Multiply this problem

12(17q+19)

Given that the volume of a rectangular prism is length x width x height, this problem can be solved by setting up the equation 2w * w * 8 = 400, where w is the width and 2w is the length. Solving this equation, we find that the width is 5 feet and the length is 10 feet.

In mathematics, the volume of a rectangular prism is given by the formula length x width x height. We are given that the volume of the storage container is 400 cubic feet, its height is 8 feet, and the length is twice the width. Let us denote the width as w, then the length is 2w.

From the given volume formula, we have:

Length x Width x Height = Volume

Substituting the values, we get:

2w * w * 8 = 400

Solving this equation, we find:

w^2 = 25

Taking the square root of both sides, we get:

w = 5

Substituting w=5 into 2w, we find the length:

Length = 2*5 = 10

So the width of the container is 5 feet and the length is 10 feet.

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Answer:

C. The growth factor of g is twice the growth factor of f.

Step-by-step explanation:

Let's find the growth factor of g(x) by getting its equation. To do it, we are using the standard exponential equation:

[tex]y=a(b+1)^x[/tex]

where

[tex]a[/tex] is the initial value

[tex]b[/tex] is the growth factor

We know form our graph that g(x) passes throughout (0, 3), so [tex]x=0[/tex] and [tex]y=3[/tex].

Replacing values

[tex]3=a(b+1)^0[/tex]

[tex]3=a(1)[/tex]

[tex]a=3[/tex]

We also know from our graph the g(x) passes throughout (1, 12), so [tex]x=1[/tex] and [tex]y=12[/tex].

Replacing values

[tex]y=a(b+1)^x[/tex]

[tex]12=3(b+1)^1[/tex]

[tex]12=3(b+1)[/tex]

[tex]b+1=\frac{12}{3}[/tex]

[tex]b+1=4[/tex]

[tex]b=4-1[/tex]

[tex]b=3[/tex]

The growth factor of g(x) is 4.

Now, to find the growth factor of f(x), we just need to equate 1+b with [tex]\frac{5}{2}[/tex] and solve for b:

[tex]1+b=\frac{5}{2}[/tex]

[tex]b=\frac{5}{2} -1[/tex]

[tex]b=\frac{3}{2}[/tex]

[tex]b=1.5[/tex]

Finally, we can divide the growth factor of g(x) by the growth factor of f(x) to find how many times bigger is the growth factor of g(x):

[tex]\frac{3}{1.5} =2[/tex]

We can conclude that the growth factor of g is twice the growth factor of f.

Answer:

C

Step-by-step explanation:

ANSWER

r is not a set of ordered pair

EXPLANATION

A relation is a correspondence between two sets.

In a relation, the elements from one set set (domain) maps on to the elements in a second set(co-domain).

The relation can then be written as an ordered pair (x,y).

The given listing is

r={√3,√5,√7, √13}

This is not an ordered pair so it cannot be a relation.

The third choice is correct.

Answer:

Choice C is correct, r is not a set of ordered pairs

Step-by-step explanation:

A relation between sets of data is a collection of ordered pairs which contain one object from each set. If the element x is from the first set and its corresponding object y from the second set, then the objects are said to be related if the ordered pair (x,y) is in the relation.

X comprises of the domain while Y makes up the range.

Therefore, r is not a relation since it is not a set of ordered pairs.

