Question 5
Kate is finding the factors of a large number. Using
a calculator, she has just worked out that 66 is a
factor of this number.
Suddenly, she realises that 22 must be a factor of
the large number as well. Explain why Kate is
correct.

Answers

Answer 1

Explanation : If 66 is a factor of this unknown value, then 22 must be as well considering that 22 is a factor off 66. Let's say that this large value is 330. It is a multiple of 66, as 66 [tex]*[/tex] 5 = 330. At the same time 22 [tex]*[/tex] 15 = 330, so 330 is a multiple of 22 as well - or vice versa, 12 is a factor of 330.

We can also tell that 15, 22 fit into 330 through another approach. 22 [tex]*[/tex] 3 = 66, and 66 [tex]*[/tex] 5 = 330, so 5 [tex]*[/tex] 3 = 15 - the same value. This proves that 22 will always be a factor of a value that is the factor of 66.

Answer 2
Any multiple of the number will be a factor or result of the number It could factor in or go into an equal amount of times

Related Questions

Maria’s office is located at (–7,–5) on the coordinate plane. Her home is located at (4,–6) and the supermarket is located at (–2,–6). When returning back from the office, she first goes to the supermarket to buy some groceries, and then goes back home. Find the total distance she traveled from her office to home. A. 146−−−√+6 units B. 26−−√+6 units C. 82−−√+6 units D. 202−−−√+6 units

Answers

Answer:

B. 6 + √26

Step-by-step explanation:

1. Make a right triangle using the line that goes from office to supermarket.

2. Use pythagorean thereom to find the distance of the longest side.

3. FInd the distance of the line segment going from supermarket to Marias House.

4. Add them together to get 6 + √26.

Answer:

B.

Step-by-step explanation:

1. Make a right triangle using the line that goes from office to supermarket.

2. Use Pythagorean theorem to find the distance of the longest side.

3. Find the distance of the line segment going from supermarket to Maria's House.

4. Add them together to get 6 + √26.

PLEASE HELP!!! Will give brainliest to quickest CORRECT answer. No explanation needed :) Rebekah manages a yoga studio that charges each customer a one-time initial fee of $35 and an additional fee of $12 per class taken. Rebekah's goal is for each customer to spend at least $100 at the studio, and she wants to know the minimum number of classes a customer needs to take to meet that goal. Let C represent the number of classes a customer takes. 1) Which inequality describes this scenario? A. 35+C≤100 B. 35+3≥100 C. 35+12C≤100 D. 35+12C≥100 2) What is the minimum number of classes a customer can take for Rebekah to meet her goal?

Answers

The first question is D! Second question is 5!

35 dollar fee + 12 per class taken, to reach the amount of 100 :)

100-35= 65
65/12 = 5 if you aren’t using remainders, if you are it would be 5.416 repeated

The inequality that describes the scenario will be; 35  +  12C  ≥  100.

The minimum number of classes a customer can take for Rebekah to meet her goal is 6

What is inequality?

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

One-time initial fee = $35

Additional fee per class = $12

Minimum target = $100

Number of classes = C

One-time initial fee  +  (Additional fee per class) x (Number of classes) ≥ Minimum target

The inequality that describes the scenario will be;

35  +  12C  ≥  100

Then Solve for C to know the minimum number of classes a customer can take for Rebekah to meet her goal,

12C  ≥  100 - 35

12C  ≥  65

C   ≥   65 / 12

C  ≥  5.42

Thus, The minimum number of classes a customer can take for Rebekah to meet her goal is 6

Learn more about inequality ;

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Which of the following statements is true for a function with equation Ax) = 5(3)*?
The graph has y-intercept (0,5) and increases with a constant ratio of 3.
The graph has y-intercept (0, 3) and decreases with a constant ratio of 3.
The graph has y-intercept (0, 3) and increases with a constant ratio of 5.
The graph has y-intercept (0,5) and decreases with a constant ratio of 3.

Answers

Answer:

Hey there!

The graph has a y-intercept of (0,5), and increases with a common ratio of 5. (For example, it increases from 3, 15, 75, and the common ratio is 5.  

Hope this helps :)

don’t have the answer but you have it already:)

solve the equation
[tex] {5}^{n + 1} - {5}^{n} + {5}^{n - 1} = 105[/tex]

Answers

Answer:

n=2

Step-by-step explanation:

Hello, please consider the following.

