Answer :
Sure, let's solve the problems step-by-step.
1. Finding the value of [tex]$y$[/tex]:
We have the equation:
[tex]\[
\frac{5}{6} = \frac{y}{72}
\][/tex]
To solve for [tex]$y$[/tex], we can use cross-multiplication. This means we multiply the numerator of one fraction by the denominator of the other fraction. So, we get:
[tex]\[
5 \times 72 = 6 \times y
\][/tex]
Calculating the left side:
[tex]\[
5 \times 72 = 360
\][/tex]
Now we have:
[tex]\[
360 = 6 \times y
\][/tex]
To solve for [tex]$y$[/tex], divide both sides by 6:
[tex]\[
y = \frac{360}{6}
\][/tex]
So, the value of [tex]$y$[/tex] is 60.
2. Finding the value of [tex]$x + x_5$[/tex]:
We start with the equation:
[tex]\[
x + x_5 = \frac{32}{40}
\][/tex]
First, simplify the fraction [tex]$\frac{32}{40}$[/tex]. We do this by finding the greatest common divisor (GCD) of 32 and 40, which is 8. So, divide both the numerator and the denominator by 8:
[tex]\[
\frac{32}{40} = \frac{32 \div 8}{40 \div 8} = \frac{4}{5}
\][/tex]
Now, convert the fraction to a decimal to find that [tex]$x + x_5 = 0.8$[/tex].
In conclusion, the value of [tex]$y$[/tex] is 60, and the value of [tex]$x + x_5$[/tex] is 0.8.
1. Finding the value of [tex]$y$[/tex]:
We have the equation:
[tex]\[
\frac{5}{6} = \frac{y}{72}
\][/tex]
To solve for [tex]$y$[/tex], we can use cross-multiplication. This means we multiply the numerator of one fraction by the denominator of the other fraction. So, we get:
[tex]\[
5 \times 72 = 6 \times y
\][/tex]
Calculating the left side:
[tex]\[
5 \times 72 = 360
\][/tex]
Now we have:
[tex]\[
360 = 6 \times y
\][/tex]
To solve for [tex]$y$[/tex], divide both sides by 6:
[tex]\[
y = \frac{360}{6}
\][/tex]
So, the value of [tex]$y$[/tex] is 60.
2. Finding the value of [tex]$x + x_5$[/tex]:
We start with the equation:
[tex]\[
x + x_5 = \frac{32}{40}
\][/tex]
First, simplify the fraction [tex]$\frac{32}{40}$[/tex]. We do this by finding the greatest common divisor (GCD) of 32 and 40, which is 8. So, divide both the numerator and the denominator by 8:
[tex]\[
\frac{32}{40} = \frac{32 \div 8}{40 \div 8} = \frac{4}{5}
\][/tex]
Now, convert the fraction to a decimal to find that [tex]$x + x_5 = 0.8$[/tex].
In conclusion, the value of [tex]$y$[/tex] is 60, and the value of [tex]$x + x_5$[/tex] is 0.8.