Answer:

1. 5:3:2

2. 4:5

3. 6:5

4. 2:5:6

5. 2:5

6. 7:5

7. 3:1:2

8. 1.0:0.6

9. 1:1.5

10. 0.2:0.5:0.8

Step-by-step explanation:

1. divide everything by 3

2. divide everything by 4

3. divide everything by 6

4. divide everything by 6

5. divide everything by 6

6. divide everything by 8

7. divide everything by 4

8. divide everything by 7

9. divide everything by 3

10. divide everything by 6

Answer::

1. 5:3:2

2. 4:5

3. 6:5

4. 2:5:6

5. 2:5

6. 7:5

7. 3:1:2

8. 1.0:0.6

9. 1:1.5

10. 0.2:0.5:0.8

I hope this helps! :-)

Answer:

A

Step-by-step explanation:

3x² + 6 - 2x + 5x - 4x² + 9

Combine like terms:

3x² - 4x² - 2x + 5x + 6 + 9

-x² + 3x + 15

Final answer:

To simplify the polynomial, combine like terms by adding or subtracting coefficients of terms with the same variable and exponent. The terms simplify to -x^2 + 3x + 15, matching option A.

Explanation:

The subject of the student's question involves simplifying a polynomial. To simplify the given polynomial 3x2 + 6 - 2x + 5x - 4x2 + 9, we need to combine like terms. This process involves adding or subtracting the coefficients of terms with the same variable and exponent. Let's go through the steps:

Combine the terms with x2: 3x2 - 4x2 = -1x2

Combine the terms with x: -2x + 5x = 3x

Add the constant terms: 6 + 9 = 15

Putting it all together, the simplified form of the polynomial is -x2 + 3x + 15, which matches option A.

Remember, when simplifying polynomials, always look for like terms that can be combined and ensure the final expression is written in standard form, with terms ordered from highest to lowest degree.

Answer:

35

Step-by-step explanation:

The geometric mean of n numbers is the n-th root of their product.

The geometric mean of these two numbers is ...

√(245·5) = √1225 = 35

Answer:

35

Step-by-step explanation:

Take the product of the two numbers, then get the square root of the product.

[tex]245*5=1225\\\sqrt{1225} = 35[/tex]

Answer:

Step-by-step explanation:

-3x²-(4x²-x)

=-3x²-4x²+x

=-7x²+x

Answer:

[tex]-7x^2+x[/tex]

Step-by-step explanation:

(4x2-x) from -3x2 is

Subtract [tex]4x^2-x from -3x^2[/tex]

[tex]-3x^2 - (4x^2-x)[/tex]

Remove the parenthesis by multiplying negative sign inside the parenthesis

[tex]-3x^2 - 4x^2+x[/tex]

Now combine like terms, add -3 and -4 and it becomes -7

[tex]-7x^2+x[/tex]

Answer:

x = 15

Step-by-step explanation:

Answer:

x = 15

Step-by-step explanation:

13+6+2x-18=4x-29​

Combine like terms

2x + 1 = 4x - 29

Subtract 4x from both sides

-2x + 1 = - 29

Subtract 1 from both sides

-2x = -30

Divide both sides by -2

x = 15

The median of these numbers is: 7

3,4,5,5,6,7,7,8,10,10,10

Answer:

the median would be 7

Step-by-step explanation:

Answer:

A. (x - 1)(x - 8)

Step-by-step explanation:

By looking at the graph, we can see that the polynomial has roots at x = 1 and 8. This means that the function in factored form would look like (x - 1)(x - 8).

Answer:

A) (x - 1)(x - 8)

Step-by-step explanation:

Apex

Here is what i figured out.

Answer:

First, to find the median, we have to order all numbers, from least to highest:

Now, we calculate the position of each quartile:

[tex]Q_{k}=\frac{k(n+1)}{4}\\Q_{1}=\frac{1(15+1)}{4}=4\\Q_{2}=\frac{2(15+1)}{4}=8\\Q_{3}=\frac{3(15+1)}{4}=12[/tex]

So, the first quartile is in the fourth position, the thirds quartile is in the twelfth position:

So, first quartile is 6.1. Second quartile is 14.6, and the third quartile is 27.1.

It's important to remember that the second quartile is the median. So the median is 14.6

Lastly, the interquartile range is the difference between the third and first quartile. So:

[tex]Q_{3}-Q_{1}=27.1-6.1=21[/tex]

Therefore, the interquartile range is 21.

