Solve the system of equations -2x-3y=48 and -x+2y=-11 by combining the equations to find x and y ( , )

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)

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

$25=r^{2}$

$r=5\ cm$

<em>step 2</em>

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

<em>Find the area of the larger circle</em>

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

How do I solve this?

Artemon [7]

a^2 - b^2 = (a + b)(a - b)

In this case

49x^4y^2 - 4z^2

= (7x^2y)^2 - (2z)^2

= (7x^2y + 2z)(7x^2y - 2z)

Factors are (7x^2y + 2z) and (7x^2y - 2z)

Answer:

D) 7x^2y + 2z

8 0

2 years ago

If a cat with short brown hair (llBb) is crossed with a cat with long black hair (Llbb), what is the likelihood that there will

Advocard [28]

Bb = brown hair phenotype

bb = black hair phenotype

we see that B = brown hair is the dominant gene while b = black hair is the recessive gene

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ll = short hair, this is a lowercase L

Ll = long hair

In this case, l = short hair is the recessive gene while L = long hair is the dominant gene.

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Check out the diagram below to see the dihybrid crosses for each of the hair color and hair length genotypes. From there, I show all of the genotypes possible for any offspring. Those genotypes are

LlBb = long brown hair (comes up 4 times)
Llbb = long black hair (comes up 4 times)
llBb = short brown hair (comes up 4 times)
llbb = short black hair (comes up 4 times)

-----------------------------------

If we are talking about 1 offspring, then it is not possible for him/her to have both "long black hair AND short brown hair" as the instructions state. So let's consider two offspring instead.

The probability of having long black hair is 4/16 = 1/4 as there are 4 cases of Llbb out of 16 cases total. Similarly, the probability of getting llBb is 4/16 = 1/4 as well, for pretty much the same reasons.

The probability of having both events occur is (1/4)*(1/4) = 1/16

The multiplication of probabilities is valid because the two events are independent.

==============================================

<h3>Final Answer: A) 1/16</h3>

5 0

2 years ago

Three wooden cube blocks each have a side length of 6cm. What is the combined volume of the three wooden blocks in cm?

aleksklad [387]

Answer:

c

Step-by-step explanation:

what you do is you find how many sides there are witch is 6 and multiply that by 6 witch would equal 36 now all you do is multiply 3x36 witch equals 108cm square

4 0

2 years ago

Read 2 more answers

How many inches are in three fourths of a yard

guapka [62]

The answer is 27 inches. I am 90% sure of it. It is 27 because a yard has 36 inches. So you do the rule of three. 36/4*3. 36/4 is 9. 9*3=27. I hope you pass your test! :D

3 0

3 years ago