The function h(x) is a translation of the exponential function g(x) = 2(3)x − 4. What's h(x) if the translation is a vertical stretch by a factor of 2, a vertical shift upward 9 units, and a horizontal shift to the right 7 units? Question 11 options: A) h(x) = 4(3)x − 7 + 9 B) h(x) = 4(3)x − 9 + 7 C) h(x) = 4(3)x – 7 + 7 D) h(x) = 4(3)x + 7 − 9

Answers

Answer 1

The function h(x) is a translation of the exponential function [tex]g(x) = 2(3)^{x - 4}[/tex] , is  [tex]h(x) = 4(3)^{x + 7} - 9[/tex]

What are exponential functions?

When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function.

There usual form is specified below. They are written in several such equivalent forms.

The function h(x) is a translation of the exponential function given as

[tex]g(x) = 2(3)^{x - 4}[/tex]

We have to determine, the h(x) if the translation is a vertical stretch by a factor of 2, a vertical shift upward of 9 units, and a horizontal shift to the right 7 units.

The function h(x) is vertically stretched by 2.

  [tex]h(x) = 2 (2(3)^{x - 4})\\\\h(x) = 4((3)^{x - 4})[/tex]      

Vertically shift upward by 9,

[tex]h(x) = 4((3)^{x - 4})\\\\h(x) = 4((3)^{x - 4})- 9[/tex]                    

And a horizontal shift to the right 7 units,

[tex]h(x) = 4((3)^{x - 7})- 9[/tex]                    

The function h(x) is a translation of the exponential function [tex]g(x) = 2(3)^{x - 4}[/tex] , is  [tex]h(x) = 4(3)^{x + 7} - 9[/tex]

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Related Questions

Directions:Solve this equation
[tex]5 + 5x= 12x - \frac{12}{5} \times 7\div 5[/tex]
Thanks to whoever answers! <3​

Answers

Answer:

-3.21538461538

Step-by-step explanation:

[tex]\mathrm{Equation\;Given:}\; 5+5x=\frac{12x-\frac{12}{5}\cdot \:7}{5}[/tex]

[tex]\mathrm{Multiply\;both\;sides\;by\;5}:[/tex]   [tex]5\cdot \:5+5x\cdot \:5=\frac{12x-\frac{12}{5}\cdot \:7}{5}\cdot \:5[/tex]

[tex]\mathrm{Now\;we\;have\;}:[/tex]  [tex]25+25x=12x-\frac{84}{5}[/tex]

[tex]\mathrm{Subtract\;by\;sides\;by\;25}:[/tex]   [tex]25+25x-25=12x-\frac{84}{5}-25[/tex]

[tex]\mathrm{Thus\;we\;have}:[/tex]  [tex]25x=12x-\frac{209}{5}[/tex]

[tex]\mathrm{Subtracting\;12x\;from\;both\;sides}:[/tex]  [tex]25x-12x=12x-\frac{209}{5}-12x[/tex]

[tex]\mathrm{So\;then\;we\;have:}[/tex] [tex]13x=-\frac{209}{5}[/tex]

[tex]\mathrm{Now\;divide\;both\;sides\;by\;13}:[/tex]  [tex]\frac{13x}{13}=\frac{-\frac{209}{5}}{13}[/tex]

[tex]\mathrm{Hence\;we\;have}:\;\;x=-\frac{209}{65}[/tex]

[tex]\mathrm{Decimal\;form}:-3.21538461538[/tex]

Kavinsky

Which is the graph of f(x)=3^x

Answers

The third graph from the figure represents the exponential function f(x) = 3ˣ, since the function contains the point (x, y) = (5, 243) on the cartesian plane.

How to determine the graph associated with a given function

In this question we must compare a given exponential function with a set formed by four functions. As the function is crescent and monotonous, then  we can choose the correct graph by a evaluating the function for a given x-value and find the graph that matches with such finding:

f(5) = 3⁵

f(5) = 243

The third graph from the figure represents the exponential function f(x) = 3ˣ, since the function contains the point (x, y) = (5, 243) on the cartesian plane.

