\(\displaystyle P=2l+ 2w\)

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 42=2l+2(7)\)

\(\displaystyle 42=2l+14\)

Subtract \(\displaystyle 14\) from both sides

\(\displaystyle 42-14=2l+14-14\)

\(\displaystyle 28=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{28}{2}=\frac{2l}{2}\)

\(\displaystyle 14=l\)

The fence is going around the backyard, so this is a perimeter problem. 

\(\displaystyle P=2l+2w\)

\(\displaystyle P=2(10)+2(5)\)

\(\displaystyle P=20+10\)

\(\displaystyle P=30\)

A straight line has a measurement of \(\displaystyle 180^\circ\). We can subtract to find how much more we'd need to have a straight line. 

\(\displaystyle 180-32=148\)

This is an isosceles triangle because an isosceles triangle has two equal sides. 

This triangle is a not scalene triangle because a scalene triangle has side lengths of all different lengths.

This is not an equilateral triangle because an equilateral triangle has to have all sides equal in length. 

This is not a right triangle because a right triangle has to have a right angle, an angle that measures \(\displaystyle 90^\circ\).

When you are trying to decide if a line represents a line of symmetry you can think about folding the figure across that line. Once you make the fold, do all of the parts line up on top?

If yes, then the line represents a line of symmetry. 

If no, then the line does not represent a line of symmetry. 

This line represents a line of symmetry because if you fold on the black line, then one side would lay on top of the other and the parts would match up. 

This is an equilateral triangle because the sides are all equal, and an equilateral triangle has to have all sides equal in length. 

This triangle is not a scalene triangle because all of the side lengths are not different lengths.

This is not an isosceles triangle because an isosceles triangle has only two equal sides. 

This is not a right triangle because a right triangle has to have a right angle, an angle that measures \(\displaystyle 90^\circ\). 

\(\displaystyle \frac{12}{100}\) is twelve hundredths. 

\(\displaystyle .12\) is twelve hundredths. When we say a decimal, we say the number and add the place-value of the last digit. 

In this problem we are making equivalent fractions. In order to make equivalent fractions you have to multiply the numerator and the denominator by the same number. 

\(\displaystyle 1\times3=3\)

\(\displaystyle 7\times3=21\)

To compare fractions, we need to first make common denominators. 

\(\displaystyle \frac{7}{8}\times\frac{5}{5}=\frac{35}{40}\)

\(\displaystyle \frac{2}{5}\times\frac{8}{8}=\frac{16}{40}\)

Now that we have common denominators, we can compare numerators. The fraction with the bigger numerator has the greater value. 

\(\displaystyle \frac{35}{40}>\frac{16}{40}\)

To solve this problem, we first need to find out how many of Justin's toys will fit on the shelves. If we have \(\displaystyle 4\) shelves, and \(\displaystyle 8\) toys fit on each shelf, we can multiply those two numbers together to find out the total number of toys that will fit. Let's let \(\displaystyle f\) represent the number of toys that will fit. 

\(\displaystyle 4\times8=f\)

\(\displaystyle 32=f\)

Justin has \(\displaystyle 40\) toys, so to find out how many don't fit on the shelves we need to know what is left over, so we subtract. Let's let \(\displaystyle t\) represent the number of toys left over. 

\(\displaystyle 40-32=t\)

\(\displaystyle 8=t\)