Determine whether each statement about the design from the rug is true.

Which expression is equivalent to r to the 9th over r to the 3rd

alisha [4.7K]

Answer:

$r^{6}$

Step-by-step explanation:

To make this a bit easier to see, we'll expand that expression.

R to the 9th is just r times itself 9 times. R to the third is r times itself 3 times.

(excuse my bad formatting)

The expression:

r • r • r • r • r • r • r • r • r • 1

r • r • r • 1

Remember, anything and everything has a coefficient or denominator of 1.

So, we can cancel 3 r's from the numerator and denominator.

r • r • r • r • r • r • 1

1

Simplify....

$\frac{1r^{6}}{1}$

That just equals $r^{6}$ .

3 0

3 years ago

50 POINTS!!! In rectangle ABCD, AB = 6 cm, BC = 8 cm, and DE = DF. The area of triangle DEF is one-fourth the area of rectangle

aalyn [17]

Answer:

$EF=4\sqrt{3}$

Step-by-step explanation:

In rectangle ABCD, AB = 6, BC = 8, and DE = DF.

ΔDEF is one-fourth the area of rectangle ABCD.

We want to determine the length of EF.

First, we can find the area of the rectangle. Since the length AB and width BC measures 6 by 8, the area of the rectangle is:

$A_{\text{rect}}=8(6)=48\text{ cm}^2$

The area of the triangle is 1/4 of this. Therefore:

$\displaystyle A_{\text{tri}}=\frac{1}{4}(48)=12\text{ cm}^2$

The area of a triangle is half of its base times its height. The base and height of the triangle is DE and DF. Therefore:

$\displaystyle 12=\frac{1}{2}(DE)(DF)$

Since DE = DF:

$24=DF^2$

Thus:

$DF=\sqrt{24}=\sqrt{4\cdot 6}=2\sqrt{6}=DE$

Since ABCD is a rectangle, ∠D is a right angle. Then by the Pythagorean Theorem:

$(DE)^2+(DF)^2=(EF)^2$

Therefore:

$(2\sqrt6)^2+(2\sqrt6)^2=EF^2$

Square:

$24+24=EF^2$

Add:

$EF^2=48$

And finally, we can take the square root of both sides:

$EF=\sqrt{48}=\sqrt{16\cdot 3}=4\sqrt{3}$

6 0

3 years ago

Read 2 more answers

When Akiko measured a rose, its height was 5.8 in. After 10 weeks, the height was 1 1/3 times the original height. What was the

kramer

The solution is in the attachment

8 0

3 years ago

A brace for a shelf has the shape of a right triangle. Its hypotenuse is 16 inches long and the two legs are equal in length. Ho

Flura [38]

Using pythag a^2+b^2=16^2
16^2=256
and since a=b the equation is 2x^2=256
/ each side by 2
x^2=128
x=sq rt of 128=11.31 roughly

8 0

3 years ago

The lassos high school senior class raised funds for an end of the year cruise getaway. The city gave them a special package for

kirill115 [55]

Answer:

Step-by-step explanation:

x = total number of students

1500 + 367x = 16,600

367x = 16,600 - 1500

367x = 15100

x = 15100 / 367

x = 41.14.......rounds to 41 students <==

this only works if the port fees and taxes that the city gave them are included in the money the class raised

5 0

3 years ago