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3 years ago

Special right triangles 45-45-90 & 30-60-90 formula!! finding missing side lengths

Mathematics

1 answer:

nordsb [41]3 years ago

4 0

The formula you need to know is that the side opposite of the 30° angle is always half the hypotheneus. For example in question 2 X should be 6 since 3 is opposite side of the angle 30°. In a 45 45 90 triangle, it is important to know that the straight sides are always the same length (since they are the same angle). For example in question 9, v is also 9√2.

When you have two sides, you can figure out the third side with a² + b² = c² since they are all right triangles. Good luck

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It's for a test, I have to show some work and answer, I will give brainliest

natka813 [3]

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3 years ago

jenna's rectangular garden borders a wall. she buys 80 ft of fencing. what are the dimensions of the garden that will maximize i

FrozenT [24]

Answer:

The dimensions are x =20 and y=20 of the garden that will maximize its area is 400

Step-by-step explanation:

Step 1:-

let 'x' be the length and the 'y' be the width of the rectangle

given Jenna's buys 80ft of fencing of rectangle so the perimeter of the rectangle is 2(x +y) = 80

x + y =40

y = 40 -x

now the area of the rectangle A = length X width

A = x y

substitute 'y' value in above A = x (40 - x)

A = 40 x - x^2 .....(1)

Step :2

now differentiating equation (1) with respective to 'x'

$\frac{dA}{dx} = 40 -2x$ ........(2)

Find the dimensions

$\frac{dA}{dx} = 0$

40 - 2x =0

40 = 2x

x = 20

and y = 40 - x = 40 -20 =20

The dimensions are x =20 and y=20

length = 20 and breadth = 20

Step 3:-

we have to find maximum area

Again differentiating equation (2) with respective to 'x' we get

$\frac{d^2A}{dx^2} = -2$

Now the maximum area A = x y at x =20 and y=20

A = 20 X 20 = 400

Conclusion:-

The dimensions are x =20 and y=20 of the garden that will maximize its area is 400

verification:-

The perimeter = 2(x +y) =80

2(20 +20) =80

2(40) =80

80 =80

8 0

3 years ago

What is the solution to the system of equations 2x-y=7 and y=2x+3

Yuri [45]

Make y the subject in both equations

$2x-y=7$

$-y=-2x+7$

$y=2x-7$

For the second equation

$y=2x+3$

The two equations are parallel because they have the same gradient or slope but different y intercepts.

This type of equations have no solution because they will never intersect.

$NO SOLUTION$

The correct answer is C

6 0

3 years ago

Dan says he ran twice as far as Karim what possiblities for the distance they each could run

Lelechka [254]

If Karim ran one mile, Dan ran two miles.
If Karim ran three miles, Dan ran six miles.

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3 years ago

What is the solution and the inequality ?

Nikolay [14]

Inequality : 19.50n+24≤$110

Solution: Alyssa can buy 4 DVDs

Work: 110-24=86
86/19.50 = 4.4

You can't have a fraction of a DVD, so you have to round down to 4.

4 0

3 years ago