Find the value of x and y.

The area if a rectangular frame is 32 square inches. The perimeter of the frame is 24 inches. Which shows the correct dimensions

Zarrin [17]

Answer:

8 x 4

Step-by-step explanation:

Lets say the length is x and the width is y.

xy = 32

2x + 2y = 24

Rearranging the second equation, we get:

2x = 24 - 2y

/2 /2

x = 12 - y

substitute into the first equation

y(12 - y) = 32

12y - y^2 = 32

-32 -32

-y^2 +12y - 32 = 0

x -1 x -1

y^2 - 12y + 32 = 0

(y - 8)(y - 4) = 0

y = 8 or 4

substitute into x = 12 - y.

x = 12 - 8 = 4

x = 12 -4 = 8

so the correct dimensions are 4 x 8, as either x = 4 and y =8, or x = 8 and y = 4.

Hope I helped!

8 0

3 years ago

6. Determine if the two functions are inverses of one another.

-BARSIC- [3]

It will be yesssssssssssssssssssssssssssssssss

6 0

3 years ago

Raven bought a TV originally priced at $225. She got a 22% discount. If she gave the cashier $200, how much change did she get b

sergeinik [125]

Answer:

She would get 49.50 back

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

I have no clue what do you, can someone please explain

fiasKO [112]

Answer:

a = 3 b = -18 c = 11 d = 0

Step-by-step explanation:

The table tells you what value the function will product (y) if you input the corresponding value of x.

So, for example, if you input the value of x = 1 into the function, you will get y = -4.

If we substitute x = 0 and y = 0 into the function we can find the value of d immediately:

0 = a(0)³ + b(0)² +c(0) + d

0 = 0 + 0 + 0 + d

0 = d

As d = 0, we can now eliminate d and write the function as:

y = ax³ + bx² + cx

Now substitute the remaining pairs of values into y = ax³ + bx² + cx to create 3 equations:

1) When x = 1, y = -4

⇒ a(1)³ + b(1)² + c(1) = -4

⇒ a + b + c = -4

2) When x = 2, y = -26

⇒ a(2)³ + b(2)² + c(2) = -26

⇒ 8a + 4b + 2c = -26

⇒ 4a + 2b + c = -13

3) When x = 3, y = -48

⇒ a(3)³ + b(3)² + c(3) = -48

⇒ 27a + 9b + 3c = -48

⇒ 9a + 3b + c = -16

Now solve the system of 3 equations simultaneously to find the value of a, b and c. To do this, reduce this to 2 equations with 2 unknowns by eliminating one of the unknowns from two pairs of equations:

Eliminate c by subtracting equation 1) from equation 2) to create equation 4):

2) 4a + 2b + c = -13

1) a + b + c = -4

4) 3a + b = -9

Eliminate c by subtracting equation 2) from equation 3) to create equation 5):

3) 9a + 3b + c = -16

2) 4a + 2b + c = -13

5) 5a + b = -3

Now use equations 4) and 5) to find a and b, by subtracting equation 4) from equation 5) to find a:

5) 5a + b = -3

4) 3a + b = -9

6) 2a = 6

⇒ a = 6 ÷ 2 = 3

and substituting the found value of a into equation 4) or 5) to find b:

5) 5(3) + b = -3

15 + b = -3

⇒ b = -18

Now substitute the found values for a and b into one of the original 3 equations to find c:

1) a + b + c = -4

3 - 18 + c = -4

⇒ c = 11

Therefore, the function is y = 3x³ - 18x² + 11x

3 0

3 years ago

Jodi bought a new car with a 14-gallon gas tank. Around town she is able to drive 336 miles on one tank of gas. On her first tri

gizmo_the_mogwai [7]

Part A:

Answer:

$336\leq 14m\leq 448$

Step-by-step explanation:

Step 1:

Jodi bought a new car with a 14-gallon gas tank.

Around town, she can drive 336 miles on one tank of gas.

She drove 448 miles on one tank on a trip on the highway

m will represent the number of miles per gallon of gas.

Step 2:

If m represents the number of miles per gallon of gas she gets and her tank holds 14 gallons then 14m represents the number of miles she can drive.

14 gallons · $\frac{m}{1} = 14m$

Around town, she was able to drive 336 miles and on the highway, she was able to drive 448

So... $336\leq 14m\leq 48$

Part B:

Answer:

The compound inequality is two simple inequalities separated by "and" is $336\leq 14m$ and $14m < 448$ .

Step-by-step explanation:

Step 1:

We are told Jodi bought a new car with a 14-gallon gas tank.

Around town, she can drive 336 miles on one tank of gas. She drove 448 miles on one tank of gas on her first trip traveling on highways

Here we need to rewrite the compound inequality

Let $m$ represent the number of miles per gallon of gas.

Step 2:

Since $14m$ must greater than or equal to $336$ and less than or equal to $448$ :

The two simple inequalities must be separated by the word "and"

$336\leq 14m$ and $14m$

Part C:

Answer:

The solution of simple inequality is $24\leq m$ and $m\leq 32$

Step- by step explanation:

Step 1:

We are given Jodi bought a new car with a 14-gallon gas tank. Around town, she can drive 336 miles on one tank of gas. She drove 448 miles on one tank of gas on her first trip traveling on highways.

Step 2:

Solve each simple inequality by dividing both sides by 14:

$336\leq 14m$ and $14m\leq 448$

$\frac{336}{14}\leq \frac{14m}{14}$ and $\frac{14m}{14} \leq \frac{448}{14}$

$24\leq m$ and $m\leq 32$

Part D:

Answer:

The solution of the compound inequality is $24\leq m\leq 32$

Step 1:

We are given Jodi bought a new car with a 14-gallon gas tank. Around town, she can drive336miles on one tank of gas. She drove 448 miles on one tank of gas on her first trip traveling on highways. To solve the compound inequality without rewriting it as two simple inequalities

Step 2:

Solving compound $336\leq 14m\leq 448$ for $m$ by dividing all sides by 14

$226\leq 14m\leq 448\\$

$\frac{336}{14}\leq \frac{14m}{14} \leq \frac{448}{14}$

$24\leq m\leq 32$

Part G:

Answer:

Download docx

5 0

2 years ago

Read 2 more answers