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Roman55 [17]
2 years ago
7

PLEASE HELP Given the function f(x) = 3x2 – 4

Mathematics
1 answer:
Zarrin [17]2 years ago
7 0

Answer:

15

Step-by-step explanation:

Rate of change is the slope of the tangent which will be the derivative of the function

if f(x) = 3x² - 4

f'(x) = 6x

as the derivative is linear, the average rate of change will occur at the midpoint of the interval

f'(2.5) = 6(2.5) = 15

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The sum of the squares of two consecutive negative integers is 61. Find the smaller of the two integers
Marysya12 [62]
x^2+(x+1)^2=61\\ x^2+x^2+2x+1-61=0\\ 2x^2+2x-60=0\ \ /:2\\ x^2+x-30=0\\ \Delta=1^2-4\cdot(-40)=1+120=121\ \ \Rightarrow\ \  \sqrt{\Delta} =11\\ \\ x_1= \frac{-1-11}{2} = \frac{-12}{2} =-6,\ \ \ \ x_2= \frac{-1+11}{2} = \frac{10}{2}=5\\ \\Ans.:x=-6
3 0
3 years ago
A) 75YARDS B) 85 YARDS C)80 YARDS D) 90 YARDS
Amanda [17]

Answer:

________________

I think it's 85 yards

7 0
3 years ago
Need help solving algebraically!
alekssr [168]
We need to account for both x values on either side of the length, and width.
Thus, the length becomes 10 + x + x = 10 + 2x
and the width becomes 5 + x + x = 5 + 2x

For the second question, I'm assuming we don't account for the area that is covered by the garden.
Then we can say that the path is measured by: (5 + 2x)(10 + 2x) - 50, which is the area of the garden itself.

(5 + 2x)(10 + 2x) - 50 = 54

Expanding the brackets:
50 + 10x + 20x + 4x^{2} - 50 = 54
4x^{2} + 30x = 54
2x^{2} + 15x - 27 = 0
2x^{2} - 3x + 18x - 27 = 0
x(2x - 3) + 9(2x - 3) = 0

(x + 9)(2x - 3) = 0
x = -9, or x = 3/2

Since x > 0, then x ≠ -9
Thus, the only x-value we can take is x = 3/2
6 0
3 years ago
Two dice are numbered 1,2,3,4,5,6 and 1,1,2,2,3,3 respectively. They are rolled and
Alexxx [7]

Answer:

P(2) = 1/18

P(3) = 1/9

P(4) = 1/6

P(5) = 1/6

P(6) = 1/6

P(7) = 1/6

P(8) = 1/9

P(9) = 1/18

Step-by-step explanation:

Each die has six possible outcomes, so both dice together have 6*6 = 36 outcomes:

(1,1), (1,1), (1,2), (1,2), (1,3), (1,3),

(2,1), (2,1), (2,2), (2,2), (2,3), (2,3),

(3,1), (3,1), (3,2), (3,2), (3,3), (3,3),

(4,1), (4,1), (4,2), (4,2), (4,3), (4,3),

(5,1), (5,1), (5,2), (5,2), (5,3), (5,3),

(6,1), (6,1), (6,2), (6,2), (6,3), (6,3).

The sum of the values for each outcome is:

2, 2, 3, 3, 4, 4,

3, 3, 4, 4, 5, 5,

4, 4, 5, 5, 6, 6,

5, 5, 6, 6, 7, 7,

6, 6, 7, 7, 8, 8,

7, 7, 8, 8, 9, 9.

To find the probability of each sum, we just need to divide the number of times this sum appears over the total number of possibilities (36), so we have:

P(2) = 2/36 = 1/18

P(3) = 4/36 = 1/9

P(4) = 6/36 = 1/6

P(5) = 6/36 = 1/6

P(6) = 6/36 = 1/6

P(7) = 6/36 = 1/6

P(8) = 4/36 = 1/9

P(9) = 2/36 = 1/18

8 0
3 years ago
6/24 divided by 12/16
garri49 [273]
The answer is would be 1/3
7 0
3 years ago
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