If f(1) =7 and f(n)=-5f(n-1)-n

then find the value of
f(4)

Answers

Answer 1

Final answer:

Using the recursive relationship f(n) = -5f(n-1) - n, we calculated the values step by step to find that f(4) is -914.

Explanation:

The question asks us to find the value of f(4) given that f(1) = 7 and the recursive relationship f(n) = -5f(n-1) - n.

To find f(4), we need to compute it in a step-by-step manner by first finding f(2) and f(3), and using those results to finally compute f(4).

Starting with f(1) = 7, we calculate f(2):

f(2) = -5f(1) - 2 = -5*7 - 2 = -35 - 2 = -37.

Next, calculate f(3):

f(3) = -5f(2) - 3 = -5*(-37) - 3 = 185 - 3 = 182.

Finally, calculate f(4):

f(4) = -5f(3) - 4 = -5*182 - 4 = -910 - 4 = -914.

Therefore, the value of f(4) is -914.

Answer 2

Final answer:

Using the recursive function given, by computing step by step from f(1) up to f(4), we find that f(4) equals -914.

Explanation:

To find the value of f(4), we must use the given recursive relation f(n) = -5f(n-1) - n, starting with the base case f(1) = 7.

Find f(2):
f(2) = -5f(2-1) - 2 = -5f(1) - 2 = -5(7) - 2 = -35 - 2 = -37Find f(3):
f(3) = -5f(3-1) - 3 = -5f(2) - 3 = -5(-37) - 3 = 185 - 3 = 182Find f(4):
f(4) = -5f(4-1) - 4 = -5f(3) - 4 = -5(182) - 4 = -910 - 4 = -914

Therefore, f(4) = -914.


Related Questions

A triangle has a base of 12 and one-third centimeters and height of 3 centimeters. Which expression could be used to determine the area of the triangle shown? One-half + 12 and one-third + 3 One-half (3) (12) (one-third) 12 and one-third times 3 One-half (12 and one-third) (3)

Answers

Answer:

One-half (3) (12) (one-third)

Step-by-step explanation:

Area of a triangle bus expressed as shown.

Area of a triangle = 1/2bh

B is the base

H is the height

Given base = 12 1/3xm

Height =3cm

Area =>1/2 (3) 12(1/3)

Area = One-half (3) (12) (one-third)

Answer:

One-half (12 and one-third) (3) option D/ the last one

Step-by-step explanation:

I took it and got it right on e2020

The pie chart shows information about the grades achieved by all of the candidates in Keval's school who took AS Level English in 2015. 8 candidates achieved grade C. Work out the number of candidates in Keval's school who took AS Level English in 2015, showing your working out (2 marks)

Answers

Answer:

you have to put the pie chart to get an answer

Step-by-step explanation:

graph the function
h(x)= 6(4/3)^x

Answers

Graph of the function h(x)= 6(4/3)ˣ will be a positive exponential.

What is an exponential function?

A mathematical function with the formula f (x) = eˣ is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, which equates to about, is the exponential-function basis that is most frequently encountered.

One of the key mathematical operations is the exponential function (though it would have to admit that the linear function ranks even higher in importance). We allow the exponent to be the independent variable to create an exponential function.

The exponential function increases quickly, as shown in the graph of f above. The simplest kinds of dynamical systems have solutions in the form of exponential functions. For instance, straightforward models of bacterial development produce an exponential function.

Growth or decay can both be described by an exponential function. The function h(x)= 6(4/3)ˣ

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Suppose that 200 flies are ee, 150 flies are ee, and 150 flies are ee. calculate the frequencies of the 3 genotypes for this population. do not leave your answers as fractions!

Answers

Complete Question

Imagine a large Source [tex](S_o)[/tex] population of 500  files at a particular time we will call [tex]T_s[/tex].The files have brown ebony bodies. Suppose that 200 flies are ee, 150 flies are Ee, and 150 flies are EE. calculate the frequencies of the 3 genotypes for this population. do not leave your answers as fractions!