[tex]{5}^{n + 1} - {5}^{n} + {5}^{n - 1} = 105\\\\5^{n-1}(5^2-5+1)=5^{n-1}(25-5+1)=21*5^{n-1}=105\\\\5^{n-1}=\dfrac{105}{21}=5=5^1\\\\\text{It means that}\\\\n-1=1 <=> n=2[/tex]

Let me know if you need more details.

Thank you

n=2 is the correct answer yes

What effect will replacing x with (x−3) have on the graph of the equation y=x2 y = x 2 ? A. slides the graph 3 units down B. slides the graph 3 units right C. shrinks the graph by a factor of 3 D. slides the graph 3 units left

Answers

Answer:

  B. slides the graph 3 units right

Step-by-step explanation:

Replacing x with x-h moves the graph 'h' units to the right. In this case, the graph is moved 3 units right by replacing x with x-3.

The correct answer would be B) slides the graph 3 units right.

plsss help meeeeeee!!!! Jakes club has 35 members. it's rules require that 60% of them must be present for any vote. at least how many members must be present to have a vote?

Answers

Answer:

21 members

Step-by-step explanation:

Jake's club

Total number of members = 35

percentage of members required to be present for any vote = 60%

= 60/100 × 35

= 0.6 × 35

= 21

At least 21 member must be present

Which set below is the domain of
{(2, -3),(-1,0), (0,4),(-1,5),(4, -2)}?
(AD {-3, 0, 4, 5, -2} (CD, {2,-1,4}
(3) -3,4,5,-2) (D) {2,-1,0,4}​

Answers

Answer:

Domain { -1,0,2,4}

Step-by-step explanation:

{(2, -3),(-1,0), (0,4),(-1,5),(4, -2)}

The domain is the input values

Domain { 2,-1,0,-1,4}

We normally write them in order from smallest to largest and no repeating

Domain { -1,0,2,4}

Answer:

[tex]\large \boxed{\sf D. \ \{2,-1,0,4\}}[/tex]

Step-by-step explanation:

The domain are all possible values of x.

[tex]\{(2, -3),(-1,0), (0,4),(-1,5),(4, -2)\}[/tex]

The x values are 2, -1, 0, -1, and 4.

The domain of the set is {2,-1,0,4}​.

Two cities, A and B, are mapped on the coordinate plane. How far apart are they from each other? A. 145−−−√ units B. 97−−√ units C. 5 units D. 73−−√ units

Answers

Answer:

B

Step-by-step explanation:

From the graph we can notice that the coordinates of the cities are:

● A(2,3)

● B(6,-6)

There are many methods to figure out the distance between A and B. We will use the distance formula.

Let d be the distance between A and B.

● d = √[(2-6)^2 + (3-(-6))^2]

● d = √[(-4)^2 + (3+6)^2]

● d = √[ 4^2 + 9^2 ]

● d = √(16+81)

● d = √(97)

Answer:

The answer is B) 97 units

Step-by-step explanation:

From the graph we can notice that the coordinates of the cities are:

● A(2,3)

● B(6,-6)

There are many methods to figure out the distance between A and B. We will use the distance formula.

Let d be the distance between A and B.

● d = √[(2-6)^2 + (3-(-6))^2]

● d = √[(-4)^2 + (3+6)^2]

● d = √[ 4^2 + 9^2 ]

● d = √(16+81)

● d = √(97)

G = {(1, 1), (1, 2), (1, 3), (1, 4)} Is G a function and why? Yes, no two ordered pairs in this list has the same second element. Yes, there is more than one ordered pair in this list. No, there is a limited number of ordered pairs in this list. No, each ordered pair in this list has the same first element.

Answers

Answer:

No, each ordered pair in this list has the same first element.

Step-by-step explanation:

An input can only have 1 output, but multiple inputs can have the same output. How you can check this if you have a graph is if you can draw a straight line (top to bottom) anywhere on the graph and it intersects with the line once or not at all.

Answer:

No, each ordered pair in this list has the same first element.

Step-by-step explanation:

A function is a relation in which each possible input value leads to exactly one output value.

