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3 years ago

Find the solution of the system of equations . - 5x + 9y = 11 x - 3y = - 7 how do i solve this

Mathematics

1 answer:

DIA [1.3K]3 years ago

3 0

Answer:

<em>Solution: x=5, y=4</em>

Step-by-step explanation:

<u>System of Equations</u>

We need to solve:

- 5x + 9y = 11

x - 3y = - 7

There are several ways to solve a system of linear equations. We'll take advantage of the second equation since it has the x with coefficient 1 and solve it for x:

x = - 7 + 3y

Now replace it into the first equation:

- 5(- 7 + 3y) + 9y = 11

Operate:

35 - 15y + 9y = 11

Simplify:

35 - 6y = 11

Rearrange:

- 6y = 11 - 35 = -24

Solve:

y = -24 / -6

y = 4

Finally, since

x = - 7 + 3y

x = - 7 + 3*4

x = - 7 + 12

x = 5

Solution: x=5, y=4

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Answer:

5 degrees colder

Step-by-step explanation:

You take the starting point then subract the ending point and you get your answer. But in order to know if its colder or warmer is to know that the higher the number, the hotter, and the lower the number, the colder.

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3 years ago

Read 2 more answers

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.

3 0

2 years ago

What is 3 to the sixth power times 3 there is a picture please help worth 12 pts.!!!!!

Diano4ka-milaya [45]

Answer:

2187 ( 3 to the 7th)

Step-by-step explanation:

3 to the 6th= 729

729 x 3 = 2187

6 0

2 years ago

Could someone break it down. I am not catching on.

sleet_krkn [62]

$\bf -0.04y+0.11(9000-y)=0.35y
\\\\\\
-0.04y+990-0.11y=0.35y
\\\\\\
990-0.15y=0.35y\implies 990=0.35y+0.15y
\\\\\\
990=0.50y
\implies 
\cfrac{990}{0.5}=y\implies 1980=y$

6 0

3 years ago

Step by step answer please

Sergio [31]

Answer:

Not a right triangle

Step-by-step explanation:

Find AC by doing 22-13=9

Use Pythagorean Theorem to determine if it is a right triangle.

8 squared plus 5 squared=89

Square rt= 9.43

And 9.43 is not equal to 9.

3 0

2 years ago