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3 years ago

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The diagonals of rectangle nopq intersect at point r. if oq=2(x+3) and pr=3x-5, solve for x.

2 answers:

OverLord2011 [107]3 years ago

8 0

The diagonals of a rectangle are always congruent. We have the whole length of OQ to be 2x + 6, and we have only half of NP. Therefore, OQ = 2(PR). 2x+6=2(3x-5). 2x+6 = 6x-10. 16 = 4x so x = 4. That means that each diagonal is 14 units long.

tatuchka [14]3 years ago

4 0

Answer:

$x=4$

Step-by-step explanation:

Please find the attachment.

We have been given that the diagonals of rectangle nopq intersect at point r.

We know that diagonals of rectangle are always congruent. Line segment oq is diagonal of our given rectangle.

We also know that diagonals of parallelogram bisect each other, so length of diagonal np will be two times pr.

$np=2\times pr$

$np=2(3x-5)$

Now, we will equate np with oq to solve for x as:

$2(3x-5)=2(x+3$

$6x-10=2x+6$

$6x-10+10=2x+6+10$

$6x=2x+16$

$6x-2x=2x-2x+16$

$4x=16$

$\frac{4x}{4}=\frac{16}{4}$

$x=4$

Therefore, the value of x is 4.

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Solving equations with variables on both sides <br><br><br> 7+9x=6x-2

katrin2010 [14]

Answer:

Here

Step-by-step explanation:

We move all terms to the left:

7+9x-(6x-2)=0

We get rid of parentheses

9x-6x+2+7=0

We add all the numbers together, and all the variables

3x+9=0

We move all terms containing x to the left, all other terms to the right

3x=-9

x=-9/3

x=-3

3 0

2 years ago

Read 2 more answers

K=am+3mx solve for m

Otrada [13]

Assuming the variables are constants, you isolate m. So move am to the left. K-am=emx. Now divide ex. This gives you, m=(K-am/ex)

7 0

3 years ago

Use the distributive property to simplify each expression<br> (2b - 10) 3.2

Darya [45]

Answer: 6.4b - 32

Step-by-step explanation:

4 0

3 years ago

max2010maxim [7]

Hello!

So, this is quite the complex question, and here are the following steps:

What is the quotient of $\frac{6-3\sqrt[3]{6}}{\sqrt[3]{9}}$ ?

$\frac{(6 - 3\sqrt[3]{6})\sqrt[3]{9^{2}}}{9}$ (rationalize the denominator)

$\frac{3(2 -\sqrt[3]{6})\sqrt[3]{9^{2}}}{9}$ (factor 3 from the expression)

$\frac{(2-\sqrt[3]{6})\sqrt[3]{9^{2}}}{3}$ (reduce the fraction with 3)

$\frac{2\sqrt[3]{9^{2}}-\sqrt[3]{9^{2}}}{3}$ (distributive property)

$\frac{2\sqrt[3]{81}-\sqrt[3]{486}}{3}$ (simplify 3 · 9²)

$\frac{6\sqrt[3]{3}-3\sqrt[3]{18}}{3}$ (simplify the radical)

$\frac{3(2\sqrt[3]{3}-3\sqrt[3]{18})}{3}$ (factor 3 from the expression)

$2\sqrt[3]{3}-\sqrt[3]{18}$ (reduce the fraction)

The answer, is simply, choice A, $2\sqrt[3]{3} -\sqrt[3]{18}$ ≈ 0.263758.

5 0

3 years ago

Point G is the midpoint of PQ. <br> PG equals 2X plus 3 and GQ equals 5X -5. what is X?

borishaifa [10]

Answer:

$x=\frac{8}{3}=2\frac{2}{3}\approx{2.667}$

Step-by-step explanation:

$\overline{PG}=2x+3\\\overline{GQ}=5x-5$

Since they're equidistant (equal distances), we can set them equal to one another and solve for x:

$2x+3=5x-5$

Adding 5 to both sides:

$2x+8=5x$

Subtracting 2x from both sides:

$8=3x$

Dividing both sides by 3:

$\frac{8}{3}=x$

Therefore:

$x=\frac{8}{3}=2\frac{2}{3}\approx{2.667}$

6 0

3 years ago