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3 years ago

Write an equation that can be used to answer the question. Then solve. Round to the nearest tenth if necessary.

Mathematics

1 answer:

tensa zangetsu [6.8K]3 years ago

7 0

Answer:

5^2+h^2=12^2, the answer would be ~10.97 ft.

Step-by-step explanation:

I would use the Pythagorean theorem to solve this problem. Put in the things that you know, so in this image we are given one of the legs and the hypotenuse of the triangle.

Pythagorean theorem is :

a^2+b^2=c^2 with a and b being the legs and c being the hypotenuse.

Once you plug in the hypotenuse and one of the legs, solve for the other leg by subtracting a^2 (5^2) from 12^2 (c^2), which will give you 119, and then take the square root of 119 and you will get your answer.

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A farmer knows that a crop she is growing requires 24 kg of fertilizer throughout the season. She has a measuring flask which wh

Papessa [141]

Answer:

48 times

Step-by-step explanation:

From the above question, we know that:

2 times = 1 kg of fertilizer

A crop requires 24 kg of fertilizer

Hence:

1 kg of fertilizer = 2 times

24 kg of fertilizer = x

Cross Multiply

x = 24 kg × 2 times/1 kg

x = 48 times

She need to fill the flask 48 times to make the required amount of fertilizer for the crop

8 0

3 years ago

what is peter's number? "if you subtract 12 from my number and multiply the difference by -3, the result is -54

lara31 [8.8K]

Answer:

Step-by-step explanation:

-54/-3 = 18

18+12 = 30

7 0

3 years ago

Find the measure of the arc.<br><br> 146°E<br><br> mFD =

Verizon [17]

Answer:

arc FD = 236°

Step-by-step explanation:

The measure of the arc is equal to the measure of the central angle it subtends, thus

arc FD = arc FE + arc ED = 146° + 90° = 236°

4 0

3 years ago

Find an equation of the sphere that passes through the origin and whose center is (-2, 2, 3). Be sure that your formula is monic

Andrei [34K]

Answer:

$\bold{(x+2))^2+(y-2)^2+(z-2)^2=17}$

Step-by-step explanation:

Given the center of sphere is: (-2, 2, 3)

Passes through the origin i.e. (0, 0, 0)

To find:

The equation of the sphere ?

Solution:

First of all, let us have a look at the equation of a sphere:

$(x-a)^2+(y-b)^2+(z-c)^2=r^2$

Where ( $x,y,z$ ) are the points on sphere.

$(a, b, c)$ is the center of the sphere and

$r$ is the radius of the sphere.

Radius of the sphere is nothing but the distance between any point on the sphere and the center.

We are given both the points, so we can use distance formula to find the radius of the given sphere:

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$

Here,

$x_1 =0 \\y_1 =0 \\z_1 =0 \\x_2 =-2 \\y_2 =2 \\z_2 =3$

So, Radius is:

$r = \sqrt{(-2-0)^2+(2-0)^2+(3-0)^2}\\\Rightarrow r = \sqrt{4+4+9} = \sqrt{17}$

Therefore the equation of the sphere is:

$(x-(-2))^2+(y-2)^2+(z-2)^2=(\sqrt{17})^2\\\bold{(x+2))^2+(y-2)^2+(z-2)^2=17}$

4 0

3 years ago

10. Two lighthouses are located on a north-south line.

Kamila [148]

The question is an illustration of bearing (i.e. angles) and distance (i.e. lengths)

The distance between both lighthouses is 5783.96 m

I've added an attachment that represents the scenario.

From the attachment, we have:

$\mathbf{\angle A = 180^o - 120^o\ 43'}$

Convert to degrees

$\mathbf{\angle A = 180^o - (120^o +\frac{43}{60}^o)}$

$\mathbf{\angle A = 180^o - (120^o +0.717^o)}$

$\mathbf{\angle A = 180^o - (120.717^o)}$

$\mathbf{\angle A = 59.283^o}$

$\mathbf{\angle B = 39^o43'}$

Convert to degrees

$\mathbf{\angle B = 39^o + \frac{43}{60}^o}$

$\mathbf{\angle B = 39^o + 0.717^o}$

$\mathbf{\angle B = 39.717^o}$

So, the measure of angle S is:

$\mathbf{\angle S = 180 - \angle A - \angle B}$ ---- Sum of angles in a triangle

$\mathbf{\angle S = 180 - 59.283 - 39.717}$

$\mathbf{\angle S = 81}$

The required distance is distance AB

This is calculated using the following sine formula:

$\mathbf{\frac{AB}{\sin(S)} = \frac{AS}{\sin(B)} }$

Where:

$\mathbf{AS = 3742}$

So, we have:

$\mathbf{\frac{AB}{\sin(81)} = \frac{3742}{\sin(39.717)}}$

Make AB the subject

$\mathbf{AB= \frac{3742}{\sin(39.717)} \times \sin(81)}$

$\mathbf{AB= 5783.96}$

Hence, the distance between both lighthouses is 5783.96 m

Read more about bearing and distance at:

brainly.com/question/19017345

5 0

2 years ago

Write an equation that can be used to answer the question. Then solve. Round to the nearest tenth if necessary. ​

Write an equation that can be used to answer the question. Then solve. Round to the nearest tenth if necessary.