All categories

1 year ago

in rectangle ABCD, BD and AC are diagonals and intersect at E. If BD = 84 units and AE = 6y, what is the value of y

Mathematics

1 answer:

goldfiish [28.3K]1 year ago

3 0

Answer:

y = 7

Step-by-step explanation:

The diagonals of a rectangle are congruent and bisect each other, then

AC = BD , that is

AE + EC = BD [ AE = EC = 6y ]

6y + 6y = 84

12y = 84 ( divide both sides by 12 )

y = 7

You might be interested in

getting home from trick or treat celia and emma counted their candies. half of celias candies is equal to 2/3 of emmas candies.

blagie [28]

Candies with celias and emmas is 60 and 45 respectively.

<u>Solution:</u>

Given, Getting home from trick or treat celia and emma counted their candies. Half of celias candies is equal to 2/3 of emmas candies.

They had a total of 105 candies altogether.

We have to find how many candies did each of them have.

Let the number of candies with celias be n, then number of candies with emma will be 105 – n.

Now according to given condition.

$\begin{array}{l}{\frac{1}{2} \times \text { celias candies count }=\frac{2}{3} \times \text { emmas candies count }} \\\\ {\rightarrow \frac{1}{2} \times n=\frac{2}{3} \times(105-n)} \\\\ {\rightarrow 3 \times n=2 \times 2 \times(105-n)} \\\\ {\rightarrow 3 \times n=2 \times 2 \times(105-n)} \\\\ {\rightarrow 3 n=4(105-n)} \\\\ {\quad \rightarrow 3 n=420-4 n} \\\\ {\rightarrow 3 n=420-4 n} \\\\ {\rightarrow 3 n+4 n=420} \\\\ {\rightarrow 7 n=7 \times 60} \\\\ {\rightarrow n=60}\end{array}$

Hence, candies with celias and emmas is 60 and 45 respectively.

4 0

3 years ago

Marcus has a square shaped garden that has an area of 4(x^2-y^2) square feet. If the garden has four equal sections, what is the

SpyIntel [72]

Answer:

x^2-y^2

Step-by-step explanation:

took a quiz and got it right

8 0

2 years ago

The difference between two numbers is 7. The sum of twice the larger number and three times the smaller number is 19.

Alex17521 [72]

Answer:

x= 8 y= 1

Step-by-step explanation:

First, you identify your variables:

x= larger number

y= smaller number

Second, you find your equations:

x - y = 7

2x + 3y = 19

Third, (I used the substitution method) you make "y" by itself for the 1st equation.

y = x - 7

2x + 3y = 19

Then, you plug in the 1st equation for "y" in the 2nd equation

2x + 3(x - 7) = 19

Then, you distribute and simplify.

2x + 3x - 21 = 19

5x - 21 = 19

5x = 40

x = 8

Finally, you plug in the variable you found ( x ) into one of the equations and solve,

8 - y = 7

- y = -1

y = 1

6 0

2 years ago

What is the quotient <br> 13632 divided by 48

Brilliant_brown [7]

Answer:

284 is the answer

7 0

2 years ago

Is the measure of Z1 equal to the measure of Z2?<br> Why?

VMariaS [17]

Answer:

Angles with the same measure are congruent, so Z1 = Z2.

Step-by-step explanation:

5 0

3 years ago