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What is the sum of the first thirteen terms in a geometric series with a
r = 3 a1= -10

Answers

The sum of the first thirteen terms of the geometric series is -7971615.

What is Geometric series?

This is the sum of an infinite number of terms that has a constant ratio between successive terms.

To calculate the sum of the first thirteen terms of the geometric series, we use the formula below.

Formula:

S₁₃ = a(rⁿ-1)/(r-1).............. Equation 1

Where:

S₁₃ = Sum of the first thirteen terms of the geometric series.a = First term of the seriesr = Common ratio

Given:

a = -10r = 3n = 13

Substitute these values into equation 1

S₁₃ = -10(3¹³-1)/(3-1)S₁₃ = -7971615

Hence, the sum of the first thirteen terms of the geometric series is -7971615.

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What is the surface area?
2 mm
9 mm
3 mm

Answers

Answer:

Surface area of rectangular prism

=P×h

=2(l+w)×h

=2(3+9)×2

=48mm²

[tex] \boxed{ \frak{Answer}}[/tex]

Given,

Length (l) = 9 mm

Breadth (b) = 3 mm

Height (h) = 2 mm

To find: The surface of it.

We, know that

Surface area of a cuboid = 2(lb + bh + lh)

By using the formula,

= 2(lb + bh + lh)

= 2(9*3 + 3*2 + 9*2)

= 2( 27 + 6 + 18)

= 2(51)

= 102 mm²

Therefore the required surface area is 102 mm²

[tex] \boxed{ \frak{Keep \: Learning }}[/tex]

Can someone answer theese questions

Answers

Question 1 ) A ray has one endpoint and continues forever in the opposite direction

Question 2)

IG

Question3)

DC

Hope this helps!

GIVING BRAINLIEST AND 5 STARS TO BEST ANSWER!!! I HAVE 1 HOUR LEFT!!!!!!

Answers

Answer:

The origin is where x,y lines meet. I put a cirlce there with no label there. Sorry it's messy

Step-by-step explanation:

I'm only a 6th grader. No hate, please. I only did what I learned from my teacher.

The sum of Two numbers is 9. The
sum of the squares of the numbers is
41. Find the numbers.

Answers

Answer:

4 and 5

Step-by-step explanation:

Assuming your 2nd sentence should be: "The sum of the squares of the two numbers is 41"

X + Y = 9   {equation 1}

X² + Y² = 41  {equation 2}

from equation 1:  y = 9-x

Substitute that into equation 2

x² + (9-x)² = 41

x² + 81 - 18x + x²= 41

2x² - 18x + 40 = 0

We can factor out a 2

x² - 9x + 20 = 0

(x-5)(x-4) = 0

x = 5 or 4

checking

Your two numbers are 4 and 5

4² + 5² 

= 16 + 25

= 41

Simplify (3^-2)^4
O A. 1 /3^2
O B. 3^2
O c. 3^8
OD.1/3^8

Answers

[tex](3^{-2})^4 = 3^{-2 \times 4} = 3^{-8} = \dfrac 1{3^8}\\\\\text{Hence the answer is D.}[/tex]

Answer:

1/3^8

Step-by-step explanation:

[tex]\hookrightarrow (3^{-2} )^{4} \\[/tex]

As,

x⁻²=1/x²

Then,

[tex]\hookrightarrow (\frac{1}{3^{2} } )^{4} \\\\\hookrightarrow (\frac{1}{9} )^{4} \\\\\hookrightarrow ((\frac{1}{3} )^{2})^{4} \\\\\hookrightarrow (\frac{1}{3})^{8}[/tex]

Miguel is flying a kite, holding his hands a distance of 3.5 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 25


. If the string from the kite to his hand is 150 feet long, how many feet is the kite above the ground? Round your answer to the nearest tenth of a foot if necessary.

