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3 years ago

The length of the rectangle is x + 12. The width of the rectangle is x + 3. Please determine the area of the rectangle.

Mathematics

1 answer:

OverLord2011 [107]3 years ago

3 0

Answer:

For part A, the product of (-5 + x)(x + 4) is equal to x^2 - x - 20. For part B, the product of -5 + x and x + 4 is not equal to the product of 5 + x and x - 4. And for part C the product of (3 + 5)(3^2 + 4 - 3) equals 70.

Step-by-step explanation:

I will tell you how I came up with those answers.

The product of (-5 + x)(x + 4) can be found using the FOIL method(First, Outer, Inner, Last).

Start with multiplying -5 and x. -5 * x = -5x.

Now multiply -5 and 4. -5 * 4 = -20.

Next, multiply x and x. x * x = x^2.

Finally, multiply x and 4. x * 4 = 4x.

And now it is time to simplify and change to standard form.

-5x - 20 + x^2 + 4x.

x^2 - 5x - 20 + 4x.

x^2 - 5x + 4x - 20.

x^2 - x - 20.

The final answer for part A is x^2 - x - 20.

For part B, the product of -5 + x and x + 4 is already known.

But now we need to figure out the product of 5 + x and x - 4.

We can use the FOIL method again to solve for the new product.

Start by multiplying 5 and x. 5 * x = 5x.

Next, multiply 5 and -4. 5 * -4 = -20.

Now multiply x and x. x * x = x^2.

Finally, multiply x and -4. x * -4 = -4x.

And now we can simplify and arrange the terms into standard form.

5x - 20 + x^2 - 4x.

x^2 + 5x - 20 - 4x.

x^2 + 5x - 4x - 20.

x^2 + x - 20.

The final answer for part B is that the products of

(-5 + x)(x + 4) and (5 + x)(x - 4) are not equivalent. They look similar except the difference between them is the "x" value. The x value of the first equation's product is -x while the x value of the second equation's product is x.

For part C, use the FOIL method as used in the last questions to find the answer.

2 * 3^2 = 2 * 9 = 18.

2 * 4 = 8.

2 * -3 = -6.

5 * 3^2 = 5 * 9 = 45.

5 * 4 = 20.

5 * -3 = -15.

Now combine the numbers to get the final answer for part C.

Follow PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition and Subtraction).

The only operations are subtraction and addition. The rule is the add before subtracting, but this does not always apply. For this being true, we only need to perform the first operation from the left side.

18 + 8 - 6 + 45 + 20 - 15.

26 - 6 + 45 + 20 - 15.

20 + 45 + 20 - 15.

65 + 20 - 15.

85 - 15.

70.

So the last answer to part C is 70.

Also the area of the rectangle is x^2 + 15x + 36. I forgot that part, my apologies.

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Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are sum

Naddika [18.5K]

Answer:

P(A) = 86/100

P(B) = 79/100

P(A') = 14/100

P(A U B) = 95/100

P(A' U B) = 84/100

Step-by-step explanation:

i. P(A) = number of disks with high shock resistance/total number of disks

= (70+16)/100

= 86/100

ii. P(B) = number of disks with high scratch resistance/total number of disks

= (70+9)/100

= 79/100

iii. P(A') = number of disks without high shock resistance/total number of disks

= (100-86)/100

= 14/100

iv. P(AUB) = number of disks with high shock resistance or high scratch resistance/total number of disks

= (70+9+16)/100

= 95/100

v. P(A'UB) = number of disks without high shock resistance or with high scratch resistance/total number of disks

= (5+9+70)/100

= 84/100

3 0

3 years ago

Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to p

zalisa [80]

General Idea:

(i) Assign variable for the unknown that we need to find

(ii) Sketch a diagram to help us visualize the problem

(iii) Write the mathematical equation representing the description given.

(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE

Applying the concept:

Given: x represents the length of the pen and y represents the area of the doghouse

Statement 1: "The pen is 3 feet wider than it is long"

$Length \; of\; the \; pen = x\\ Width \; of\; the\; pen=x+3$

------

Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"

$Area \; of\; the\; Dog \; house=y\\ Perimeter \; of\; Dog\; house=y$

------

Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."

$Area \; of \; the\; Pen - Area \;of \;the\;Dog \;House=\;Space\;inside\;Pen\\ \\ x \cdot (x+3)-y=178\\ Distributing \;x\;in\;the\;left\;side\;of\;the\;equation\\ \\ x^2+3x-y=178\Rightarrow\; 1^{st}\; Equation\\$

------

Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."

$Perimeter\; of\; the\; Pen=3\; \cdot \; Perimeter\; of\; the\; Dog\; House\\ \\ 2(x \; + \; x+3)=3 \cdot y\\ Combine\; like\; terms\; inside\; the\; parenthesis\\ \\ 2(2x+3)=3y\\ Distribute\; 2\; in\; the\; left\; side\; of\; the\; equation\\ \\ 4x+6=3y\\ Subtract \; 6\; and \; 3y\; on\; both\; sides\; of\; the\; equation\\ \\ 4x+6-3y-6=3y-3y-6\\ Combine\; like\; terms\\ \\ 4x-3y=-6 \Rightarrow \; \; 2^{nd}\; Equation\\$

Conclusion:

The systems of equations that can be used to determine the length and width of the pen and the area of the doghouse is given in Option B.

$178=x^2+3x-y\\ \\ -6=4x-3y$

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4 years ago

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James went out for. a long walk . he walked 3/4 mile and then sat down to take rest. then walked 1/8 of a mile how far did he wa

scoundrel [369]

Answer:

7/8 mile

Step-by-step explanation:

3/4 = 6/8

6/8+ 1/8 = 7/8

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3 years ago

Your sister is getting married this summer and she has asked you to help her select a D.J.

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So Dave charges 150 at first and then 10.50 per each hour, so if your sister has the party going for say "h" hours, then his total charges will then be 150 + 10.5h.

now, Marvin's Mobile Music charges 135 at first, but then is more expensive per hour is 15 bucks per each hour, so if she has a party for "h" hours, then his total charges are 135 + 15h.

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so, 3 and a third of a hour, or 3 hours and 20 minutes, they both will cost your sister the same amount, so it wouldn't matter who's hired if the party is only 3 hours and 20 minutes long.

however, after that, the one with higher hourly rate, Marvin's, gets more expensive, and she's better off hiring the one with cheaper hourly rate.

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4 years ago

27 + 5 x 6 A Little Problem With this so some help please?

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Answer:

Step-by-step explanation:

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4 years ago

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