MATHEMATICS HIGH SCHOOL

Which systems of equations have exactly one solution?Choose all answers that are correct.
1. y = 2x
y=2x+1

2 . x =5
y = -4

3. y = x+6
y -6 =x

4 . y= 3x+ 4
y =3

Answers

Answer 1
Answer: 1.
y=2x \n y=2x+1 \n \n2x=2x+1 \n2x-2x=1 \n0=1 \nnot \ true - no \ solution

2.
x=5 \ny=-4 \nalready \ solved - one \ solution

3.
y=x+6 \ny-6=x \n \ny=x+6 \ny=x+6 \n \nx+6=x+6 \nx-x=6-6 \n0=0 \ntrue - infinitely \ many \ solutions

4.
y=3x+4 \ny=3 \n \n3=3x+4 \n3-4=3x \n-1=3x \nx=-(1)/(3) \n \n(x,y)=(-(1)/(3),3) - one \ solution

The answer is 2 and 4.

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Answers

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Which are sums of perfect cubes? Check all that apply.A=8x6 + 27
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Answers

I think these are the sums of perfect cubes. 

A = (2x²)³ + (3)³
B = (x³)³ + (1)³
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Answers

I am only in the seventh grade so it might not be right, but this is what I would do:

Set up a proportion: 77/2.194/70.2 = 100/x/y = 240/z/123.9

Then solve for x: if 77 equals 100, that means 2.194 is 77% of x. So x equals 2.849350649

*the 350649 repeats

Then solve for y: Like mentioned before 70.2 is going to only be 77% of y, so if you set that up in a proportion, it is: 70.2/77 = y/100. So when you solve you get 91.16883116883117...

Then finally we solve for z: 100 is only 41.6% of 240, so that means 2.849350649 is only 41.6% of z. So then we set it up as a proportion: 141.6/100 = z/2.849350649, then we solve. It equals 4.034680518984.

Sorry if my answer was redundant, but hope this helped!

The product of two consecutive positive even integers is 14 more than their sum

Answers

X(x+2)=x+x+2+14
x^2+2x=2x+16
x^2=16
x=4 or x =-4

Answer:

x=4,-4

Step-by-step explanation:

Guy decides to get in shape by running. The first day, he runs 1 mile in 12 minutes. Two months later he has decreased his mile time by 25%. What is his mile time now?

Answers

If you would like to know what is his mile time two months later, you can calculate this using the following steps:

25% of 12 minutes = 25% * 12 = 25/100 * 12 = 3 minutes

12 minutes - 3 minutes = 9 minutes

The correct answer would be 9 minutes.

Answer: 9 minutes.

Step-by-step explanation: 12-3=9.

3 x 4 = 12, 3 x 3 x 3=9, 3 x 3 x 3 x 3=12, 4+4+4=12. So if you think about it, three goes into twelve four times, just like a quarter goes into a dollar four times, or 25 goes into 100 four times. So, if you take twelve minus three and equal it, it is nine.

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C. 1
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Answers

The scaling factor of the given function, f(x) = 3|x| is equal to 3. This is evident because the equation suggests that whatever is the absolute value of x from the equation is, multiply it only by 3 and then we determine the value of y. The answer to this question is letter D. 3.
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