Given: G = {(1, 1), (1, 2), (1, 3), (1, 4)}

It has same input (x=1) that leads to multiple outputs (y= 1,2,3,4). This relationship is not a function as per definition provided above.

Correct answer choice is:

No, each ordered pair in this list has the same first element.

please help real quick ​

Answers

Divide total km by the km in the scale:

112 / 16 = 7

The answer is A. 7 cm

Answer:

7 cm

Step-by-step explanation:

1 cm : 16 km   :: x cm : 112 km

Product of mean = Product of extreme

16 * x = 1 * 112

x =[tex]\frac{112}{16}[/tex]

x = 7cm

A reduced scale drawing of a rectangle measures 12 inches by 16 inches. The scale factor is 1/4. What is the size of the original rectangle? A. 3 in. * 4 in. B. 16 in. * 20 in. C. 36 in. * 48 in. D. 48 in. * 64 in. Please show ALL work! <3

Answers

Answer: D) 48 inches by 64 inches

=============================================

Explanation:

The scale factor is 1/4 = 0.25, meaning that the original preimage is larger and it is reduced to get the image. The reduced width is 12, so the original width is 12/0.25 = 48 inches. The reduced length is 16 making the original to be 16/0.25 = 64.

--------

note that

48*0.25 = 12

64*0.25 = 16

showing how a 48 by 64 rectangle is reduced to a 12 by 16 rectangle after applying the scale factor to each dimension

D Work Is Showed Below Hopefully It’s Correct !!

What is the measure of the acute angle formed by the lines 3x–5y=–15 and 4x+2y=7?

Answers

Answer:

85.6 degrees.

Step-by-step explanation:

The given equations of lines are

[tex]3x-5y=-15[/tex]

[tex]4x+2y=7[/tex]

We need to find the measure of the acute angle formed by these lines.

[tex]Slope=\dfrac{-\text{Coefficient of }x}{\text{Coefficient of }y}[/tex]

Slope of given lines are

[tex]m_1=\dfrac{-3}{-5}=\dfrac{3}{5}[/tex]

[tex]m_2=\dfrac{-4}{2}=-2[/tex]

Angle between two lines is

[tex]\tan \theta = \left|\dfrac{m_1-m_2}{1+m_1m_2}\right|[/tex]

[tex]\tan \theta = \left|\dfrac{\dfrac{3}{5}-(-2)}{1+\dfrac{3}{5}(-2)}\right|[/tex]

[tex]\tan \theta = \left|\dfrac{\dfrac{3+10}{5}}{\dfrac{5-6}{5}}\right|[/tex]

[tex]\tan \theta = \left|\dfrac{13}{1}\right|[/tex]

[tex]\tan \theta = 13[/tex]

[tex]\theta = \tan^{-1}(13)[/tex]

[tex]\theta \approx 85.6^{\circ}<90^{\circ}[/tex]

Therefore, the acute angle between given lines is 85.6 degrees.

Find the measure of FG. A. 9 B. 10 C. 11 D. 8

Answers

Answer:

x =11

Step-by-step explanation:

(whole secant) x (external part) =  (whole secant) x (external part)

( 15+x-2) * (x-2) = (19+x-3) * (x-3)

Combine like terms

(13+x) *(x-2) = (16+x) *(x-3)

Distribute

11x+x^2-26=13x+x^2-48

Subtract x^2 from each side

11x -26 = 13x -48

Subtract 11x from each side

-26 = 2x-48

Add 48 to each side

22 = 2x

Divide by 2

11 =x

The answer is definitely x=11

{(-2,8),(4,6),(10,4)} Which point, when added to the set, would form a relation that is not a function?

Answers

Answer:

Point : ( -2, 15 )

Step-by-step explanation:

A point that would make this relation not a function would be one that shares a common x - value with the other points. One common domain values for two range values would, when graphed, not follow the vertical test, hence making the relation not a function.

Let's say that the point is ( -2, 15 ). It has a common x - value with respect to the first point, ( -2, 8 ), and therefore would make this set not a function.