Answer:

It all depends on the type of coins stacked

The stack of coins with the greatest volume is the one with the largest number of coins and the largest diameter.

Final Answer: The stack of coins with the greatest volume is the one with the largest number of coins and the largest diameter.

To calculate the volume of a stack of coins, we can use the formula for the volume of a cylinder,[tex]V = πr^2h,[/tex] where V is the volume, r is the radius of the coin, and h is the height of the stack.

Since each stack has the same height, we only need to compare the volumes based on the number of coins and their diameter.

First, let's assume the radius of each coin is r and the height of each stack is h. Let's denote the number of coins in each stack as n.

Now, let's calculate the volume for each stack:

1. Stack 1: Volume = [tex]πr^2 * h * n1[/tex]

2. Stack 2: Volume = [tex]πr^2 * h * n2[/tex]

3. Stack 3: Volume = [tex]πr^2 * h * n3[/tex]

Since all stacks have the same height (h), we can disregard it in the comparison.

To compare the volumes, we need to compare the number of coins (n) and the radius of the coins (r).

Let's assume Stack 1 has the largest number of coins, followed by Stack 2 and then Stack 3.

If all stacks have the same number of coins, then the one with the largest diameter (which is the radius times 2) would have the greatest volume.

After calculating the volumes for each stack, we can determine which stack has the greatest volume based on the number of coins and their diameter.

Complete question:

If each stack of coins has the same height, which stack of coins has the greatest volume?

Answer: Option A

[tex]\sigma ^ 2 = 2.25[/tex]

Step-by-step explanation:

The number of faces obtained by flipping the coin 9 times is a discrete random variable.

If we call this variable x, then, the probability of obtaining a face in each test is p.

Where [tex]p = 0.5[/tex]

If we call n the number of trials then:

[tex]n = 9[/tex]

The distribution of this variable is binomial with parameters

[tex]p = 0.5\\\\n = 9[/tex]

For a binomial distribution, the variance "[tex]\sigma^2[/tex]" is defined as

[tex]\sigma ^ 2 = np(1-p)[/tex]

[tex]\sigma ^ 2 = 9(0.5)(1-0.5)[/tex]

[tex]\sigma ^ 2 = 9(0.5)(0.5)[/tex]

[tex]\sigma ^ 2 = 2.25[/tex]

Answer:

480

Step-by-step explanation:

Answer:

480

Step-by-step explanation:

4/100 is 4% so find 4% of 12,000

12,000(.04) = 480

Answer:

the radius of sphere X is 2 times larger than the radius of sphere T

Step-by-step explanation:

Given

Surface area of sphere, T =452.16

Surface area of sphere, X= 1808.64

how many times larger is the radius of sphere X than the radius of sphere T?

Finding radius of both spheres:

Surface area of sphere is given as

A=4πr^2

Now putting value of Ta=452.16 in above formula

452.16=4πrt^2

rt^2=452.16/4π

rt^2=35.98

Taking square root on both sides

rt=5.99

Now putting value of Xa=1808.64 in above formula

1808.64=4πrx^2

rx^2=1808.64/4π

rx^2=143.92

Taking square root on both sides

rx=11.99

Comparing radius of sphere X and the radius of sphere T

rx/rt=11.99/5.99

      = 2.00

rx=2(rt)

Hence the radius of sphere X is 2 times larger than the radius of sphere T!

The answer is:

The radius of the  sphere X is 2 times larger than the radius of the sphere T

To solve the problem, we need to find the radius of both spheres using the following formula:

[tex]Area=\pi *radius^{2}\\\\radius=\sqrt{ \frac{Area}{\pi }}[/tex]

Where,

Area, is the area of the circle.

r, is the radius of the circle.

