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.

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

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.

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

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 .

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

Answer:

Step-by-step explanation:

rectangular prism=lwh

cylinder=πr²h

cone=1/3 πr²h

sphere=4/3 πr³

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 %

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

Answer:

Step-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

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.

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

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!

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

Answer:

$2046

Step-by-step explanation:

Add 1947 and 99 because he is depositing, as in adding, 99 dollars

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.

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

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

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)

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.

Answer:

3*4=12

Step-by-step explanation:

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 !

:)

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

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]

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)

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%.

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:

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

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]

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.