The measures of the consecutive angles of a quadrilateral are in the ratio $5 : 7 : 11 : 13 .$ Find the measure of each angle. draw a quadrilateral that satisfies the requirements, and explain why two sides must be parallel.

What is the ratio of the measure of an interior angle to the measure of an exterior angle in a regular hexagon? A regular decagon? A regular $n$ -gon?

A team's best hitter has a lifetime batting average of $.320 .$ He has been at bat 325 times. a. How many hits has he made?b. The same player goes into a slump and doesn't get any hits at all in his next ten times at bat. What is his current batting average to the nearest thousandth?

A basketball player has made 24 points out of 30 free throws. She hopes to make all her next free throws until her free-throw percentage is 85 or better. How many consecutive free throws will she have to make?

Points $B$ and $C$ lie on $\overline{A D}$ . Find $A C$ if $\frac{A B}{B D}=\frac{3}{4}, \frac{A C}{C D}=\frac{5}{6},$ and $B D=66$

This question is in the process of being solved. The video shown is an answer to a question that covers similar topics.

The perimeter of a triangle is 132 $\mathrm{cm}$ and the lengths of its sides are in the ratio $8 : 11 : 14 .$ Find the length of each side.

$32 : 44 : 56$

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The perimeter of an isosceles triangle is $\sqrt{50}$ feet. The lengths of the sides are in the ratio $3 : 3 : 4$ . Find the length of each side of the triangle.

An isosceles triangle has sides that are $5 \mathrm{cm}, 5 \mathrm{cm},$ and 8 $\mathrm{cm}$ long. Find its area and the lengths of the three altitudes.

Mass Find the mass of the solid region bounded by the parabolic surfaces $z=16-2 x^{2}-2 y^{2}$ and $z=2 x^{2}+2 y^{2}$ if the density of the solid is $\delta(x, y, z)=\sqrt{x^{2}+y^{2}}$

For the following exercises, graph the parabola, labeling the focus and the directrix.$$x^{2}+4 x+2 y+2=0$$

For the following exercises, graph the parabola, labeling the focus and the directrix.$$3 x^{2}+30 x-4 y+95=0$$

A wedge like the one in Exercise 22 has dimensions $a=2$ , $b=6,$ and $c=3 .$ The density is $\delta(x, y, z)=x+1 .$ Notice that if the density is constant, the center of mass will be $(0,0,0)$ .

Convert each angle in degrees to radians. Write the answer as a multiple of $\pi$.$$15^{\circ}$$

Can you neutralize a strong acid solution by adding an equal volume of a weak base having the same molarity as the acid? Support your position.

In Fig. $8-60,$ the pulley has negligible mass, and both it and the inclined plane are frictionless. Block $A$ has a mass of $1.0 \mathrm{kg},$ block $B$ has a mass of $2.0 \mathrm{kg},$ and angle $\theta$ is $30^{\circ} .$ If the blocks are released from restwith the connecting cord taut, what is their total kinetic energy when block $B$ has fallen 25 $\mathrm{cm} ?$

For each statement in Exercises $5-10$ copy and complete a table like the one shown below.$$\text {If }\underline{?} \text { then }\underline{?} \text { True\False}.$$$$\begin{array}{|l|l|}\hline {\text { Statement }} & {?} & {?} \\ \hline {\text { Contrapositive }} & {?} & {?} \\ \hline {\text { Converse }} & {?} & {?} \\ \hline {\text { Inverse }} & {?} & {?} \\ \hline \end{array}$$If a triangle is scalene, then it has no congruent sides.

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## Discussion

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## Recommended Questions

The perimeter of an isosceles triangle is $\sqrt{50}$ feet. The lengths of the sides are in the ratio $3 : 3 : 4$ . Find the length of each side of the triangle.

An isosceles triangle has sides that are $5 \mathrm{cm}, 5 \mathrm{cm},$ and 8 $\mathrm{cm}$ long. Find its area and the lengths of the three altitudes.

Mass Find the mass of the solid region bounded by the parabolic surfaces $z=16-2 x^{2}-2 y^{2}$ and $z=2 x^{2}+2 y^{2}$ if the density of the solid is $\delta(x, y, z)=\sqrt{x^{2}+y^{2}}$

For the following exercises, graph the parabola, labeling the focus and the directrix.

$$x^{2}+4 x+2 y+2=0$$

For the following exercises, graph the parabola, labeling the focus and the directrix.

$$3 x^{2}+30 x-4 y+95=0$$

A wedge like the one in Exercise 22 has dimensions $a=2$ , $b=6,$ and $c=3 .$ The density is $\delta(x, y, z)=x+1 .$ Notice that if the density is constant, the center of mass will be $(0,0,0)$ .

Convert each angle in degrees to radians. Write the answer as a multiple of $\pi$.

$$15^{\circ}$$

Can you neutralize a strong acid solution by adding an equal volume of a weak base having the same molarity as the acid? Support your position.

In Fig. $8-60,$ the pulley has negligible mass, and both it and the inclined plane are frictionless. Block $A$ has a mass of $1.0 \mathrm{kg},$ block $B$ has a mass of $2.0 \mathrm{kg},$ and angle $\theta$ is $30^{\circ} .$ If the blocks are released from rest

with the connecting cord taut, what is their total kinetic energy when block $B$ has fallen 25 $\mathrm{cm} ?$

For each statement in Exercises $5-10$ copy and complete a table like the one shown below.

$$\text {If }\underline{?} \text { then }\underline{?} \text { True\False}.$$

$$\begin{array}{|l|l|}\hline {\text { Statement }} & {?} & {?} \\ \hline {\text { Contrapositive }} & {?} & {?} \\ \hline {\text { Converse }} & {?} & {?} \\ \hline {\text { Inverse }} & {?} & {?} \\ \hline \end{array}$$

If a triangle is scalene, then it has no congruent sides.