The graph below shows the quadratic function f, and the table below shows the quadratic function g.
x -1 0 1 2 3 4 5
g(x) 13 8 5 4 5 8 13
Which statement is true?
A.
The functions f and g have the same axis of symmetry and the same y-intercept.
B.
The functions f and g have different axes of symmetry and different y-intercepts.
C.
The functions f and g have the same axis of symmetry, and the y-intercept of f is greater than the y-intercept of g.
D.
The functions f and g have the same axis of symmetry, and the y-intercept of f is less than the y-intercept of g.
Answers
Answer:
D
Step-by-step explanation:
The true statement is:
The functions f and g have the same axis of symmetry, and the y-intercept of f is greater than the y-intercept of g.
What is Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
As, per the graph and table is:
From the graph of f(x):
Axis of symmetry will be at x = 2
The maximum value of f(x) = 10
From the table of g(x):
Axis of symmetry will be at x = 2
The minimum value of g(x) = 4
thus, The functions f and g have the same axis of symmetry, and the y-intercept of f is greater than the y-intercept of g.
Learn more about Function here:
https://brainly.com/question/9753280
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Related Questions
Can somebody help me with parametric equations?
I do not have a TI-84 at the moment! Thanks!
1. Graph the following set of parametric equations on your calculator and select the matching graph.
2. Transform the given parametric equations into rectangular form. Then identify the conic.
Answers
Answer:
Attachment 1 : Graph B
Attachment 2 : Option B
Step-by-step explanation:
( 1 ) The equation x = t² - 3 is represented by exponential growth, ( t² ) so it's graph will be similar to the first graph, graph 1, in our options. Then again we have to consider the equation y = √t - 2, which will be similar to graph 4, but with a greater slope. This leaves us with a solution of graph b.
( 2 ) We have the following system of equations at hand here.
{ x = 5 cot(t), y = - 3csc(t) + 4 }
Now instead of isolating the t from either equation, let's isolate cot(t) and csc(t) --- Step #1,
x = 5 cot(t) ⇒ x - 5 = cot(t),
y = - 3csc(t) + 4 ⇒ y - 4 = - 3csc(t) ⇒ y - 4 / - 3 = csc(t)
Now let's square these two equations, adding them --- Step #2
We know that csc²θ - cot²θ = 1, so let's subtract the equations
( y - 4 / - 3 )² = (csc(t))²
- ( x - 5 / 1 )² = (cot(t))²
___________________
(y - 4)² / 9 - x² / 25 = 1
And as we are subtracting the two expressions, this is an example of a hyperbola. Therefore your solution is option b.
someone please help it's Multiple Coordinate Transformations
Answers
Answer:
Step-by-step explanation:
Coordinates of the vertices of the given rectangle are,
A(-4, 5), B(-2, 5), C(-2,1) and D(-4, 1).
If the given rectangle ABCD is translated by 1 unit right and 4 units down,
Rule for the translation will be,
(x, y) → [(x + 1), (y - 4)]
Therefore, coordinates of A, B, C and D after translation will be,
A(-4, 5) → A'(-3, 1)
B(-2, 5) → B'(-1, 1)
C(-2, 1) → C'(-1, -3)
D(-4, 1) → D'(-3, -3)
Then A', B', C' and D' are reflected about the y-axis.
