Write an equivalent expression dor 8x + 6 using distributive property

Solve the problem.A plane flying a straight course observes a mountain at a bearing of 35° to the right of its course. At that t

Mice21 [21]

Given:

A plane flying a straight course observes a mountain at a bearing of 35° to the right of its course.

The distance between plan and mountain is 10 km.

A short time later, the bearing to the mountain becomes 45°.

Here NM is the distance between the plane from the mountain when the second bearing is taken.

We need to find the measure of NM.

$We\text{ know that }\angle INM\text{ and }\angle\text{XNM are supplementary angles.}$

The sum of the supplementary angles is 180 degrees.

$\angle INM+\angle XNM=180^o$ $\text{Substitute }\angle XNM=45^o\text{ in the equation.}$

$\angle INM+45^o=180^o$

$\angle INM=180^o-45^o$

$\angle INM=135^o$

We know that the sum of all three angles of the triangle is 180 degrees.

$\angle INM+\angle NIM+\angle INM=180^o$ $\text{Substitute }\angle INM=135^o\text{ and }\angle NIM=35^o\text{ in the equation.}$

$135^o+35^o+\angle INM=180^o$

$170^o+\angle INM=180^o$

$\angle INM=180^o-170^o$

$\angle INM=10^o$

Consider the sine law.

$\frac{\sin N}{IM}=\frac{\sin M}{IN}=\frac{\sin I}{NM}$

Take the equation to find the measure of NM.

$\frac{\sin N}{IM}=\frac{\sin I}{NM}$ $\text{Substitute }\angle N=135^o,\angle I=35^o,\text{ and IM=10 in the equation.}$

$\frac{\sin 135^o}{10}=\frac{\sin35^o}{NM}$

$NM=\frac{\sin 35^o}{\sin 135^o}\times10$ $NM=8.11$

Hence the measure of NM is 8.1 km.

The plane is 8.1 km far from the mountain when the second bearing is taken.

5 0

1 year ago

You are hiding a treasure you go from your house to the store that is 10 miles straight down from your house to by a shovel. You

vovikov84 [41]

The hypotenuse will 18 miles

I hope this helps

-Ayden

8 0

3 years ago

I need help pls on math

Rina8888 [55]

$x^2-x-12=x^2+3x-4x-12=x(x+3)-4(x+3)=(x+3)(x-4)\\\\x^2-2x-8=x^2+2x-4x-8=x(x+2)-4(x+2)=(x+2)(x-4)\\\\4x^2=2x\cdot2x$

$\dfrac{x^2-x-12}{2x}:\dfrac{x^2-2x-8}{4x^2}=\dfrac{x^2-x-12}{2x}\cdot\dfrac{4x^2}{x^2-2x-8}\\\\=\dfrac{(x+3)(x-4)}{2x}\cdot\dfrac{2x\cdot2x}{(x+2)(x-4)}=\dfrac{(x+3)}{1}\cdot\dfrac{2x}{(x+2)}\\\\=\boxed{\dfrac{2x^2+6x}{x+2}}$

4 0

4 years ago

Find the perimeter of the rectangle below.<br> 5x2 - 6<br> 2x2

PIT_PIT [208]

The answer Is 4! Good luck

5 0

3 years ago

A half-filled cylindrical water tank has a water level of 20 feet high. The tank can hold 6000 cubic feet of water. Find the dia

Anettt [7]

Answer:

d = 13.8 feet

Step-by-step explanation:

Because we are talking about cubic feet of water, we need the formula for the VOLUME of a cylinder. That formula is

$V=\pi r^2h$

We will use 3.141592654 for pi; if the tank HALF filled with water is at 20 feet, then the height of the tank is 40 feet, so h = 40; and the volume it can hold in total is 6000 cubic feet. Filling in then gives us:

$6000=(3.141592654)(r^2)(40)$

Simplify on the right to get

$6000=125.6637061r^2$

Divide both sides by 125.6637061 to get that

$r^2=47.74648294$

Taking the square root of both sides gives you

r = 6.90988299

But the diameter is twice the radius, so multiply that r value by 2 to get that the diameter to the nearest tenth of a foot is 13.8

5 0

4 years ago