Answer:

The frequency of  genotype ee is  [tex]f_{ee}= 0.4[/tex]

The frequency of  genotype Ee is [tex]f_{Ee} = 0.3[/tex]

The frequency of  genotype EE is [tex]f_{EE} = 0.3[/tex]

Step-by-step explanation:

From the question we are told that

   The number of files with genotype ee is [tex]ee = 200[/tex]

    The number of files with genotype Ee is [tex]Ee = 150[/tex]

    The number of files with genotype  [tex]EE[/tex] is [tex]EE = 150[/tex]

The frequency of  genotype ee is mathematically evaluated as

      [tex]f_{ee} = \frac{200}{500}[/tex]

      [tex]f_{ee}= 0.4[/tex]

The frequency of  genotype Ee is mathematically evaluated as

      [tex]f_{Ee} = \frac{150}{500}[/tex]

      [tex]f_{Ee} = 0.3[/tex]

The frequency of  genotype EE is mathematically evaluated as

      [tex]f_{EE} = \frac{150}{500}[/tex]

      [tex]f_{EE} = 0.3[/tex]

PLS HELPP Mr. Clark needed to rent a moving van. Company A charges a rate of $90 per hour plus a $50 truck
fee. Company B charges $70 per hour plus a $90 truck fee. For what number of rental hours is the cost
for both companies the same?​

Answers

Answer:

2 hours

Step-by-step explanation:

According to the information provided you can say that for company A, the total cost is equal to 90 for the number of hours plus the 50 fee. For company B, the total cost is equal to 70 for the number of hours plus 90.

90x+50= 70x+90

x= number of rental hours

Then, you have solve for x:

90x-70x=90-50

20x=40

x=40/20

x= 2

The cost for both companies is the same for 2 rental hours.

Answer:

h = 2 hrs

Step-by-step explanation:

Mr Clark needed to rent a moving Van.

Company A charges

cost = 50 + 90(h)

where

h = number of hours used

Company B charges

cost = 90 + 70(h)

where

h = number of hour used

The number of rental hours when both companies cost is same is when both the cost equation is equal to each other.

Therefore,

50 + 90(h) = 90 + 70(h)

50 - 90 = 70h - 90h

-40 = -20h

divide both sides by -20

h = -40/-20

h = 2 hrs

PLEASE HELP 50 POINTS


Assume the whole pizza was 12 inches across and cut into 8 pieces.

Answers

Answer:

14.14 inches squared

Step-by-step explanation:

We basically just want to find the area of one slice of pizza.

We know that the whole pizza was 12 inches across, which means its diameter was 12. Radius is 1/2 of the diameter, so r = 12/2 = 6 inches.

The area of a circle (the pizza, I assume, was circular) is: [tex]A=\pi r^2[/tex], where r is the radius. Here, r = 6, so:

[tex]A=\pi r^2[/tex]

[tex]A=\pi *6^2=36\pi[/tex]

But this is the area of the entire pizza. We need to divide it by 8:

[tex]36\pi /8[/tex] ≈ 14.14 inches squared

Hope this helps!

Answer:

14.13 in²

Step-by-step explanation:

Diameter: 12 inches

Radius: 12/2 = 6 inches

Area of the entire pizza:

pi × r²

3.15 × 6²

113.04 in²

Area of each slice:

113.04/8

14.13 in²

Grace is having trouble deciding what to order for dessert. The options are 4 different flavors of ice cream, 3 different flavors of cake, or 2 different flavors pie. If she were to choose one item at random, what is the probability that she will choose a cake?

Answers

Answer: The probability that she would choose cake is 0.33 (or 33%)

Step-by-step explanation: The number of all possible outcomes is given as follows;

4 (ice cream) + 3(cake) + 2(pie), that is 4 + 3 + 2 = 9  

This means there is a possibility of 9 different outcomes if she decided to choose her dessert at random.

However, there are 3 flavors of cake available which means the possibility of choosing cake is 3.

Therefore the probability that she will choose a cake is give as,

P(Cake) = Number of required outcomes/Number of all possible outcomes

P(Cake) = 3/9

P(Cake) = 1/3 or 0.33

Therefore the probability that she would choose cake is 0.33 or 33%

Find the percent markdown for an $80 jacket that is in sale for $48

Answers

Answer:

40 percent off

Step-by-step explanation:

40 percent off 80.00 is 48.00

Our school had a pizza party.The school ordered 847 slices of pizza for the party. The students ate 628 slices. How many slices of pizza are left over?

