If the mZSRW=85 degrees what are the measures of ZVRU and ZURW?​

If The MZSRW=85 Degrees What Are The Measures Of ZVRU And ZURW?

Answers

Answer 1

Answer:

m<VRU = 80°

m<URW = 15°

Step-by-step explanation:

<SRW and <VRT are vertical opposite angles. Vertical opposite angles are equal. Therefore:

[tex] 2x + 15 = 85 [/tex]

Use this expression to solve for the value of x

[tex] 2x + 15 - 15 = 85 - 15 [/tex]

[tex] 2x = 70 [/tex]

[tex] \frac{2x}{2} = \frac{70}{2} [/tex]

[tex] x = 35 [/tex]

Find m<VRU by plugging in the value of x in the expression for its angle given.

m<VRU = [tex] 2x + 10 [tex]

[tex] 2(35) + 10 = 70 + 10 = 80 [tex]

m<VRU = 80°

FIND m<URW.

m<URW = 180° - (m<VRU + m<SRW) (angles on a straight line is 180°)

m<URW = 180 - (80 + 85)

= 180 - 165

m<URW = 15°


Related Questions

if x=10^a , y=10^b and x^b.y^a=100.prove that xy=1​

Answers

Answer:

ab=1

Step-by-step explanation:

Assuming that you meant ab=1

[tex]x=10^{a}\\\\y=10^b\\\\x^b*y^a=100\\\\(10^a)^b*(10^b)^a=100\\\\10^{ab}*10^{ba}=100\\\\10^{ab+ba}=100\\\\10^{2ab}=100\\\\(10^2)^{ab}=100\\\\100^{ab}=100\\\\ab=1[/tex]this is because the exponents have to be equal

A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue. Trapezoid E F G H is shown. F G is Maple Drive, G H is Garden road, E H is Pine avenue, and E F is Elm Street. Sides F G and E H are parallel. Angle G is 108 degrees. In trapezoid EFGH, EF ≅ HG. What is the measure of the angle between Elm Street and Pine Avenue? 54° 72° 108° 144°

Answers

Answer: Option B -- 72°

Step-by-step explanation:

If a town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue. Using Trapezoid E F G H is shown. F G is Maple Drive, G H is Garden road, E H is Pine avenue, and E F is Elm Street. Sides F G and E H are parallel. Angle G is 108 degrees. In trapezoid EFGH, EF ≅ HG. The measure of the angle between Elm Street and Pine Avenue is 72°

Answer:

b

Step-by-step explanation:

Jacob needs 48 ounces of tomatoes for the spaghetti sauce. He is choosing between two brands of tomatoes. Find the unit rate for each brand. Round to the nearest cent (hundredth)

Answers

Answer:

unit rate = cost/weight

Step-by-step explanation:

To find the unit rate, divide the cost by the weight of each brand.

The lower unit rate represents a lower price, so that is the one you choose.

Answer:

Brand B.

Step-by-step explanation: Jacob should pick Brand B because he will save money. This is because if he buys 8 ounces 6 times, he will have to pay about $17.94, but if he buys 16 ounces 3 times, he will only spend $14.97.

Hope this helps! :)

There are two routes Lucas can take to walk to school. Route A is 2 and StartFraction 1 over 8 EndFraction miles and is StartFraction 3 over 8 EndFraction mile longer than route B. The equation b + StartFraction 3 over 8 EndFraction = 2 and StartFraction 1 over 8 EndFraction can be used to represent this situation, where b is the length of route B. How many miles will Lucas walk if he takes route B?

Answers

Answer:

1 3/4

Step-by-step explanation:

i took this quiz its the correct answer...

Answer:

B. ! 3/4 miles

Step-by-step explanation:

I got it right on edge.

