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3 years ago

Paul is growing a rectangular rose garden. His area is 5x2+ 8x +3. What are the dimensions of his rectangle?

Mathematics

1 answer:

irina [24]3 years ago

6 0

Answer:

$Length = 5x + 3$

$Width = x +1$

Step-by-step explanation:

Given

$Area = 5x^2 + 8x + 3$

Required

Determine the dimensions

To do this, we simply factorize the given expression.

$Area = 5x^2 + 8x + 3$

Expand

$Area = 5x^2 + 5x +3x+ 3$

Factorize

$Area = 5x(x + 1) +3(x+ 1)$

Factor out x + 1

$Area = (5x +3) (x+ 1)$

Area is calculated as:

$Area = Length * Width$

So:

$Length = 5x + 3$

$Width = x +1$

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For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perim

ICE Princess25 [194]

Answer:

Part a) The area of the figure is $\frac{9}{2}(4+\pi )\ cm^{2}$

Part b) The perimeter of the figure is $3(2+2\sqrt{2}+ \pi)\ cm$

Step-by-step explanation:

Step 1

Find the area of the figure

In this problem we have that

The figure ABC is the half of a square and the other figure is a semicircle

Find the area of the figure ABC

we have

$AB=6\ cm, BC=6\ cm$

The area of the half square ABC is equal to find the area of triangle ABC

$A1=\frac{1}{2}*6*6=18\ cm^{2}$

Find the area of the semicircle

The area of the semicircle is equal to

$A2=\pi r^{2}/2$

we have that

$r=6/2=3\ cm$

substitute

$A2=\pi (3)^{2}/2$

$A2=(9/2) \pi\ cm^{2}$

The area of the figure is equal to

$18\ cm^{2}+(9/2) \pi\ cm^{2}= \frac{9}{2}(4+\pi )\ cm^{2}$

Step 2

Find the perimeter of the figure

The perimeter of the figure is equal to

$P=AB+AC+length\ CB$

we have

$AB=6\ cm$

Applying Pythagoras theorem

$AC=\sqrt{6^{2}+6^{2}}\\AC=6\sqrt{2}\ cm$

Remember that

the circumference of a semicircle is equal to

$C=\frac{1}{2}2\pi r=\pi r$

$r=6/2=3\ cm$

$C=\pi(3)$

$C=3 \pi\ cm$

The perimeter of the figure is equal to

$P=6\ cm+6\sqrt{2}\ cm+3 \pi\ cm$

Simplify

$P=3(2+2\sqrt{2}+ \pi)\ cm$

5 0

3 years ago

A truck that can carry no more than 6900 lb is being used to transport refrigerators and upright pianos. Each refrigerator weigh

Sloan [31]

Well, first, you need to add up the amount of ten fridges and ten pianos. than you see if its heavier or lighter... > or <....... do you remember how to graph?

8 0

3 years ago

Mark deposited $450, $312, $125, and $432 in his bank account this

IgorLugansk [536]

By knowing how much Mark deposits, how much he deducts and what is his initial balance, we can know what the final balance is.

We will see that the balance at the end of the month is $2224.

We know that:

Mark deposited:

$450, $312, $125, and $432.

The total deposit is: $450 + $312 + $125 + $432 = $1319

The deductions are:

$205 and $123

The total deductions are: $205 + $123 = $328

The initial balance is $1233.

The final balance will be equal to the initial balance plus what Mark deposits minus what Mark deducts, this is:

Final balance = $1233 + $1319 - $328 = $2224

We can conclude that the balance at the end of the month is $2224

If you want to learn more, you can read:

brainly.com/question/19245500

8 0

3 years ago

HELP PRETTY PRETTY PLEASE!!!!!!!!!!!!!!!!!

klio [65]

Simplify the answer so its ( x+1 over (x-2)(x-4) ) where the answer should be D all real numbers except 2 and 4.
hope it helped !!

4 0

3 years ago

Read 2 more answers

Find two consecutive whole numbers that 137 lies between

kondor19780726 [428]

Consecutive means right behind each other basically.

1,2,3,4,5 are consecutive numbers because they are in order.

the numbers got 135, 136, 137, 138, 139, 140

137 lies between 136 and 138.

136 and 138 is your answer

7 0

3 years ago