What is the difference between -10 and 17 on a number line?

Answers

Answer 1

Answer: The difference would be 7

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Karla is riding vertically in a hot air balloon, directly over a point P on the ground. Karla spots a parked car on the ground at an angle of depression of 30o. The balloon rises 50 meters. Now the angle of depression to the car is 35 degrees. How far is the car from point P?

Answers

Answer:

407 m

Step-by-step explanation:

Refer the attached figure

Karla spots a parked car on the ground at an angle of depression of 30° i.e. ∠BDP = 30°

Now the balloon rises 50 meters.i.e. AB = 50 m

So, the angle of depression to the car is 35 degrees. i.e.∠ADP = 35°

Let DP be the distance of the car prom point P

Let BP be x

In ΔBDP

$Tan\theta = (Perpendicular)/(Base)$

$Tan 30^(\circ) = (BP)/(DP)$

$(1)/(√(3))= (x)/(DP)$

$DP= (x)/((1)/(√(3)))$ --1

In ΔADP

$Tan\theta = (Perpendicular)/(Base)$

$Tan 35^(\circ) = (AP)/(DP)$

$0.70020= (50+x)/(DP)$

$DP= (50+x)/(0.70020)$ --2

So, equating 1 and 2

$(50+x)/(0.70020) = (x)/((1)/(√(3)))$

$(50+x)/(x) = (0.70020)/((1)/(√(3)))$

$(50+x)/(x) =1.21278$

$50+x =1.21278x$

$50 =1.21278x-x$

$50 =0.21278x$

$(50)/(0.21278)=x$

$x=234.982$

Substitute the value of x in 1

$DP= (234.982)/((1)/(√(3)))$

$DP= 407.0007$

Hence the car is at a distance of approximately 407 m from point P

We form 2 similar rt. triangles:

Triangle #1.
X = Hor. side = dist. from P to the car.
Yi = Ver. side.
A = 30o.

Triangle #2.
X = Hor. side = Dist. from P to the car.
Y2 = Y1+50 = Ver. side.
A = 35o.

Use aw of Sines.
sin30/Y1 = sin35/(Y1+50).
Cross multiply:
(Y1+50)sin30 = Y1*sin35
Y1/2+25 = 0.574Y1
Multiply both sides by 2:
Y1+50 = 1.148Y1
1.148Y1-Y1 = 50
0.148Y1 = 50
Y1 = 337.8 m.

tan30 = Y1/X = 337.8/X
X = 337.8/tan30 = 585 m. 714 feet away hope that helps if not tell me.

A
-2
1
B.
1
-1
The midpoint of AB = ([?],[ ])

Answers

Answer:

midpoint of AB = (-1/2 , 0)

Step-by-step explanation:

A(-2 , 1) = (x1 , y1)

B(1 , -1) = (x2 , y2)

midpoint formula:

=(x1 + x2/2 , y1 + y2/2)

=(-2 + 1/2 , 1 + (-1)/2)

=(-1/2 , 0/2)

(-1/2 , 0)

Which of the following is a zero for the function f(x) = (x − 15)(x + 1)(x − 10)?X=-15
X=-10
X=1
X=15

Answers

we have the function

$f(x)=(x-15)(x+1)(x-10)$

we know that

The zero's of the function are the values of variable x when the value of the function is equal to zero

in the given function the zero's are

$x=15\nx=-1\nx=10$

therefore

the answer is

$x=15$

The answer should be x=15 because once u subtract 15-15 u get 0 and then u substitute 15 in "x" and then. Multiply 0 by everything else n u get 0:))

22 kilometers is the same as how many miles?Hint: 1km≈0.6mi
Round your answer to the nearest tenth.

Answers

Because the problem says 1km≈0.6, in this case the answer would be 13.2 miles.
22 (km) x 0.6 (mi) = 13.2 miles

What is the answer to this problem
8x-2=-9+7×

Answers

8x−2=−9+7x

Simplify:

8x−2=−9+7x

8x+−2=−9+7x

8x−2=7x−9

Subtract 7x from both sides.

8x−2−7x=7x−9−7x

x−2=−9

Add 2 to both sides.

x−2+2=−9+2

x=−7

you want like terms on the same side. so you want x on the same side
subtract 7x from 8 x = x
add 2-9 = -7
now you have x= -7

Find the area of a circle with a diameter of 12 inches. Use 3.14 for pi.37.68 in2
113.04 in2
339.12 in2
452.16 in2

Answers

Answer: 113.04 inch²

Step-by-step explanation: Since area of circle=pi×r²

where r=radius of circle

and radius=diameter/2

hence r=12/2=6 inches

hence Area =pi×6²

Area =3.14×36

Area =113.04 inch²

Aloha there! :) The answer to your question is 113.04 sq inches.

Hope I helped! =D

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