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3 years ago

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F(x)=3x−4 Input is x=3 , Output is

1 answer:

Pepsi [2]3 years ago

6 0

f(x)=3x−4 Input is x=3 , Output is

3X3-4= 5

f(x)=−4x+3 Input is x=−3 , Output is

4x-3 +3 = -9

f(x)=−x−1 Input is x=−4 , Output is

-(-4-1) =-(-5) =5

f(x)=x2 Input is x=5 , Output is

5x2=10

hope it will help you

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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

An irregular parallelogram rotates 360° about the midpoint of its diagonal. How many times does the image of the parallelogram c

Kazeer [188]

Answer:

2.

Step-by-step explanation:

Rotating a figure about the midpoint of its diagonal, the figure will coincide with its pre-image two times: at 180° and at 360°.

This is different than rotating about the origin; for a rotation about the origin, a 180° rotation does not always coincide with the pre-image.

hope that answers ur question :))))

4 0

3 years ago

Oleg, Sasha, and Dima share 600 toys. Sasha has twice as many toys as Oleg. Dima has 40 more toys than Oleg. How many toys does

Anika [276]

Answer: 140

Oleg, Sasha, and Dima shared 600 toys. Sasha had twice as many toys as Oleg. Dima had 40 more toys than Oleg.

Let the number of toys Oleg has = x

Let the number of toys Sasha has = y

Let the number of toys Dima has = z

Sasha had twice as many toys as Oleg

So y = 2*x= 2x

Dima had 40 more toys than Oleg.

z = x + 40

Oleg, Sasha, and Dima shared 600 toys

x + y + z= 600

We know y=2x and z=x+40

Replace it for y and z

Subtract 40 on both sides

Divide by 4 on both sides

Oleg had 140 toys

Step-by-step explanation:

6 0

4 years ago

A frustum is made by removing a small cone from a similar large cone in the diagram shown the height of a small cone is a quarte

lesantik [10]

Answer:

Volume of the frustum = ⅓πh(4R² - r²)

Step-by-step explanation:

We are to determine the volume of the frustum.

Find attached the diagram obtained from the given information.

Let height of small cone = h

height of the large cone = H

The height of a small cone is a quarter of the height of the large cone:

h = ¼×H

H = 4h

Volume of the frustum = volume of the large cone - volume of small cone

volume of the large cone = ⅓πR²H

= ⅓πR²(4h) = 4/3 ×π×R²h

volume of small cone = ⅓πr²h

Volume of the frustum = 4/3 ×π×R²h - ⅓πr²h

Volume of the frustum = ⅓(4π×R²h - πr²h)

Volume of the frustum = ⅓πh(4R² - r²)

6 0

4 years ago

Solve -4(2x - 1) = -6(x + 2) - 2<br> A.-5<br> B.5<br> C.9<br> D.9

Oksanka [162]

$Hello$ $There!$

<u>The answer is...</u>

<u />

C. 9

Hopefully, this helps you!!

$AnimeVines$

8 0

3 years ago