So,

We are given:

[tex]T_{area}=452.16units^{2}\\X_{area}=1808.64units^{2}[/tex]

Now, calculating we have:

For the sphere X,

[tex]X_{radius}=\sqrt{ \frac{X_{area}}{\pi }}=\sqrt{\frac{1808.64units^{2} }{\pi } }\\\\X_{radius}=\sqrt{\frac{1808.64units^{2} }{\pi }}=\sqrt{575.71units^{2} }=23.99units[/tex]

For the sphere T,

[tex]T_{radius}=\sqrt{ \frac{T_{area}}{\pi }}=\sqrt{\frac{452.16units^{2} }{\pi } }\\\\X_{radius}=\sqrt{\frac{452.16units^{2} }{\pi }}=\sqrt{143.93units^{2} }=11.99units[/tex]

Then, dividing the radius of the X sphere by the  T sphere to know the ratio (between their radius), we have:

[tex]ratio=\frac{23.99units}{11.99units}=2[/tex]

Hence, we have the radius of the sphere X is 2 times larger than the radius of the sphere T.

Have a nice day!

ANSWER

[tex]a_{7}= - 20[/tex]

EXPLANATION

The sequence is defined recursively by:

[tex]a_{n+1}=-2a_n+4[/tex]

Where

[tex]a_1=1[/tex]

[tex]a_{2}=-2a_1+4[/tex]

[tex]a_{2}=-2(1)+4 = 2[/tex]

[tex]a_{3}=-2a_2+4[/tex]

[tex]a_{3}=-2(2)+4 = 0[/tex]

[tex]a_{4}=-2a_3+4[/tex]

[tex]a_{4}=-2(0)+4 = 4[/tex]

[tex]a_{5}=-2a_4+4[/tex]

[tex]a_{5}=-2(4)+4 = - 4[/tex]

[tex]a_{6}=-2a_5+4[/tex]

[tex]a_{6}=-2( - 4)+4 = 12[/tex]

[tex]a_{7}=-2a_6+4[/tex]

[tex]a_{7}=-2(12)+4 = - 20[/tex]

Answer:

not really sure what answer you want. but you have a 50/50 chance of picking a green or purple marble.

Step-by-step explanation:

Answer:

10/20 = 1/2

Step-by-step explanation:

There are 10 purple marbles and 20 marbles in total. The chances of picking a purple marble is 10/20. 10/20 simplifies to 1/2.

Answer:

4.68

Step-by-step explanation:

Remember to line up the decimal point. Subtract as ordinarily.

8.31

-3.43

--------

4.68

4.68 is your answer

~

The graph fourth represents the inequality x ≤ 4000 if in the past 15 years, a business owner has made at most $4,000 in profits each week option fourth is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.

We have:

Over the past 15 years, a business owner has made at most $4,000 in profits each week.

So the peak value is $4,000

Let's suppose the business owner earns $x profit each week, then we can frame an inequality:

x ≤ 4000

From the above inequality, the value of x will be:

x belongs to (0, 4000)

Thus, the graph fourth represents the inequality x ≤ 4000 if in the past 15 years, a business owner has made at most $4,000 in profits each week option fourth is correct.

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Answer:

First question: The common ratio r is 3

Second question: The average rate of change is 297.92

Third question: The function's graph of h(x) = 0.5(2^x) + 0.5 has a

y-intercept of 1

Fourth question: The ordered pairs lie on the graph of f(x) are (2 , 18)

and (0 , 2)

Step-by-step explanation:

First question:

* Lets revise the rule of the geometric sequence

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)

* General term (nth term) of a Geometric sequence:

- U1 = a  ,  U2  = ar  ,  U3  = ar2  ,  U4 = ar3  ,  U5 = ar4

- Un = ar^n-1, where a is the first term , r is the constant ratio

 between each two consecutive terms  and n is the position

 of the term in the sequence

* Now lets solve the question

∵ The sequence is 16 , 48 , 144 , 432 , ................

