - f(a))/(b - a)
Here the function is g(x) = -x² − 9x + 27 and the interval is [-9, -1], we can evaluate g(x) in both ends of our interval, then we will get the two values needed for the numerator, here we will get:
g(-1) = -(-1)² − 9*-1 + 27 = -1 + 9 + 27 = 35
g(-9) = -(-9)² -9*-9 + 27 = 27
Replacing that in the formula we can get the rate of change is:
R = (35 - 27)/(-1 + 9) = 8/8 = 1
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Find the Independent and Dependent variables in the below Research Question.
Is there a difference in time finding a parking spot at SDSU than across other San Diego universities?
Answers
The independent variable in the research question is the location of the universities, with SDSU being the specific location of interest. The dependent variable is the time it takes to find a parking spot.
The research question is seeking to compare the time it takes to find a parking spot at SDSU to the time it takes at other San Diego universities, with the location being the independent variable that may affect the dependent variable, which is the time taken to find a parking spot.
By identifying the independent and dependent variables in the research question, researchers can design a study that will collect data on these variables, analyze the data, and
draw conclusions about whether there is a significant difference in the time it takes to find a parking spot at SDSU compared to other universities in San Diego.
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Your goal is to create a college fund for you child. Suppose you find a fund that offers an apt of 6% . How much should you deposit monthly to accumulate $80,00 in 14 years
Answers
The amount to be invested now is $173.9.
What is the present amount?
The amount to be invested now can be calculated using the formula for future value of an annuity as shown below;
FV = A x ((1 + r)ⁿ⁻¹) / r
where:
FV = future value of the annuityA = monthly paymentr = annual interest rate / 12 n = number of months = 14 yrs x 12 = 168 monthsMonthly rate becomes;
r = 6% / 12 = 0.5% = 0.005
The amount is calculated as;
80,000 = A x ((1 + 0.005)¹⁶⁸ ⁻ ¹) / 0.005
80,000 =460A
A = 80,000/460
A = $173.9
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PLEASE HELP ME :( PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME
Answers
Answer:
Step-by-step explanation:
...Negative.
Answer:
Negative
Step-by-step explanation:
Mark and his three friends ate out at Applebee's. Their bill totaled $52.35. If they left the server a 20% tip, how much would each person pay splitting the bill evenly?
Answers
Step-by-step explanation:
so the total with the tip is $62.82 then divide by 3 so I believe your answer is $20.94
$15.70
Step-by-step explanation:
20% tip on $52.35 is $10.47
$10.47 + $52.35 = $62.82
$62.82 ÷ 4(him and 3 friends) = $15.70
So, each person would pay $15.70 if they split the bill evenly.
What is the constant of proportionality in this table?
X
2
5
7.5
y
31
77.5
116.25
Answers
In this table, the constant of proportionality is 15.5.
What is the constant of proportionality?The constant of proportionality is the ratio that one value has compared to another.
In other words, the constant of proportionality is the quotient of the numerator and the denominator.
The constant of proportionality can also be referred to as the slope, gradient, or unit rate.
X y Constant of Proportionality
2 31 15.5 (31/5)
5 77.5 15.5 (77.5/5)
7.5 116.25 15.5 (116.25/7.5)
Thus, the constant of proportionality, which can also be computed as the slope or unit rate is 15.5.
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What is the volume of a hemisphere with a radius of 9.8 in, rounded to the nearest tenth of a cubic inch?
Answers
The volume of the hemisphere is approximately 1970.2 cubic inches.
Given that:
Radius, r = 9.8 inches
The formula for the volume of a hemisphere is given as:
V = (2/3) x π x r³
V = (2/3) x π x (9.8 in)³
V = (2/3) x 3.14 x 941.192
V = 1970.2 cubic inches
Therefore, the volume of the hemisphere is approximately 1970.2 cubic inches.
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HURRY ASAP!!! NEED THE ANSWER
The graph shows f(x). The absolute value function g(x) is described in the table.
The graph shows a v-shaped graph, labeled f of x, with a vertex at 0 comma 2, a point at negative 1 comma 3, and a point at 1 comma 3.
x g(x)
−1 5
0 4
1 3
2 2
3 3
If g(x) = f(x + k), what is the value of k?
k = −2
k is equal to negative one half
k is equal to one half
k = 2
Answers
Answer:
A
Step-by-step explanation:
help fill in these answers please
Answers
This has to do with the solution the quadratic equation given as: y=x² - 5x -14.
What is the solution and related quantities?
To factorize the quadratic equation - y = x² - 5x -14, we need to find two numbers that multiply to -14 and add up to -5.
We can list out the factors of -14 as follows:
-1 and 14
1 and -14
-2 and 7
2 and -7
Out of these pairs, the numbers that add up to -5 are -2 and 7.
Therefore, we can factorize the equation as:
y = (x - 2)(x + 7)
To find the zeros or x-intercepts, we set each factor equal to 0 and solve for x:
x - 2 = 0, x + 7 = 0
x = 2, x = -7
So the solutions are (2, 0) and (-7, 0).
