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Mathematics

1 answer:

VARVARA [1.3K]3 years ago

7 0

Answer:

Here is the answer to your question it is in this picture

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a bottle of juice holds 3/8 gallon when it is full. if 1/3 of the juice has been poured out, how much juice is left in the bottl

taurus [48]

Let's get the denominators of both fractions to be the same before moving on, aka finding the least common multiple of the denominators.

8 and 3 have a LCM of 24. So, we have to multiply 1/3 by 8 and 3/8 by 3.

1/3 * 8/8 = 8/24

3/8 * 3/3 = 9/24

There is only 1/24 of juice left in the bottle if the remaining amount of juice has 1/3 poured out.

Hope that helped.

4 0

3 years ago

Ages of sylvans daughters are consecutive even integers. The sum of their ages is 60. Write an equation representing and find ag

notka56 [123]

Consecutive even integers are 2 apart
they are
x,x+2,x+4
total sum is 60
x+x+2+x+4=60
3x+6=60
minus 6 both sides
3x=54
divide both sides by 3
x=18
x+2=20
x+4=22

the ages are
18,20,22

3 0

3 years ago

AABC has vertices at A(1, -9), B(8,0), and C(9,-8).

Rainbow [258]

Check the picture below.

$~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{-9})\qquad B(\stackrel{x_2}{8}~,~\stackrel{y_2}{0}) ~\hfill AB=\sqrt{[ 8- 1]^2 + [ 0- (-9)]^2} \\\\\\ AB=\sqrt{7^2+(0+9)^2}\implies AB=\sqrt{7^2+9^2}\implies \boxed{AB=\sqrt{130}} \\\\[-0.35em] ~\dotfill$

$B(\stackrel{x_1}{8}~,~\stackrel{y_1}{0})\qquad C(\stackrel{x_2}{9}~,~\stackrel{y_2}{-8}) ~\hfill BC=\sqrt{[ 9- 8]^2 + [ -8- 0]^2} \\\\\\ BC=\sqrt{1^2+(-8)^2}\implies \boxed{BC=\sqrt{65}}$