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2 years ago

Teresa drove 936 miles in 13 hours. At the same rate, how many miles would she drive in 9 hours?

Mathematics

1 answer:

Drupady [299]2 years ago

6 0

$\dfrac{936\text{ mi}}{13\text{ hr}}=\dfrac{x\text{ mi}}{9\text{ hr}}$
$\implies x=\dfrac{936\times9}{13}=648$

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Find the value of x using angle properties & the measure of

Jobisdone [24]

Answer:

15.

$x = 20$

16.

$\angle BFH$ = $100\textdegree$

$\angle CBD$ = $100\textdegree$ (if needed)

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17.

$x = 7$

18.

$\angle BFH$ = $68\textdegree$

Step-by-step explanation:

15. The two following angles, which is $\angle CBD$ and $\angle BFH$ , are Corresponding Angles. Write an expression by using the following measurements from $\angle CBD$ and $\angle BFH$ . Then, solve the expression for the value of $x$ :

$\angle CBD$ = $5x$

$\angle BFH$ = $3x + 40$

$5x = 3x + 40$

Solve for $x$ :

$5x = 3x + 40$

$5x - 3x = 3x - 3x + 40$

$2x = 40$

$\frac{2x}{2} = \frac{40}{2}$

$x = 20$

16. After you have the value $x$ use it to find the actual measurements of both $\angle CBD$ and $\angle BFH$ , by applying $x$ to the following expressions from both $\angle CBD$ and $\angle BFH$ and solve them:

-The value of $x$ :

$x = 20$

-Solve for $\angle CBD$ :

$\angle CBD$ = $5x$

$5(20)$

$100$

-The actual measurement of $\angle CBD$ :

$\angle CBD$ = $100\textdegree$

-Solve for $\angle BFH$ :

$\angle BFH = 3x + 40$

$3(20) + 40$

$60 + 40$

$100$

-The actual measurement of $\angle BFH$ : (if needed)

$\angle BFH$ = $100\textdegree$

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17. The two following angles, which is $\angle BFE$ and $\angle DBF$ are Alternate Interior Angles .Write an expression by using the following measurements from $\angle BFE$ and $\angle DBF$ . Then, solve the expression for the value of $x$ :

$\angle BFE$ = $16x$

$\angle DBF$ = $4x + 84$

$16x = 4x + 84$

-Solve for $x$ :

$16x = 4x + 84$

$16x - 4x = 4x - 4x + 84$

$12x = 84$

$\frac{12x}{12} = \frac{84}{12}$

$x = 7$

18. After you have the value $x$ use it to find the actual measurement of $\angle DBF$ , by applying $x$ to the expression from $\angle DBF$ and solve it and find the actual measurement of an angle that is not labeled, which is $\angle BFH$ :

-The value of $x$ :

$x = 7$

Solve for $\angle DBF$ :

$\angle DBF$ = $4x + 84$

$4(7) + 84$

$28 + 84$

$112$

-The actual measurement of $\angle DBF$ :

$\angle DBF$ = $112\textdegree$

-Since both $\angle DBF$ and $\angle BFH$ are supplementary (two angles that equals to $180\textdegree$ ), and you want to find the actual measurement of $\angle BFH$ , Use the measurement of $\angle DBF$ and subtract it from $180\textdegree$ :