All categories

3 years ago

A rectangular skateboard park has an area of 2 + 15 + 56. What are possible dimensions of the park?

Mathematics

1 answer:

const2013 [10]3 years ago

8 0

Answer:

The possible dimensions of the park are (x + 7) and (x + 8) where x is any number

Step-by-step explanation:

If an area of a rectangle is A = ax² + bx + c, then the dimensions of the rectangle are the factors of ax² + bx + c

∵ A rectangular skateboard park has an area of x² + 15x + 56

∴ A = x² + 15x + 56

- Lets factorize the trinomial x² + 15x + 56 into two factors

∵ The last sign of it is (+)

∴ The two factors have the same middle sign

∵ The middle sign of it is (+)

∴ The two factors have (+) as a middle sign

∵ x² = x × x

∵ 56 = 7 × 8

∵ 7 × x + 8 × x = 15x ⇒ middle term

- That means the factors of x² + 15x + 56 are (x + 7) and (x + 8)

∴ The factors of x² + 15x + 56 are (x + 7) and (x + 8)

∵ A = x² + 15x + 56

∴ A = (x + 7)(x + 8)

∵ Area of the rectangle = The product of its dimensions

∴ (x + 7) and (x + 8) are the dimensions of the park

The possible dimensions of the park are (x + 7) and (x + 8) where x is any number

You might be interested in

Question 1

8090 [49]

The correct answer is C. The 13 moose are the individuals. There is one categorical variable and four quantitative variables.

Explanation:

In research, the individuals refer to the participants or population that is being analyzed. For example, if the purpose of the research is to know how many hours highschool students sleep, the individuals are high school students. In this context, the individual or population of this study ae the 13 moose.

Moreover, this research focuses on different variables such as gender, height, the number of hours each moose spends in the water, the weigh of the food eaten on average by each moose, and the average weight of food eaten every day. From these variables, the last four variables are quantitative because they can be measured using numbers, for example, the height is measured in inches. On the other hand, the first variable is categorical because each moose can be classified in only two categories: male or female.

7 0

3 years ago

Two cars leave town at the same time going in the same direction. One travels 55 miles per hour and the other travels 48 miles p

Amanda [17]

Answer:

Question 160644: Two cars leave town at the same time going in opposite directions. One travels 55 mph and the other travels 48 mph. In how many hours will they be 206 miles apart? T=2 HOURS THEY WILL BE 206 MILES APART

Ok thank you

4 0

2 years ago

Read 2 more answers

A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to spli

Rudik [331]

Answer:

1) The equation 1/8(x+16)=76/8 represents the situation, where x is the food bill.

2) The solution x=60 represents the total food bill.

These both answers are correct.

Step-by-step explanation:

Since there are 8 group of friends, and the total amount spent by them is $76 including the tip i.e $16.

If x is the food bill our equation can be:

(x+16)/8 = 76/8

Solving the equation

(x+16)/8 = 9.5

x+16= 9.5*8

x= 76 -16

x= 60

The food bill is x=60.

6 0

3 years ago

Read 2 more answers

I need help! Will mark Brainliest for full answer!!!

Softa [21]

Answer:

Part a .............> x = 11

Part b .............> k = 57.2

Part c .............> y = 9.2

Explanation:

The three problems deal with inverse variation between two variables

An inverse variation relation between two variables means that when one of the variables increases, the other will decrease (and vice versa)

Mathematically, an inverse variation relation is represented as follows:

$y = \frac{k}{x}$

where x and y are the two variables and k is the constant of variation

Now, let's check the givens:

Part a:

We are given that y = 3 and k = 33

Substitute in the original relation and solve for x as follows:

$y = \frac{k}{x}\\ \\3 = \frac{33}{x}\\ \\x=\frac{33}{3}=11$

Part b:

We are given that y = 11 and x = 5.2

Substitute in the original relation and solve for k as follows:

$y=\frac{k}{x}\\ \\11=\frac{k}{5.2}\\ \\k=11*5.2=57.2$

Part c:

We are given that x=7.8 and k=72

Substitute in the original relation and solve for y as follows:

$y=\frac{k}{x}=\frac{72}{7.8}=9.2$ to the nearest tenth

Hope this helps :)

6 0

2 years ago

Angela shared a cab with her friends. When they arrived at their destination, they evenly divided the $j fare among the 3 of the

igor_vitrenko [27]

Answer:

(j/3)+5

thats the answer

8 0

3 years ago