I’m not sure what it’s asking

Answers

Answer:

A, D, E, F and G

Step-by-step explanation:

It is asking for the elements of the set A which are integers

how many minutes are in 17 years​

Answers

Answer:

Step-by-step explanation:  

8.935e+6

Answer:

8.935e+6 minutes

Step-by-step explanation:

[tex]1 calendar year = 525600\\17 years\:\:\:\:\:\:\: = x\\\\x = 525600\times 17\\\\=8935200[/tex]

Solve for m.
0 = -12 + m​

Answers

Answer:

[tex]\huge \boxed{m=12}[/tex]

Step-by-step explanation:

[tex]m+-12=0[/tex]

[tex]\sf Add \ 12 \ to \ both \ sides.[/tex]

[tex]m+-12+12=0+12[/tex]

[tex]m=12[/tex]

If a=mg-kv2/m,find,correct to the nearest whole number the value of v when a=2.8,m=12,g=9.8 and k=8/3

Answers

Answer:

v = 23

Step-by-step explanation:

Formatting the question gives;

a = mg - kv² / m

Make v subject of the formula as follows;

(i) Multiply both sides by m

ma = m²g - kv²

(ii) Collect like terms

kv² = m²g - ma

(iii) Divide through by k

v² = (m²g - ma) / k

(iv) Take the square root of both sides

v = √ [(m²g - ma) / k]            --------------(ii)

From the question:

a = 2.8

m = 12

g = 9.8

k = 8/3

Substitute these values into equation (i) as follows;

v = √ [(12²(9.8) - 12(2.8)) / (8/3)]

v = √ [(1411.2 - 33.6) / (8/3)]

v = √ [1377.6 / (8/3)]

v = √ [1377.6 x (3/8)]

v = √ [1377.6 x 3 / 8)]

v = √ [516.6]

v = 22.73

v = 23 [to the nearest whole number]

Therefore v = 23 to the nearest whole number    

33 + 2(5+8) - (6-2)2 =

Answers

Answer:

51

Step-by-step explanation:

33+2(5+8)-(6-2)2

open the brackets FIRST

2(5+8) = 26

33+26-(6-2)2

33+18

= 51

hat are the two decisions that you can make from performing a hypothesis​ test? What are the two decisions that you can make from performing a hypothesis​ test? Select all that apply. A. make a type II error B. make a type I error C. reject the alternative hypothesis D. fail to reject the alternative hypothesis E. reject the null hypothesis F. accept the null hypothesis G. accept the alternative hypothesis H. fail to reject the null hypothesis

Answers

Answer:

One is :

C. reject the alternative hypothesis

F. accept the null hypothesis

The other is :

E. reject the null hypothesis

G. accept the alternative hypothesis

Another type of decision is when we

D. fail to reject the alternative hypothesis

E. reject the null hypothesis

and

H. fail to reject the null hypothesis

C. reject the alternative hypothesis

Step-by-step explanation:

There are two types of decisions that we can make .

One is :

C. reject the alternative hypothesis

F. accept the null hypothesis

The other is :

E. reject the null hypothesis

G. accept the alternative hypothesis

Another type of decision is when we

D. fail to reject the alternative hypothesis

E. reject the null hypothesis

and

H. fail to reject the null hypothesis

C. reject the alternative hypothesis

It is clear from the above that when we reject one hypothesis we accept the other hypothesis.

or

When we fail to reject one hypothesis we reject the other hypothesis.

Enter the number that belongs in the green box

Answers

Answer:

1

Step-by-step explanation:

Hi!

First we need to translate 2 units down. That means we need to subtract 2 from the y value. So now we have (-1,1).

For a 270 degree counterclockwise rotation the rule is to go from (x,y) to (y,-x)

So now we have (1,1). Since they're only asking for the x value, the answer is 1.

Answer:

[1, 1]

Step-by-step explanation:

Translation → [-1, 3] moves down to [-1, 1]

Now, a 90°-clockwise rotation is the exact same as a 270°-counterclockwise rotation, and according to the 270°-counterclockwise rotation [90°-clockwise rotation] rule, you take the y-coordinate, bring it over to your new x-coordinate, and take the OPPOSITE of the x-coordinate and set it as your new y-coordinate:

Extended Rotation Rules

270°-clockwise rotation [90°-counterclockwise rotation] >> (x, y) → (-y, x)

270°-counterclockwise rotation [90°-clockwise rotation] >> (x, y) → (y, -x)

180°-rotation >> (x, y) → (-x, -y)

Then, you perform your rotation:

270°-counterclockwise rotation [90°-clockwise rotation] → [-1, 1] moves to [1, 1]

( not my answer cr BasketballEinstein on brainly, i just saw that the same question like this one was already answered FULLY somewhere else )

Roger pays $1187.20 for a computer. The price includes 6% sales tax. What is the price of the computer
itself?

