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2 years ago

Solve the system of linear equations by substitution. 5x+2y=9 y-x= 8

Mathematics

2 answers:

mylen [45]2 years ago

6 0

From equation 2(y-x=8)
y=8+x.....name equation 3
Sub equation 3 in equation 1
5x+2(8+x)-9=0 (Transpose the 9)
5x+16+2x-9=0 (Group the like terms)
5x+2x+16-9
7x+7
x=7+7=14
x=14

Varvara68 [4.7K]2 years ago

5 0

Answer:

x=1

y=9

Step-by-step explanation:

5x+2y=9 , y-x= 8

y=8+x

put 8+ x anywhere we see y

5x+2(8+x)=9

5x+16+2x=9

5x+2x+16=9

7x+16=9

16-9=7x

7=7x

divide both sides by 7

x=1

if x=1, then y-1=8

y=8+1

y=9

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A sphere has a radius of 12 inches. A second sphere has a radius of 9 inches. What is the difference of the volumes of the spher

just olya [345]

Answer:

Solution given;

for sphere

radius [r]:12inches

another

radius [R]:9inches

Now

difference in volume of sphere:

volume of sphere of having radius [r-R]

= $\frac{4}{3} πr³$ - $\frac{4}{3} πR³$

= $\frac{4}{3} π$ (12³-9³)

= 1332π cubic inches

The volume of the larger sphere is <u>___1332</u>__π cubic inches greater than the volume of the smaller sphere.

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2 years ago

IRISSAK [1]

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6 0

3 years ago

Read 2 more answers

The volume of a box is 143.4 in3. find the volume of a larger, similarly shaped box that has a scale factor of 3. round your ans

just olya [345]

Answer:

1,290.6 in3

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2 years ago

An electrical pole is 12.4m tall. It is supported by a guy wire that is 17.3 long. how far is the anchor of the guy wire to the

kari74 [83]

The anchor of the guy wire is 12.06 meters away form base of electrical pole.

Further explanation:

The whole given scenario forms a right angle triangle. The pole is standing straight so it is the perpendicular while the guy wire goes from the top of pole to the anchor so it will be the hypotenuse. We have to finds the base.

Pythagoras theorem will be used.

Pythagoras theorem states that:

$H^2=B^2+P^2$

Given

Base=?

Perpendicular=12.4 m

Hypotenuse = 17.3 m

Putting the values

$(17.3)^2=B^2+(12.4)^2\\299.29=B^2+153.76\\B^2=299.29-153.76\\B^2=145.53\\Takeing\ Square\ root\ on \both\ sides\\\sqrt{B^2}=\sqrt{145.53}\\B=12.06\ m$

The anchor of the guy wire is 12.06 meters away form base of electrical pole.

Keywords: Pythagoras theorem, Hypotenuse

Learn more about Pythagoras theorem at:

#LearnwithBrainly

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3 years ago

Why can’t we use the rules for exponents when the bases are not common?

Kazeer [188]

Answer:

Ok, the rules of the exponent come from a logic construction.

If we have x^n

this means that n is multiplied by itself n times.

If we decompose n into a + b, we have:

x by itself a times, and then x by itself b times, and for how the product works, this is equivalent:

if n = 5, a= 2 and b = 3

x^5 = (x*x*x*x*x) 5 times-

x^5 = x^(2 + 3) = (x^2)*(x^3) = (x*x*)*(x*x*x) = x*x*x*x*x = x^5

And the same for the other rules:

(x^n)^b = x^n*b and such.

Obviusly, this only works when we have a common base.

So the correct answer is that we constructed the exponential rules in a way that only can be used when we have a common base, and this happens because to construct them, we started with common bases.

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3 years ago