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3 years ago

Find the value of x and y in the following figure where ABCD is a parallelogram

Mathematics

1 answer:

asambeis [7]3 years ago

5 0

Answer:

x = 3

y = 2

Step-by-step explanation:

Diagonals of a parallelogram bisect each other into two equal segments. Therefore:

3x - 1 = 2(x + 1)

Solve for x

3x - 1 = 2x + 2

Collect like terms

3x - 2x = 1 + 2

x = 3

Also:

5y + 1 = 6y - 1

Collect like terms

5y - 6y = -1 - 1

-y = -2

Divide both sides by -1

y = -2/-1

y = 2

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A pool has a depth of 12 feet and a width of 14 feet.If it holds 1680 cubic feet of water, what is the length of the pool?

Novay_Z [31]

12 x 14 x L = 1680

168 x L = 1680

L = 1680 / 168

L = 10 feet

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2 years ago

A building casts a shadow that is 36 feet long. At the same time of day, a nearby 9-foot tall tree casts a shadow that is 4 feet

ANTONII [103]

Answer:

16 feet is the correct answer to this problem.

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2 years ago

eXCUSE ME!!! I NEED HELP PRONTO!! BRAINLIEST PLS! in a fraction the denominator is 4 less than the numerator. If 3 is added to b

avanturin [10]

7/5 = 14/10 = 28/20

Numerator = x

Denominator = x-4

Add 3 to both:

x +3 / (x-4+3)

x+3 = 14

(x-4 +3) = 10 = x-1 = 10

x = 11

Check:

11 -4 = 7 ( denominator is 4 less than the numerator.)

add 3 to both:

11+3 = 14

7+3 = 10

14/10 reduces to 7/5

The original fraction would be 11/7

8 0

3 years ago

A spice store charges $2.75 for 25 grams of paprika. It also charges 5% of the purchase price for shipping any order

zlopas [31]

Answer:

Part a) The expression is $3.2445x$

Part b) Customer cannot buy 2.5 ounces of paprika and have it shipped for less than $8.00

Step-by-step explanation:

<u><em>The complete question is</em></u>

A spice store charged 2.75 for 25 grams of paprika. It also charges 5% of the purchase price for shipping any order.

Part a) Write and simplify an expression to determine the cost of buying and shipping x ounces of paprika. Use 1 ounce = 28 grams

Part b) Can a customer buy 2.5 ounces of paprika and have it shipped for less than 8.00? Explain

step 1

Convert grams to ounces

Remember that

$1\ oz=28\ g$

To convert grams to ounces divide by 28

$25\ g=25/28= 0.89\ oz$

The unit price is

$2.75/0.89=3.09\frac{\$}{oz}$

Let

x ----> the number of ounces of paprika

y ----> the cost of buying and shipping x ounces of paprika

5%=5/100=0.05

$y=3.09x+(3.09x)0.05\\y=3.09x[1+0.05]\\y=3.2445x$

Part b) For x=2.5 oz

substitute in the equation

$y=3.2445(2.5)=\$8.11$

$\$8.11 > \$8.00$

therefore

Customer cannot buy 2.5 ounces of paprika and have it shipped for less than $8.00

3 0

2 years ago

The volume of the rectangular prism is 648 feet. The rectangular base is 6 feet by 9 feet. What is the height of the prism?

IrinaK [193]

Answer:

$h=12ft$

Step-by-step explanation:

The formula one would use for finding the volume of a rectangular prism is as follows:

Volume = length × width × height , $V=l*w*h$

With this in mind, let's plug in the given variables in the question for this formula.

$V=648ft^3$

$l=6ft$

$w=9ft$

$h=$ ?

We don't know the height, but that's just fine. We will plug in all our values and isolate $h$ .

$V=lwh\\648ft^3=(6ft)(9ft)h$

I'm leaving in units just because I want to show that units aren't just for show. They can be used when in doubt of how to go about your math.

$648ft^3=(6ft)(9ft)h\\648ft^3=(54ft^2)h\\\frac{648ft^3}{54ft^2}=\frac{(54ft^2)h}{54ft^2}$

Notice, that the units on the left side cancel out, leaving only the unit $ft$ left next to the solution. In the same way, the units on the right side cancel out too, leaving only $h$ , height.

$\frac{648ft^3}{54ft^2}=\frac{(54ft^2)h}{54ft^2}\\12ft=h$

If involving units only confuses you, like it does for me, you can remove them like so, you just need to know what units your solution uses instead of being able to come to the proper units by using math.

$V=lwh\\648=(6)(9)h\\648=54h\\\frac{648}{54}=\frac{54h}{54}\\12ft=h$

5 0

3 years ago

Find the value of x and y in the following figure where ABCD is a parallelogram​

Find the value of x and y in the following figure where ABCD is a parallelogram