The graph of a system of equations with the same slope and the same y-intercepts will have no solutions.A. Always
B. Sometimes
C. Never

Answers

Answer 1
Answer: I think the correct answer from the choices listed above is option C. The graph of a system of equations with the same slope and the same y-intercepts will never have no solutions. Rather, it has an infinite number of solutions since all points of the lines intersects.

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The number of aluminum cans used each year varies directly as the number of people using the cans. If 500 people use 120000 cans in one year, how many cans are used each year in a city which has a population of 130000?

Answers

Answer

31,200,000


Explanation

Firstly, calculate the constant of proportionality.

Al ∝ N

Al = kN     Where Al = number of aluminium cans, k = constant and N = number of people using the can.

Al = kN

k = Al/N

  = 120000/500

  = 240

Equation becomes;

Al = 240N

For 130000 cans;

Al = 240 × 130000

   = 31,200,000


Which of the following is the function representing the graph below?

Answers


You need to pick a point on the graph, then go through the list of choices
and see which one can produce the point you picked.

Look at the point on the graph right above the origin, where the graph
crosses the y-axis.  At that point, x=0 and f(x) (or 'y') = 1 .

Now look at the choices, one at a time, and see whether  (0, 1)  fits.
I'll start at the bottom of the list:

-->  f(x) = 4^(x-3)
When x=0, f(x) = 4^(-3) .
4^(-3) is not '1', so our point is not on this f(x).

-->  f(x) = 4^x + 3
When x=0, f(x) = 4⁰ + 3  =  1 + 3  =  4
'4' is not '1', so our point is not on this f(x).

-->  f(x) = 4^x - 3
When x=0, f(x) = 4⁰ - 3  =  1 - 3  =  -2
'-2' is not '1', so our point is not on this f(x).

(Only one choice left.)

--> f(x) = 4^x
When x=0, 4^x = 4⁰  =  1
That's it !  Our point is on this f(x).
Which is lucky, because we were out of choices.


Which of the following statements is true?

Answers

Answer:

option C is correct.

Step-by-step explanation:

Checking equation A

(9x^3 + 12x) + (16x^3 -4x+1)= 24x^3 +16x-1\n9x^3+16x^3+12x-4x+1=24x^3+16x-1\n25x^3+8x+1\neq 24x^3+16x-1

Checking equation B

(3x+2x^2-4)-(x^2+x-5)=2x+x^2-9\n3x-x+2x^2-x^2-4+5=2x+x^2-9\n2x+x^2+1\neq 2x+x^2-9

Checking equation C

(10x^3+2x^2-11)+(9x^2+2x-2)=10x^3+11x^2+2x-13\n10x^3+2x^2+9x^2+2x-11-2=10x^3+11x^2+2x-13\n10x^3+11x^2+2x-13=10x^3+11x^2+2x-13

Checking equation D

(-7x^2+12)-(5-4x^2)=11x^2-17\n-7x^2+4x^2+12-5=11x^2-17\n-3x^2+7\neq 11x^2-17

Hence, only option C is correct.

The warehouse of the Alpha DistributionCompany measures 450 feet by 300 feet. If
65% of the floor space is covered, how many square feet are NOT covered?

Answers

Answer:

47,250 ft^2

Step-by-step explanation:

Area: 450 * 300 = 135,000 ft^2
65% of 135,000 =

135,000 * 0.65 = 87,750 ft^2 (space covered)
135,000 - 87,750 = 47,250

What is the midpoint of OA ?A: (2m, n)


B: (m, n)


C: (m – n, 0)


D: (m, 2n)

Answers

Answer:

(m,n)

Step-by-step explanation:

Since O is at the origin, we can take the coordinates of point A and divide them by 2 to find the midpoint

( 2m/2,2n/2)

The midpoint is at (m,n)

Maggie has 7 tiles with pictures of plants and 2 tiles with pictures of animals. Maggie keeps all the tiles on a mat with the pictures hidden and mixes them up. She then turns one tile face up and finds the picture of a plant on it. She removes this tile from the mat and turns over another tile without looking. What is the probability that the second tile that Maggie turns over has a plant on it? 22.2%
28.6%
65.0%
75.0%

Answers

Answer: The probability that the second tile that Maggie turns over has a plant on it, is 75.0 %.

Step-by-step explanation:

We have,

Number of tiles with pictures of plants = 7

And, number of tiles with pictures of animals = 2,

⇒ Total numbers of tiles = 7 + 2 = 9,

After removing one picture of plant tile,

The remaining number of plant tiles = 7 - 1 = 6,

And, total numbers of remaining tiles = 9 - 1 = 8.

Since,

\text{ The probability of plant tile in second trial}=\frac{\text{Remaining plant tiles}}{\text{Total remaining tiles}}

=(6)/(8)

=0.75 = 75\%     (Because, 0.01 = 1% ⇒ 0.75 = 75% )

Thus, the probability that the second tile that Maggie turns over has a plant on it, is 75.0 %.

7 tiles with plants and 2 tiles with animals...total of 9 tiles

she flips a plant tile, and does not replace it.

probability that 2nd tile is a plant = 6/8 = 0.75 = 75%