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3 years ago

PLEASE HELP!!!

Mathematics

1 answer:

Marta_Voda [28]3 years ago

3 0

Answer:

19.5 in²

Step-by-step explanation:

A applicable formula for the area of the smaller triangle is ...

A = (1/2)ab·sin(C) . . . . where a, b are the given sides and C is the angle between them.

The side lengths are 3 in and 13 in, so the area is ...

A = (1/2)(3 in)(13 in)sin(C) = (19.5 in²)sin(C)

The sine function is a maximum at C=90°, at which angle it has the value 1. So, the maximum area is that of a right triangle of sides lengths 3 and 13 inches.

The maximum area is 19.5 in².

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Write an equation of a line that passes through (-12, -14) with slope 6.

damaskus [11]

The slope intercept form of a line is y = mx + b

m = slope
b = y-intercept

Plug in the slope, 6, into m.

Rewrite the equation;

y = 6x + b
We need to find b, your y-intercept, to finish this equation.

Plug in your point coordinate, (x, y) ⇒ (-12, -14) into the equation.

-14 = 6(-12) + b

Solve for b to find the y-intercept.

-14 = -72 + b
58 = b

Your new equation (your answer) is<em> </em>y = 6x + 58.

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4 years ago

2. How can we tell if a number is divisible by 4?

Akimi4 [234]

Answer:

Step-by-step explanation:

The last two digits of the number are divisible by 4

Example: 5624

last two digit 24 and 24 is divisible by 4. 5624 is divisible by 4

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4 years ago

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3 years ago

Find the lengths of the sides of the triangle PQR. P(2, −3, −4), Q(8, 0, 2), R(11, −6, −4) |PQ| = Incorrect: Your answer is inco

Aloiza [94]

Answer:

the length PQ is 9 units,the length QR is 9 units,the length PR is 9.48 units,the triangle is not a right triangle,this is a isosceles triangle

Step-by-step explanation:

Hello, I think I can help you with this

If you know two points, the distance between then its given by:

$P1(x_{1},y_{1},z_{1} ) \\P2(x_{2},y_{2},z_{2})\\\\d=\sqrt{(x_{2}-x_{1} )^{2} +(y_{2}-y_{1} )^{2}+(z_{2}-z_{1} )^{2} }$

Step 1

use the formula to find the length PQ

Let

P1=P=P(2, −3, −4)

P2=Q=Q(8, 0, 2)

$d=\sqrt{(8-2)^{2} +(0-(-3))^{2}+(2-(-4))^{2}} \\ d=\sqrt{(6)^{2} +(3)^{2}+(6 )^{2}}} \\d=\sqrt{36+9+36}\\d=\sqrt{81} \\d=9\\$

the length PQ is 9 units

Step 2

use the formula to find the length QR

Let

P1=Q=Q(8, 0, 2)

P2=R= R(11, −6, −4)

$d=\sqrt{(11-8)^{2} +(6-0))^{2}+(-4-2 )^{2}} \\\\\\d=\sqrt{(3)^{2} +(6)^{2}+(-6 )^{2}}} \\d=\sqrt{9+36+36}\\d=\sqrt{81} \\d=9\\$

the length QR is 9 units

Step 3

use the formula to find the length PR

Let

P1=P(2, −3, −4)

P2=R= R(11, −6, −4)

$d=\sqrt{(11-2)^{2} +(-6-(-3)))^{2}+(-4-4 )^{2}} \\\\\\d=\sqrt{(9)^{2} +(-6+3)^{2}+(-4-(-4) )^{2}}} \\d=\sqrt{81+9+0}\\d=\sqrt{90} \\d=9.48\\$

the length PR is 9.48 units

Step 4

is it a right triangle?

you can check this by using:

$side^{2} +side^{2}=hypotenuse ^{2}$

Let

side 1=side 2= 9

hypotenuse = 9.48

Put the values into the equation

$9^{2} +9^{2} =9.48^{2}\\ 81+81=90\\162=90,false$

Hence, the triangle is not a right triangle

Step 5

is it an isosceles triangle?

In geometry, an isosceles triangle is a type of triangle that has two sides of equal length.

Now side PQ=QR, so this is a isosceles triangle

Have a great day

3 0

3 years ago

What is an equation of the line that passes through the point (3,-1) and is perpendicular to the equation y=-3x+2

Alex17521 [72]

If it is perpendicular then the slope of it will be:

$-3 \times x = -1\\\\x = \frac{1}{3}$

y = 1/3 x + b

-1 = (1/3)(3) + b

-1 = 1 + b

b = -2

The equation is:

$y = \frac{1}{3}x - 2$

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4 years ago