Answers

Answer:

66.9 ft

Step-by-step explanation:

Kite string forms a right triangle with the horizontal 3.5 feet off of the ground

sin 25  = opp / hyp  = height / 150

sin 25 = height / 150

150 sin25 = height      but it is 3.5 feet off of the ground...add that in

3.5  + 150 sin25 = true height = ~ 66.9 ft

Use the substitution method to determine the solution to the system of equations below. y-2x+2=1 6x - 3y = 3​

Answers

Answer:

y = 2x - 1

Step-by-step explanation:

y - 2x + 2 = 1

6x - 3y = 3​

[tex]y - 2x + 2 = 1 \\ +2x - 2 +2x - 2\\y = 2x - 1[/tex]

Plug in for y:

6x - 3(2x - 1) = 3​

6x - 6x + 3 = 3

Simplified, 3 = 3

Answer: this solution has infinite solutions

Step-by-step explanation:

original system:

y-2x+2 = 1

6x-3y = 3

Move 2 to right side of equation

y    -2x = -1

-3y+6x = 3

solve for y in first equation

⇒ y = 2x - 1

insert y into second equation

⇒ -3(2x-1) + 6x = 3

simplify

⇒ -6x+3+6x = 3

simplify once more

⇒ 3 = 3

this solution has infinite solutions

find the greatest common factor of 21 35 70​

Answers

Answer:

7

Step-by-step explanation:

21 = 3 x 7

35 = 7 x 5

70 = 2 x 5 x 7

The greatest common factor of 21, 35 and 70 is 7.

Note : -

The greatest common factor ( GCF ) of a set of numbers is the largest factor that all the numbers share.

Give the degree of the polynomial. 10yx^5w^4-w^3v^5-5x^11-6​

Answers

10yx⁵w⁴ - w³v⁵ - 5x¹¹ - 6

Degree = biggest exponent = 11

There are 24 students in a class and a decrease of 15%. How many students would you have?

Answers

Answer:

20

Step-by-step explanation:

85% of 24 is 20

What is the probability that a person with an iron deficiency is 20 years or older?
A.
0.23
B.
0.34
C.
0.60
D.
0.78

Answers

The answer to this is:

0.34

The probability that a person with an iron deficiency is 20 years or older will be 0.34. Then the correct option is B.

What is probability?

Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of occurrences.

The table is given below.

Then the probability that a person with an iron deficiency is 20 years or older will be

P = 102 / 300

P = 0.34

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Someone please check my answers for 5 & 6, correct me if they are incorrect. May someone also please help me with 7 & 8? Thank you!

Answers

For part 5 the total value is $1845, for part 6 the total net worth is $3200, and for part 7 the debt to assets value is 0.433.

What is debt?

It is defined as the amount one party needs to pay to another party as the first party borrowed an amount that will be credited by the second party. Debt occurs when one party cannot be able to purchase something under normal circumstances.

5)

Total value = 20×30 + 18×40 + 35×15 = $1845

6)

Net worth = (3500 + 300 + 600) - (1000+200) = $3200

7)

Total debt value = 2000+3200 = $5200

Total assets value = 10000+1300+700 = $12000

Debt to assets value = 5200/12000 = 0.433

Similarly, we can find any debt to assets value by using the formula:

Debt to assets value = Total debt/Total assets

Thus, for part 5 the total value is $1845, for part 6 the total net worth is $3200, and for part 7 the debt to assets value is 0.433.

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i need this answer fast and as soon as possible

Find the volume of the podium in the shape of a prism.

Answers

Answer:

8640

Step-by-step explanation:

1) Volume of the lower prism:

V1 = 27*20*12 = 6480

2) Volume of the higher prism:

V2 = 9*20*12 = 2160

3) Volume of the podium: V1 + V2 = 8640

How much should you invest at 3.7% simple interest in order to earn $70 interest in 11 months?

