MATHEMATICS HIGH SCHOOL

Which algebraic expression is equivalent to the expression below?7(2x - 6)







A.

7x - 8

B.

7x - 1

C.

14x + 42

D.

14x - 42

Answers

Answer 1
Answer: Using the formula a(b+c) = ab + ac, then 7(2x-6) = 14x - 42. The answer is D.

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Which of the following ordered pairs represents a solution to the equation below?
y = 3x−2

Answers

Answer:

(0,-2) (1,1) (2,4)

Step-by-step explanation:

A manufacturing firm wants to package its product in a cylindrical container 2ft. high with surface area 6ft^2.
What should the radius of the circular top and bottom​ be?

Answers

To solve the problem above, we will be using the equation in solving the surface area of a cylinder which goes. A = 2pi r^2 + 2pi r h, A is for the surface area, pi is 3.1416; h is the height and r is the radius. Basing on this formula the radius will be 0.3982 ft both top and bottom.

You drive 1400 miles in 3.5 days. You drive an equal number of miles each day. How many miles do you drive each day.

Answers

Answer:

400 Miles Per Day

Step-by-step explanation:

If you drive an equal amount of miles each day, you know the total miles driven will be the amount of miles per day. Therefore (1400 Miles)/(3.5 Days) = 400 (Miles)/(Day)

Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The three pens are to have the same area. Express the area function for the three pens in terms of x. Determine the domain and range for the area function

Answers

Answer:

The area function is

A=(135)/(2)x-(9)/(2)x^2.

The domain and range of A is (0,15m) and (0, 253.125 m^2].

Step-by-step explanation:

The given length of fencing is 90 m.

Let the length and width of each pen be x and y respectively as shown in the figure.

As there are 3 pens, so, the total area,

A= 3 xy \;\cdots (i)

From the figure the total length of fencing is 6x+4y.

Here, for a significant area for the animals, x>0 as well as y>0 as x and y are the sides of ben.

From the given value:

6x+4y=90\;\cdots (ii)

\Rightarrow y=\frac {45}{2}-(3x)/(2)

Now, from equation (i)

A=3x\left(\frac {45}{2}-(3x)/(2)\right)

\Rightarrow A=(135)/(2)x-(9)/(2)x^2\;\cdots (iii)

This is the required area function in the terms of variable x.

For the domain of area function, from equation (ii)

x=15-(2y)/(3)

\Rightarrow x<15 m [as y>0]

So, the domain of area function is (0,15m).

For the range of area function:

As x \rightarrow 0 or y\rightarrow 0, then A\rightarrow 0 [from equation (i)]

\Rightarrow A>0

Now, differentiate the area function with respect to x .

\frac {dA}{dx}=(135)/(2)-9x

Equate \frac {dA}{dx}  to zero to get the extremum point.

\frac {dA}{dx}=0

\Rightarrow (135)/(2)-9x=0

\Rightarrow x=(15)/(2)

Check this point by double differentiation

\frac {d^2A}{dx^2}=-9

As,  \frac {d^2A}{dx^2}<0, so, point x=(15)/(2) is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

A=(135)/(2)* \frac {15}{2}-(9)/(2)* \left(\frac {15}{2}\right)^2

\Rightarrow A=253.125 m^2

Hence, the range of area function is (0, 253.125 m^2].

Final answer:

The area of each pen can be expressed as A(x) = x * (90 - 2x) / 3. The domain of this function is 0 < x < 45, and the range is 0 < A(x) < 300

Explanation:

In this problem, since Pam has to divide the petting zoo into three parts, we can consider the width of each pet pen to be x and the total length of the three pens to be (90 - 2x)/3, given that the total fence is 90m and we have two fences that are x meters long separating the pens. So, the area, A of each pen can be expressed as a function of x: A(x) = x * (90 - 2x) / 3. The domain of this function, or the possible values of x, would be all the values that make the area positive, which are 0 < x < 45. For the range of the function, we analyze the quadratic function which will have a maximum value at x = 15, as the area will be largest when the space is divided evenly, so the maximum area is A(15)= 15 * (60) / 3 = 300. Therefore, the range of the function is 0 < A(x) < 300.

Learn more about Area and Functions here:

brainly.com/question/29292490

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you are planting a rectangle garden. it is 5 feet longer than 3 times its width. the area of the garden is 250 feet. find the dimensions

Answers

l=3w+5
2(3w+5)+2w=250 (both w and l have to be multiplied by two because there are two sides)
This can be simplified to: 6w+10+2w=250
Now subtract 10 from both sides and add the two w's together.
This makes: 8w=260
Divide both by 8: 32.5-w=32.5
32.5 times 2=65
250-65=185, divided by 2=92.5

Length=92.5
Width=32.5

hope this helped!

Separate 185 into two parts so that one part is 31 more than the other part. Find each part.

Answers

9514 1404 393

Answer:

  108, 77

Step-by-step explanation:

Let x represent the larger part. Then ...

  x + (x -31) = 185

  2x = 216

  x = 108

  x -31 = 77

The two parts are 108 and 77.
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