Rule for the reflection about y-axis will be,
(x, y) → (-x, y)
New coordinates after the reflection will be,
A'(-3, 1) → A"(3, 1)
B'(-1, 1) → B"(1, 1)
C'(-1, -3) → C"(1, -3)
D'(-3, -3) → D''(3, -3)
Finally these points are rotated 270° clockwise about the origin,
Rule to be followed,
(x, y) → (-y, x)
Therefore, new coordinates will be,
A"(3, 1) → A"'(-1, 3)
B"(1, 1) → B'"(-1, 1)
C"(1, -3) → C"'(3, 1)
D"(3, -3) → D"'(3, 3)
Oregon State University is interested in determining the average amount of paper, in sheets, that is recycled each month. In previous years, the average number of sheets recycled per bin was 59.3 sheets, but they believe this number may have increase with the greater awareness of recycling around campus. They count through 79 randomly selected bins from the many recycle paper bins that are emptied every month and find that the average number of sheets of paper in the bins is 62.4 sheets. They also find that the standard deviation of their sample is 9.86 sheets. What is the value of the test-statistic for this scenario
Answers
Answer:
The test statistic is [tex]t = 2.79[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 59.3[/tex]
The sample size is [tex]n = 79[/tex]
The sample mean is [tex]\= x = 62.4[/tex]
The standard deviation is [tex]\sigma = 9.86[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 62.2 - 59.3 }{ \frac{ 9.86}{ \sqrt{ 79} } }[/tex]
[tex]t = 2.79[/tex]
Find y when x = 4 (30 points)
Answers
Answer:
y = 54/25
Step-by-step explanation:
y = p×q^(x-1)
when x = 1 then y = 10
so,
10 = p×q^(1-1)
or, 10 = p×1
or, p = 10
when x = 6 then y = 0.7776
0.7776=p×q^(6-1)
or, 0.7776=p×q^5
or, 0.7776=10×q⁵
[0.7776 = 7776/10000 = 486/625]
or, 486/625 = 10×q⁵
or, 486/6250=q⁵
or, [tex] \frac{ \sqrt[5]{486} }{ \sqrt[5]{6250} } = q[/tex]
or, [tex]q = \frac{3 \sqrt[5]{2} }{5 \sqrt[5]{2} } [/tex]
or, q = 3/5
so, when x = 4
y = p×q^(x-1)
y = 10×(3/5)^(4-1)
y = 10×(3/5)^3
y = 10×27/125
y = 54/25
PLEASE HELP!!! Sarah had a balance of $155 in her bank account at the start of the week. She withdrew $65.50 on Monday, $23.25 on Wednesday, and $26.45 on Thursday. On Friday she deposited $165.30. Write an expression that represents Sarah's spending. *
Answers
Answer:
155.00-65.50-23.25-26.45+165.30
Step-by-step explanation:
Answer:
155 + 165.3 - 65.5 - 23.25 - 26.45
Step-by-step explanation:
She had $155 dollars in the starting = +155
She withdrew $65.5 = -65.5
She withdrew another $23.25 = -23.25
She withdrew another $26.45 = -26.45
She deposited $165.3 = +165.3
The expression looks like:
155 + 165.3 - 65.5 - 23.25 - 26.45
We could solve the expression:
155 + 165.3 - 65.5 - 23.25 - 26.45
=> 320.3 - 88.75 - 26.45
=> 320.3 -115.2
=> 205.1
At the end of the week, she had a total of $205.10.
In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft. For a group of 1013 adults, the mean of those who do not worry about identify theft is closest to ________.
Answers
Answer: 669
Step-by-step explanation:
Given, In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft.
i.e. The proportion of adults said that they worry about identity theft. (p) = 0.66
Sample size : n= 1013
Then , Mean for the sampling distribution of sample proportion = np
= (1013) × (0.66)
= 668.58 ≈ 669 [Round to the nearest whole number]
Hence, the mean of those who do not worry about identify theft is closest to 669 .
The seventh-grade class is raising money
to have a class trip at the end of the year.
They began the year with $1,500. Now they
have $1,650 in the account.
What is the percent of increase for the
money the class has raised? I
a.
b.
Make Sense and Persevere The
class figured out that if the percent
increase is 99% from the beginning of
the year, the class will have enough
money for every student to go on the
field trip. How much money will the
class need to raise for every student to
go.
Answers
Answer:
The percent of the increase for the money the class raised is 10 %
Step-by-step explanation:
Because if you divide 1500 by 10 you get 150 that means 150 is 10 % of 1500 and if you add 150 to 1500 you get 1650 so the increase of money the class raised is 10 %
John and mike got paid $40.00 for washing
car. John work one hour, mike worked 1.5 hrs.
How much do they get paid for time worked?
Answers
The manager of the video department at a department store plans to purchase a large number of DVDs of a recent movie. One supplier is selling boxes of 20 DVD movies for $240, and a second supplier is selling boxes of 14 DVD movies for $170. Only complete boxes of DVD movies can be purchased. Complete part a) and b) below. a)
a) If the manager can purchase boxes of DVD movies from either or both suppliers, determine the maximum number of DVD movies that can be purchased for $415. Indicate how many boxes of 20 and how many boxes of 14 will be purchased.
— box(es) of 20 and — box(es) of 14
b) How much will the DVD movies cost?