Answers

Answer:

209

Step-by-step explanation:

837-628

least to greatest. 26.2, 262%, 2 3/5 (two and three fifths)
in all decimal or percent form please and i need an answer soon please help!!!

Answers

Answer:

Step-by-step explanation:

BACD

Final answer:

The numbers from least to greatest are 2.62 (262%), 2.6 (2 3/5), and 26.2.

Explanation:

To arrange the numbers 26.2, 262%, and 2 3/5 from least to greatest in all decimal or percent forms, we need to convert them into the same form.

First, we know that 262% as a decimal is 2.62. The mixed number 2 3/5 can be converted to a decimal by dividing the numerator by the denominator and adding it to the whole number, resulting in 2 + 0.6 = 2.6.

Now we have the numbers in decimal form: 26.2, 2.62, and 2.6.

To order them from least to greatest:

2.62 (262%)2.6 (2 3/5)26.2

When converting back to percent form, remember to multiply by 100. Thus, 2.62 is already given as 262%, and 2.6 becomes 260%.

Find the simplified product where x=0: √5x (√8²−2√x)

Answers

Answer:

D Is the answer on edge

Step-by-step explanation:

hope this helps!

The product of the polynomials √(5x) and √(x²) - 2√(x) will be 8√(5x) - 2x√5.

What is a polynomial?

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

The polynomials are given below.

√(5x) and √(8²) - 2√(x)

The product of the polynomials √(5x) and √(x²) - 2√(x) will be given as,

⇒ [√(5x)] [√(8²) - 2√(x)]

⇒ √(5x)√(8²) - 2√(x)√(5x)]

⇒ 8√(5x) - 2x√5

The product of the polynomials √(5x) and √(x²) - 2√(x) will be 8√(5x) - 2x√5.

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F(x)=x^2 - 1/x - 4
Can someone please help me with this

Answers

That is a really hard one so I think that you should just do a new one honestly keeping it a buck 100 witcha lil brah


Use the formula A = h(b1 + b2).
What is the area of the trapezoid?
square units

Answers

Answer:

75 square units

Step-by-step explanation:

The area of the trapezoid is 75 sq.units.

What is a Quadrilateral?

A quadrilateral is a polygon with four sides.

It is of various types,

Trapezoid, which have one pair of parallel sides,

Parallelogram, it has two pairs of parallel sides,

Rhombus, it has all sides equal,

Rectangle, opposite sides are parallel and equal, and,

Square, all sides are equal and opposite sides are parallel, and all angles have measure of 90 degree.

The quadrilateral ABCD with lengths of three of its sides is 16, 6, and 14.

The height of the quadrilateral is 5.

The area of the quadrilateral has been asked to determine using the formula,

A = (1/2) h ( b1 + b2)

The parallel sides are 14 and 16, so b1 = 14 and b2 = 16, h = 5

The area is determined using the formula

A = (1/2) * 5 * ( 14+16)

A =  (1/2) * 5 * ( 30 )

A = 75 sq.units

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The radius of a circle is 7 ft. Find its area to the nearest tenth.

Answers

The required area of the circle with a radius of 7 ft is given as 153.9 ft².

What is an area circle?

The area of the circle is given by the pie times square of the radius. Or defined as the area enclosed within the circumference of the circle.

here,
Area of the circle = πr²

From the given data radius is 7ft,
plugging the value in the area formula of the circle,
Area of the circle = 3.14 × 7² = 153.9 ft²

Thus, the required area of the circle with a radius of 7 ft is given as 153.9 ft².

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Triangle A B C is shown. Angle A C B is a right angle. The length of hypotenuse A B is 12 centimeters, the length of C B is 9.8 centimeters, and the length of A C is 6.9 centimeters.
Which expressions can be used to find m∠BAC? Select three options.

cos−1(StartFraction 6.9 Over 12 EndFraction)
cos−1(StartFraction 9.8 Over 12 EndFraction)
sin−1(StartFraction 6.9 Over 12 EndFraction)
sin−1(StartFraction 9.8 Over 12 EndFraction)
tan−1(StartFraction 6.9 Over 9.8 EndFraction)

Answers

Final answer:

To find measure of angle BAC in a right triangle, we can use the trigonometric functions cos⁻¹(6.9/12), sin⁻¹(6.9/12), and tan⁻¹(6.9/9.8), corresponding to the sides AC and CB with respect to the hypotenuse AB.

