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3 years ago

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A man drove 14 mi directly east from his home, made a left turn at an intersection, and then traveled 5 mi north to his place of

work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?

1 answer:

Stels [109]3 years ago

4 0

Answer:

14.9 miles

Step-by-step explanation:

If the road was created, the 3 different roads would form a right triangle where the new road would be the hypotenuse and the other 2 roads would be the legs.

We can use the pythagorean theorem to find the length of the hypotenuse, or the new road:

a² + b² = c²

14² + 5² = c²

221 = c²

14.9 = c

= 14.9 miles

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$\huge \boxed{\mathfrak{Question} \downarrow}$

Solve the following using Substitution method

2x – 5y = -13

3x + 4y = 15

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$\left. \begin{array} { l } { 2 x - 5 y = - 13 } \\ { 3 x + 4 y = 15 } \end{array} \right.$

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

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Choose one of the equations and solve it for x by isolating x on the left-hand side of the equal sign. I'm choosing the 1st equation for now.

$2x-5y=-13$

Add 5y to both sides of the equation.

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$x=\frac{5}{2}y-\frac{13}{2} \\$

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$\frac{15}{2}y-\frac{39}{2}+4y=15 \\$

Add $\frac{15y}{2} \\$ to 4y.

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Divide both sides of the equation by 23/2, which is the same as multiplying both sides by the reciprocal of the fraction.

$\large \underline{ \underline{ \sf \: y=3 }}$

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Multiply 5/2 times 3.

$x=\frac{15-13}{2} \\$

Add $-\frac{13}{2}\\$ to $\frac{15}{2}\\$ by finding a common denominator and adding the numerators. Then reduce the fraction to its lowest terms if possible.

$\large\underline{ \underline{ \sf \: x=1 }}$

The system is now solved. The value of x & y will be 1 & 3 respectively.

$\huge\boxed{ \boxed{\bf \: x=1, \: y=3 }}$

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