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3 years ago

What are the values of h and x in the right triangle? Explain.

Mathematics

1 answer:

alexandr402 [8]3 years ago

3 0

Answer:

h = 60 ; x = 25

Step-by-step explanation:

You are going to want to use Pythagorean Theorem to solve these.

Pythagorean Theorem: a² + b² = c²

h² + 144² = 156²

h² + 20736 = 24336

h² = 3600

h = 60

x² + 60² = 65²

x² + 3600 = 4225

x² = 625

x = 25

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3 years ago

the graph of part of linear function G is shown on thw grid. which inequality best represents the range of the part shown?

valentinak56 [21]

It should be -9 < x <= 2

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2 years ago

a line whose perpendicular distance from the origin is 4 units and the slope of perpendicular is 2÷3. Find the equation of the l

GrogVix [38]

Answer:

$\huge\boxed{y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{2}{3}x+\dfrac{4\sqrt{13}}{3}}$

Step-by-step explanation:

The equation of a line:

$y=mx+b$

We have

$m=\dfrac{2}{3}$

substitute:

$y=\dfrac{2}{3}x+b$

The formula of a distance between a point and a line:

General form of a line:

$Ax+By+C=0$

Point:

$(x_0,\ y_0)$

Distance:

$d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+b^2}}$

Convert the equation:

$y=\dfrac{2}{3}x+b$ |subtract $y$ from both sides

$\dfrac{2}{3}x-y+b=0$ |multiply both sides by 3

$2x-3y+3b=0\to A=2,\ B=-3,\ C=3b$

Coordinates of the point:

$(0,\ 0)\to x_0=0,\ y_0=0$

substitute:

$d=4$

$4=\dfrac{|2\cdot0+(-3)\cdot0+3b|}{\sqrt{2^2+(-3)^2}}\\\\4=\dfrac{|3b|}{\sqrt{4+9}}$

$4=\dfrac{|3b|}{\sqrt{13}}\qquad|$ |multiply both sides by $\sqrt{13}$

$4\sqrt{13}=|3b|\iff3b=-4\sqrt{13}\ \vee\ 3b=4\sqrt{13}$ |divide both sides by 3

$b=-\dfrac{4\sqrt{13}}{3}\ \vee\ b=\dfrac{4\sqrt{13}}{3}$

Finally:

$y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{4\sqrt{13}}{3}$

4 0

3 years ago

Diane has a rope that is 8 meters long. She cuts away a piece that is 1.67 meters long. How long is the remaining piece of rope?

Readme [11.4K]

Answer:

6.33 m

Step-by-step explanation:

Total length of the rope = 8 m

Cut length of the rope = 1.67 m

We need to find the remaining piece of the rope.

Remaining piece = Total length - cur length

= 8 m - 1.67 m

= 6.33 m

So, 6.33 m is the remaining piece of the rope.

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3 years ago

A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 22 feetfeet less than th

ivann1987 [24]

So basically the ladder is creating a right triangle with the ground and the wall. Ladder is the hypotenuse (h), building = b, ground = g
b = h - 22 ft
g = 1010 ft
use Pythagorean Theorem to determine the length of h:
${c}^{2} = {a}^{2} + {b}^{2} \\ {h}^{2} = {(h - 22)}^{2} + {1010}^{2} \\ {h}^{2} = {h}^{2} - 44h + 484 + 1020100$
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$0 = - 44h + 484 + 1020100 \\ 44h = 1020584 \\ 44h \div 44 = 1020584 \div 44 \\ h = 23195.1 \: feet$

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3 years ago