Answers

1187.20 + 6/100*1187.20
= 1187.20 + 71.232
= 1258.432

a pharmaceutical salesperson receives a monthly salary of $5000 plus a commission of 7% of sales. write a linear equation for the salesperson’s monthly wage W in terms of monthly sales S. NEED TO TURN IT IN TODAY

Answers

Equation for the monthly wage will be → W = 0.07S + 5000

   Given in the question,

Monthly salary of the sales-person = $5000Commission = 7% of total sales

Let the total sales of a month = $S

Therefore, commission on this sale = 7% of $S

                                                            = $0.07S

Salary of the month = $5000

Total earnings (W) of the sales person = $(0.07S + 5000)

     Therefore, equation for the monthly wage will be,

W = 0.07S + 5000

Learn more,

https://brainly.com/question/25362379

Suppose a team of doctors wanted to study the effect of different types of exercise on reducing body fat percentage in adult men. The 57 participants in the study consist of men between the ages of 40 and 49 with body fat percentages ranging from 32%â34%. The participants were each randomly assigned to one of four exercise regimens.Ten were instructed to complete 45 min of aerobic exercise four times a week.Eleven were instructed to complete 45 min of anaerobic exercise four times a week.Nine were instructed to complete 45 min of aerobic exercise twice a week and 45 minutes of anaerobic exercise twice a week.Nine were instructed not to exercise at all.All participants were asked to adhere to their assigned exercise regimens for eight weeks. Additionally, to control for the effect of diet on weight loss, the doctors provided the participants with all meals for the duration of the study. After eight weeks, the doctors recorded the change in body fat percentage for each of the participants.The doctors plan to use the change in body fat percentage data in a one-way ANOVA F?test. They calculate the mean square between as MSbetween=11.632991 and the mean square within as MSwithin=1.261143. Assume that the requirements for a one-way ANOVA F?test have been met for this study.Choose all of the correct facts about the F statistic for the doctors' ANOVA test.A. The F statistic increases as the differences among the sample means for the exercise groups increase.B. The F statistic is 0.1084.C. The F statistic has 3 degrees of freedom in the numerator and 35 degrees of freedom in the denominator.D. The F statistic indicates which exercise treatment groups, if any, are significantly different from each other.E. The F statistic has 4 degrees of freedom in the numerator and 38 degrees of freedom in the denominator.F. The F statistic is 9.2242.

Answers

Answer:

A. The F statistic increases as the differences among the sample means for the exercise groups increase.

C. The F statistic has 3 degrees of freedom in the numerator and 35 degrees of freedom in the denominator.

F. The F statistic is 9.2242.

Step-by-step explanation:

Given that

Observations                     Samples                             Total

40-49             10       11              9         9                        39

The degrees of freedom is given by

For numerator= k-1 = 4-1=3

For denominator= n-k= 39-4= 35

F statistic is given by

F= MS between/ MS within

=11.632991 / 1.261143 = 9.2242

Where

Mean Square Between = MS between = 11.632991

Mean Square Within = MS within = 1.261143

Hence the correct choices are  A, C and F

A. The F statistic increases as the differences among the sample means for the exercise groups increase.

C. The F statistic has 3 degrees of freedom in the numerator and 35 degrees of freedom in the denominator.

F. The F statistic is 9.2242.

Suppose we have

Mean Square Between = MS between = 18.632991

Mean Square Within = MS within = 1.261143

Then F statistic would be = 14.77468 > 9.2242

which tells that The F statistic increases as the differences among the sample means for the exercise groups increase.

