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The value of the car will be £2,621 after 5 years.

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time.

Given that, The value of a second-hand car is £8,000. Each year it loses 20% of its value, we are asked to find its value after 5 years.

This is a situation of exponential decay.

Hence, using the exponential decay formula =

A = P(1-r)ⁿ

Where A is final value, P is principal value, r is rate of decrease and n is the number of years.

Here, we will find A, and we have,

P = £8,000.

r = 20% = 0.20

t = 5

Therefore,

A = 8000(1-0.20)⁵

A = 8000(0.80)⁵

A = 8000(0.32768)

A ≈ 2,621

Hence, the value of the car will be £2,621 after 5 years.

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Answer:

8/13

Step-by-step explanation:

5 + 5 + 3 = 13 total

5 red balls + 3 green balls = 8

Answer:

M<1 is 43 degrees and M<2 is 137

Step-by-step explanation:

This is a case of supplementary angles. M<1 and M<2 are supplementary, which means that their angle degrees added together will be equal to 180. The same is for M<2 and M<3, and M<3 and M<4, and M<1 and M<4. Basically, two angles are supplementary when they form a straight line, or 180 degrees

First, we know that M<1 and M<2 added together is 180. We know M<1 is 7x+1, so then, we have:

(7x+1) + (M<2) = 180

Therefore, we have 180-(7x+1) = M<2. We can't solve the equation further on from there, so we move on.

Next, we know that M<2 and M<3 added together is 180. We know that M<3 is 12x-29, so then, we have:

(12x-29) + (M<2) = 180

Therefore, we have 180-(12x-29) = M<2. Now, we have two equations to solve x:

180-(7x+1) = M<2 and 180-(12x-29) = M<2. As both equations equal M<2, they equal each other. Thus, we have:

180-(7x+1) = 180-(12x-29)

We can cancel out 180, so:

-(7x+1) = -(12x-29)

-7x-1 = -12x+29

-30 = -5x

x = 6.

Now that we have x, we can find M<1, M<3, and M<2. M<1 is (7x+1), so we use substitution, putting 6 for x, and M<1 is evaluated to 43 degrees.

Now that we have M<1, we can find M<2 easily. M<1 + M<2 = 180, so 43 + M<2 must be 180. Therefore, M<2 is 137 degrees.

We can do the same for M<3, but the problem does not require it.

Answer:

It's Both

Step-by-step explanation:

for the first two co-ordinates, there are many y-value for a single x-value, then for the last two co-ordinates theres a single y-value for one x-value

Answer:

The area of the new triangle would be A = (1/2) * 30ft * 40ft = (1/2) * 1200ft^2 = 600ft^2

Step-by-step explanation:

To increase the size of a triangle by a scale factor of 10/3, you can multiply each side length of the triangle by 10/3.

The new dimensions of the triangle would be (10/3) * 9ft = 30ft and (10/3) * 12ft = 40ft.

The area of a triangle is given by the formula A = (1/2) * b * h, where b is the length of the base and h is the height of the triangle.

Using the new dimensions of the triangle, the area of the new triangle would be A = (1/2) * 30ft * 40ft = (1/2) * 1200ft^2 = 600ft^2.

Answer:

Total number of package Deli made = 48 package

Step-by-step explanation:

Given:

Amount of cheese block = 12 pound

Amount of cheese in each package = 1/4 pound

Find:

Total number of package Deli made

Computation:

Total number of package Deli made = Amount of cheese block / Amount of cheese in each package

Total number of package Deli made = 12 / [1/4]

Total number of package Deli made = 12 x 4

Total number of package Deli made = 48 package

Answer: 48 packages

Answer:

V≈1150.35cm³

Step-by-step explanation:

Using the formulas

V=4 /3πr3

d=2r

Solving for V

V=1/ 6πd^3=1/ 6·π·13^3≈1150.34651cm³

The answer to this is A. I hope this helps

Answer:

9.0 ft

Step-by-step explanation:

Let the distance from the bottom of the board to the edge of the wall be represented as "x"

Angle measure = θ = 53.13°

Hypotenuse = 15 ft

Adjacent side = x ft

The trigonometric ratio we would apply would be CAH:

Thus,

Cosine θ = Adjacent/Hypotenuse

Plug in the values

Cos 53.13° = x/15

Multiply both sides by 15

15 * Cos 53.13 = x

9.00002143 = x

x ≈ 9.0 ft (nearest tenth)

Therefore, distance from the bottom of the board to the edge of the wall = 9.0 ft

Answer:

(x-c) is a factor of f(x)

The value of the tan(α) is -0.2624.