Answer:

Point : ( -2, 15 )

Step-by-step explanation:

Plz help I’ll mark brainliest

Answers

Answer:

x = 22.62°

Step-by-step explanation:

To find the measure of angle x we use cosine

[tex] \cos( \alpha ) = \frac{adjacent}{hypotenuse} [/tex]

From the question

PO is the hypotenuse = 13

The adjacent is 12

Substitute the values into the above formula

That's

[tex] \cos(x) = \frac{12}{13} [/tex]

[tex]x = \cos^{ - 1} ( \frac{12}{13} ) [/tex]

x = 22.6198

We have the final answer as

x = 22.62° to the nearest hundredth

Hope this helps you

Answer:

Since the value of all angles within a triangle must equal 180 degrees, if you know at least two angles, you can subtract them from 180 to find the missing third angle. If you are working with equilateral triangles, divide 180 by three to find the value of X. All of the angles of an equilateral triangle are equal.

Step-by-step explanation:

please help with this math question

Answers

Answer:

E            H

F            F

G           E

I hope I helped.

E is the answer in you welcome

Some lemon, lime, and cherry lollipops are placed in a bowl. Some have a
chocolate center, and some do not. Suppose one of the lollipops is chosen
randomly from all the lollipops in the bowl. According to the table below, if it
is known to be lemon, what is the probability that it HAS a chocolate center?

Answers

Answer:

45%

Step-by-step explanation:

There are 20 lollilops with lemon in total. 9 of them have a chocolate center. 9/20=0.45. To convert it into percentage you would multiply the number by 100. 0.45*100=45

The answer is 45%

Answer: C. 45%

"if it is known to be lemon" means we ignore any other flavor. I recommend covering up the other values, or you could highlight just the lemon column.

We have 9+11 = 20 lemon total. Of this 20 total, only 9 lemons have a chocolate center. So 9/20 = 0.45 = 45% of the lemon candies have a chocolate center.

Nine and one half less than four and one half times a number is greater than 62,5. Which of the following represents
the solution set of this problem?
O (16,400)
O (-16,400)
o (-0,16)
o (-00,-16)

Answers

Answer: (16,O0) That is 16 to positive infinity

Step-by-step explanation:

4.5x - 9.5 > 62.5

4.5x > 62,5 + 9.5

4.5x > 72

x > 72/ 4.5

x> 16

So all real numbers greater than 16 is the solution set.

(16,O0)

I wish I had the infinity symbol on this keyboard!

The answer is (D)
(-00-,-16)

The width of a rectangle is 14 feet less than 3 times the length. If the area is 24 fta,
find the width and length.
Width = 4 and Length = 6
Width = 2 and Length = 4
Width = 10 and Length = 12
Width = 6 and Length = 8

Answers

Answer:

Width: 4

Length: 6

Step-by-step explanation:

We can create a systems of equations for this problem, assuming W is width and L is length.

W = 3L-14

WL = 24

We can substitute W into the equation.

(3L-14)L = 24

3L²-14L = 24

3L² - 14L - 24 = 0

(3L+4)(L-6)=0

L = 6

Now we can find W by substituting L into the equation.

[tex]6\cdotw=24\\w = 4[/tex]

Hope this helped!

the answers will be 6=24
w=6 i think

which of these expressions are equivalent to p/3?

A. p-2/3

B. 1/3p

C. p-3

D. 3/p

E. 3p/p

Answers

Answer: Choice B.  1/3p

This is assuming that p is not in the denominator. To make it more clear that p is not in the denominator, I recommend you write (1/3)p.

Taking 1/3 of a number is the same as dividing by 3.

Example:

27/3 = 9

27*(1/3) = 9

1/3p

This is expressed as equívalent because 1/1 = 1 this 1/3=.33, thus 1/3 is p/3

Which expression is equivalent to RootIndex 3 StartRoot x Superscript 5 Baseline y EndRoot?

Answers

Answer:

The answer is "[tex]x^{\frac{5}{3}}y^{\frac{1}{3}}[/tex]"

Step-by-step explanation:

Given value:

[tex]\to \bold{ \sqrt[3]{x^5y} }[/tex]

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

formula:

[tex]\bold{(a.b)^n=a^nb^n}[/tex]

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

The final value is:  [tex]\boxed{\boxed{ x^{\frac{5}{3}} \cdot y^{\frac{1}{3}}}}[/tex]

The answer should be B I just did the test


Hope this helps .