Subtract (x^2+3x-4) -(4x-2x^2-3)

Answers

Answer:

3 x^2 - x + -1

Step-by-step explanation:

Simplify the following:

-(4 x - 2 x^2 - 3) + x^2 + 3 x - 4

Factor -1 out of -2 x^2 + 4 x - 3:

--(2 x^2 - 4 x + 3) + x^2 + 3 x - 4

(-1)^2 = 1:

2 x^2 - 4 x + 3 + x^2 + 3 x - 4

Grouping like terms, 2 x^2 + x^2 + 3 x - 4 x - 4 + 3 = (x^2 + 2 x^2) + (3 x - 4 x) + (-4 + 3):

(x^2 + 2 x^2) + (3 x - 4 x) + (-4 + 3)

x^2 + 2 x^2 = 3 x^2:

3 x^2 + (3 x - 4 x) + (-4 + 3)

3 x - 4 x = -x:

3 x^2 + -x + (-4 + 3)

3 - 4 = -1:

Answer: 3 x^2 - x + -1

Rearrange the equation so w is the independent variable.
u-5= -4(w - 1)

Answers

Answer:

w = ((u-5)/-4) + 1

Step-by-step explanation:

To make w an independent variable, it must be by itself, so we have

u - 5 = -4(w-1)

We divide both sides by -4

(u-5)/-4 = -4(w-1)/-4

(u-5)/-4 = w-1

Now we add 1 to both sides,

(u-5)/-4+1 = w-1+1

((u-5)/-4) + 1 = w

w = ((u-5)/-4) + 1

Answer:

u = -4w + 9.

Step-by-step explanation:

If w is the independent variable, it will be the variable you are changing.

u - 5 = -4(w - 1)

u - 5 = -4w + 4

u = -4w + 9.

Hope this helps!

Hello! Stay safe and Please answer In a hurry Thanks!

Answers

Answer:

4

Step-by-step explanation:

An equilateral triangle has 3 equal sides.

So

4(x-1) = x +8

4x-4=x+8

3x=12

x=4

Same result obtained when comparing the other pairs of equations.

Answer:

Explanation:

Since it is an equilateral Triangle their sides are the same.

Thus, 4(x - 1) = x + 8 = 2x + 4

But we can take 2 sides to work with:
To solve for x:

4(x - 1) = x + 8
4x - 4 = x + 8
4x - x = 8 + 4
3x = 12
x = 12/3
x = 4

Therefore, x = 4 and the equation involving x is 4(x - 1) = x + 8

Need to find the volume of these composite figures. Thank You!​

Answers

Answer:

3. V = 1,498.24. V = 2,813.445. V = 96.293

Step-by-step explanation:

3. Formula of a Cylinder + Formula of a Cone = Total

V=πr^2h + V=πr^2h

/3 = total

V = 3.14 * 36 * 10 + V = 3.14 * 36 * 10/3

V = 1,130.4 + V = 376.8 = Total

V = 1,498.2

4. Formula of Cone + Formula of Cone = Total

V=πr^2h

/3 + V=πr^2h

/3 = Total

V = 3.14 * 36 * 8/3 + V = 3.14 * 100 * 8 = Total

V = 301.44 + 2,512 = Total

V = 2,813.44

5. Formula of a cylinder + formula of a sphere = Total

V=πr^2h + V=4

/3πr^3 = Total

V = 3.14 * 4 * 5 + V = 4/3 * 3.14 * 8

V = 62.8 + V = 33.493 = Total

V = 96.293

DEFINITELY hope this helped,

Kavitha

3. Why can the numerator and denominator of a rational expression be divided by their common factors? What conditions must be placed on the value of the variables when a rational expression is simplified?

Answers

Answer:

Step-by-step explanation:

Hello, do you agree that for any real number a (different from 0)

[tex]\dfrac{a}{a}=1[/tex]

?

5/5 = 1 for instance.

So, when you have the same common factor at the numerator and at the denominator you can eliminate it. For instance.

[tex]\dfrac{10}{4}=\dfrac{5*2}{2*2}=\dfrac{5}{2}\cdot \dfrac{2}{2}=\dfrac{5}{2}[/tex]

You just need to be careful with 0, as dividing by 0 is not allowed.

Hope this helps

Thank you.

How many acres are contained in a parcel described as follows: The NE ¼ of the NW ¼; the N ½ of the NW ¼, NE ¼, of Section 10?

Answers

Answer:

   1.25 acres

Step-by-step explanation:

If we assume that both the semicolon (;) and the comma (,) mean "of the", then this will be ...

  (1/4)(1/4)(1/2)(1/4)(1/4) of 640 acres = 1.25 acres

Trigonometry-Logarithm Question..Please help..

