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shepuryov [24]
3 years ago
9

HELP! ASAP! 3x - 4y = -7 and 4x + 3y = 24 solve for x and y

Mathematics
2 answers:
pav-90 [236]3 years ago
6 0

Answer:

x = 3

y = 4

Step-by-step explanation:

3x -4y = -7

4x + 3y = 24

write the first equation in terms of y

3x - 4y = -7

3x + 7 = 4y

3x/4 + 7/4 = y

now substitute that into the second equation

4x + 3y = 24

4x + 3(3x/4 + 7/4) = 24

4x + 2.25x + 5.25 = 24

6.25x + 5.25 = 24

6.25x = 24 - 5.25

6.25x = 18.75

x = 18.75/6.25

x = 3

last step, substitute x for 3 in the equation.

y = 3x/4 + 7/4

y = 3*3/4 + 7/4

y = 9/4 + 7/4

y = 4

Sindrei [870]3 years ago
3 0

Answer:

\boxed{x = 3 \: and \: y = 4}

Step-by-step explanation:

3x - 4y = -7.....(eq)1 \\ 4x + 3y = 24 .....(eq)2 \\ \boxed{step \:   1}\\ \times 4....3x - 4y = -7 \\  \times 3....4x + 3y = 24  \\\boxed{step \:   2} \\ 12x - 16y =  - 28 \\ 12x + 9y = 72 \\ \boxed{step \:   3} \\ 12x - 12x  - 16y - ( + 9y) =  - 28 - 72 \\  - 25y =  - 100 \\ y =  \frac{ - 100}{ - 25}  \\\boxed{ y = 4}\\.................. \\  \boxed{step \:   4} \\ substitute \: the \: value \: of \: y \: in \: .....(eq)1 \\ 3x - 4y = -7 \\ 3x - 4(4) =  - 7 \\ 3x - 16 =  - 7 \\ 3x =  - 7 + 16 \\ 3x = 9 \\ x =  \frac{9}{3}  \\ \boxed{ x = 3}

♨Rage♨

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A square name tag has sides that are 5 centimeters long. What is the name tag's area?
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WILL MAKE BRAINLIEST!!! A Ferris wheel has a diameter of 220 feet and the center of the wheel is 125 feet above the ground. The
daser333 [38]
Since the radius of a circle is half its diameter, the radius of our Ferris wheel is r= \frac{220}{2} =110ft

Next, we are going to convert from revolutions per minute to degrees per second.
We know that t<span>he wheel makes a complete turn every 2 minutes, so it makes a complete turn in 120 seconds. Since there are 360° in a complete turn, we can set up our conversion factor:
</span>\frac{1*360}{120}=3 degrees per second 
<span>
Now, lets find the height:
</span>We know that <span>the passenger is at the lowest point on the wheel when t=0; since the wheel is 125 feet above the ground, at t=0 h=125. To find t at the top, we are going to take advantage of the fact that the wheel will turn 180° from the lowest point to the top and that it turns 3° every second:
</span>t= \frac{180}{3}
t=60
Notice that the height at the top is the diameter of the wheel plus the height above the ground, so h=220+125=345.

To model the situation we are going to use the cosine function, but notice that cos (\alpha) is 1 when \alpha =0 and -1 wen \alpha =180. Since we want the opposite, we are going to use negative cosine.
Notice that we want \alpha =180 when t=60, so we are going to use -cos(3t). Next, we are going to multiply our cosine by the radius of our wheel: -110cos(3t), and last but not least we are going to add the sum of the radius of the wheel plus the height above the ground:
h=110+125-110cos(3t)
h=225-110cos(3t)

Now that we have our height function lets check if everything is working:
<span>the passenger is at the lowest point at t=0; we also know that the lowest point is 125 feet above the ground, so lets evaluate our function at t=0:
</span>h=225-110cos(3t)
h=225-110cos(3*0)
h=125 feet 
So far so good. 
We also know that at t=60, our passenger is 345 feet above the ground, so lets evaluate our function at t=60 and check if coincides:
h=225-110cos(3t)
h=225-110cos(3*60)
h=225-110cos(180)
h=345feet 

We can conclude that cosine function that express the height h (in feet) of a passenger on the wheel as a function of time t (in minutes) ) is: h=225-110cos(3t)
8 0
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bulgar [2K]
A. 145
EXPLANATION:
There are 2 angles in the picture.
Both angles mist add up to 180
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