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2 years ago

What is the coordinates after (x+2, y + 3)

Mathematics

1 answer:

emmainna [20.7K]2 years ago

8 0

Answer:

L is (2,4) M (3,1,) N(0,4)

Step-by-step explanation:

L 0+2=2 so x is 2

L 1+3=4 so y is 4

M 1+2=3 so x is 3

M -2+3=1 so y is 1

N -2+2=0 so x is 0

N 1+3=4 so y is 4

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I am Lyosha [343]

Y=3
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2 years ago

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The length of the longer leg of a right triangle is 20 inches more than twice the length of the shorter leg. The length of the h

Alex17521 [72]

Answer:

Step-by-step explanation:

Let x represent the length of the hypotenuse.

Let y represent the length of the the shorter leg.

Let z represent the length of the longer leg.

The length of the longer leg of a right triangle is 20 inches more than twice the length of the shorter leg. It means that

z = 2y + 20

The length of the hypotenuse is 22 inches more than twice the length of the shorter leg. It means that

x = 2y + 22

We would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore,

(2y + 22)² = y² + (2y + 20)²

(2y + 22)(2y + 22) = y² + (2y + 20)(2y + 20)

= 4y² + 44y + 44y + 484 = y² + 4y² + 40y + 40y + 400

4y² + 88y + 484 = y² + 4y² + 80y + 400

4y² + 88y + 484 = 5y² + 80y + 400

5y² - 4y²+ 80y - 88y + 400 - 484

y² - 8y - 84 = 0

y² + 6y - 14y - 84 = 0

y(y + 6) - 14(y + 6)

y - 14 = 0 or y + 6 = 0

y = 14 or y = - 6

The shorter length cannot be negative hence y = 14 inches

The length of the shorter side is 14 inches.

The length of the hypotenuse is

(2 × 14) + 22 = 50 inches

The length of the longer side is

(2 × 14) + 20 = 48 inches

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

A movie theater decreased the size of its popcorn bags by 20%. If the old bags held 15 cups of popcorn, how much do the new bags

vovikov84 [41]

Answer:

Your answer will be  $12$  cups of popcorn.

Step-by-step explanation:

To find out how much the new bags hold, you need to find out the discount.

$\frac{20}{100 } = .2$

$15 * .2 = 3$

We know that the discount is $3$ .

To figure out how much the new bags hold, subtract by the old bags.

$15 - 3 = 12$

The new bags hold 12 cups of popcorn. 

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3 years ago

Find the value of a and of b for which (a) the solution of x2 + ax -2<x < 4

KengaRu [80]

Answer: $a = -2$

$b = 8$

Step-by-step explanation:

Given :

$x^{2} +ax$

re - writing the equation , we have

$x^{2} +ax-b$

we need to find the value of a and b for which -2<x < 4 , this means that the roots of the quadratic equation are -2<x < 4.

The formula for finding the quadratic equation when the roots are known is :

$x^{2}$ - sum of roots(x) + product of root = 0

sum of roots = -2 + 4 = 2

product of roots = -2 x 4 = -8

substituting into the formula , we have:

$x^{2} -2x-8=0$ , which could be written in inequality form as

$x^{2} -2x-8$

comparing with $x^{2} +ax-b$ , it means that :

$a = -2$

$b = 8$

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3 years ago