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ivanzaharov [21]

3 years ago

5

If a right triangle has a hypotenuse of length 20 units and one leg of length 16 units, find the length of the other leg. A. 12

B. 656 C. 384 D. 36

2 answers:

xxTIMURxx [149]3 years ago

5 0

Answer:

12

Step-by-step explanation:

Use the Pythagorean theorem which is a^2 + b^2 = c^2

c is hypotenuse and a and b are the legs

we need to find a^2 so

a^2 + 16^2 = 20^2

a^22 + 256 = 400

then subtract 256 from 400

a^2 = 144

square root 144

= 12

kirill [66]3 years ago

3 0

Answer:

12

Step-by-step explanation:

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At the base of a pyramid, a surveyor determines that the angle of elevation to the top is °. At a point meters from the base, th

riadik2000 [5.3K]

Answer:

$\frac{(\sin 18^\circ)}{75} = \frac{(\sin 35^\circ)}{x}$

Step-by-step explanation:

Incomplete question:

<em></em> $\angle CBD = 53^\circ$ <em></em>

<em></em> $\angle CAB = 35^\circ$ <em></em>

<em></em> $AB = 75$ <em></em>

<em></em>

<em>See attachment for complete question</em>

Required

Determine the equation to find x

First, is to complete the angles of the triangle (ABC and ACB)

$\angle ABC + \angle CBD = 180$ --- angle on a straight line

$\angle ABC + 53= 180$

Collect like terms

$\angle ABC =- 53+ 180$

$\angle ABC =127^\circ$

$\angle ABC + \angle ACB + \angle CAB = 180$ --- angles in a triangle

$\angle ACB + 127 + 35 = 180$

Collect like terms

$\angle ACB =- 127 - 35 + 180$

$\angle ACB =18$

Apply sine rule

$\frac{\sin A}{a} = \frac{\sin B}{b}$

In this case:

$\frac{\sin ACB}{AB} = \frac{\sin CAB}{x}$

This gives:

$\frac{(\sin 18^\circ)}{75} = \frac{(\sin 35^\circ)}{x}$

4 0

3 years ago

Read 2 more answers

1. Manufacturing Process Incorporation plan to produce a new ergonomic chair. Before the company starts producing this chair the

Oduvanchick [21]

Answer:

1. cost per chair: $86.40

2. selling price per chair: $146.88

Step-by-step explanation:

1. The total cost per chair will be the sum of the cost of materials and the overhead cost (equipment, energy, labor, marketing). The cost of materials is ...

$500/(16 chairs) = $31.25/chair

So, the total cost is ...

cost of each chair = material cost + overhead cost

= $31.25 +55.15

cost of each chair = $86.40

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2. We assume the markup is 70% of the cost, so will be ...

0.70 · $86.40 = $60.48

Then the selling price of the chair will be ...

selling price = cost + markup

selling price = $86.40 +60.48

selling price = $146.88

3 0

3 years ago

Grade 10 math anyone?

Kisachek [45]

Answer:

6 years

Step-by-step explanation:

Here,

$I=60$

$P=200$

$R=0.05$

and we need to find $T$ .

So using the formula $I=PRT$ , we can find T by substituting the values

$60 = (200)(0.05)T$

$60=10T$

$T=\frac{60}{10} = 6$ years

8 0

3 years ago

Please help quickly this is timed

liberstina [14]

Answer:

the one you have selected is correct

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6

katrin2010 [14]

Answer:

Part a) The height of the ball after 3 seconds is $49\ ft$

Part b) The maximum height is 66 ft

Part c) The ball hit the ground for t=4 sec

Part d) The domain of the function that makes sense is the interval

[0,4]

Step-by-step explanation:

we have

$h(t)=-16t^{2} +63t+4$

Part a) What is the height of the ball after 3 seconds?

For t=3 sec

Substitute in the function and solve for h

$h(3)=-16(3)^{2} +63(3)+4=49\ ft$

Part b) What is the maximum height of the ball? Round to the nearest foot.

we know that

The maximum height of the ball is the vertex of the quadratic equation

so

Convert the function into a vertex form

$h(t)=-16t^{2} +63t+4$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$h(t)-4=-16t^{2} +63t$

Factor the leading coefficient

$h(t)-4=-16(t^{2} -(63/16)t)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$h(t)-4-16(63/32)^{2}=-16(t^{2} -(63/16)t+(63/32)^{2})$

$h(t)-(67,600/1,024)=-16(t^{2} -(63/16)t+(63/32)^{2})$

Rewrite as perfect squares

$h(t)-(67,600/1,024)=-16(t-(63/32))^{2}$

$h(t)=-16(t-(63/32))^{2}+(67,600/1,024)$

the vertex is the point (1.97,66.02)

therefore

The maximum height is 66 ft

Part c) When will the ball hit the ground?

we know that

The ball hit the ground when h(t)=0 (the x-intercepts of the function)

so

$h(t)=-16t^{2} +63t+4$

For h(t)=0

$0=-16t^{2} +63t+4$

using a graphing tool

The solution is t=4 sec

see the attached figure

Part d) What domain makes sense for the function?

The domain of the function that makes sense is the interval

[0,4]

All real numbers greater than or equal to 0 seconds and less than or equal to 4 seconds

Remember that the time can not be a negative number

6 0

3 years ago