Consider the functions:
f(x)=2/3
g(x)=2/3x-3+2
Which statement is true regarding the vertical and
horizontal translations from f(x) to g(x)?
The function flx) was translated left 3 units and up
2 units
The function f(x) was translated right 3 units and
down 2 units
O The function f(x) was translated left 3 units and
down 2 units
O The function f(x) was translated right 3 units and up
2 units

Answer:

The average rate of change from year 0 to year 2 is

[tex]change = -0.0585[/tex]

The average rate of change from year 3 to year 6 is

[tex]change = -0.0129[/tex]

Step-by-step explanation:

The average rate of change describes the average rate at which gas price in dollars per gallon is changing with respect to time (years)

The given polynomial function is

[tex]y = -0.0058x^4 +0.05x^3 -0.086x^2 - 0.04x + 2.52[/tex]

Calculate the average rate of change from year 0 to year 2.

For year x = 0

[tex]y = -0.0058(0)^4 +0.05(0)^3 -0.086(0)^2 - 0.04(0) + 2.52 \\\\y = 2.52[/tex]

For year x = 2

[tex]y = -0.0058(2)^4 +0.05(2)^3 -0.086(2)^2 - 0.04(2) + 2.52 \\\\y = -0.0928 + 0.4 - 0.344 - 0.08 + 2.52 \\\\y = 2.403[/tex]

The average rate of change from year 0 to year 2 is

[tex]change = \frac{y(2) - y(0)}{x(2) - x(0)} \\\\change = \frac{ 2.403- 2.52}{2 - 0} \\\\change = \frac{-0.117}{2} \\\\change = -0.0585[/tex]

The negative sign indicates that the gas price has decreased from year 0 to year 2.

The average rate of change from year 3 to year 6 is

For year x = 3

[tex]y = -0.0058(3)^4 +0.05(3)^3 -0.086(3)^2 - 0.04(3) + 2.52 \\\\y = -0.4698 + 1.35 - 0.774 - 0.12 + 2.52 \\\\y = 2.506[/tex]

For year x = 6

[tex]y = -0.0058(6)^4 +0.05(6)^3 -0.086(6)^2 - 0.04(6) + 2.52 \\\\y = -7.5168 + 10.8 - 3.096 - 0.24 + 2.52 \\\\ y = 2.4672[/tex]

The average rate of change from year 3 to year 6 is

[tex]change = \frac{y(6) - y(3)}{x(6) - x(3)} \\\\change = \frac{ 2.4672- 2.506}{6 - 3} \\\\change = \frac{-0.0388}{3} \\\\change = -0.0129[/tex]

The negative sign indicates that the gas price has decreased from year 0 to year 2.

Answer:

See below.

Step-by-step explanation:

It is known that a parallelogram has rotational symmetry, rotated 180 degrees about it's center point. Now by definition a parallelogram is a quadrilateral with two pairs of parallel sides, hence it's name. If you were to take a look at the attachment below, you might see the connection.

Rotational Symmetry will make it so that side AB corresponds to CD, respectively AD and CB. The sides will coincide with one another after a 180 degree rotation, so that AB = CD, and AD = CB. Hence, in the same parallelogram, opposite sides are congruent.

Proved!

Answer:

[tex]g(x) = \frac{1}{5} |x|[/tex]

Step-by-step explanation:

Given

[tex]f(x) = |x|[/tex]

Vertically compressed

Compression Factor = 5

Required

Find the equation of the new function;

Let the new function be represented by g(x)

Let c represented the compression factor;

such that c = 5

When a function f(x) is vertically compressed by factor c, the new function becomes

[tex]f(\frac{1}{c}x)[/tex]

From properties of functions;

[tex]f(\frac{1}{c}x) = \frac{1}{c} *f(x)[/tex]

This implies that

[tex]g(x) = f(\frac{1}{c}x) = \frac{1}{c} *f(x)[/tex]

[tex]g(x) = \frac{1}{c} *f(x)[/tex]

Recall that [tex]f(x) = |x|[/tex] and c = 5

[tex]g(x) = \frac{1}{5} * |x|[/tex]

[tex]g(x) = \frac{1}{5} |x|[/tex]

Hence, the new function is [tex]g(x) = \frac{1}{5} |x|[/tex]

Answer:

G(x)=1/5 |x|

Step-by-step explanation:

A p e x

Answer:

x = 20

y = 73

Step-by-step explanation:

8x - 87 + 7x - 33 = 180

15x = 180 + 87 + 33

15x = 300

x = 20

8x - 87 = y

160 - 87 = y

y = 73

Answer:

Nonlinear- it is a quadratic, which is a parabola, not a linear graph.

Step-by-step explanation:

Answer:

It's Nonlinear

Answer:

Step-by-step explanation:

k den

Answer:

1 / 4 (2x − 14) = 4.