They will cost $—
Answers
Answer:
1 box of 20 and 1 box of 14
They will cost $410
Step-by-step explanation:
1. Find how many boxes of 20 DVD movies can be bought
415 - 240 = 175
1 box of 20 DVD movies can be sold
2. Find how many boxes of 14 DVD movies can be bought from $175
175 - 170 = 5
1 box of 14 DVD movies can be bought
3. Find the cost
240 + 170 = 410
1+3^2⋅2−5 order of operations
Answers
()
^
* /
+ -
So,
1+3^2*2-5 =
1+((3^2)*2)-5 =
1+(9*2)-5 =
1+18-5 =
14
Answer:
Below
Step-by-step explanation:
● 1 + 3^2 × 2 -5
Start by calculating 3^2 wich is 9
● 1 + 9 × 2 -5
Multiply 2 by 9 (9×2=18)
● 1 + 18 -5
Add 1 to 18 (1+18 = 19)
● 19 -5
Substract 5 from 19 (19-5 = 14 )
● 14
Find the value of angle X. x = 40 x = 55 x = 109 x = 130 I will mark as Brainliest
Answers
Answer:
130 degree
Step-by-step explanation:
Interior angles of the triangle:
81, 49, (180-x)
and by sum of all angles of triangle is 180 degree,
therefore,
81 + 49 + 180 - x = 180
x = 130 degree
Write the equation in standard form.
x2 + 6 = 5x
Answers
Answer:
Step-by-step explanation:
x2 + 6 = 5x
2x-5x = -6
3x = -6
x = -6/3
x = -2
Answer:
[tex]x^{2} -5x + 6 =0[/tex]
Step-by-step explanation:
One way to calculate the target heart rate of a physically fit adult during exercise is given by the formula h=0.8( 220−x ), where h is the number of heartbeats per minute and x is the age of the person in years. Which formula is equivalent and gives the age of the person in terms of the number of heartbeats per minute?
Answers
Answer:
The answer is:
C. [tex]\bold{x = -1.25h+220}[/tex]
Step-by-step explanation:
Given:
[tex]h=0.8( 220-x )[/tex]
Where [tex]h[/tex] is the heartbeats per minute and
[tex]x[/tex] is the age of person
To find:
Age of person in terms of heartbeats per minute = ?
To choose form the options:
[tex]A.\ x=176-h\\B.\ x=176-0.8h\\C.\ x=-1.25h+220\\D.\ x=h-0.8220[/tex]
Solution:
First of all, let us have a look at the given equation:
[tex]h=0.8( 220-x )[/tex]
It is value of [tex]h[/tex] in terms of [tex]x[/tex].
We have to find the value of [tex]x[/tex] in terms of [tex]h[/tex].
Let us divide the equation by 0.8 on both sides:
[tex]\dfrac{h}{0.8}=\dfrac{0.8( 220-x )}{0.8}\\\Rightarrow \dfrac{1}{0.8}h=220-x\\\Rightarrow 1.25h=220-x[/tex]
Now, subtracting 220 from both sides:
[tex]\Rightarrow 1.25h-220=220-x-220\\\Rightarrow 1.25h-220=-x[/tex]
Now, multiplying with -1 on both sides:
[tex]-1.25h+220=x\\OR\\\bold{x = -1.25h+220}[/tex]
So, the answer is:
C. [tex]\bold{x = -1.25h+220}[/tex]
identify the roots of the equation and the multiplicities of the roots 8(x - 2)³ = 0
Answers
Answer:
The root of the equation is 2 with multiplicity 3
Step-by-step explanation:
8(x-2)^3=0
(x-2)^3=0
The root of the equation is 2 with multiplicity 3
Which numbers are 9 units from −5 on this number line?
Drag and drop all of the numbers that are 9 units from −5 to their correct position on the number line.
-14,-5 -4 4 5 9
Answers
Answer:
-14 and 4
Step-by-step explanation:
To find the values subtract 9 from -5, as well as add 9 to -5
-5-9= -14
-5+9= 4
A die is rolled 200 times with the following results. Outcome 1 2 3 4 5 6 Frequency 32 36 44 20 30 38 What is the experimental probability of rolling the given result? 3 a. 0.22 c. 0.44 b. 0.78 d. 0.23
Answers
Answer:
.22
Step-by-step explanation:
The number of times a 3 was rolled is 44 out of 200
The experimental probability is 44/200 = .22
The frequency of rolling a 3 was 44.
So... 44/200
After dividing we get 0.22
Therefore, the answer is A
Best of Luck!
A homeowner wants to build a fence to enclose a 320 square yard rectangular area in his backyard. Along one side the fence is to be made of heavy-duty material costing $9 per yard, while the material along the remaining three sides costs $1 per yard. Determine the least cost to the homeowner.
