Jocy is making a wooden picture frame that will have a width that is 12 inches shorter than its length. If he uses 100 inches of wood, what are the dimsensionsof th frame?

Answers

Answer 1

Answer: If he uses 100 inches of wood to make the frame, then 100 is double the sum of the length and the width, so 50 is the sum of the length and the width.

If the length is 12 more than the width, then the width is (50-12)/2=19. The length, then, is 19+12=31.

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Find all relative extrema of the function. use the second derivative test where applicable. (if an answer does not exist, enter dne.) f(x) = x3 − 9x2 + 2

Answers

First find the derivative of the function. The derivative is $f'(x)=3 x^(2) -18x$ . Now set it equal to 0 to find the critical numbers. $0=3 x^(2) -18x$ . Factor to solve for the zeros of the derivative. $0=3x(x-6)$ . So 3x = 0, and x = 0, or x - 6 = 0 and x = 6. We will make a table with values for -∞<x<0, 0<x<6, 6<x<∞. Pick a value within those boundaries for each interval and find the sign, positive or negative, that results from subbing that number into the derivative. If we choose -1 in the first interval f'(-1)=21, so the function is increasing from negative infinity to 0. If we choose 1 in the second interval, f'(1)=-15, so the function is decreasing from 0 to 6. If we choose 10 in the last interval, f'(10)=120, so the function is increasing from 6 to infinity. The points of extrema are found by subbing the critical x values into the original function. We know the function is increasing from negative infinity to 0, so f(0)=2, and our max point is (0, 2). We know the function is decreasing from 6 to infinity, so f(6)=-106, and our min point is (6, -106). I do this instead of the second derivative test, but they both work.

Which equation can be used to represent six added to twice the sum of a number and four is equal to one-half of the difference of three and the number?

Answers

six added to twice the sum of a number and four is equal to one-half of the difference of thee and the number.

Let x be the number.

6 + 2(x + 4) = 1/2 * (3-x)

Find the value of x.

6 + 2x + 8 = 3/2 - x/2
2x + x/2 = 3/2 - 8 - 6
2x + x/2 = 3/2 - 14
2(2x + x/2) = 2(3/2 - 14)
4x + x = 3 - 28
5x = -25
x = -25/5
x = -5

To check: x = -5

6 + 2(x + 4) = 1/2 * (3-x)

6 + 2(-5+4) = 1/2 * (3 - (-5))
6 + 2 (-1) = 1/2 * (3 + 5)
6 - 2 = 1/2 (8)
4 = 4

Answer: Opion A

(A) 6 + 2(X + 4)= 1/2(3-X) <=========+ 100 %

Step-by-step explanation:

What is the image point of (-1,8)(−1,8) after a translation right 1 unit and up 2 units?

Answers

The image point of (-1, 8) after a translation right 1 unit and up 2 units is (0, 10).

To find the image point of (-1, 8) after a translation right 1 unit and up 2 units, we need to add 1 to the x-coordinate and 2 to the y-coordinate of the given point.

The new x-coordinate is (-1 + 1) = 0, and the new y-coordinate is (8 + 2) = 10.

Therefore, the image point of (-1, 8) after the translation is (0, 10).

Learn more about translation here:

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Answer:

(0,10)

Step-by-step explanation:

Im pretty sure bc of subtracting 1 from the -1 in your x vaue and adding 2 to the 8 in you Y value

Lisa is seven times as old as her brother. She will be four times as old as her brother in three years. Represent the above situation in mathematical form.

Answers

Answer:

Let B = the brothers age now

Let L = Lisa's age now

Then today:

L = 7B

And three years from now, Lisa's current age plus 3 equals 4 times the brothers age plus 3 represented by the following formula

L+3 = 4(B+3)

Now we can substitute the value of L in the first formula for L in the second formula

7B + 3 = 4(B+3)

So the answer is C

Step-by-step explanation:

Mrs. Quotient asked her students to simplify each of the expressions below. Which of the numbered choices represents the expressions which simplified to the same result? A 71 B 72 C 73

Answers

Answer:

A and B

Step-by-step explanation:

Mrs. Quotient asked her students to simplify each of the expressions below. Which of the numbered choices represents the expressions which simplified to the same result? A 126/2 B 23 × 3 C 3 × 21

When simplifying an algebraic expression, the following steps are needed to be taken.

Firstly, remove parenthesis by multiplying the constant with the term in the parenthesis or remove parenthesis using exponent rules for parenthesis in exponent form.

Secondly Combine terms by adding coefficients of terms with the same order and lastly sum all constant.

A) 126/2

Applying the division rule give:

126/2 = 63

B) 23 × 3

Applying multiplication rule gives:

23 × 3 = 69

C) 3 × 21

Applying multiplication rule gives:

3 × 21 = 63

Both the results of expression A and expression B are simplified to the same result

B. If soil is priced at $5 per cubic yard, how much will it cost to fill your boxes?

Answers

The volume of each box is (length x width x height).
The number of boxes is ' Q '.
The cost is

($5) (Q) (length x width x height, all measured in yards) .

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