Multiply through by 4(2x - 14)

You'll get

1 = 16(2x - 14)

1 = 32x - 224

Group like terms

224 + 1 = 32x

225 = 32x

Divide both sides by 32

x = 225/ 32

Hope this helps

Answer:

O {-8, 8}

Step-by-step explanation:

[tex]-|x| = -8\\\\\frac{-|x|=-8}{-1}\\\\|x|=8\\\\\text{Apply rule: If } |u|=a, a > 0, \text {then } u=a \text { or } u=-a\\\\\boxed {x = -8, x = 8}[/tex]

Answer:

John's initial investment is Rs.150000

Step-by-step explanation:

Let the principal amount be a

We are given that John wants to invest in a simple interest savings account .The interest rate on this account is 0.7%.

Now to find simple interest in x years

Formula : [tex]Si = P \times T \times R[/tex]

Where P = Principal

T= time

R = rate of interest in decimals

So,[tex]SI=a \times 0.007 \times x[/tex]

Amount = Principal+Interest

Amount = [tex]a+a(0.007)x[/tex]

We are given that The account balance y can be modeled by the following linear equation y=150,000+150,000(0.007)x

So, On comparing a = 150000

Hence John's initial investment is Rs.150000

Answer:

4

Step-by-step explanation:

Month 1- average rating as er graph is 4 point (1,4)

Rating was 4 at the beginning, then was stable for 2 months at 3, then increased over time up to 8 at month 10, point (10, 8)

Answer: 40.9

Step-by-step explanation:

Answer:

[tex]-1868[/tex]

Step-by-step explanation:

[tex]-165 - 1703[/tex]

Subtract the numbers.

[tex]=-1868[/tex]

Answer:

-1868 is the simplified polynomial

Step-by-step explanation:

-165 -1703

= -165 + -1703

= -(165+1703)

= -(1868)

Answer:

1783 sq. Units

Step-by-step explanation:

Answer:

Jessie scored higher than Reagan.

Step-by-step explanation:

We are given that Reagan scored 1140 on the SAT. The distribution of SAT scores in a reference population is normally distributed with mean 1000 and standard deviation 100.

Jessie scored 30 on the ACT. The distribution of ACT scores in a reference population is normally distributed with mean 17 and standard deviation 5.

For finding who performed better on the standardized exams, we have to calculate the z-scores for both people.

1. Finding z-score for Reagan;

Let X = distribution of SAT scores

SO, X ~ Normal([tex]\mu=1000, \sigma^{2}=100^{2}[/tex])

The z-score probability distribution for the normal distribution is given by;

                                    Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 1000

            [tex]\sigma[/tex] = standard deviation = 100

Now, Reagan scored 1140 on the SAT, that is;

       z-score  =  [tex]\frac{1140-1000}{100}[/tex]  =  1.4

2. Finding z-score for Jessie;

Let X = distribution of ACT scores

SO, X ~ Normal([tex]\mu=17, \sigma^{2}=5^{2}[/tex])

The z-score probability distribution for the normal distribution is given by;

                                    Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 17

            [tex]\sigma[/tex] = standard deviation = 5

Now, Jessie scored 30 on the ACT, that is;

       z-score  =  [tex]\frac{30-17}{5}[/tex]  =  2.6

This means that Jessie scored higher than Reagan because Jessie's standardized score was 2.6, which is 2.6 standard deviations above the mean and Reagan's standardized score was 1.4, which is 1.4 standard deviations above the mean.

Answer:

Y = 2

E = 9

A = 1

R = 0

Step-by-step explanation:

2222 - 999 + 11 - 0 =1234

Answer:

D

Step-by-step explanation:

i beleive the answer is D

random words so brainly doesnt delete my answer again for no reason d ;lkm dfkslfjks fjdsfdnfjnv fheryqoiwr bnmxm,nxvbkfldj uyeuqiowerhtuirqgyt jbnnkfamcx vnkscjvhsdf

Answer It is the first option because it has reflectional symmetry vertically and horizontally, therefore creating 4 lines of symmetry. If that's wrong, then it's "c."

Step-by-step explanation:

because it has reflectional symmetry vertically and horizontally, therefore creating 4 lines of symmetry. If that's wrong, then it's "c."

Answer:

11

Step-by-step explanation:

7x-4=73

7x = 4+73

7x = 77

7x/7 = 77/7

x = 11

Answer:

Hi your answer should be 8 thousand

Step-by-step explanation:

Answer:

c ( 8000)

Step-by-step explanation:

A comes out 0.13

B is 0.026

c is 8000

D is 0.1

Absolutely c is the right answer.

Please mark me brainliest. I need to rank up.

Answer: 1 is not, 2 is, 3 is, 4 is, 5 is, 6 is not

Step-by-step explanation:

1 is not because 2 has two arrows coming off of it and each input can only have one output. 6 is not because if you draw a line down the graph it will hit the figure more than once( this is called the pencil drop test)

Function is an assignation that for each element of first set assigns one and only one element from second set.

1) NO    {element 2 from set one has assigned two elements (b, c) from set two}

2)  YES

3) YES     {several elements from set one can have assigned the same element from set two}

4), 5)   YES

6)  NO   {for x from about -4 to about 0.5 there are two y}

Answer:

13divided by 7

Step-by-step explanation:

[tex]4x + 3x - 4 = 17 \\ 7x - 4 = 17 \\ 7x = 17 - 4 \\ 7x = 13 \\ \frac{7x}{7} = \frac{13}{7 } \\ x = \frac{13}{7} or1 \times \frac{6}{7} [/tex]

The required number is 3 .