Explanation:

To find the measure of angle BAC in triangle ABC where angle ACB is a right angle, we can use the trigonometric ratios involving the sides of the triangle. Given that AB is the hypotenuse, CB is the adjacent side to angle BAC, and AC is the opposite side to angle BAC, we can use the following expressions:

cos⁻¹(⅓6.9/12): This represents the cosine of angle BAC, since cosine is the ratio of the adjacent side to the hypotenuse.sin⁻¹(⅓6.9/12): This represents the sine of angle BAC, since sine is the ratio of the opposite side to the hypotenuse.tan⁻¹(⅓6.9/9.8): This represents the tangent of angle BAC, since tangent is the ratio of the opposite side to the adjacent side.

Using any of these trigonometric functions, we can calculate the measure of angle BAC by inputting the ratios into a calculator that has the capability to compute the inverse trigonometric functions.

A row of plaques covers 252 square feet of space along a wall.

If the plaques are 6 feet tall, what length of the wall do they cover?
The length of the wall that the plaques will cover is feet long.

Answers

Answer:

252/6=42

Step-by-step explanation:

BRAINLIEST PLZ

Answer:

The length of the wall that the plaques will cover is 42 feet long.

Step-by-step explanation:

Wall is rectangular in shape

So Area = length × width

252 = 6 × length

length = 252/6

length = 42

what the value of the expression -2(-7/9 divided 1/3)

Answers

Answer:

lol i need

Step-by-step explanation:

ez calps plue

Answer:

14/27

Step-by-step explanation:

let me know if this is right

A couple plans on having three children. Which of the following represents the sample space for the genders of the three children? To simplify this question, we will use the binary definition of gender, with representing boy and representing girl. A (68B, BBG, BGG, GGG) B.(B,G) C.(BB, BG, GB, GG) D. (BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG) E. (BG, BG, BG)

Answers

Your answer is E (BG, BG, BG)

What is the formula to find the vertex of a parabola?

Answers

Answer:

y = a(x - h)^2 + k (please give branliest)

Step-by-step explanation:

(h,k) are coordinates of a point on the parabola

this is derived by ax^2 + bx + c

Final answer:

The formula to find the vertex of a parabola is x = -b/(2a) and y = f(x). The vertex of a parabola is represented by the coordinates (x, y).

Explanation:

The formula to find the vertex of a parabola is x = -b/(2a) and y = f(x). In the equation of a parabola y = ax² + bx + c, the vertex can be found by substituting the x-coordinate from the formula into the equation to get the y-coordinate. So, the vertex of a parabola is represented by the coordinates (x, y).

What is 10^3 x 10^9 with a single exponent ?

Answers

10^3 x 10^9 = 10^12

Step-by-step explanation:

Given that,

10^3 x 10^9

The bases of the 2 terms are same (10) and the power of the terms are 3 and 9

As the base of the 2 terms are same and the bases are in multiplication form we can add up the powers.

So,

10^3 x 10^9 = 10^(3+9)

= 10^12

deon buys candy that cost $6 per pound. he will buy at most 7 pounds. write answer as inequality

Answers

Answer:

x ≤ 42 dollars

Step-by-step explanation:

Deon will buy at most 7 pounds, and we know that it costs 6 per pound, so we multiply 7 and 6 to get 42. Deon will not buy over 7 pounds, so that means less than or equal to.

What is the slope of the line that passes through the points (-9, -3) and (1, -3)?
Write your answer in simplest form.

Answers

Answer:

The slope is 0.

Step-by-step explanation:

m= (y2-y1)/(x2-x1).

y2 is -3, y1 is -3.

x2 is 1 and x1 is -9.

m= -3 -(-3)/ 1- (-9)

m= 0/10

m=0

Final answer:

The slope of the line that passes through the points (-9, -3) and (1, -3) is 0 because the y-coordinates of both points are the same and this results in a 'change in y' of 0.

