Describe the transformation of ƒ(x) = log5 x which is given by g(x) = 3 log5 (x−7). Question 16 options: A) g(x) is shrunk vertically by a factor of 1∕3 and translated to the right 7 units compared to ƒ(x). B) g(x) is stretched vertically by a factor of 2 and translated to the left 7 units compared to ƒ(x). C) g(x) is stretched vertically by a factor of 3 and translated to the right 7 units compared to ƒ(x). D) g(x) is shrunk vertically by a factor of 1∕3 and translated to the left 7 units compared to ƒ(x)

Answer:

Hope the picture helps

Answer:

6[tex]cm^{2}[/tex] (assuming the units is in centimetres)

Step-by-step explanation:

Hi, hope this helps!

Method 1:

Calculate this shape as a trapezium. This is a trapezium because it has one pair of parallel sides. The way to calculate the area of a trapezium is this:

- Half the sum of the parallel sides

- Multiply the perpendicular height between them

In this case, 4 and 2 are parallel, so we add them together (4 + 2 = 6) then we divide by two (6 ÷ 2 = 3). Then we multiply our answer by the perpendicular length between the two parallel sides (assuming the side on the left is at a right-angle, 3 x 2 = 6).

Method 2:

Calculate this shape as a rectangle + a triangle. If you split the shape so the pointy bit on the right becomes a triangle and the left becomes a square, you can calculate the area without knowing the formula for calculating a trapezium (see above ^).

- Area of the square / rectangle = length x width = 2 x 2 = 4

- Area of the triangle = 1/2 x length x width = 2 x 2 x 1/2 = 4 x 1/2 = 4 ÷ 2 = 2

Then we add the two areas together (4 + 2 = 6).

I hope this helped and I wasn't waffling on :)

Bluey

Answer:6

Step-by-step explanation:

A cdefghijklmnop

Step-by-step explanation:

Answer:

option a) multiply by 1/2

Step-by-step explanation:

2, 1 , 1/2 , 1/4 ....

Common ratio = 2nd term ÷ 1st term

                        = (1/2)÷ 1

                        = 1/2

Each term is obtained by multiplying by (1/2) with the previous term

Answer:

Step-by-step explanation:

A =3x² + 4x + 1

B = 5x² - 3x + 8

C = 4x² - 7x - 3

B + C –A is

5x² - 3x + 8 + 4x² - 7x - 3 - ( 3x² + 4x + 1)

Expand and simplify

We have

5x² - 3x + 8 + 4x² - 7x - 3 - 3x² - 4x -1

Group like terms

5x² + 4x² - 3x² - 3x - 7x - 4x + 8 - 3 - 1

We have the final answer as

Hope this helps you

Answer:

[tex]\boxed{\angle RQS = 56 \ degrees}[/tex]

[tex]\boxed{\angle SRT = 56 \ degrees}[/tex]

Step-by-step explanation:

A) ∠QRS = 90 degrees (The angle of the triangle opposite to the diameter is always 90)

Given that QR = 68 degrees

So,

∠RSQ = [tex]\frac{1}{2} (QR)[/tex]

∠RSQ = 68/2

∠RSQ = 34 degrees

Now, Finding ∠RQS

∠RQS = 180-90-34

∠RQS = 56 degrees

B) ∠SRT = ∠QRS - ∠QRT

=> ∠QRS = 90 (Mentioned above) , ∠QRT = 56 (Given)

So,

∠SRT = 90-56

∠SRT = 34 degrees

Answer:

Bob makes 15 dollars an hour mowing lawns.

The graph would be a straight line with a slope of 15.

Step-by-step explanation:

The Constant of Proportionality is y=kx, where k is the constant.  A real world example would be:

Bob makes 15 dollars an hour mowing lawns.  (y=15x)

The graph would be a straight line with a slope of 15.

Answer:

(-1,5) and [tex](3, \frac{1}{125})[/tex] are points on the graph

Step-by-step explanation:

Given

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

Required

Determine which point in on the graph

To get which of point A to D is on the graph, we have to plug in their values in the given expression using the format; (x,g(x))

A. (-1,5)

x = -1

Substitute -1 for x in [tex]g(x) = \frac{1}{5}^x[/tex]

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

Convert to index form

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

Change / to *

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

[tex]g(x) = 5[/tex]

This satisfies (-1,5)

Hence, (-1,5) is on the graph

B. (1,0)

x = 1

Substitute 1 for x

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

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

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

(1,0) is not on the graph because g(x) is not equal to 0

C. [tex](3, \frac{1}{125})[/tex]

x = 3

Substitute 3 for x

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

[tex]g(x) = \frac{1}{5}^3[/tex]

Apply law of indices

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

[tex]g(x) = \frac{1}{125}[/tex]

This satisfies [tex](3, \frac{1}{125})[/tex]

Hence, [tex](3, \frac{1}{125})[/tex] is on the graph

D.  [tex](-2, \frac{1}{25})[/tex]

x = -2

Substitute -2 for x

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

[tex]g(x) = \frac{1}{5}^{-2}[/tex]

Convert to index form

[tex]g(x) = 1/(\frac{1}{5}^2)[/tex]

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

[tex]g(x) = 1/(\frac{1}{25})[/tex]

Change / to *

[tex]g(x) = 1*(\frac{25}{1})[/tex]

[tex]g(x) = 25[/tex]

This does not satisfy  [tex](-2, \frac{1}{25})[/tex]

Hence, [tex](-2, \frac{1}{25})[/tex] is not on the graph

Answer:

A.) P^2 - 10p + 24 = 0

B.) 6 or 4 dollars

Step-by-step explanation:

Given that a company’s weekly revenue, in thousands, is modeled by the equation

R = -p2 + 14p,

where p is the price of the product it makes. The company is considering hiring an outside source to distribute its products, which will cost the company 4p + 24 thousand dollars per week.