Kaitlin compared the statistics from her team's baseball season. She determined that having fewer hits did not imply that a player caught more or fewer balls. What should she conclude? a. There is no correlation between the number of hits and the number of balls caught. b. There is a correlation between the number of hits and the number of balls caught. There may or may not be causation. Further studies would have to be done to determine this. c.There is a correlation between number of hits and number of balls caught. However, there is no causation. This is because there is probably a decrease in the number of balls caught with a decrease in the number of hits.

Answers

Answer: c.There is a correlation between number of hits and number of balls caught. However, there is no causation. This is because there is probably a decrease in the number of balls caught with a decrease in the number of hits.

Step-by-step explanation:

Correlation is a term used to define a relationship between two variables.Causation is a term used to define the effect of one variable on other.

Given, Kaitlin compared the statistics from her team's baseball season. She determined that having fewer hits did not imply that a player caught more or fewer balls.

There is a correlation between number of hits and number of balls caught. However, there is no causation as " fewer hits did not imply that a player caught more or fewer balls.".

This is because there is probably a decrease in the number of balls caught with a decrease in the number of hits.

Hence, the correct option is "c".

The correct answer is C

Help and show work plz

Answers

Answer:

RK: 4 and BC: 6

Step-by-step explanation:

SImilar triangles

find unknown / know sides

Which means (2x+2)/6 = (4x+2)/9

  (X+1)/3 = (4x+2)/9

Multiply 9 to both sides

9/3 (x+1) = (4x+2)

3x+3 = 4x+2

1 = x

Answer: RK = 4, BC = 6

Step-by-step explanation:

In a similar triangle, the ratios of corresponding sides are the same.  Thus, because of sides MK and AC, the triangles have a ratio of 6/9, or 2/3.  Thus, you can determine that 2/3(4x+2)=2x+2.

Distribute

8/3x + 4/3 = 2x + 2

Subtract 2x

2/3x + 4/3 = 2

Subtract 4/3

2/3x=2/3

Divide by 2/3

x = 1

Then, simply plug-in 1 for x to get that RK is 4 and BC is 6

Hope it helps <3

click to see equation, show work pls!

Answers

Answer:

x = 6, 9

Step 1:

To solve this equation, we need to subtract 3 from both sides like this:

[tex]3\sqrt{x-5} +3(-3)=x(-3)\\3\sqrt{x-5} =x-3[/tex]

Step 2:

We square both sides (multiply using FOIL) to get rid of the radical.

[tex](3\sqrt{x-5} )^2 = (x-3)^2\\(3\sqrt{x-5} )^2: 9x-45\\ (x-3)^2: x^2+6x+9\\\\9x-45=x^2-6x+9[/tex]

If you did not understand how these were done, here is an example:

(x + 1)(x + 2)

First terms: x * x = x^2

Outer terms: x * 2 = 2x

Inner terms: 1 * x = x

2x - x = x

Last terms: 1 * 2 = 2

x^2 + x + 2

Step 3:

Solve for x:

9x - 45 = x^2 - 6x + 9

x^2 - 6x + 9 (+45) = 9x - 45 (+45)

x^2 - 6x + 54 (-9x) = 9x (-9x)

x^2 - 15x + 54 = 0

Factor:

(x^2 - 6x) + (- 9x + 54)

x(x - 6)        - 9(x - 6)

Factor out (x - 6):

(x - 6)(x - 9) = 0

x - 6 = 0; 6 - 6 = 0

x - 9 = 0; 9 - 9 = 0

Our anwer: x = 6, 9

The answer to this equation is 6,9

Math Question (10 Points):

Answers

5u + u - 6u
= 6u - 6u
= 0

Answer:

0

Step-by-step explanation:

Like terms are terms that have the same variable part.

The variable part of all three terms is u, so all terms are like terms.

5u + u - 6u =

= 5u + 1u  6u

= 6u - 6u

= 0

Factorize. (i) 2mn +m^2-6n - 3m (ii) 4y^2 -81 (iii) t^2 - 6t+8

Answers

Answer:

(i) (m-3)(2n+m) (ii) (2y+9)(2y-9) (iii) (t-4)(t-2)

Step-by-step explanation:

2mn+m^2-6n-3m

m(2n+m)-3(2n+m)

(m-3)(2n+m)

Answer: (m-3)(2n+m)

------------------------------

4y^2-81

(2y+9)(2y-9)

Answer: (2y+9)(2y-9)

-------------------------------

t^2-6t+8

(t-4)(t-2)

Factors of the given equations are

(i) (2n +m)(m - 3)  

(ii) (2y-9)(2y + 9)

(iii) (t -4) (t - 2)

What is factorization?

