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3 years ago

Y is inversely proportional to (x+2)² when x=1, y=2

Mathematics

1 answer:

REY [17]3 years ago

6 0

Answer:

y = 18 / (x + 2)²

Step-by-step explanation:

Inversely proportional

y * (x + 2)² = k

when x=1, y=2

k = 2 * (1 + 2)²

k = 18

-----------------------

y * (x + 2)² = 18

Divide both sides by (x + 2)²

y = 18 / (x + 2)²

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8 0

3 years ago

What is the length of AC?<br><br><br> 3 ft<br><br> 4 ft<br><br> 9 ft<br><br> 18 ft

iragen [17]

Answer: The length of AC is 18 ft.

Step-by-step explanation:

By the given diagram,

AM = MB and CN = NB

M and N are the mid points of the sides AB and CB respectively,

Thus, by the mid point theorem,

MN ║ AC,

By the alternative interior angle theorem,

∠BMN ≅ ∠BAC

∠BNM ≅ ∠BCA

Thus, by AA similarity postulate,

ΔBMN ≅ ΔBAC

By the property of similar triangles,

$\frac{BM}{BA}=\frac{MN}{AC}$

$\frac{BM}{BM+MA}=\frac{MN}{AC}$

$\frac{4}{4+4}=\frac{9}{AC}$

$\frac{4}{8}=\frac{9}{AC}$

$4AC=72\implies AC = 18\text{ ft}$

Thus, The length of AC is 18 ft.

5 0

3 years ago

Read 2 more answers

Help me out please and thank you

faust18 [17]

<h3>Answer: 1</h3>

========================================================

Explanation:

We're given the height in relation to base BC, so we need to find the length of this base. This is the same as finding the distance from B to C.

Turn to the distance formula

$d = \text{Distance from B to C}\\\\d = \sqrt{(x_1-x_2)^2+(y_1-y^2)^2}\\\\d = \sqrt{(-2-(-3))^2+(-1-(-2))^2}\\\\d = \sqrt{(-2+3)^2+(-1+2)^2}\\\\d = \sqrt{(1)^2+(1)^2}\\\\d = \sqrt{1+1}\\\\d = \sqrt{2}\\\\$

Coincidentally, the base and height are the same. This won't always be the case.

Now we can find the area of the triangle

$A = \text{Area of triangle}\\\\A = \frac{1}{2}*\text{Base}*\text{Height}\\\\A = \frac{1}{2}*\sqrt{2}*\sqrt{2}\\\\A = \frac{1}{2}*\sqrt{2*2}\\\\A = \frac{1}{2}*\sqrt{4}\\\\A = \frac{1}{2}*2\\\\A = 1\\\\$