Answers
Answer:
Determination of the least cost of fence enclosure:
= cost of heavy-duty one side of the length plus cost of remaining three sides of the fence
= $416 ($360 + $56)
= $416
Step-by-step explanation:
Rectangular Fence Area = 320 square yard
Since fence is rectangular, the two sides are length and width
Length of rectangular is always greater than the width
Length cannot be 20 yard with width as 16 yard
Therefore, length = 40 yard and width = 8 yard.
Proof: Area of a rectangular = 40 x 8 = 320 square yard
Since, parameter = 2 (Length + Width)
= 2 x (40 + 8)
= 96 yards
Therefore, along one side with heavy-duty material is one length side of the fence = 40 yard
Cost of the one length with heavy-duty material = 40 x $9 = $360
Remaining three sides = 96 - 40 = 56 yard
Cost of remaining three sides = 56 x $1 = $56
Total cost of fencing = $416 ($360 + $56)
there are 12 eggs in one box and 12 boxes in one crate. how many eggs are in a shipment of 24 crates
Answers
Answer:
Step-by-step explanation:
12 eggs in one box
12 boxes = 1 crate
12 x 12 = 144 eggs
144 x 24 crates = 3456 eggs
Answer:
3,456 eggs
Step-by-step explanation:
There are 12 eggs in one box and 12 boxes in one crate. To find out how many eggs are in a crate, multiply 12 and 12
12*12=144
144 eggs in one crate.
We want to find out what how many eggs are in 24 creates. We know there are 144 eggs in 1 crate. Therefore, we can multiply 144 and 24.
144*24=3,456
There are 3,456 eggs in 24 crates.
find the perimeter of a square of sides 10.5cm
Answers
Answer:
Perimeter = 42 cm
Step-by-step explanation:
A square has all equal sides so you would just add 10.5 + 10.5 + 10.5 + 10.5 to get 42 cm.
Answer:
42 cm
Step-by-step explanation:
Side of square = 10.5 cm (given)
Perimeter of square = Side X 4
= 10.5 X 4
= 42 cm
HOPE THIS HELPED YOU !
:)
Find the value of x.
Answers
Answer:
x=3
Step-by-step explanation:
I guessed and checked which x value would make ABC proportional to DBE. If x=3, than DB=8 which is double BE. If x=3, than AB=14 which is double BC. Since it is proportional, It should be correct. I don't remember the actual way you solve this with a formula but this makes sense to me.
Answer:
x=3
Step-by-step explanation:
We can use ratios to solve since the triangles are similar
x+5 4
------------ = ---------------
x+5 +2x 4+3
Simplifying
x+5 4
------------ = ---------------
3x+5 7
Using cross products
7(x+5) = 4(3x+5)
Distribute
7x+35 = 12x+20
Subtract 7x from each side
35 = 5x+20
Subtract 20 from each side
15 = 5x
Divide by 5
3 =x
V= pi r2h rectangular prism cylinder cone sphere
Answers
Answer:
Step-by-step explanation:
rectangular prism=lwh
cylinder=πr²h
cone=1/3 πr²h
sphere=4/3 πr³
Christopher has $1947 in his savings account. This weekend he will deposit another $99 in the account. How much money will be in Christopher savings account after this weekend
Answers
Answer:
$2046
Step-by-step explanation:
Add 1947 and 99 because he is depositing, as in adding, 99 dollars
List the sides in order from the largest to the smallest. A. XY, YW, WX B. XY, WX, YW C. WX, YW, XY D. WX, XY, YW
Answers
Answer:
Option (D)
Step-by-step explanation:
By applying Sine rule in the given triangle WXY,
[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinY}}{\text{XW}}=\frac{\text{SinX}}{\text{WY}}[/tex]
[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin82}}{\text{XW}}=\frac{\text{Sin39}}{\text{WY}}[/tex]
[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin82}}{\text{XW}}[/tex]
[tex]\frac{\text{XW}}{\text{XY}}=\frac{\text{Sin82}}{\text{Sin59}}[/tex]
= 1.1489
XW : XY ≈ 1.15 : 1
[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin39}}{\text{WY}}[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{\text{Sin59}}{\text{Sin39}}[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{1.36}{1}[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{\frac{1}{1}}{\frac{1}{1.36} }[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{1}{0.7342}[/tex]
XY : WY = 1 : 0.7342
XW : XY : WY = 1.15 : 1 : 0.7342
Therefore, WX > XY > WY
Option (D). will be the correct option.