Answers

Answer:

[tex]$x=\frac{25\pi }{12} \text{ and }x=\frac{29\pi }{12}[/tex]

Step-by-step explanation:

Solve

[tex]\log_2(2 \sin x) + \log_2(\cos x) =1[/tex]

in interval [tex]$\left(2\pi, \frac{5\pi}{2} \right)$[/tex]

Remember that logarithms follow:

[tex]f(x\cdot y)=f(x)+ f(y)[/tex]

Therefore

[tex]\log_2(2 \sin x) + \log_2(\cos x) =-1 \implies \log_2(2 \sin x \cdot \cos x) =-1[/tex]

We got a double angle of sine:

[tex]\sin(2x)= 2 \sin x \cos x[/tex]

[tex]\log_2( \sin 2x ) =-1[/tex]

[tex]2^{-1}=\sin 2x[/tex]

[tex]$\frac{1}{2} =\sin 2x$[/tex]

The solutions for it are:

[tex]$2x=\frac{\pi }{6}+2\pi n \text{ and }2x=\frac{5\pi }{6}+2\pi n, \text{ as } n\in \mathbb{Z}$[/tex]

As

[tex]$x=\frac{\pi }{12}+\pi n \text{ and }x=\frac{5\pi }{12}+\pi n, \text{ as } n\in \mathbb{Z}$[/tex]

But we have the interval

[tex]$\left(2\pi, \frac{5\pi}{2} \right)$[/tex]

Therefore, the answer is

[tex]$x=\frac{25\pi }{12} \text{ and }x=\frac{29\pi }{12}[/tex]

write the remainder when [x ^2 -1] is divided by (x-1)

Answers

Answer:

Explanation:

f(x) = x^2 - 1

x - 1 = 0
x = 1

f(1) = 1^2 - 1
f(1) = 1-1
f(1) = 0

So the remainder is 0

15x 18 + 12+ 3+ 9
Pemdas

Answers

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{294}}}}}[/tex]

Step-by-step explanation:

PEMDAS is a acronym which helps you to remember the order of operations.

PEMDAS stands for :

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Let's solve

[tex] \sf{15 \times 18 + 12 + 3 + 9}[/tex]

Multiply the numbers : 15 × 18 = 270

⇒[tex] \sf{270 + 12 + 3 + 9}[/tex]

Add the numbers : 270 + 12 + 3 + 9

⇒[tex] \sf{294}[/tex]

Hope I helped!

Best regards!!

Answer:

This would equal 294

Step-by-step explanation:

i added them up

Complete the square: x2+7x+?=(x+?)2

Answers

Answer:

[tex] {x}^{2} + 7x + \frac{49}{4} = {(x + \frac{7}{2}) }^{2} [/tex]

Explanation:

[tex] {x}^{2} + 7x + a = {(x + b)}^{2} [/tex]

[tex] {x}^{2} + 7x + a = {x}^{2} + 2bx + {b}^{2} [/tex]

compare the x co-efficient

[tex] 7 = 2b[/tex]

[tex] b = \frac{7}{2} [/tex]

compare the constants

[tex]a = {b}^{2} [/tex]

[tex]a = {( \frac{7}{2}) }^{2} [/tex]

[tex]a = \frac{49}{4} [/tex]

Solve the following (^ this sign symbolizes the power) 7). 4^2 8). 7^2 9). 6^4 10). 1^2 11) 5^3 12) 1^3

Answers

Answer:

7. 4^2 = 6

8. 7^2 = 49

9. 6^4 =1296

10. 1^2 = 1

11. 5^3 =125

12. 1^3 =1

Step-by-step explanation:

the length of a rectangle is 4 cm less than 5 times its width its perimeter is 160 cm find its length and width​

Answers

Let x= width
Length= 5x-4
2(x)+2(5x-4)=160
2x+10x-8=160
12x-8=160
+8. +8
12x=168
x=14
width=14
length= 5(14)-4=66

4(4+2x)=7(x-4)
A: The solution set is (_) Simplified
B: There is no solution
Pick one and if A then simplify the answer

Answers

Answer:

x=-44

Step-by-step explanation:

4(4+2x)=7(x-4)

[expanding the brackets]

16+8x=7x-28

[grouping like terms]

8x-7x= -28-16

x= - 44

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[tex]\boxed{x = -44}[/tex]

[tex]4(4+2x)=7(x-4)[/tex]

