Mark's favorite tree is a large oak tree in his front yard. Mark wanted to
know how tall the tree is. At the
same time of day, he measured the
length of his shadow and the length
of the shadow cast by the tree. Mark,
who is 5 feet tall, cast a shadow 10
feet long. He found that the tree's
shadow was 140 feet long. How tall is
the tree?

 The shadow of the tree is 280 feet long.

Step-by-step explanation:

We can use a ratio to solve this:

Use the Height to shadow for each. This works because the fractions must reduce to the same equivalent.

5/10 = 140/x

We can see that 5/10 is 1/2, so we need another fraction using 140 as the numerator that is equal to 1/2.  That's easy here: Multiply 140 × 2 to get the new denominator, 280 that replaces x. That is the length of the shadow.

If you have a less obvious ratio, you can use Cross Multiplication to solve the unknown value in the ratio:

5/10 = 140/x  Cross multiply the numerator of the left side times the denominator on the right side, and the denominator on the left side by the numerator on the right side:

5 × x = 10 × 140

5x = 1400  Divide both sides by 5 (the 5s "cancel" on the left)

5x/5 = 1400/5

x = 280

I hope this helps, especially when you see more questions like this in the future.

7

step-by-step explanation:

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions