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3 years ago

Find the square: (5x - 4y)2 (and please put the process of solving the equation)

1 answer:

7 0

$(5x-4y)^2$
$(5x-4y)(5x-4y)$

Multiply each term in one bracket in turn by the terms in the other bracket

$(5x)(5x) = 25x^2$
$(5x)(-4y)=-20xy$
$(-4y)(5x)=-20xy$
$(-4y)(-4y)=16y^2$

Put them together we have
$25x^2-20xy-20xy-16y^2$
$25x^2-40xy-16y^2$

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35 POINTS AVAILABLE

aliina [53]

Answer:

Part 1) The length of each side of square AQUA is $3.54\ cm$

Part 2) The area of the shaded region is $(486\pi-648)\ units^{2}$

Step-by-step explanation:

Part 1)

step 1

Find the radius of the circle S

The area of the circle is equal to

$A=\pi r^{2}$

we have

$A=25\pi\ cm^{2}$

substitute in the formula and solve for r

$25\pi=\pi r^{2}$

simplify

$25=r^{2}$

$r=5\ cm$

step 2

Find the length of each side of square SQUA

In the square SQUA

we have that

SQ=QU=UA=AS

$SU=r=5\ cm$

Let

x------> the length side of the square

Applying the Pythagoras Theorem

$5^{2}=x^{2} +x^{2}$

$5^{2}=2x^{2}$

$x^{2}=\frac{25}{2}\\ \\x=\sqrt{\frac{25}{2}}\ cm\\ \\ x=3.54\ cm$

Part 2) we know that

The area of the shaded region is equal to the area of the larger circle minus the area of the square plus the area of the smaller circle

Find the area of the larger circle

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=AB=18\ units$

substitute in the formula

$A=\pi (18)^{2}=324\pi\ units^{2}$

step 2

Find the length of each side of square BCDE

we have that

$AB=18\ units$

The diagonal DB is equal to

$DB=(2)18=36\ units$

Let

x------> the length side of the square BCDE

Applying the Pythagoras Theorem

$36^{2}=x^{2} +x^{2}$

$1,296=2x^{2}$

$648=x^{2}$

$x=\sqrt{648}\ units$

step 3

Find the area of the square BCDE

The area of the square is

$A=(\sqrt{648})^{2}=648\ units^{2}$

step 4

Find the area of the smaller circle

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=(\sqrt{648})/2\ units$

substitute in the formula

$A=\pi ((\sqrt{648})/2)^{2}=162\pi\ units^{2}$

step 5

Find the area of the shaded region

$324\pi\ units^{2}-648\ units^{2}+162\pi\ units^{2}=(486\pi-648)\ units^{2}$

7 0

3 years ago

4 is the square root of which number ?

Tom [10]

Your answer would be two

6 0

3 years ago

Three people invest at a ratio of 1:4:7. If the partnership is worth $636,000, what did each person invest?

olga_2 [115]

Answer:

See the detailed answers below

Step-by-step explanation:

Given data

Ratio= 1:4:7

combined ratio= 1+4+7= 12

Total amount= $636,000

Apply the part to all method

The first person will take

1/12= x/ 636,000

cross multiply

12x= 636,000*1

x= 636,000/12

x= 53000

The second person will take

4/12= x/ 636,000

cross multiply

12x= 636,000*4

x= 2544000/12

x= 212000

The third person will take

7/12= x/ 636,000

cross multiply

12x= 636,000*7

x= 4452000/12

x= 371000

6 0

3 years ago

Using capital letters and no periods or spaces, type the abbreviation for the congruence postulate.

jek_recluse [69]

HL is the answer got it from answer key

6 0

3 years ago

Read 2 more answers

Compute each sum below. If applicable, write your answer as a fraction.

Alex777 [14]

Answer:

First equation is -425

Second equation is 11.25

Step-by-step explanation:

First equation we can write as

$\sum_{i=0}^7 5 \times (-2)^i$

computing

When i=0 -> $5 \times (-2)^0 =5$

When i=1 -> $5 \times (-2)^1 = -10$

...

When i=7 -> $5 \times (-2)^7 = --640$

then replacing each term we have

$5 + (-10) + ( 20) + ( -40) + (80) +( -160) + 320 + (-640) = -425$

For the second equation we'll have 9 terms, solving in a similar fashion

When i=1 -> $\frac{1}{4}1=0.25$

When i=2 -> $\frac{1}{4}2=0.50$

When i=3 -> $\frac{1}{4}3=0.75$

...

When i=9 -> $\frac{1}{4}9=2.25$

So we have 0.25 + 0.50 + 0.75 + 1.00 + 1.25 + 1.50+ 1.75 +2.00 +2.25

4 0

3 years ago