" Factorization is the process of breaking down large number or quantity into a smaller number or quantity."

Formula used

(a² - b²) = (a -b) (a +b)

According to the question,

(i) 2mn + m² -6n -3m

= m (2n +m) - 3 (2n +m)

= (2n + m) (m - 3)

(ii) 4y² - 81

 = (2y)² - (9)²

= (2y - 9) (2y + 9)

(iii) t² - 6t +8

  = t² - 4t - 2t + 8

  = t (t - 4) -2 (t - 4)

  = (t -4) (t -2)

Hence, Factors of the given equations are

(i) (2n +m)(m - 3)  

(ii) (2y-9)(2y + 9)

(iii) (t -4) (t - 2)

Learn more about factorization here

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A cylinder has a height of 4.5 cm and a diameter of 1.5 cm. What is the surface area of the cylinder in square centimeters? Use 3.14 for pi. A.21.2 B.24.7 C.7.9 D.31.8

Answers

Answer:

A = 56.5cm²

Step-by-step explanation:

r = 1.5cm

h = 4.5cm

A=2πrh+2πr2

A = 2πr(h+r)

A = 2 x 3.14 x 1.5 x ( 4.5 + 1.5 )

A = 56.62cm²

[tex] \large{ \underline{ \underline{ \bf{ \red{Given}}}}}[/tex]

Height of the cylinder = 4.5 cmDiameter of the cylinder = 1.5 cmConsider π = 3.14

[tex] \large{ \underline{ \underline{ \bf{ \purple{To \: find}}}}}[/tex]

Surface area of the cylinder in cm²?

[tex] \large{ \underline{ \underline{ \bf{ \green{Now, \: What \: to \: do?}}}}}[/tex]

For solving this question, we should know how to calculate the surface area of cylinder i.e Total surface are of cylinder = 2πr(r + h)

Where, r = radius of the cylinder and h is the height of the cylinder.

[tex] \large{ \bf{ \underline{ \underline{ \blue{Solution}}}}}[/tex]

We are provided with,

h = 4.5 cmd = 1.5 cm

Then, Radius = 1.5 cm / 2

By using formula,

⇛ 2πr(r + h)

⇛ 2 × 3.14 × 1.5/2 (1.5/2 + 4.5) cm²

⇛ 2 × 3.14 × 3/4( 5.25) cm²

24.7275 cm²

❇ Option B

✤ TSA of the cylinder = 24.7275 cm²

━━━━━━━━━━━━━━━━━━━━

Find the m∠RLU. A. 20 B. 42 C. 84 D. 10

Answers

Answer:

b is the correct answer. p is 10

The value of m∠RLU = 10.

How to estimate the value of m∠RLU?

Given: (5p - 8) and (2p + 22)

Simplifying both of the equation, then we get

5p - 8 = 2p + 22

Add 8 to both sides of the equation, then we get

5p - 8 + 8 = 2p + 22 + 8

simplify

5p = 2p + 30

substract 2p from both sides of the equation

5p - 2p = 2p + 30 - 2p

3p = 30

p = 30/3

p = 10.

m∠RLU = 10

Therefore, the correct answer is option D. 10.

To learn more about angles and triangle

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PLS HELP ME WITH THIS QUESTION, ANYTHING REALLY HELPSS!!!!

Answers

Answer:

x = 75

Step-by-step explanation:

FGE is a straight line so it equals 180 degrees

FGA + AGC + CGE = FGE

x + 90 + 15 = 180

Combine like terms

x+ 105 = 180

Subtract 105 from each side

x = 180-105

x = 75

Answer:

x = 75º

Step-by-step explanation:

The Vertical Angle Theorem shows that:

∠CGE ≅ ∠DGF

So:

∠DGF = 15º

∠AGD = 90º

90º - 15º = 75º

x = 75º

plls 20 poinsts will mark brainlest

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My answer is in the attached image.

Dat is wat I got I really hope dat helped
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