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3 years ago

13

Which graph best represents the solution set of y> 5/3 x+2

1 answer:

Anna [14]3 years ago

5 0

Answer:

B

Step-by-step explanation:

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In the right ∆ABC, the hypotenuse AB = 17 cm. M is the midpoint of the hypotenuse. Find the legs if PAMC=32 cm and PBMC=25 cm

jeyben [28]

Answer:

The length of the legs is 8.64cm and 14.64cm respectively

Step-by-step explanation:

I've added an attachment to aid my explanation.

At different intervals, I'll be making reference to it.

Given

$AB = 17$

$PAMC = 32$

$PBMC = 25$

From the attachment, we have:

$y + z = AB$

Since, M is the Midpoint

$y = z = \½AB$

Substitute 17 for AB

$y = z = \½ * 17$

$y = z = 8.5$

Also, from the attachment

$v + x + z = PAMC$

$v + x + y = 32$

Substitute 8.5 for y

$v + x + 8.5 = 32$

$v + x = 32 - 8.5$

$v + x = 23.5$ --------- (1)

Also, from the attachment

$v + w + z = 25$

Substitute 8.5 for z

$v + w + 8.5 = 25$

$v + w = 25 - 8.5$

$v + w = 17.5$ ----------- (2)

Subtract (2) from (1)

$v - v + x - w = 23.5 - 17.5$

$x - w = 6$

Make x the subject

$x = 6 + w$

Apply Pythagoras Theorem:

We have that:

$AB^2 = AC^2 + BC^2$

The above can be replaced with

$17^2 = x^2 + w^2$ (see attachment)

$289 = x^2 + w^2$

Substitute 6 + w for x

$289 = (6 + w)^2 + w^2$

$289 = 36 + 12w + w^2 + w^2$

$289 - 36 = 12w + 2w^2$

$253 = 12w + 2w^2$

Reorder

$2w^2 + 12w - 253 = 0$

Solve using quadratic equation:

$w = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

Where

$a = 2$

$b = 12$

$c = -253$

$w = \frac{-12 \± \sqrt{12^2 - 4 * 2 * -253}}{2 * 2}$

$w = \frac{-12 \± \sqrt{144 + 2024}}{4}$

$w = \frac{-12 \± \sqrt{2168}}{4}$

$w = \frac{-12 \± 46.56}{4}$

Split:

$w = \frac{-12 + 46.56}{4}$ or $w = \frac{-12 - 46.56}{4}$

$w = \frac{34.56}{4}$ or $w = \frac{-58.56}{4}$

$w = 8.64$ or $w = -14.64$

But length can't be negative

So:

$w = 8.64$

Recall that: $x = 6 + w$

$x = 6 + 8.64$

$x = 14.64$

<em>Hence, the length of the legs is 8.64cm and 14.64cm respectively</em>

5 0

3 years ago

What is the value of the expression

Gelneren [198K]

Answer:32

Step-by-step explanation: First you do 4×4×4×

=64 then you divide by 2.. 64÷2=32

8 0

4 years ago

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√200 in consecutive integers and in simplified form

myrzilka [38]

√200 = √2·100 = √2 · √100 = 10√2

4 0

3 years ago

The side lenghts of a square measures 10x+5. the side lenghts of a triangle are 30x,3x and 6x+30. the square and triangle have t

Goshia [24]

(10x+5)4 = 30x + 3x + 6x +30

40x + 20 = 39x + 30

X = 10

perimeter of the square= 420
perimeter of the triangle= 420

5 0

3 years ago

Pls help 10 points!!! No links or else

ddd [48]

Answer:

7,8

Step-by-step explanation:

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3 years ago

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