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olya-2409 [2.1K]
3 years ago
10

A) Find an equation of the line:

Mathematics
1 answer:
nikklg [1K]3 years ago
6 0

A) y=-2x-2

y/x=slope -4/2=-2 y-intercept=b=-2 (put in y=mx=b form)

B) y=15/4x-1 or y=3.75x-1

C) y=-0.6664x-3(I DONT THINK THIS ONE IS RIGHT CHECK IT FIRST)

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(Hehe...Please ignore the markings)
inysia [295]

Answer:

See below:

Step-by-step explanation:

Problem 1:

Multiply Equation 1 by 4, keep Equation 2 the same.

x+y=8, multiply each term by 4:

4*x=4x, 4*y=4y, 8*4=32

so, the equivalent system is: 4x+4y=32 and x-y=2

Solve the system of equations:

x-y=2 becomes x=y+2

plug into 4x+4y=32 to solve for y

4(y+2)+4y=32---> 4y+8+4y=32--->8y=24---> y=3

Plug into x-y=2---> x-3=2---> x=5

Problem 1 Answer:

Equivalent system: 4x+4y=32, x-y=2; solution: x=5, y=3

Problem 2:

Keep Equation 1 the same. Add 1 and 2.

To add an equation, add the left sides together, and then the rights.

so: x+y=8 + x-y=2 gives us: 2x=10

solve for x ---> 2x/2=10/2--->x=5

plug x into x+y=8--->5+y=8--->y=3

Problem 2 answer:

Equivalent system: x+y=8, 2x=10; solution:x=5, y=3

Problem 3:

Subtract Equation 2 from 1, and keep 2 the same.

To subtract an equation, subtract the left sides, then the rights. We are subtracting 1<em> from </em>2, so its 2-1.

x-y=2 - x+y=8 gives us: -2y=-6

Solve for y by dividing by -2-->-2y/-2=-6/-2---> y=3

Plug into x-y=2---> x-3=2---> x=5

Problem 3 answer:

Equivalent system: -2y=-6, x-y=2; solution: x=5, y=3

Problem 4:

Multiply the sum of Equation 1 and 2 by a factor of 3. Keep equation 2 the same.

First we add 1 and 2: (we did this earlier) ---> 2x=10 ---> now we multiply it all by 3---> 2x*(3)=10*(3)---> this gives us: 6x=30---> now divide by 6 to solve for x: 6x/6=30/6 gives us: x=5

Now, solve for y by plugging x into equation 2: x-y=2---> 5-y=2--->y=3

Problem 4 answer:

Equivalent system: 6x=30, x-y=2; solution: x=5, y=3

______

Quick Tip: One thing inherent of Equivalent systems is that they have the same set of solutions. Thus, we know the systems are equivalent when they have the same set of solutions for x and y. Moreover, you don't need to solve every time after you attempt to find an equivalent system, instead, just plug in the values found in problem 1 to each new set of equations to test if they are equivalent.

If we find x=5 and y=3 for x+y=8 and x-y=2, then all we have to do is plug them in to 6x=30 and -2y=-6 to see if they are equivalent.

6(5)=30 ---> true

-2(3)=-6 ---> true

3 0
2 years ago
Convert logx y = 1/2 to exponential form.
Lena [83]

Answer:

Exponential form: y = x^½

Step-by-step explanation:

Given

log_xy= \frac{1}{2}

Required:

The exponential form

To convert to an exponential function, we have to take exponents of both sides using the base of the logarithm function.

This gives us

x^{log_xy}= x^\frac{1}{2}

Since the base of the exponential function and the logarithm is the same (x), they'll cancel out one another

This leaves us with

y= x^\frac{1}{2}

Hence, the exponential form of the expression

log_xy= \frac{1}{2} is y= x^\frac{1}{2}

8 0
3 years ago
Two ropes are attached to a large ballon in a parade. The people holding the ropes are 40 feet apart,and the angle between the t
tankabanditka [31]

Answer:

We'll use the Law of Sines:

Sine (C) / c = Sine (B) / b

Sine (86) / 40 = Sine (52) / b

0.99756 / 40 = 0.78801 / b

0.024939  = .78801 / b

b = .78801 / .024939

side b = 31.5974978949  feet

Sine (42) / a = Sine (86) / 40

(0.66913 / a) = 0.024939

a = .66913 / .024939

side a = 26.8306668271  feet

******************************************************

I forgot to include the graphic.  

Step-by-step explanation:

8 0
3 years ago
What equations are equal to 3x-12=24
sergiy2304 [10]
According to my examination I have confirmed that I do NOT repeat do NOT know the answer to this question. Good luck!
7 0
3 years ago
1. 0 = 2x2 + 17x + 30
Anna11 [10]

Answer:

Simplify the equation and find the value of x

Step-by-step explanation:

1 = 34 + 17x \\  - 17x =  - 1 + 34 \\ 17x =  - 33 \\  \\ x =  -  \frac{33}{17}

8 0
2 years ago
Read 2 more answers
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