Answers

Step-by-step explanation:

in this condition we are given simple interest time and rate

so principal is missing so we should use the formula of principal that is

P=I×100/T×R

but we should convert that month in to years and we convert it by dividing it by 12.

What is the area of this shape?

Answers

The area of the composite shape in the image given is calculated as: 316 yd²

How to Find the Area of a Composite Shape?

To find the area of a composite shape, find the area of each of the shape that makes up the figure, then add their areas together.

The area of the composite shape = area of big rectangle + area of small rectangle + area of big triangle + area of small triangle

Area of big rectangle = (length)(width) = (5 + 4)(8) = 72 yd²

Area of small rectangle = (length)(width) = (5)(4) = 20 yd²

Area of big triangle = 1/2(base)(height) = 1/2(12)(4+5+4+7) = 120 yd²

Area of small triangle = 1/2(base)(height) = 1/2(8+5)(16) = 104 yd²

The area of the composite shape = 72 + 20 + 120 + 104 = 316 yd²

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If ( x - y ) = 2 and xy = 3 find the value of...
[tex] {x}^{3} + {y}^{3} [/tex]........

Answers

Answer: 4:7

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

Given :

x - y = 2xy = 3

Solving :

2 values which satisfy the given conditions are x = 3 and y = 1

Evaluating the expression :

x³ + y³(3)³ + (1)³27 + 128


A square has a perimeter of 40 feet. Find the length of the
diagonal of the square.

Answers

Answer:

14.14

Step-by-step explanation:

Answer:

The length of the diagonal of the square is about 14.142 feet

Step-by-step explanation:

Step 1:  Determine the length

[tex]P = 4(l)[/tex]

[tex]40\ ft = 4(l)[/tex]

[tex]\frac{40\ ft}{4}=\frac{4(l)}{4}[/tex]

[tex]10\ ft = l[/tex]

Step 2:  Determine the diagonal length

Pythagorean theorem → [tex]a^2 + b^2 = c^2[/tex]

a and b are going to be the sides of the square which are both 10 ft so we just plug those in and solve for c

[tex](10)^2 +(10)^2 =c^2[/tex]

[tex]100+100=c^2[/tex]

[tex]\sqrt{200}=\sqrt{c^2}[/tex]

[tex]14.142=c[/tex]

Answer:  The length of the diagonal of the square is about 14.142 feet

One number is ten more than twice another. Their sum is one. Find the numbers.​

Answers

answer:

x = 4

y = -3

steps :

x = 10 + 2y

x + y = 1

2y = x - 10 -> y = 1/2x - 5

x + y = 1 -> y = 1 - x

since theyre both equal to y they are equal to each other

1/2x - 5 = 1 - x

3/2x = 6

x = 4

plug 4 back where x is

y = 1 - 4

y = -3

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please help need asap

Answers

brainly.com/question/27661391 yo im begging some one to help

Step-by-step explanation:

Find the volume of the candle:

3^2 x 3.14 x 4= 113.04cubic inches.


now divide total wax used by volume of a candle.


3278.16 / 113.04 = 29 candles.

4.5,4.316,4.32,4.312 from least to greatest

Answers

4.5, 4.316, 4.32, 4.312

= 4.500, 4.316, 4.320, 4.312

Look at the thousandths and hundreths place in the decimal section.

Least to greatest = 4.312 < 4.316 < 4.32 < 4.5

4.312, 4.316, 4.32, 4.5 from least to greatest

5.
In the parallelogram ABCD, the diagonals AC and BD
are equal in length. What is the measure of the angle A
?
two
(A) 30
(B) 45
(C) 60
(D) 75
(E) 90
How to solve this?

Answers

Answer:

  (E) 90°

Step-by-step explanation:

The diagonals of a parallelogram are equal in length if and only if the parallelogram is a rectangle.

Any angle of a rectangle is 90°.

