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3 years ago

Please provide steps. I have a test soon.

Mathematics

1 answer:

marishachu [46]3 years ago

6 0

Answer:

B) 5x+15y=30

5x-5y=10

Step-by-step explanation:

First, we solve the top equations by addition. Multiply the first one by -4.

-4x-12y=-24

4x-8y=4

This equals -20y=-20, so y=1. Now we put that back into either equation and find that x=3. So the solution set is (3,1)

Plugging those into each of the possible choices, we find that the answer is

B) 5x+15y=30. 5(3)+15(1)=30 15+15=30. 30=30 CHECK

5x-5y=10 5(3)-5(1)=10. 15-5=10. 10=10. CHECK

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3 years ago

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Sean operates a lawn-cutting business. He charges $15 for a single lawn and $25 for a front and back lawn. Sean made $475 from 2

topjm [15]

The system of equations that models the given situation is given as follows:

x + y = 25.

15x + 25y = 475.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

Variable x: Number of single lawns cut.

Variable y: Number of front and back lawns cut.

He had 25 customers, hence:

x + y = 25.

He charges $15 for a single lawn and $25 for a front and back lawn, and made a total of $475, hence:

15x + 25y = 475

More can be learned about a system of equations at brainly.com/question/24342899

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2 years ago

Wich of the following appear in the diagram below NEED ANSWER QUICK

valina [46]

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3 years ago

A 140 kg camera is suspended by two wires over a 40 metre wide football field to get shots of the action from above. At one poin

Katen [24]

Answer:

Please red the answer below

Step-by-step explanation:

In order to determine the length of each cable you use the Newton second law for each component of the forces involved in the situation.

For the x component you have:

$T_1cos\theta_1-T_2cos\theta_2=0$ (1)

T1: tension of the first cable = 1500N

T2: tension of the second cable = 800N

θ1: angle between the horizontal and the first cable

θ2: angle between the horizontal and the first cable

For the y component you have:

$T_1sin\theta_1+T_2sin\theta_2-W=0$ (2)

W: weight of the camera = Mg = (140kg)(9.8m/s^2) = 1372N

You can squared both equations (1) and (2) and the sum the two equations:

$T_1^2cos^2\theta_1=T_2^2cos^2\theta_2\\\\T_1^2sin^2\theta_1=T_2^2sin^2\theta_2-2WT_2sin\theta_2+W^2$

Then, you sum the equations:

$T_1^2(cos^2\theta_1+sin^2\theta_1)=T_2^2(sin^2\theta_2+cos^2\theta_2)-2Wsin\theta_2+W^2$ (3)

Next, you use the following identity:

$sin^2\theta+cos^2\theta=1$

and you obtain in the equation (3):

$T_1^2=T_2^2-2WT_2sin\theta_2+W^2\\\\sin\theta_2=\frac{T_2^2-T_1^2+W^2}{2WT_2}=\frac{(800N)^2-(1500)^2+(1372N)^2}{2(800N)(1372N)}=0.066\\\\\theta_2=sin^{-1}0.066=27.23\°$

With this values you can calculate the value of the another angle, by using the equation (1):

$\theta_1=cos^{-1}(\frac{T_2cos(27.23\°)}{T_1})=cos^{-1}(\frac{(800N)(cos27.23\°)}{1500N})\\\\\theta_1=61.69\°$

Now, you can calculate the length of each cable by using the information about the width of the football field. You use the following trigonometric relation:

$l_1cos\theta_1=40-d\\\\l_2cos\theta_2=d\\\\$

d: distance to the right side of the field

By using the cosine law you can fins a system of equation and then you can calculate the values of l1 and l2.

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3 years ago

Kx^2 + 6x + k = 0 find k

ICE Princess25 [194]

Answer:

Step-by-step explanation:

kx^2 + 6x + k = 0

k= 6x/x^2+1

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3 years ago