Is (-8, -10) a solution to this system of equations?

A cable for a power transformer forms

posledela

Answer:

32 ft

Step-by-step explanation:

From the diagram, the side opposite the 60° angle is 28 feet.

We are looking for the approximate length of the cable.

The approximate length of the cable is the hypotenuse of the triangle shown.

Recall the sine ratio from SOH-CAH-TOA

Which means Sine of the angle is Opposite/Hypotenuse

Let the hypotenuse be h, then we have:

$\sin(60) = \frac{28}{h}$

$0.866 = \frac{28}{h}$

$h = \frac{28}{0.866}$

$h = 32.33$

The length of the cable is approximately 32 feet

3 0

3 years ago

1. Find the area of the composite figure to the nearest hundredth.

Leto [7]

Answer:

#1: 751.56 mm²

#2: 477 km²

Step-by-step explanation:

First I noted the semicircle on the left, which has a radius of 12.5 mm. The formula for finding the area of a semicircle is 1/2(πr²).

1/2(3.14 * (12.5)²)

12.5 squared is 156.25.

1/2(3.14 * 156.25)

Multiply 3.14 by 156.25 to get 490.625.

1/2(490.625)

Divide 490.625 by 2 to get 245.3125.

245.3125 mm² for the semicircle

Then, I split the rest of into a 12.5 by 25 rectangle and a 31 by 12.5 triangle.

(12.5 * 25) + 1/2(31 * 12.5)

Multiply 12.5 by 25 to get 312.5.

312.5 + 1/2(31 * 12.5)

Multiply 31 by 12.5 to get 387.5.

312.5 + 1/2(387.5)

Multiply 1/2 by 387.5 to get 193.75

312.5 + 193.75

Add 312.5 and 193.75 to get 506.25.

506.25 mm² for the rest of the figure.

Now add the two measures, and you have your answer for #1.

245.3125 + 506.25 = 751.5625 mm², which rounds to 751.56 mm².

The area of the composite figure is 751.56 mm².

Now for #2. First, find the area of the triangle.

1/2(40 * 27)

Multiply 40 by 27 to get 1080.

1/2(1080)

Multiply 1/2 by 1080.

590 km² for the triangle.

Now find the area of the circle.

3.14 * 6²

3.14 * 36

113.04 km² for the circle.

Now subtract the area of the circle from the area of the triangle.

590 - 113.04

476.96 km², which rounds to 477.0 km².

The area of the shaded region is 477 km².

6 0

3 years ago

Read 2 more answers

A welder produces 7 welded assemblies during the first day on a new job, and the seventh assembly takes 45 minutes (unit time).

likoan [24]

Answer:

(a). 72.9%.

(b). 13.6 hr.

Step-by-step explanation:

So, we are given the following data or parameters or information which is going to assist us in solving this question/problem;

=> "A welder produces 7 welded assemblies during the first day on a new job, and the seventh assembly takes 45 minutes (unit time). "

=> The worker produces 10 welded assemblies on the second day, and the 10th assembly on the second day takes 30 minutes"

So, we will be making use of the Crawford learning curve model.

T(7) + 10 = T (17) = 30 min.

T(7) = T1(7)^b = 45.

T(17 ) = T1(17)^b = 30.

(T1) = 45/7^b = 30/17^b.

45/30 = 7^b/17^b = (7/17)^b.

1.5 = (0.41177)^b.

ln 1.5 = b ln 0.41177.

0.40547 = -0.8873 b.

b = - 0.45696.

=> 2^ -0.45696 = 0.7285.

= 72.9%.

(b). T1= 45/7^ - 045696 = 109.5 hr.

V(TT)(17) = 109.5 {(17.51^ - 0.45696 – 0.51^ - 0.45696) / (1 - 0.45696)} .

V(TT) (17) = 109.5 {(4.7317 - 0.6863) / 0.54304} .

= 815.7 min .

= 13.595 hr.

8 0

3 years ago

How do you factor this in the form (x+b)(x+c)

faust18 [17]

So you have your polynomial. To factor this out, you need to find the factors of -45 that will add up to 3. These two factors would be -5 and 8. So, you have factored your polynomial! (x-5)(x+8). If you are still unsure, simply use the FOIL method to check and see if you get the same polynomial back. Hope this helps!

7 0

3 years ago

Solve the system of equations by graphing, elimination or

vladimir1956 [14]

Answer:

Solve the system of equations by graphing, elimination or

subod

Step-by-step explanation:

8 0

2 years ago