∵ a = 16

∵ ar = 48

∴ r = 48/16 = 3

∴ The sequence is geometric withe common ratio 3

* The common ratio r is 3

Second question:

* Lets revise the average rate of change of a function

- When you calculate the average rate of change of a function,

  you are finding the slope of the secant line between the two points

  on the function

- Average Rate of Change  for the function y = f (x) between

 x = a and x = b is:

 change of y/change of x = [f(b) - f(a)]/(b - a)

* Now lets solve the problem

∵ g(x) = 50(12^x), where x ∈ [-1 , 1]

∵ a = -1 and b = 1

∵ f(-1) = 50(12^-1) = 50/12

∵ f(1) = 50(12^1) = 600

∴ Average Rate of Change  = [600 - 50/12]/[1 - (-1)]

∴ Average Rate of Change  = [595.8333]/[2] = 297.92

* The average rate of change is 297.92

Third question:

* Lets talk about the y- intercept

- When any graph intersect the y-axis at point (0 , c), we called

 c the y-intercept

- To find the y- intercept, substitute the value of x in the

  function by zero

* Now lets check which answer will give y- intercept = 1

∵ h(x) = 0.5(2^x) + 0.5 ⇒ put x = 0

∴ h(0) = 0.5(2^0) + 0.5 = 0.5(1) + 0.5 = 1

∵ h(x) = (0.5)^x + 1 ⇒ put x = 0

∴ h(0) = (0.5)^0 + 1 = 1 + 1 = 2

∵ h(x) = 5(2^x) ⇒ put x = 0

∴ h(0) = 5(2^0) = 5(1) = 5

∵ h(x) = 5(0.5)^x + 0.5

∴ h(0) = 5(0.5)^0 + 0.5 = 5(1) + 0.5 = 5.5

* The function's graph of h(x) = 0.5(2^x) + 0.5 has a y-intercept of 1

Fourth question:

* Lets study how to find a point lies on a graph

- When we substitute the value of x of the point in the function

 and give us the same value of y of the point, then the point

 lies on the graph

* Now lets solve the problem

∵ f(x) = 2(3)^x

∵ The point is (2 , 18) ⇒ put x = 2

∴ f(2) = 2(3)² = 2(9) = 18 ⇒ the same y of the point

∴ The point (2 , 18) lies on f(x)

∵ The point is (0 , 2) ⇒ put x = 0

∴ f(0) = 2(3)^0 = 2(1) = 2 ⇒ the same y of the point

∴ The point (0 , 2) lies on f(x)

∵ The point is (-1 , 1) ⇒ put x = -1

∴ f(-1) = 2(3)^-1 = 2(1/3) = 2/3 ⇒ not the same y of the point

∴ The point (-1 , 1) does not lie on f(x)

∵ The point is (3 , 56) ⇒ put x = 3

∴ f(3) = 2(3)³ = 2(27) = 54 ⇒ not the same y of the point

∴ The point (3 , 56) does not lie on f(x)

* The ordered pairs lie on the graph of f(x) are (2 , 18) and (0 , 2)

Answer:

3eeddw

Step-by-step explanation:

[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ \cline{1-1} a_1=21\\ r=2\\ n=25 \end{cases} \\\\\\ S_{25}=21\left( \cfrac{1-2^{25}}{1-2} \right)\implies S_{25}=21\left( \cfrac{-33554431}{-1} \right) \\\\\\ S_{25}=21(33554431)\implies S_{25}=704643051[/tex]

A = (1/2)(x)(y)

Let x = diagonal 1

Let y = diagonal 2

The product of xy = 144.

This means that x = 12 and y = 12.

So, 12 • 12 = 144

Each diagonal is 12 feet.