_____

Adjacent angles of a parallelogram are supplementary. If the diagonals are the same length, the triangles formed by either diagonal are congruent with the triangles formed by the other diagonal. This means adjacent angles are congruent. Congruent supplementary angles are 90°.

1/3x + 5 x= -6 need expression 1/3x = 5 is equal to __ when x = -6

Answers

Answer:

  3

Step-by-step explanation:

To evaluate an expression with a particular value of the variable, put that value where the variable is and do the arithmetic.

__

  1/3(-6) +5 = -2 +5 = 3

For x = -6, the value of the expression is 3.

The graphs below have the same shape. What is the equation of the graph of g(x)?
A. g(x)=x²-2
B. g(x) = (x + 2)²
C. g(x)=(x-2)^2
D. g(x)=x^2+2

Answers

Answer:

B. g(x) = (x + 2)²

Step-by-step explanation:

We got the graph of g by translating the graph of the parent function

f(x) = x² two units to the left

Therefore the equation of the graph of g is (x + 2)²


Work out 3 1/2 x 1 3/7, giving your answer in its simplest form?

Answers

let's firstly convert the mixed fractions to improper fractions and then get their product.

[tex]\stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} ~\hfill \stackrel{mixed}{1\frac{3}{7}}\implies \cfrac{1\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{10}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{2}\cdot \cfrac{10}{7}\implies \cfrac{7}{7}\cdot \cfrac{10}{2}\implies 1\cdot 5\implies 5[/tex]

how much is 27.99$ with 25% extra

Answers

Answer:

34.98

Simply add the 27.99 with 25%

= 34.98

Suppose the lengths of 3-year-old cats are normally distributed with a mean of 30 inches and a
standard deviation of 2.92 inches. Find each of the following:

1. The percent of cats between 24.16 and 35.84
2. The percent of cats who are longer than 35.84
3. The percent of cats shorter than 24.16 inches

Answers

1.  The percent of cats between 24.16 and 35.84 is 95%

2. The percent of cats who are longer than 35.84 is 2.28 %

3. The percent of cats shorter than 24.16 inches is 2.28%

What is the empirical rule formula in statistics?

The empirical rule - formula

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

Mean, u = 30 inches

Standard Deviation, s = 2.92 inches

Formula for z-score = (x-u)/s

1. We have to find the percent of cats between 24.16 and 35.84 inches.

24.16, z-score = -2

35.84, z-score = 2

According to the empirical rule,

95% of the data values are within 2 standard deviations of the mean.

So, 95% of the cats are between 24.16 and 35.84 inches.

2. Here, x = 35.84

   z=(35.84-30)/2.92

   z= 2

According to the Empirical Rule,

95% of the values lie within 2 standard deviations of the mean.

So, the percent of cats who are longer than 35.84

100 - 97.72 = 2.28%

3. Now, x = 36.22

Using the formula mentioned above, we get:

z= 24.16-30/2.92

z=-2

According to empirical rule,

68% of the values lie within 1 standard deviation of the mean.

i.e., remaining 32% are outside the 1 standard deviation and  half of the values i.e. 16% are below 1 standard deviation.

The percent of cats shorter than 24.16 inches is 2.28%

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Given

μ = 30 inσ = 2.92 in

Find z-scores for x = 24.16 and x = 35.84

Use formula

z = (x - μ)/σ 1) z = (24.16 - 30)/2.92 = - 22) z = (35.84 - 30)/2.92 = 2

Find the corresponding percentage from z-score table

z = - 2 ⇒ 2.28%z = 2 ⇒ 97.72%

Now find the answers#1

The percent of cats between 24.16 and 35.84

97.72 - 2.28 = 95.44%#2

The percent of cats who are longer than 35.84

100 - 97.72 = 2.28%#3

The percent of cats shorter than 24.16 inches

2.28%

Write a sequence of dilations and translations that maps circle D onto circle C and that shows the two circles you created are similar.

Answers

Answer: Circle d

Step-by-step explanation:

Circle D is the answer I believe
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