Chapter 9

Solve each proportion. $$\frac{84}{52}=\frac{m}{13}$$

Solve each equation. Round to the nearest tenth, if necessary. $$5 p^{2}=315$$

Solve each proportion. $$\frac{2.8}{h}=\frac{4.2}{12}$$

Europe's largest town square is the Rynek Glowny located in Krakow, Poland. It covers approximately \(48,400\) square yards. How many feet long is a side of the square?

Solve each equation. Round to the nearest tenth, if necessary. $$2 d^{2}=162$$

Solve each equation. Round to the nearest tenth, if necessary. $$190.5=1.5 b^{2}$$

Find the negative square root of 1000 to the nearest tenth.

Solve each equation. Round to the nearest tenth, if necessary. $$0.1 x^{2}=0.169$$

If \(x=\sqrt{5000},\) what is the value of \(x\) to the nearest tenth?

State three numbers that could be the measures of the sides of a right triangle. Justify your answer.

City code requires that a reception hall must allow 4 square feet for each person on the dance floor. The reception hall wants to have a dance floor that is a square and that is large enough for 100 people at a time. What is the length of each side of the dance floor?

PHYSICS The formula \(h=16 t^{2}\) measures the time \(t\) in seconds that it takes for an object to fall from a height of \(h\) feet and hit the ground. How long would it take a marble to hit the ground if it was dropped off a cliff with a height of 150 feet? Round to the nearest tenth.

Estimate the perimeter of a square that has an area of 2080 square meters. Then calculate the perimeter. Round to the nearest tenth.

Determine whether each statement is sometimes, always, or never true. A whole number is an integer.

The hypotenuse of an isosceles right triangle is 8 inches. Is there enough information to find the length of the legs? If so, find the length of the legs. If not, explain why not.

Write a number for which the negative square root is not an integer. Then graph the negative square root.

Determine whether each statement is sometimes, always, or never true. An irrational number is a negative integer.

How do the lengths of the sides of a right triangle relate to each other? Include an example of a set of numbers that represents the measures of the legs and hypotenuse of a right triangle.

What are the possibilities for the ending digit of a number that has a whole number square root? Explain your reasoning.

Determine whether each statement is sometimes, always, or never true. A repeating decimal is a real number.

Find the amount of edging needed to enclose the triangular flower bed. A 10 yd B 16 yd C 18 yd D 24 yd

Use the following information. Squaring a number and finding the square root of a number are inverse operations. That is, one operation undoes the other operation. Use inverse operations to evaluate each expression. $$(\sqrt{64})^{2}$$

Determine whether each statement is sometimes, always, or never true. An integer is a whole number.

Use the following information. Squaring a number and finding the square root of a number are inverse operations. That is, one operation undoes the other operation. Use inverse operations to evaluate each expression. $$(\sqrt{100})^{2}$$

Numbers that can be represented by a triangular arrangement of dots are called triangular numbers. The first three triangular numbers are \(1,3,\) and 6 Find the next three triangular numbers.

FLOORING A square room has an area of 324 square feet. The homeowners plan to cover the floor with 6 -inch square tiles. How many tiles will be in each row on the floor?

Use the following information. Squaring a number and finding the square root of a number are inverse operations. That is, one operation undoes the other operation. Use inverse operations to evaluate each expression. $$(\sqrt{169})^{2}$$

Give a counterexample for each statement. All square roots are irrational numbers.

Give a counterexample for each statement. All rational numbers are integers.

How are square roots related to factors? Give an example of a number between 100 and 200 whose square root is a whole number and an example of a number between 100 and 200 whose square root is a decimal that does not terminate.

Give a counterexample for each statement. What is the value of \(x\) to the nearest tenth if \(x^{2}-4^{2}=\sqrt{15^{2}} ?\)

Name all of the sets of numbers to which each real number belongs. Let \(N=\) natural numbers, \(\mathbf{W}=\) whole numbers, \(\mathbf{Z}=\) integers, \(\mathbf{Q}=\) rational numbers, and $\mathbf{I}=\text { irrational numbers. $$-5$$

A long piece of paper is folded so that the lower edge of the strip forms a right angle with itself. Classify \(\angle 3\). F. acute H. right G. obtuse J. straight

GEOMETRY Use the formula for the area of a circle \(A=\pi r^{2}\) where \(A\) represents the area, \(r\) represents the radius, and \(\pi\) is approximately equal to 3.14 , to find the radius of the circle with an area of 28.26 square inches.

Name all of the sets of numbers to which each real number belongs. Let \(N=\) natural numbers, \(\mathbf{W}=\) whole numbers, \(\mathbf{Z}=\) integers, \(\mathbf{Q}=\) rational numbers, and $\mathbf{I}=\text { irrational numbers. $$0 . \overline{4}$$

Solve each equation. Round to the nearest tenth, if necessary. $$m^{2}=81$$

Name all of the sets of numbers to which each real number belongs. Let \(N=\) natural numbers, \(\mathbf{W}=\) whole numbers, \(\mathbf{Z}=\) integers, \(\mathbf{Q}=\) rational numbers, and $\mathbf{I}=\text { irrational numbers. $$\sqrt{63}$$

Solve each inequality. $$4 y>24$$

Solve each equation. Round to the nearest tenth, if necessary. $$196=y^{2}$$

Name all of the sets of numbers to which each real number belongs. Let \(N=\) natural numbers, \(\mathbf{W}=\) whole numbers, \(\mathbf{Z}=\) integers, \(\mathbf{Q}=\) rational numbers, and $\mathbf{I}=\text { irrational numbers. $$7.4$$

Solve each inequality. $$\frac{a}{0.3}<-7$$

Solve each equation. Round to the nearest tenth, if necessary. $$168=2 p^{2}$$

OPEN ENDED Give an example of a number that is an integer and a rational number.

Tobias' average for five quizzes is \(86 .\) If he wants to have an average of at least 88 for six quizzes, what is the lowest score he can receive on his sixth quiz?

Solve each inequality. $$18 \geq-2 k$$

Solve each equation. Round to the nearest tenth, if necessary. $$\frac{x^{2}}{2}=51$$

CHALLENGE Tell whether the product of a rational number like 8 and an irrational number like \(0.101001000 \ldots\) is rational or irrational. Explain your reasoning.

Simplify each expression $$(2+6)^{2}+(-5+6)^{2}$$

Solve each inequality. $$2 x+5<17$$

Estimate each square root to the nearest whole number. Do not use a calculator. $$-\sqrt{5.25}$$