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3 years ago

5^(11x+23)=125^(7x) how to solve for x

1 answer:

8 0

Answer: x= 23/10 or x= 2.3
First... 5^11x-23=5^21x
Cancel out the 5
Secondly... 11x+23 =21x
Switch 21 and 23 to make...
11x=21x-23. Switch again to make...
11x-21x=23
Now subtract 11 and 21
-10x=-23
Divide to get
x=23/10 or x=2.3

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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)

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

HELP MEEE OMGGGG JESSUS AMENNN

irina1246 [14]

Answer:

Answers in the pics

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ;)

8 0

3 years ago

Three students spent $12 on school lunch. At that rate, find the amount 10 students would spend on the same school lunch.

Naddika [18.5K]

12 divided by 3 is 4. the answer would be 40 as 4x10 is equal to 40

7 0

3 years ago

Read 2 more answers

In Exercises 8-10, sketch the figure described.

Lunna [17]

The sketch answers to question 8, 9 and 10 is given in the image attached.

<h3>What is an intersecting lines?</h3>

A link is known to be intersecting if two or more lines are said to have cross one another in a given plane.

Note that the intersecting lines are known to be one that often share a common point, and it is one that can be seen on all the intersecting lines, and it is known to be the point of intersection.

Looking at the image attached, you can see how plane A and line c intersecting at all points on line c and also GM and GH and line CD and plane X as they are not intersecting

Therefore, The sketch answers to question 8, 9 and 10 is given in the image attached.

Learn more about intersecting lines from

brainly.com/question/2065148

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6 0

1 year ago

Please help with this question!

Nostrana [21]

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a ) Two matrices cannot be multiplied.

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b )

The answer is | 20 - 4 - 12 |

| 8 2 19 - |

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7 0

3 years ago