Solution :

[tex]4(4+2x)=7(x-4)[/tex]

[tex]( 2x + 4 ) = 7 ( x - 4 )[/tex]

[tex]4 . 2x + 4 . 4 = 7x - 7 . 4[/tex]

[tex]8x + 16 = 7x - 28[/tex]

[tex]( 8x + 16) + ( -16 - 7x ) = ( 7x - 28 ) + ( -16 - 7x )[/tex]

[tex]( 8x + 16 ) + ( -7x - 16) = (7x - 28 ) + ( -7x - 16)[/tex]

[tex]8x + 16 - 7x - 16 = 7x - 28 - 7x - 16[/tex]

[tex]8x - 7x + 16 - 16 = 7x - 7x - 28 - 16[/tex]

[tex]x = -44[/tex]

( A: The solution set is (_) Simplified )

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Have a great day/night!

❀*May*❀

Let f(x) = x2 - 4x and g(x) = 2x – 3. Find f(g(4))

Answers

Answer:

[tex]f(g(4)) = 5[/tex]

Step-by-step explanation:

f(x) = x² - 4x

g(x) = 2x – 3

To find f(g(4)) we must first find f(g(x))

To find f(g(x)) substitute g(x) into f(x) that's for every x in f(x) replace it with g (x)

That's

[tex]f(g(x)) = ({2x - 3})^{2} - 4(2x - 3) \\ = 4x^{2} - 12x + 9 - 8x + 12 \\ = 4 {x}^{2} - 12x - 8x + 9 + 12[/tex]

We have

[tex]f(g(x)) = {4x}^{2} - 20x + 21[/tex]

Now to find f(g(4)) substitute the value of x that's 4 into f(g(x)) that's replace every x in f(g(x)) by 4

We have

[tex]f(g(4)) = 4( {4})^{2} - 20(4) + 21 \\ = 4(16) - 80 + 21 \\ = 64 - 80 + 21 \\ = 85 - 80[/tex]

We have the final answer as

[tex]f(g(4)) = 5[/tex]

Hope this helps you

Answer:

Answer:

f(g(4)) = 5f(g(4))=5

Step-by-step explanation:

f(x) = x² - 4x

g(x) = 2x – 3

To find f(g(4)) we must first find f(g(x))

To find f(g(x)) substitute g(x) into f(x) that's for every x in f(x) replace it with g (x)

That's

\begin{lgathered}f(g(x)) = ({2x - 3})^{2} - 4(2x - 3) \\ = 4x^{2} - 12x + 9 - 8x + 12 \\ = 4 {x}^{2} - 12x - 8x + 9 + 12\end{lgathered}

f(g(x))=(2x−3)

2

−4(2x−3)

=4x

2

−12x+9−8x+12

=4x

2

−12x−8x+9+12

We have

f(g(x)) = {4x}^{2} - 20x + 21f(g(x))=4x

2

−20x+21

Now to find f(g(4)) substitute the value of x that's 4 into f(g(x)) that's replace every x in f(g(x)) by 4

We have

\begin{lgathered}f(g(4)) = 4( {4})^{2} - 20(4) + 21 \\ = 4(16) - 80 + 21 \\ = 64 - 80 + 21 \\ = 85 - 80\end{lgathered}

f(g(4))=4(4)

2

−20(4)+21

=4(16)−80+21

=64−80+21

=85−80

We have the final answer as

f(g(4)) = 5f(g(4))=5

Hope this helps you

1/5 divided by 3 is what

Answers

Answer:

the answer would be 1/15, or approximately 0.067.

Step-by-step explanation:

You are considering a certain telephone company. They charge S0.18 per minute of talking, plus a fixed base monthly fee of S70.If M represents the number of minutes you talk in a month, and C is the total monthly charge, which of these is the correct relationship between M and C? Select the correct answer below
a) C = 0.18M + 70
b) M = 0.70C + 18
c) C = 0.70M + 18
d) M = 0.18C + 70

Answers

Answer:

a) C = 0.18M + 70

Step-by-step explanation:

Charges:

1. Monthly fee = S702. Charge for talking = S0.18 per minute

Totals, considering number of minutes:

S70 + S0.18*M

So the equation would be:

C = 0.18M + 70

This is the option a)

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