The axis of symetry is the average of the x-intercepts
This is (2 - 7)/2 = -2.5.
Substituting this value into the equation:
y = (-2.5 )² - 5 (-2.5 ) - 14 = - 20.25
So the vertex is ( -2.5, -20.25).
The domain of the function is all real numbers, since there are no restrictions on the input x.
The range of the function is y ≥ -20.25, since the vertex is the lowest point of the parabola and the graph extends upward from there. See the graph attached.
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The population of a particular country was 23 million in 1981; in 1987, it was 32 million. The
exponential growth function A =23ekt describes the population of this country t years after 1981. Use
the fact that 6 years after 1981 the population increased by 9 million to find k to three decimal places.
Answers
K's value is around 0.055 to three decimal places.
Let's first use the given information to set up two equations:
A(0) = 23 (the initial population in millions)
A(6) = 32 (the population 6 years later in millions)
Substituting these values into the exponential growth function A = 23e^(kt), we get:
[tex]23 = 23e^(k0) = > e^{(k0)} = 1\\32 = 23e^{k*6}[/tex]
Dividing the second equation by the first, we get:
[tex]32/23 = e^{6k}[/tex]
Taking the natural logarithm of both sides, we get:
ln(32/23) = 6k
Solving for k, we get:
k = ln(32/23)/6
k ≈ 0.055
Rounding to three decimal places, we get k ≈ 0.055.
Therefore, the value of k to three decimal places is approximately 0.055.
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S = [10, 11, 13, 19, 21, 23, 29, 30]
A = The number is At least 21
B = the number is Between 12 and 25
O = number is Odd
L = number is a Less than 25
Find the P(A and L) = [____] Round to 2 d.p
Answers
The probability of A and L is 0.25, rounded to two decimal places
To find the probability of A and L, we need to find the number of elements in the intersection of A and L and divide by the total number of elements in the set S.
A = {x ∈ S | x ≥ 21}
= {21, 23, 29, 30}
L = {x ∈ S | x < 25}
= {10, 11, 13, 19, 21, 23}
A ∩ L = {x ∈ S | x ≥ 21 and x < 25}
= {21, 23}
Therefore, the probability of A and L is:
P(A and L) = |A ∩ L|/|S|
= 2/8
= 0.25
Therefore, the required probability of A and L is 0.25, rounded to two decimal places
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Please solve piecewise
Answers
The numeric values of the piecewise function in this problem are given as follows:
f(-4) = -4.f(0) = 0.f(3) = 1.How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
A piecewise function is a function that has different definitions, based on the input x of the function.
For values of x that are of 1 or less, the function is defined as follows:
f(x) = x.
Hence the numeric values in this interval are given as follows:
f(-4) = -4.f(0) = 0.For values of x that are greater than 1, the function is defined as follows:
f(x) = -x + 4.
Hence, at x = 3, the numeric value of the function is given as follows:
f(3) = -3 + 4 = 1.
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graph the following linear inequalities; <-2x+7
Answers
The graph of the linear inequality can be seen in the image at the end.
How to graph the linear inequality?I can assume that the linear inequality you want to graph is:
y < -2x + 7
To graph this inequality, what we need to do is graph the line:
y = -2x + 7
With a dashed line, and then shade all the region below that line.
To graph the line just find two points in the line, for example:
if x = 0
y = -2*0 + 7 = 7 ----> (0, 7)
if x = 1
y = -2*1 + 7 = (1, 5)
now graph the points and connect them with a dashed line, and then shade all the region below.
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Ms. Garcia bought 3 packs of red notepads,
5 packs of yellow notepads, and 8 packs of
green notepads. There were 3 notepads in each
package. How many notepads did Ms. Garcia
buy in all?
Answers
3•5=15
3•8=24
9+15+24=48
Answer: red = 9, yellow = 15 green = 24, total = 48 notepads were bought.
Step-by-step explanation:
3 x 3 = 9, so 9 red. 3 x 5 = 15, so 15 yellow. 3 x 8 = 24, so 24 green. In total this is equal to 48 notepads. 9 + 15 + 24 = 48.
Pls help, this is for geometry
Answers
I'm not 100 percent sure so please only rate after you see if it's right.
ANSWER: $1090
STEP 1:
The volume of one brick is given by multiplying its length, width, and height:
V = (7 1/4) in x 3 in x (2 1/4) in
V = (29/4) in x 3 in x (9/4) in
V = 2187/16 cubic inches
STEP 2:
The cost of one brick is given by multiplying the volume by the cost per cubic inch:
C = (2187/16 cubic inches) x $0.05/in^3
C = $1.09/brick
STEP 3: To find the cost of 1000 bricks, we simply multiply the cost of one brick by 1000:
Cost of 1000 bricks = 1000 x $1.09/brick
Cost of 1000 bricks = $1090
Therefore, the cost of 1000 bricks is $1090, rounded to the nearest cent.