Explanation:

In mathematics, the slope of a line passing through two given points can be calculated by the formula: (y2 - y1) / (x2 - x1). Where y2 and y1 represent the y-coordinates of the two points and x2 and x1 represent the x-coordinates of the two points. However, in this particular case, we see that the y-coordinates of both points (-9, -3) and (1, -3) are the same as -3.

This means our 'change in y', or (y2 - y1), is equal to zero (-3 - -3 = 0). Any fraction with 0 as the numerator (0 divided by any number) is itself equal to 0. Therefore, the slope of the line that passes through the points (-9, -3) and (1, -3) is 0.

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A motel finds it can rent 180 rooms when the room rate is $ 60 per day. For each $ 2 increase in the rate, two fewer rooms are rented. Find the room rate that maximizes daily revenue. The rate that maximizes revenue is $ .

Answers

Answer:

$7,200

Step-by-step explanation:

r=p × n

where

r=revenue

p = price per item

n = number of items sold

A change in price changes quantity ( number sold)

Variable x changes with price, then

Let

p+x=a dollar price increase

p-x= a dollar price decrease

n+x= an increase in quantity sold

n-x= a decrease in quantity sold

Therefore,

A $2 dollar increase in price=p+2x

2 decrease in room quantity sold= n-2x

Substituting in the above equation

r=(p+2x)*(n-2x)

P=$60

n=180

Then

r=(60+2x)*(180-2x)

r=10,800-120x+360x-4x^2

r=-4x^2-240x+10,800

Solve the quadratic equation

The maximum value of x in the vertex = - b/2*a

Where

b=240

a=-4

Value of x=-240/2*(-4)

X=30

r=-4x^2-240x+10,800

=-4(30)^2-240(30)+10,800

=-4(900)-7200+10,800

=3,600-7200+10800

=$7,200

The rate that maximises revenue=$7,200

Answer:

The rate that maximizes revenue is $14,000

Step-by-step explanation:

First of all, you should know that the income equation is:

R = p * n

where:

p = price per item n = number of items sold

On the other hand, if p + x means a price increase, while n - x means a decrease in the number of an item sold.

In this case, reference is made to rooms, where 60 + 2x is the increased price and 180-2x is the decrease in rooms for rent.

So:

R=(60+2x)*(180-2x)

Expressing this in another way, applying distributive property:

R=60*180+60*(-2)x+2x*180+2x*(-2)x

R=10,800+240x-4x² equation (A)

This is a quadratic equation that is graphically represented by a parabola. If a, the coefficient that accompanies the term x², has a positive value, the parabola will be oriented upwards. On the contrary, if a has a negative value, the parabola will be oriented downwards. In this case, the value of a is -4, with the parabola facing down. The vertex is a point that is part of the parabola, which has the value as ordered minimum or maximum function. In this case, since the parabola faces downward, the vertex will be its maximum value.

The value of x in the vertex is [tex]-\frac{b}{2*a}[/tex]. In this case:

a=-4b=240

Replacing:

[tex]x=-\frac{240}{2*(-4)}[/tex]

Solving:

x=40

To find the rate that maximizes income you simply replace this value in equation (A)

R=10,800+240*40-4*(40)²

R=14,000

The rate that maximizes revenue is $14,000

16x+9=8x+46 can someone help?

Answers

Answer:

37/8

Step-by-step explanation:

Subtract 8x from both sides and get 8x+9=46 subtract 9 from both sides and get 8x=37 divide by 8 and get 37/8

Answer:

x=4.625

Step-by-step explanation:

16x+9=8x+46

-8x

8x+9=46

-9

8x=37

/8

x=4.625

The amount of slushy left in the cup (in milliliters) as a function of time (in seconds) is graphed. How fast did Sean drink the slushy?

Answers

The initial amount of slushy in the cup is 600 mm.

A linear equation has the following form:

y = mx + b

where y and x are variables, m represents the rate of change, and b represents the initial value of y.

Let y be the amount of slushy remaining in the cup (in milliliters) and x the time (in seconds).

The y intercept on the graph is 600.

As a result, the initial amount of slushy in the cup is 600 mm.

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The following question may be like this:

Sean drank a slushy as fast as he could.