Prove:

72 feet = (1/2)(12)(12) feet

72 feet = (1/2)(144) feet

72 feet = 72 feet

To find the length of each diagonal of the rhombus, we'll use the relationship between the area of a rhombus and its diagonals. The formula for the area (A) of a rhombus in terms of its diagonals (d1 and d2) is given by:
\[ A = \frac{d1 \cdot d2}{2} \]
Additionally, we are given the product of the diagonals, which means:
\[ d1 \cdot d2 = 144 \]
Since we are also given the area of the rhombus, which is 72 square feet, we can write:
\[ 72 = \frac{d1 \cdot d2}{2} \]
\[ 144 = d1 \cdot d2 \]
We have two equations with two variables, which we can solve simultaneously. However, in this case, since both equations involve the product of d1 and d2, we can use the given product directly. We know that:
\[ 2 \cdot 72 = 144 \]
\[ d1 \cdot d2 = 144 \]
We can use a property of numbers that states that the product of two numbers is equal to the square of their average if and only if the two numbers are the same. However, here we are interested in finding two different numbers whose product is 144.
We can do this by breaking down 144 into pairs of factors and then checking which pair would satisfy the condition that their product divided by 2 is equal to 72. The pair of factors of 144 that add up to 144 when multiplied and divide to 72 when halved are the actual lengths of the diagonals.
One way to determine the pair is through the process of factoring 144:
\[ 144 = 1 \times 144 \]
\[ 144 = 2 \times 72 \]
\[ 144 = 3 \times 48 \]
\[ 144 = 4 \times 36 \]
\[ 144 = 6 \times 24 \]
\[ 144 = 8 \times 18 \]
\[ 144 = 9 \times 16 \]
\[ 144 = 12 \times 12 \]
We need to find two different factors since a rhombus's diagonals are not equal. Among the listed factors, the pair 18 and 8 satisfy the condition because:
\[ \frac{18 \cdot 8}{2} = \frac{144}{2} = 72 \]
So, the lengths of the diagonals of the rhombus are 18 feet and 8 feet.

C=$0.25m+$15 because 0.25 is the slope and 15 is the y-intercept.

C stands for Cost

M stands for Minute

Final answer:

The cost of international calls can be calculated using the explicit function rule C(m) = 15 + 0.25m, where m is the number of minutes and $15 is the flat fee.

Explanation:

The student asks for an explicit function rule that represents the monthly cost of international calls given a $15 flat fee and a rate of $0.25 per minute. To address this, we introduce a function where C(m) represents the total cost of making international calls for m minutes in a month.

The cost function is C(m) = 15 + 0.25m. The term $15 flat fee is the initial cost regardless of call duration, and $0.25 per minute is the variable rate that depends on the total minutes used.

If for example, a user talked for 100 minutes, the calculation would be C(100) = 15 + 0.25(100) = 15 + 25 = $40.

Answer:

(x + 2)²(x - 1)

Step-by-step explanation:

Factorise the denominators of both fractions

x² + 4x + 4 ← is a perfect square = (x + 2)²

x² + x - 2 = (x + 2)(x - 1)

The fractions can be expressed as

[tex]\frac{x(x-1)}{(x+2)^2(x-1)}[/tex] and [tex]\frac{2(x+2)}{(x+2)^2(x-1)}[/tex]

least common multiple is (x + 2)²(x - 1)

Answer:

Step-by-step explanation:

We have the square in the base with side a = 4in and four triangles with base a = 4in and height h = 6.9in.

The formula of an area of a square:

A = a²

Substitute:

As = 4² = 16 in²

The formula of an area of a triangle:

A = (ah)/2

Substitute:

At = [(4)(6.9)]/2 = 27.6/2 = 13.8 in²

The Surface Area:

S.A. = As + 4At

Substitute:

S.A. = 16 + 4(13.8) = 16 + 55.2 = 71.2 in²

Answer:5

Step-by-step explanation:

6:30 is the ration

6/30 reduced is 1/5

1:5

so its 5

Max walks 0.2 laps per minute around the track. This conclusion was reached by dividing the total number of laps (6) by the total number of minutes (30).

The Mathematics problem posed is one concerning rates. It is given that Max walks 6 laps in 30 minutes. We need to find out how many laps would Max be able to walk in 1 minute.

