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3 years ago

The average of A and B is 6. The average of X, Y, and Z is 16. What is the average of A, B, X, Y, and Z?

Mathematics

1 answer:

ser-zykov [4K]3 years ago

4 0

Answer:

Step-by-step explanation:

Average of A and B is 6

(A+B) /2 = 6

Multiply each side by 2

A+B = 12

average of X, Y, and Z is 16

(X+Y+Z)/3 = 16

Multiply each side by 3

(X+Y+Z) = 48

To find the average of all of them

(A+B+X+Y+Z)/5

replace A+B with 12 and X+Y+Z with 48

(12+48)/5

60/5 = 12

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Explain how you know which method you should use to solve a rational equation.

notsponge [240]

<u>Methods to solve rational equation:</u>

Rational equation:

A rational equation is an equation containing at least one rational expression.

Method 1:

The method for solving rational equations is to rewrite the rational expressions in terms of a common denominator. Then, since we know the numerators are equal, we can solve for the variable.

For example,

$\frac{1}{2}=\frac{x}{2}\Rightarrow x=1$

This can be used for rational equations with polynomials too.

For example,

$\frac{1+x}{x-3}=\frac{4}{x-3}\Rightarrow(1+x)=4 \Rightarrow x=3$

When the terms in a rational equation have unlike denominators, solving the equation will be as follows

$\frac{x+2}{8}=\frac{3}{4}$

$\Rightarrow\frac{x+2}{1}=\frac{3\times8}{4}\Rightarrow{x+2}=2\times3$

$\Rightarrow{x+2}=6\Rightarrow x=6-2\Rightarrow x=4$

Method 2:

Another way of solving the above equation is by finding least common denominator (LCD)

$\frac{x+2}{8}=\frac{3}{4}$

Factors of 4: $1\times2\times2$

Factors of 8: $1\times2\times2\times2$

The LCD of 4 and 8 is 8. So, we have to make the right hand side denominator as 8. This is done by the following step,

$\Rightarrow\frac{x+2}{8}=\frac{3}{4}\times{2}{2}$

we get,

$\Rightarrow\frac{x+2}{8}=\frac{6}{8}$

On cancelling 8 on both sides we get,

$\Rightarrow(x+2)=6\rightarrow x=6-2\rightarrow x=4$

Hence, these are the ways to solve a rational equation.

7 0

3 years ago

Wo cyclists, 72 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as the other. If they m

Trava [24]

Answer:

the faster cyclist was going 18 mph

the slower cyclist was going 9 mph

Step-by-step explanation:

72 ÷ 4 = 18

18 ÷ 2 = 9

3 0

3 years ago

Read 2 more answers

What’s the answer to this equation <br> 3x+6t=?

GaryK [48]

are there any options

7 0

3 years ago

Which Two Numbers Add Up To Negative 26 And Multiply To 11?

Fynjy0 [20]

Xy=11
x+y=-26

x+y=-26
minus x both sides
y=-26-x

sub for y
x(-26-x)=11
-26x-x^2=11
add 26x+x^2 both sides
x^2+26x+11=0

ax^2+bx+c=0
x= $\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}$

a=1
b=26
c=11

x= $\frac{-26+/-\sqrt{26^{2}-4(1)(11)} }{2(1)}$
x= $\frac{-26+/-\sqrt{676-44} }{2}$
x= $\frac{-26+/-\sqrt{632} }{2}$
x= $\frac{-26+/-2\sqrt{158} }{2}$
x= $-13+/-\sqrt{158}$

x= $-13+\sqrt{158}$ or $-13-\sqrt{158}$

aprox

x=-0.420195 or -25.5698

those are the numbers

5 0

3 years ago

What is the solution to the system of equations?

melamori03 [73]

Answer:

it is b

Step-by-step explanation:

dam gurll, how many questions u gon' ask

3 0

3 years ago