In trigonometry, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

In other words, it is the ratio of sine and cosine function of an acute angle such that the value of cosine function should not equal to zero.

Given that, the angle α intersects the unit circle at point (-0.2538, 0.9673). We need to find the value of tan(α),

We know that, the tangent of the angle is the ratio of the perpendicular and the base,

So,

tan(α) = -0.2538 / 0.9673

= -0.2624

Hence, the value of the tan(α) is -0.2624.

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LJ and LI are the figure's two congruent portions. Congruency means that the segments' sizes and shapes will be comparable.

Two triangles are said to be congruent to one another according to the Side-Angle-Side Congruence Theorem (SAS) if the included angle and corresponding two sides of one triangle match those of the other. Two sides that are being considered are determined to have an included angle. Therefore, using the SAS Congruence Theorem to prove that two triangles are congruent based on the fact that they have two pairs of corresponding sides and one pair of corresponding angles is insufficient.

given

The two segments LI and LJ that are marked in the illustration are congruent to one another.

Congruency means that the segments will have the same size and shape.

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Answer:

(0,-4),(1,1)(2,6)

Step-by-step explanation:

The area of the square having the same length of the base of the triangle is 7245 square inches.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

From the given figure as the base of the triangle is an equal length of the side of a square we can obtain the area of the square by first applying Pythagoras on the right angle triangle having a height of 87 inches and a hypotenuse of 18 inches.

So,

Base = {√(87² - 18²)}.

Base = √(7245) inches.

Base = 85.11 inches.

Now, We also know that the area of a square is (side)².

Therefore it is (87.11)² which is the same as 7245 sq inches.

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Answer:

c

Step-by-step explanation:

Answer:

I believe it would be 64 in 2 correct me if I am wrong.

Answer: Hmmmmmm

Explanation

Answer:

Yes, Anna and Sharon both created triangles that are congruent. Their triangles are congruent because they have 2 corresponding, congruent side-lengths and an included angle that is congruent. Therefore, their triangles are congruent by SAS (Side-Angle-Side).

Answer:

1.40

Step-by-step explanation:

Given that

the number of customers are 130

The variance is 256

And, the sample mean is $21.50

We need to find out the standard error

So , the standard deviation is

= sqrt(variance)

= sqrt(256)

= 16

As we know that

standard error of mean = standard deviation ÷ sqrt(n)

= 16 ÷ sqrt(130)

= 1.40

Answer:

10cm

Step-by-step explanation:

Since ABC and DEF are similar, the ratio of their side is always the same.

The ratio here is:

DF/AC = 6/4 = 1.5

Therefore, it means that BC x 1.5 = EF

So:

BC x 1.5 = 15

BC = 15 / 1.5 = 10cm.

Answer:

It should be 2.016 m cubed

Step-by-step explanation:

the formula is V= 1/3 ( l × w × h ) if you want to check

Answer:

box 2 and 3

Step-by-step explanation:

the rays are the only two that form the angle of 1

The expression 1.7 x 5.5  can be an area model of the rectangle where the length is 1.7 and the width is 5.5

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

The expression 1.7 x 55 is an area model.

Area of rectangle = length x width

Now,

Length = 1.7

Width = 55

Area = 1.7 x 5.5

Thus,

The expression 1.7 x 5.5 can be an area model.

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Answer:

6

Step-by-step explanation:

The straight line (at the bottom) measures a total of 180 degrees. So we can write an equation where the sum of all of the angles = 180:

180 = 5x + x + 54 + 90

90 comes from the square indicating a right angle.

Using that equation, solve for x.

180 = 5x + x + 54 + 90

First, combine like terms.

180 = 6x + 144

Then subtract 144 from both sides

36 = 6x

Divide both sides by 6 to isolate x

6 = x

So x = 6°

Answer:

5148 months

Step-by-step explanation:

the equation that can be used to represent this question is :

100 + 50x = total amount that would be saved in x month

x = number of months

100 + 50x = 257,500

collect like terms

50x = 257,500 - 100

50x = 257,400

x = 257,400 / 50

x = 5148 months

Answer:

I love algebra anyways  

the ans is in the picture with the steps  

(hope it helps can i plz have brainlist :D hehe)

Step-by-step explanation:

9514 1404 393

Answer:

  (C)  SAS

Step-by-step explanation:

The obtuse angles in each triangle are "corresponding" with respect to the segments marked parallel and the horizontal transversal.

Those angles are between pairs of proportional sides:

  60/42 = 40/28 = 10/7

so, the applicable theorem is SAS. The triangles can be proven similar using the SAS theorem.