Isaiah is jogging near his college. He runs south along Capitol Street for about 0.75 miles and east along H Street for about 1.2 miles. He then turns left and runs along Florida Avenue until he reaches his starting point. How long is his total run to the nearest hundredth of a mile?

A triangle. The sides are Capitol Street, H Street, and they hypotenuse is Florida Avenue.

2.89 miles
3.37 miles
3.67 miles
3.92 miles

Choose one option.

As shown in the figure, Isaiah's track forms a right triangle. Hence, we can apply the pythagorean theorem.

First, we find the hypotenuse or the longest side of the right triangle. The equation is: c^2 = a^2 + b^2, where c is hypotenuse, whereas a and b are the two shorter legs.

c = √(0.75^2 +1.2^2) = 1.415 miles

Therefore, the total distance is 1.415 + 0.75 + 1.2 = 3.37 miles

$200

Step-by-step explanation:

For this one, you want to make algebraic equations. In this case, they would be r+7v=120 and r+10v=150 (where r is the register fee and v is the cost of a visit).

To solve simultaneous equations with a like term (when they have the same sign in front), you can solve by subtracting one equation from the other. This gives (r-r)+(10v-7v)=(150-120) or 3v=30, which can be solved to v=10.

To work out r, we can sub the known value of v (10) for v in either equation. This gives r+(10×10)=150 or r+100=150. This can be solved to r=50.

This makes the expression c=50+10n (where c is the total cost and n is the number of visits.

Lisa went 15 times, so this becomes c=50+(10×15) or c=50+150, which gives c=200.

**This content involves writing and solving simultaneous equations from worded questions, which you may wish to revise. I'm always happy to help!