The amount of slushy left in the cup (in milliliters) as a function of time (in seconds) is graphed. How much slushy was initially in the cup? ​

What’s the measure of angle C if tan C = 0.5773

Answers

Answer:

C =29.998°

Step-by-step explanation:

To find the measure of angle C if tan C = 0.5773, we will follow the steps below;

tan C = 0.5773

take the tan⁻¹ of both-side of the equation

that is;

 tan⁻¹ tan C =  tan⁻¹0.5773

On the left-hand side of the equation tan and  tan⁻¹ will cancel-out leaving us with just c

C =  tan⁻¹0.5773

C =29.998°

C≈30°

Which fraction is closest to 1 1/2?

Answers

Answer:

7/13

Step-by-step explanation:

To determine which answer choice is closest to 1/2, we can subtract 1/2 from each answer choice. The difference that is closest to zero will indicate the fraction that is closest to 1/2. Since 1/26 is closest to zero, 7/13 is closest to 1/2.

Answer:

4/2

THATS ITTT

A right cylinder has a radius of 2 units and a height of 5 units.

A right cylinder has a radius of 2 units and a height of 5 units.

What is the volume of the cylinder? Round to the nearest tenth.

a
31.4 cubic units
b
62.8 cubic units
c
157.1 cubic units
d
314.2 cubic units

Answers

Answer:

The volume of the cylinder is 62.8 cubic units.

Step-by-step explanation:

The volume of a cylinder is given by the following formula:

volume = (base area)*h

base area = pi*r²

volume = pi*r²*h

In order to solve this problem we need to apply the data given to the formula above as shown below:

volume = 3.14*(2)²*5 = 3.14*4*5

volume = 62.8 cubic units

The volume of the cylinder is 62.8 cubic units.

Answer:

The correct answer is option (b) 62.8 cubic units

Step-by-step explanation:

Solution

Recall that,

A right cylinder has a radius of = 2 units

Height of  = 5 units

Now,

We define the volume of a cylinder, which is represented below.

Recall that,

A right cylinder has a radius of = 2 units

Height of  = 5 units

Now,

We define the volume of a cylinder, which is represented below.

Volume of the cylinder is defined as  = base * height

The base=Pi*radius*radius,  or π* r

Where,

The base=3.1416*2*2,

The height=5

Thus,

The Volume=3.1416*2*2*5

Volume =62.8 cubic units.

Therefore the volume of the cylinder is 62.8 cubic units.of the cylinder is = base * height

The base=Pi*radius*radius,  or π* r

Where,

The base=3.1416*2*2 ,

The  height=5

Thus,

The Volume=3.1416*2*2*5

Volume =62.8 cubic units.

Therefore the volume of the cylinder is 62.8 cubic units.

A play started at 2:35 P.M after the play was over , Jamie talked to a friend for 15 minutes She left the theatre at 4:10 P.M how long was the play? Would fine this super helpful thank you so much

Answers

Answer:

1 hour 20 minutes

Step-by-step explanation:

The play started at 2:35 PM.

After the play, Jamie talked to her friend for 15 mins and then left the theater at 4:10 PM.

She started talking to her friend once the play was over, hence, to find the time she started talking, we subtract 15 mins from 4:10 PM:

  H     M

  04 : 10

-  00 : 15

  03 : 55

She started talking around 3:55 PM.

Hence, to find how long the play lasted:

   H    M

  03 : 55

- 02 : 35

  01 : 20

Hence, the play lasted for 1 hour 20 minutes.

Circle V is shown. Line segments Y V and W V are radii. Tangents Y X and W X intersect at point X outside of the circle. The length of V Y is 5. Angle V is a right angle. What is the measure of circumscribed ∠X? A 45 B 50 C 90 D95

Answers

Answer:

The correct option is;

C 90°

Step-by-step explanation:

Here we have;

Angle V = 90°

Whereby, YX and WX are tangents, and YV and WV are radii then ;

Angle Y = 90° and

Angle  W = 90°

Therefore we have sum of angles V, Y, W and X given by the following relation;

V + Y + W + X = 360° (Sum of interior angles of a polygon angle)

Therefore;

90° + 90° + 90° + X = 360°

270° + X = 360

X = 360° - 270° = 90°

Hence the correct option is X = 90°.

Answer:

Correct answer is C

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