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lina2011 [118]
3 years ago
14

Help -------------------------

Mathematics
1 answer:
34kurt3 years ago
8 0

Answer:

(A) -3 ≤ x ≤ 1

Step-by-step explanation:

The given function is presented as follows;

h(x) = x² - 1

From the given function, the coefficient of the quadratic term is positive, and therefore, the function is U shaped and has a minimum value, with the slope on the interval to the left of <em>h</em> having a negative rate of change;

The minimum value of h(x) is found as follows;

At the minimum of h(x), h'(x) = d(h(x)/dx = d(x² - 1)/dx = 2·x = 0

∴ x = 0/2 = 0 at the minimum

Therefore, the function is symmetrical about the point where x = 0

The average rate of change over an interval is given by the change in 'y' and x-values over the end-point in the interval, which is the slope of a straight line drawn between the points

The average rate of change will be negative where the y-value of the left boundary of the interval is higher than the y-value of the right boundary of the interval, such that the line formed by joining the endpoints of the interval slope downwards from left to right

The distance from the x-value of left boundary of the interval that would have a negative slope from x = 0 will be more than the distance of the x-value of the right boundary of the interval

Therefore, the interval over which <em>h</em> has a negative rate of change is -3 ≤ x ≤ 1

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Asa saves dimes and quarters so that he will have exact change for he bus. He dabs and then dumps the container that he has been
koban [17]

Asa has 15 dimes and 32 quarters.

Step-by-step explanation:

Given,

Total coins = 47

Worth of coins = $9.50 = 9.50*100 = 950 cents

1 dime = 10 cents

1 quarter = 25 cents

Let,

Number of dimes = x

Number of quarters = y

According to given statement;

x+y=47      Eqn 1

10x+25y=950   Eqn 2

Multiplying Eqn 1 by 10

10(x+y=47)\\10x+10y=470\ \ \ Eqn\ 3

Subtracting Eqn 3 from Eqn 2

(10x+25y)-(10x+10y)=950-470\\10x+25y-10x-10y=480\\15y=480

Dividing both sides by 15

\frac{15y}{15}=\frac{480}{15}\\y=32

Putting y=32 in Eqn 1

x+32=47\\x=47-32\\x=15

Asa has 15 dimes and 32 quarters.

Keywords: linear equation, elimination method

Learn more about elimination method at:

  • brainly.com/question/2670657
  • brainly.com/question/2821386

#LearnwithBrainly

7 0
3 years ago
Write absolute value of the following rational number -6/11 , 15/21 , -9 , -21/-37 , 31/-54​
Dahasolnce [82]

Answer:

6/11, 15/21, 9, 27/37, 31/54

Step-by-step explanation:

Absolute value is when you determine the distance between a value and zero . Since you will always have a positive distance, your absolute values are positive as well.

4 0
3 years ago
Write in standard form 4,000,000+3,000+50+2
Andreas93 [3]
4,003,052 is the answer to the problem
7 0
3 years ago
Read 2 more answers
Can someone answer these questions
Finger [1]
23. -7
24. greater. For example, when u subtract -5 from 10, the answer is 15, which is greater than 10
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3 years ago
An investment offers a simple interest rate of 3% per year.
Step2247 [10]

Answer:

sh 23000

Step-by-step explanation:

i = \frac{prt}{100}  =  \frac{20000 \times 3 \times 5}{100}  = 3000

Amount = principal + interest = 20000+3000 = sh 23000

6 0
3 years ago
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