It is required to find the number.

A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

Given:

Let the number be x

According to given question we have,

4x+3x-4=17

Compare the like terms we get,

7x=17+4

7x=21

x=3

The number is 3 .

Therefore, the required number is 3 .

Learn more details about algebra here:

https://brainly.com/question/24875240

#SPJ2

Answer:

B:5

Step-by-step explanation:

5 - 5/5= 5

5/5 = 1

5-1= 4

Answer:

D

Step-by-step explanation:

[tex]\frac{a^{2}}{a}-\frac{5}{a} = 4[/tex]

[tex]\frac{a^{2}-5}{a} = 4[/tex]

[tex]a^{2} -5 = 4a[/tex]

a= -1

1 - 5 = 4.-1

a = 5

25 - 5 = 4.5

Hope this helps ^-^

Answer:

State A was the 12th state to enter the Union. State B was the 11th state to enter the Union.

Step-by-step explanation:

Let's call x to the order-of-entry of State B, therefore the order-of-entry of State A is x+1. Given that he product of their order-of-entry numbers is 132:

x*(x+1) = 132

x² + x - 132 = 0

Using quadratic formula:

[tex]x = \frac{-b \pm \sqrt{b^2 -4(a)(c)}}{2(a)} [/tex]

[tex]x = \frac{-1 \pm \sqrt{1^2 -4(1)(-132)}}{2(1)} [/tex]

[tex]x = \frac{-1 \pm 23}{2} [/tex]

[tex]x_1 = \frac{-1 + 23}{2} [/tex]

[tex]x_1 = 11 [/tex]

[tex]x_2 = \frac{-1 - 23}{2} [/tex]

[tex]x_2 = -12[/tex]

The negative solution has no sense in the context of our problem, then the solution is x = 11.

Answer:

C

Step-by-step explanation:

male musicians practice an avg 2/hrs a day

The inferences can be made from the data on average, male musicians practice for two hours per day. Then the correct option is C.

A diagram is made up of rectangles whose size is related to a variable's frequency and whose width is comparable to the training sample.

A social scientist surveyed a random sample of male musicians at a university about their practice habits.

The graph below displays the amount of time typically spent practicing their instrument daily.

From the graph, we can conclude that on average, male musicians practice for two hours per day.

Then the correct option is C.

More about the histogram link is given below.

https://brainly.com/question/16819077

#SPJ2

Answer:

A & F

Step-by-step explanation:

if you look at the other question I answered for you, you can see the work. but basically you can figure out slope by doing m=y2-y1/x2-x1.

so we now know the slope is 1/4. which eliminates choices B, D, E.

we see that C will not work because the x and y values are switched.

according to point slope formula A & F work.

Step-by-step explanation:

because we know that both of these parts have to do with right triangles, we know that we can use the Pythagorean theorem.

since q is the right angle, you know that any line segment with q is a leg of the triangle

A.)

a^2 + b^2 = c^2 (add in values)

8^2 + 15^2 = c^2  (a=pq and b=qr) SIMPLIFY

64 + 225 = 289 (add)

find the square root of 289 = 17 so pr = 17

B.

This time we are using one leg (pq) and the hypotenuse (pr) to find the other leg

a^2 + b^2 = c^2 (sub the numbers in)

a^2 + 8^2 = 10^2 (simplify)

a^2 + 64 = 100 (subtract 64 on both sides)

a^2 = 36

the square root of 36 is 6 so qr = 6

Answer:

a is the answer

have a great day. brainliest please

Step-by-step explanation:

Answer:

the answer is A. :)

Step-by-step explanation:

the answer A. is 10 so just think what 2 times what will equal 10 so....2 x 5 = 10 and we got 10 so that is how we get our answer

Brainliest please thank you! and good luck!

Answer:

add a picture

Step-by-step explanation:

Answer:

x⁴ + x³ + 4x² - 5x

Step-by-step explanation:

The polynomials given in the question are:

x⁴ - 3x + 1

4x² - 2x + 8

x³ - 9

We have to add all them

First write all the polynomial in the summation form:

(x⁴ - 3x + 1) + (4x² - 2x + 8) + (x³ - 9)

Open the brackets:

x⁴ - 3x + 1 + 4x² - 2x + 8 + x³ - 9

Group together the similar terms

(x⁴) + (x³) + (4x²) + (-3x -2x) + (1 + 8 - 9)

Finding the sum in brackets:

x⁴ + x³ + 4x² + (-5x) + (0)

x⁴ + x³ + 4x² - 5x

Note that the sum is in descending powers of x

Answer:

x=54 degrees

Step-by-step explanation:

These two angles are complementary, meaning that they add to 90 degrees.

If one angle is 36 degrees, then we can write this equation: 36+x=90

We want to find what x is, so we should isolate x.

We can isolate x by subtracting 36 on both sides.

x=90-36

x=54

Answer:

54°

Step-by-step explanation:

∠PQR +∠RQS =∠PQS

36° + x° = 90°

x = 90 - 36 = 54°