If the company want to break even, the cost of hiring distributors will be equal to the revenue per week.

Therefore,

-P^2 + 14p = 4p + 24

Collect the like terms

-P^2 + 14p - 4p - 24 = 0

-P^2 + 10p - 24 = 0

Multiply all by minus sign

P^2 - 10p + 24 = 0

B.) To find P, factorize the equation above.

P^2 - 10p + 24 = 0

- 6 x - 4 = 24 and - 6 - 4 = 10

P^2 - 4p - 6p + 24 = 0

P( p - 4 ) - 6( p - 4 )

P - 6 = 0 or p - 4 = 0

P = 6 or 4

Substitute both back into the equation to test their authenticates

When p = 6

6^2 - 10(6) + 24 = 0

When p = 4

4^2 - 10(4) + 24 = 0

Answer: The correct answer is 3.6 miles

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

Well there is a .5 chance you get each side so in order for them all to land on the same side you do .5^3 which is .125 or 1/8

Answer: There are ways now to get from Andy's house to Willie's house.

Step-by-step explanation:

Given, from Dan's ranch one road is built to get to Andy's house and two roads are built to get to Willie's house.

Then, the number of ways to get from Andy's house to Willie's house =

(Number of ways to Andy's house) x (Number of ways to get Willie's house)   [Using fundamental counting principle]

= 1 x 2 = 2

Hence, there are ways now to get from Andy's house to Willie's house.

Answer:

Step-by-step explanation:

Displacement vector R = 2i + j +  3k

Unit vector along displacement vector

= R / I R I

= ( 2i + j +  3k )  / √ ( 2² + 1² + 3² )

= ( 2i + j +  3k )  / √ 14

Now force F acts in the direction of this unit vector . It is magnitude of 20 N

So this vector can be represented by the following expression

F = 20 [  ( 2i + j +  3k )  / √ 14 ]

[tex]F= \frac{20}{\sqrt{14} } \times ( 2i+j+3k)[/tex]

Answer:

The distance Ted will run in 285 minutes is 60 km

Step-by-step explanation:

The information in the question states as follows;

The distance Ted can run in 95 minutes = 20 km

Therefore, from the equation of speed, we have;

Speed = Distance covered ÷ Time taken

Ted speed, s = 20 km/(95 minutes) = 4/19 = 0.21 km/minute

Therefore, the distance, d Ted will cover in 285 minutes is given as follows;

d = Speed × Time = 0.21 km/minute × 285 minutes = 60 kilometres

The distance Ted will run in 285 minutes = 60 kilometres.

Answer:

285km=60

Step-by-step explanation:

Answer:

The awnser is 64

Step-by-step explanation:

It is 64 because you devide the perimiter (32) by 4, to get all sides, and then multiply 1 side by the other to get 64

THIS METHOD ONLY WORKS FOR A SQUARE

Answer: 5x - 2yz

Step-by-step explanation:

Answer:

112

Step-by-step explanation:

Answer:

112

Step-by-step explanation:

7² = 7 * 7 = 49    

4² = 4 * 4 = 16

7² + 3(4² + 3 + 2) = 49 + 3(16 + 3 + 2)

                           = 49  + 3 * 21

                           = 49 + 63

                           = 112

Answer:

P=2x +2y

2x=2y-p

As given that 2x=2(10)+88

x=108/2

x=54cm

May be it's help you;)

Answer:

The length of each of the two equally long sides is 26 cm

The length of the longer side is 36 cm

Step-by-step explanation:

Let the length of each of the two equal sides be represented by x

The other side = 10 + x

Perimeter of triangle (P) = sum of all sides of the triangle

88 = x + x + 10 + x

88 = 3x + 10

3x = 88 - 10

3x = 78

x = 78/3 = 26

Length of each of the two equally long sides (x) = 26 cm

Length of the longer side = 10 + x = 10 + 26 = 36 cm

Answer:

(-2, 21) and (8, 8)

Step-by-step explanation:

Use the two coordinate pairs (-2, 21) and (8, 8).  As we go horizontally from the first to the second, the run (change in x) is 10 and the rise (change in y) is -13.  Thus, the slope of the line through (-2, 21) and (8, 8) is m = rise / run = -13/10.

The equation of this line follows y - k = m(x - h):

y - 8 = (-13/10)(x - 8)

Answer:

(-32,0)

Step-by-step explanation:

Answer:

The correct answer is A. 600 square centimetres

Step-by-step explanation:

Let's recall that the formula of the surface area of a cube is:

A = 6s², where s  is the side length of the cube.