Find f(x) and g(x) so the function can be expressed as y = f(g(x)). y= [tex]\frac{2}{x^2}[/tex]+3
Answers
Answer:
One possible answer is:
f(x) = (2/x) + 3 and g(x) = x².
Step-by-step explanation:
Explanation:
We are to write this equation as y = f(g(x)). This means we want it to be a composite of functions; in f(x), we take the value of g(x) and use in place of x.
If we let g(x) = x², this means everywhere we see an x in f(x), we will replace it with x². To make our equation y = 2/x² + 3, working backward we would substitute x for x²; this would give us f(x) = 2/x + 3.
find the area of right-andled triangled whose sight-angled
making side are 3cm and 4cm
Answers
Answer:
3*4=12
Step-by-step explanation:
I NEED HELP ASAP
191 of the 288 high school students surveyed at a local school said they went outside more during school hours as elementary school students than they do now as high school students. Calculate the Margin of Error, rounded to the nearest tenth of a percent. Is it reasonable that the state education department claims the percentage for the entire state is 73%? Justify your answer.
Answers
Answer:
It is not reasonable that the state education department claims the percentage for the entire state is 73%.
Step-by-step explanation:
We are given that 191 of the 288 high school students surveyed at a local school said they went outside more during school hours as elementary school students than they do now as high school students.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of high school students who went outside more during school hours as elementary school students than they do now as high school students = [tex]\frac{191}{288}[/tex] = 0.66
n = sample of high school students = 288
p = population percentage for the entire state
Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.
The margin of error is given by;
M.E. = [tex]2 \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]
= [tex]2 \times \sqrt{\frac{0.66(1-0.66)}{288} }[/tex]
M.E. = 0.056 or 5.6%
So, the confidence interval so formed = [tex]\hat p \pm \text{Margin of error}[/tex]
= [[tex]0.66 - 0.056 , 0.66 + 0.056[/tex]]
= [0.604, 0.716]
Since the above interval does not include 0.73 or the population proportion of 73% falls outside the above interval. So, it is not reasonable that the state education department claims the percentage for the entire state is 73%.
The force of gravity on an object varies directly with its mass. The constant of variation due to gravity is 32.2 feet per second squared. Which equation represents F, the force on an object due to gravity according to m, the object’s mass? F = 16.1m F = F equals StartFraction 16.1 Over m squared EndFraction. F = 32.2m F = F equals StartFraction 32.2 Over m squared EndFraction.
Answers
Answer:
F = 32.2mStep-by-step explanation:
According to newton second law, the force of gravity on an object varies directly with its mass and it is expressed mathematically as Fαm i.e
F = mg where;
F is the force of gravity
m is the mass of the body
g is the proportionality constant known as the acceleration due to gravity.
If the constant of variation due to gravity is 32.2ft/s², the equation that represents F, the force on an object due to gravity according to m, the object’s mass can be gotten by substituting g = 32.2 into the formula above according to the law as shown;
F = m*32.2
F =32.2m
Hence the required equation is F = 32.2m
Help me please I dont know what to do
Answers
Answer:
It's option A. ± √60
Step-by-step explanation:
x^2 = 60
here ^2 will move to the other side and when it does it'll become a square root to 60.
so, x = √60
now, the answer in its simplified form would be 2√15 and -2√15.
The answer of this square root will be negative as well as positive, so, ±√60.
Answer:
±√60
You'll have to remove the square from the x by squaring the 60, hence the ±60 as the answer
What is the constant of proportionality between y and x in the graph?
Answers
Answer:
4
Step-by-step explanation:
Constant of proportionality refers to the slope of the line in this case, the slope of the line is (4-0)/(1-0)=4
Consider population data with μ = 30 and σ = 3. (a) Compute the coefficient of variation. (b) Compute an 88.9% Chebyshev interval around the population mean. Lower Limit Upper Limit
Answers
Answer:
A. 10%
B. Lower limit= 21
Upper limit = 39
Step-by-step explanation:
Mean = 30
SD = 3
a. COV = SD/|x| × 100
= 3/30 × 100
= 10%
= 0.1
B. For 88.9 chevbychev interval:
= (1 - 1/K²) = 0.889
= 1/K² = 1 - 0.889
= 1/K² = 0.111
= K² = 1/0.111
= K² = 9
= K = √9
K = 3
Lower limit = 30 - 3(3)
Lower limit = 21
Upper limit = 30 + 3(3)
Upper limit = 39
Therefore lower limit is 21 and upper limit is 39