To do this, we divide the total number of laps walked by the total number of minutes. In this case, we would divide 6 laps by 30 minutes.

6 laps ÷ 30 minutes = 0.2 laps per minute

Therefore, Max walks 0.2 laps around the track in 1 minute.

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Answer:

42,223 gallons

Step-by-step explanation:

Find the volume of the pool and then multiply that by the conversion factor 1 ft³: 7.5 gallons.

If the pool diameter is 32 feet, then the pool radius is 16 feet.

The volume here is V = πr²h, or V = π(16 ft)²(7 ft) = 5629.73 ft³

Multiplying this volume by 1 ft³: 7.5 gallons, we get:

(5630 ft³)(7.5 gallons / 1 ft³) = 42,223 gallons

10 in Actual 35 ft

20 in Actual 70ft

Part B 735 dollars

ANSWER

A. 38°

EXPLANATION

The tangent, AC to the circle meets the diameter AB to the circle at right angle.

This implies that,

[tex]m \angle BAY + m \angle YAC = 90 \degree[/tex]

Substitute the given angle:

[tex]52 \degree + m \angle YAC = 90 \degree[/tex]

[tex]m \angle YAC = 90 \degree - 52 \degree[/tex]

[tex]m \angle YAC = 38 \degree[/tex]

Using the tangent theorem and the inscribed angle theorem, m∠YAC is: A. 38°

According to the tangent theorem, a right angle (90°) is formed at the point of intersection between the radius and the tangent of a circle.

m∠BAY = m(BY) = 52° (inscribed angle theorem)

m∠BAC = 90° (tangent theorem)

m∠YAC = m∠BAC - m∠BAY

Substitute

m∠YAC = 90 - 52 = 38°

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Answer:

Statement b is true; statement a is false

Step-by-step explanation:

Best to write out (f o g)(x) and then determine its domain:

"(f o g)(x)" indicates that g(x) is used as the input to f(x):

(f o g)(x) = 5(√x+6) + 7, or 5√x + 30 + 7, or 5√x + 37.

The domain of this composite function is [0, infinity).

Thus, statement b is true:  "9 is part of the domain of (f o g)(x) = 5(√x+6) + 7"

To determine which statement is true, we will need to look at the functions f(x) and g(x) and their composition (f ° g)(x), which means we plug g(x) into f(x).
The given functions are:
f(x) = 5x + 7
g(x) = √x + 6
The composition of the functions (f ° g)(x) is f applied to g(x), which would be:
(f ° g)(x) = f(g(x)) = f(√x + 6)
This simplifies to:
(f ° g)(x) = 5(√x + 6) + 7
To be able to plug a number into (f ° g)(x), it must first be in the domain of g(x), and then the result of g(x) must be in the domain of f(x). The domain of g(x) is defined by the set of all x for which g(x) is real and defined. Since g(x) includes a square root, x must be non-negative (x ≥ 0). For f(x), the domain is all real numbers since linear functions are defined for all real x.
So, to determine if 9 is in the domain of (f ° g)(x), we will do the following:
1. Verify if 9 is in the domain of g(x). Since the domain of g(x) includes all x ≥ 0 and 9 ≥ 0, 9 is in the domain of g(x).
2. Calculate g(9) to determine if the output is within the domain of f(x):
  g(9) = √9 + 6
  g(9) = 3 + 6 (because √9 is 3)
  g(9) = 9, which is a real number and thus in the domain of f(x).
3. Since we have that g(9) is in the domain of f(x), we can compute (f ° g)(9):
  (f ° g)(9) = f(g(9))
  (f ° g)(9) = f(9)
  (f ° g)(9) = 5 * 9 + 7
  (f ° g)(9) = 45 + 7
  (f ° g)(9) = 52
Thus, we have found that 9 is in the domain of g(x), and that (f ° g)(9) is defined and equals 52. This means that statement B, "9 is in the domain of f ° g," is true.