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2 years ago

Simplify -3/4(5p-12)+2(8-1/4p)

Mathematics

1 answer:

PSYCHO15rus [73]2 years ago

8 0

Answer:

-17p-100/4

Step-by-step explanation:

-17p-100/4

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In the figure, the ratio of the perimeter of rectangle ABDE to the perimeter of triangle BCD is . The area of polygon ABCDE is s

Gekata [30.6K]

Step 1

Find the perimeter of rectangle ABDE

we know that

the perimeter of rectangle is equal to

$P=2b+2h$

In this problem

$b=ED=2\ units$

$h=AE=6\ units$

substitute

$P=2*2+2*6=16\ units$

Step 2

Find the perimeter of triangle BCD

we know that

the perimeter of triangle is equal to

$P=BD+DC+BC$

In this problem we have

$BD=AE=6\ units$

$DC=BC$

Applying the Pythagoras theorem

$DC^{2}=4^{2}+3^{2}$

$DC^{2}=25$

$DC=5\ units$

substitute

$P=6+5+5=16\ units$

Find the ratio of the perimeter of rectangle ABDE to the perimeter of triangle BCD

we have

the perimeter of rectangle is equal to

$P=16\ units$

the perimeter of the triangle is

$P=16\ units$

the ratio is equal to

$\frac{16}{16} =1$

therefore

<u>the answer Part 1) is the option B</u>

$1$

Step 3

Find the area of polygon ABCDE

we know that

The area of polygon is equal to the sum of the area of rectangle plus the area of triangle

Area of rectangle is equal to

$A=AE*BD=6*2=12\ units^{2}$

Area of the triangle is equal to

$A=\frac{1}{2}AEh$

the height h of the triangle is equal to $4\ units$

substitute

$A=\frac{1}{2}(6)(4)=12\ units^{2}$

The area of polygon is

$12\ units^{2}+12\ units^{2}=24\ units^{2}$

therefore

<u>the answer part 2) is the option C</u>

$24\ units^{2}$

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2 years ago

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A group of 5 friends decides to share the cost of a party together. If the party costs $1,100, how much does each friend pay?

seraphim [82]

Answer:

1,100 dollars divided by 5 friends is 220 dollars so each friend would have to pay 220 dollars

Step-by-step explanation:

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1 year ago

Sheila places a 54 square inch photo behind a 12-inch-by-12-inch piece of matting.

nata0808 [166]

The are of a rectangle is calculated by multiplying the length and the width of the shape. First, we determine the dimensions of this figure. We do as follows:

Width = 12 - 2x - 2x = 12 - 4x
Length = 12 - x - x = 12 - 2x

Area = (Length)(Width)
Area = (12 - 2x )(12-2x)

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2 years ago

Determine the slope of the line 3x − 5y − 6 = 0

ivolga24 [154]

Answer:

slope 3/5

Step-by-step explanation:

3x − 5y − 6 = 0

To find the slope, we want to solve for y

(y = mx+b slope intercept form of the equation(

Add 5y to each side

3x − 5y+5y − 6 = 0+5y

3x-6 = 5y

Divide by 5

3/5x -6/5 = 5y/5

3/5 x -6/5 = y

The slope is 3/5 and the y intercept is -6/5

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he data set gives the number of hours it took each of the 10 students in a cooking class to master a particular technique. {5, 3

sergeinik [125]

The best measure of center tendency for this set of data would be the median. It is the best measurement because the data set has an outlier. The outlier is the 30. So to find the median we first order the data set and then find out if the set is an even or odd set. This set is even so we just chose the middle number. If the set was even, we would add the two center number and divide them by 2.

3, 3, 4, 4, 4, 5, 5, 5, 30

The center tendency = 4

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