Replacing with the value we know, we have:

A = 6 * 10²

A = 6 * 100

A = 600 square centimetres

The correct answer is A. 600 square centimetres

For question 7, the output from left to right is:

20, 30, 40,  50, 60

For question 9, the output from left to right is:

6, 12, 18, 24

Explanation:

Using the rule (10=d-b) we can just add 10 to the input.

The same thing results with #9. We just need to add 4 to the input so that in the end u(output)-g(input)=4.

Hope this helps!! <3

Answer:

Step-by-step explanation:

7. Rule: 10=d-b

20-10=10

30-10=20

40-10=30

50-10=40

60-10=50

9. Rule: u-g=4

6-2=4

12-4=8

18-4=14

24-4=20

HOPE THIS HELPS!!!!!:)

Answer:

171 points.

Step-by-step explanation:

If five test scores have a mean of 90, all the scores added together will be 5 * 90 = 450.

The middle score is 91, so the other four scores added together will be 450 - 91 = 359.

The mode is higher than the median, so we can assume that the highest two numbers are the same: 94. 94 * 2 = 188. 359 - 188 = 171.

That means that the sum of the two lowest test scores is 171 points.

Hope this helps!

Answer:

The sum of the two lowest test scores is 171.

Step-by-step explanation:

We see that there are 5 test scores, so the median ( middle score ) was not taken to be the average of the two middle scores. It is an element present in the set of five test scores. The mode of course has to be present in the set, but multiple times. If we can figure out how many times this mode is present in the set, it would help us.

As 91 is the middle value, there has to be two above 91. Therefore, as 94 appears the most frequent, is must appear twice.

Now another key thing we need here is the sum of all 5 numbers. Given a mean of 90, 90 [tex]*[/tex] 5 = the sum of all 5 numbers = 450. Therefore, the sum of the two lowest test scores should be = 450 - 94 - 94 - 91 = 171 - which is our solution.

Answer:

320

Step-by-step explanation:

0.83333333x384=319.9999999=320

Answer:

25 in ^2

Step-by-step explanation:

First find the area of the circle

A = pi r^2

A = 3.14 ( 4.3)^2

A =58.0586

The take the fraction of the circle that is shaded

A circle is 360 degrees

155/360

155 /360 * the  total area = area shaded

31/72 * 58.0586 = 24.99745278 in ^2

Rounding yields 25 in ^2

Answer:

25[tex]in^2[/tex]

Step-by-step explanation:

To find the area we need to use the expression [tex]\frac{x}{360}[/tex] · [tex]\pi r^2[/tex]

When you substitute and solve you should get 25[tex]in^2[/tex]

Answer:

irrational

Step-by-step explanation:

rational - a number that can turn into a fraction (you could do this with a perfect square)

Irrational - a number that cannot be expressed as a fraction

The square root of 29 is an irrational number because it can not be expressed as a fraction.

To determine whether the square root of 29 is rational or irrational, we need to check if it can be expressed as a fraction (ratio) of two integers.

Assuming that the square root of 29 is rational, we can represent it as √29 = a/b, where a and b are integers with no common factors other than 1, and b is not equal to 0.

Squaring both sides of the equation (√29)² = (a/b², we get 29 = (a²)/(b²).

This implies that 29 is equal to the ratio of two integers (a²)/(b²), which means that 29 can be expressed as a fraction. However, this is not true because 29 is a prime number and cannot be written as a fraction of two integers.

Therefore, the square root of 29 cannot be expressed as a fraction and is therefore irrational.

Hence, the square root of 29 is an irrational number.

To learn more about irrational numbers;

https://brainly.com/question/33006214

#SPJ6

Answer:

(x + 3.5 ) / (x - 4 )  = 20 / 8

8x + 28 = 20x -80

12x = 108

x = 9

Step-by-step explanation:

Answer:

70 years

Step-by-step explanation:

35 years before Christ and then another 35 years after:  35 + 35 = 70 years

Answer:

Last graph showing 10 cookies and 5 brownies.

Step-by-step explanation:

There are more cookies (y-axis) than brownies (x-axis), the slope is 2.0 so the line must be > 45 degrees.  

Answer is the last graph which shows 10 cookies and 5 brownies.

Answer:

The graph that is closest to standing straight up.

Step-by-step explanation:

The bakery is preparing twice as many cookies than brownies, so for every brownie, the bakery bakes two cookies, which is represented in the graph.

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Work Shown:

A = area of larger rectangle

A = length*width = 9*15 = 135 square feet

B = area of smaller rectangle

B = length*width = 7*4 = 28 square feet

C = area of shaded region

C = difference in areas of A and B

C = A - B = 135 - 28 = 107 square feet

Answer:

242,000 is the present value of the house.

Step-by-step explanation:

Answer:

242,000 represents the value of the house

Step-by-step explanation:

Answer:

Well to convert it into a decimal we do 1 / 280 which is 0.00357142857.

Well the lengh of the non repeating is only 3 numbers .003.

And the lenght of the repeating block is 6 numbers 571428