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3 years ago

Does 21.6,28.8,36 equal a right triangle

1 answer:

3 0

21.6 < 28.8 < 36

<span>if they are the lengths of the sides of a right triangle then:

$21.6^2+28.8^2=36^2\\\\L_s=466.56+829.44=1296\\\\R_s=1296\\\\L_s=R_s$

therefore it's the right triangle.</span>

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If x=-7 and y=3x+2, then y equals what number?

kati45 [8]

Answer:

y = -19

Step-by-step explanation:

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3 years ago

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2. If the ratio of two supplementary angles is 4:5, then what are the measures<br> of both angles?

ivann1987 [24]

Answer:

4x+5x=90

9x=90

x=90/9

x=10

4x=40

5x=50

hence the angles are 40 degree and 50 degree respectively.

Hope this may help you

Thank you

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2 years ago

The altitude of a triangle is 6 cm greater than its base .if its area is 108 cm ,find its base

xeze [42]

Area of the triangle = (1/2)*base*height

base = x

height = altitude = x+6

Area of the triangle = (1/2)*x*(x+6) = 108

(1/2)*x*(x+6) = 108

x²+6x-216 =0

(x+18)(x-12)=0

x=-18, or x=12

We can use only positive value, so x=12.

Base =12 cm.

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3 years ago

Find the minimum and maximum of f(x, y, z) = y + 4z subject to two constraints, 2x + z = 4 and x2 + y2 = 1. g

yuradex [85]

$L(x,y,z,\lambda_1,\lambda_2)=y+4z+\lambda_1(2x+z-4)+\lambda_2(x^2+y^2-1)$

$L_x=2\lambda_1+2\lambda_2 x=0\implies\lambda_1+\lambda_2x=0$
$L_y=1+2\lambda_2y=0$
$L_z=4+\lambda_1=0\implies\lambda_1=-4$
$L_{\lambda_1}=2x+z-4=0$
$L_{\lambda_2}=x^2+y^2-1=0$

$\lambda_1=-4\implies \lambda_2x=4\implies\lambda_2=\dfrac4x$
$1+2\lambda_2y=0\implies\lambda_2y=-\dfrac12\implies8y=-x$

$x^2+y^2=1\implies (-8y)^2+y^2=65y^2=1\implies y=\pm\dfrac1{\sqrt{65}}$
$y=\pm\dfrac1{\sqrt{65}}\implies x=\mp\dfrac8{\sqrt{65}}$
$2x+z=4\implies z=4\pm\dfrac{16}{\sqrt{65}}$

We have two critical points to consider: $\left(-\dfrac8{\sqrt{65}},\dfrac1{\sqrt{65}},4+\dfrac{16}{\sqrt{65}}\right)$ and $\left(\dfrac8{\sqrt{65}},-\dfrac1{\sqrt{65}},4-\dfrac{16}{\sqrt{65}}\right)$ .

At these points, we respectively have a maximum of $16+\sqrt{65}$ and a minimum of $16-\sqrt{65}$ .

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3 years ago

A model is made of a car. the car is 9 feet long and the model is 6 inches long. what is the ratio of the length of the ar to th

avanturin [10]

1 feet = 12 inches
length of car in inches = 108 inches
length of model = 6 inches

length of car/ length of model = 108/6 = 18:1

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3 years ago

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