MATHEMATICS MIDDLE SCHOOL

Imagine that you are given two linear equations in slope-intercept form. You notice that the slopes are the same, but the y-intercepts are different. How many solutions would you expect for this system of equations?A. Cannot be determined
B. 0
C. 1
D. Infinitely many

Answers

Answer 1
Answer:

B

If two lines have the same slope and different intercepts, then they will never cross each other; they are parallel lines. Therefore, they have no solutions since a solution is where the lines cross.

Answer 2
Answer:

Answer:B

Step-by-step explanation:

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The graph of a line passes through the points (0, -2) and (6.0). What isthe equation of the line?

Answers

Answer:

y=(1)/(3)x-2

Step-by-step explanation:

The equation of a line is given in the form  y=mx+b

Where

m is the slope with formula  m=(y_2-y_1)/(x_2-x_1)

and

b is the y-intercept [y axis cutting point of line]

Given the two points (0, -2) and (6,0),

x_1 = 0

y_1 = -2

x_2 = 6

y_2 = 0

Now, we find m using formula:

m=(0+2)/(6-0)=(1)/(3)

Now we have

y=(1)/(3)x+b

Finding b, we plug in any (x,y) point. Lets put (6,0) and find b:

y=(1)/(3)x+b\n0=(1)/(3)(6)+b\n0=2+b\nb=-2

Thus,

equation of line = y=(1)/(3)x-2

On the moon, the distance d (in feet) that an object falls intime t (in seconds) is modeled by the function d(t) = 8/3 t
Suppose an astronaut on the moon drops a tool. How long
does it take the tool to fall 4 feet?

Answers

Answer:

3/2

Step-by-step explanation:

If d = feet and the question is how long it takes if a tool falls down 4 feet then plug that in the equation, which is 4 = 8/3 t

Then bring the 3 to the other side by multiplying which is 8x = 12

Lastly it is 12/8, simplified to 3/2

Final answer:

The astronaut's tool would take 1.5 seconds to fall 4 feet on the moon when using the given function d(t) = 8/3 t.

Explanation:

To find the time it takes the tool to fall 4 feet on the moon, we would need to set the distance d equal to 4 in the given mathematical expression and solve for t. So we would use the given function d(t) = 8/3 t.

  1. Set d(t) equal to 4: 4 = 8/3 t
  2. Solve for t by multiplying both sides with the reciprocal of 8/3 which is 3/8: t = 4 * 3/8
  3. Simplify to find: t = 1.5 seconds

So the astronaut's tool would take 1.5 seconds to fall 4 feet on the moon.

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Find (g•f)(3)
F(x)=|x+2|
g(x)=-x^2

Answers

f(x)=|x+2|\n\ng(x)=-x^2\n\n(g\circ f)(x)=-x^2|x+2|=-|x^2|\cdot|x+2|=-|x^2(x+2)|=-|x^3+2x^2|\n\n(g\ \circ\ f)(3)=-|3^3+2(3)^2|=-|27+2(9)|=-|27+18|=-45

I^37 is what?


A: i

B: -i

C: 1

D: -2

Answers

First off, i is equal to the square root of -1. The square of i, therefore is -1. An even exponent applied to i is -1. An odd exponent applied would denote -i, therefore. Your answer should be B.

The effect of the time of day a science class is taught on test scores is beingstudied in an experiment. Giving every student in the experiment the same
final exam is an example of which experimental design principle?

A. Randomization
B. Blocking
C. Direct control
D. Replication

Answers

Answer:replication

Step-by-step explanation:

Final answer:

In the experiment, giving every student the same final exam is an example of direct control. This experimental design principle ensures that all other variables are kept constant so that any differences in the outcome can be attributed only to the variable being tested.

Explanation:

In this experiment studying the effect of the time of day a science class is taught on test scores, giving every student in the experiment the same final exam is an example of the experimental design principle known as direct control. The direct control principle ensures that all other variables except the one being tested (in this case, the time of day) are kept constant. This is done to make sure that any differences observed in the outcome (the test scores in this case) can be attributed only to the variable being tested. Therefore, all students taking the same exam ensures that the difficulty of the test doesn't affect the results.

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WILL MARK BRAINLIEST!The multipliers of this system of equations have been determined to create opposite terms of the y-variable.

4 (one-fourth x minus three-fourths y = 34) right-arrow x minus 3 y = 136
24 (three-fourths x + one-eighth y = negative 12) right-arrow 18 x + 3 y = negative 288

Answers

Answer:

thus, x=-34 and y=170/-3

Step-by-step explanation:

4((1/4)*x-(3/4)*y)=34

x-3y=136

24((3/4)*x+(1/8)*y)=12

18x+3y=-288

4x-3y=34⇒x-3y=136

18x+3y=12⇒18x+3y=-288

lets solve 4x-3y=34⇒x-3y=136 first:

4x-3y=34

x-3y=136

4x-3y=34    

-x+3y=-136

3x=-102

x=-102/3

x=-34

lets plug in x to one of the equations, since both equations are equal to each other:

4x-3y=34

4(-34)-3y=34

-136-3y=34

-3y=170

y=170/-3

now lets solve: 18x+3y=12⇒18x+3y=-288

18x+3y=12

18x+3y=-288

18x+3y=12

-18x-3y=288

0\neq300

so, this system doesn't work

thus, x=-34 and y=170/-3
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