Some the system of equationsY=2x^2 - 3
Y=3x - 1

How many real number solutions are there to the equation 0=3x^2 + x - 4?

What are the solutions of the system
Y=x + 5
Y=x^2 - x + 2

Answers

Answer 1

Answer: y = 2x² - 3
y = 3x - 1

2x² - 3 = 3x - 1
  + 1 + 1
2x² - 2 = 3x
  2x² - 3x - 2 = 0
  2x² - 4x + x - 2 = 0
2x(x) - 2x(2) + 1(x) - 1(2) = 0
2x(x - 2) + 1(x - 2) = 0
(2x + 1)(x - 2) = 0
2x + 1 = 0 or x - 2 = 0
- 1 - 1 + 2 + 2
2x = -1 or x = 2
2 2
x = -0.5

  y = 3x - 1      or    y = 3x - 1
  y = 3(-0.5) - 1        or      y = 3(2) - 1
   y = -1.5 - 1       or      y = 6 - 1
  y = -2.5 or    y = 5
(x, y) = (-0.5, -2.5) or (x, y) = (2, 5)
————————————————————————————————
3x² + x - 4 = 0
  3x² - 6x + 2x - 4 = 0
3x(x) - 3x(2) + 2(x) - 2(2) = 0
3x(x - 2) + 2(x - 2) = 0
  (3x + 2)(x - 2) = 0
3x + 2 = 0 or x - 2 = 0
- 2 - 2 + 2 + 2
  3x = -2 or x = 2
3 3
x = ⁻²/₃
There are two real number solutions in the equation.
————————————————————————————————
y = x + 5
y = x² - x + 2

x + 5 = x² - x + 2
+ x + x
2x + 5 = x² + 2
- 2   - 2
2x + 3 = x²
0 = x² - 2x - 3
0 = x² - 3x + x - 3
0 = x(x) - x(3) + 1(x) - 1(3)
0 = x(x - 3) + 1(x - 3)
0 = (x + 1)(x - 3)
0 = x + 1 or 0 = x - 3
- 1   - 1 + 3 + 3
-1 = x    or   x = 3

  y = x + 5 or y = x + 5
  y = -1 + 5 or   y = 3 + 5
  y = 4 or y = 8
(x, y) = (-1, 4) or (x, y) = (3, 8)

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The mean score on a calculus exam was 40, and the standard deviation was 5. The teacher decided to double everyone’s score and then added 7 points. What are the values of the mean and standard deviation of the distribution of transformed exam scores? (Options: mean = 80 and standard deviation = 5, mean = 80 and standard deviation = 10, mean = 87 and standard deviation = 5, mean = 87 and standard deviation = 10, mean = 87 and standard deviation = 17)

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The new mean becomes 87 (40*2+7), while the new standard deviation becomes 10 (5*2). The correct option is then option D.

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a rectangular garden has dimensions of 100 feet by 10, next season, the garden decreased to 2/5 of its size. what is the scale of the drawing for the new garden

Answers

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What is the length of the diagonal, d, of the rectangular prism shown below?

Answers

Answer:

d = 10√10 ≈ 31.62

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Answer:

d = 10√10 ≈ 31.62

Step-by-step explanation:

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How do i solve this
(-15b - 7) - (-2b)

Answers

Answer:

13b + 7

Step-by-step explanation:

Combine like terms. (-15b - 7) - (-2b), add -15b to both sides, the equation then becomes (-7) - (13b). Swap the equation around to become (13b) - (-7), a subtraction sign and then a negative makes the negative a positive. The equation then becomes 13b + 7.

One number is five more than another, and their sum is three less than three times the smaller. Find the numbers.If x represents the smaller number, which equation could be used to solve for x?

A. x 2 + 5 = 3x - 3
B. 2x + 5 = 3x - 3
C. 2x + 5 = 3(x - 3)