Solving Equations and Inequalities

The formula for the area of a circle with diameter d is $A=\pi {\left(\frac{d}{2}\right)}^2$. Write an expression to represent the area of the circle.

Find the value of $a{b}^n$ if $n=3, a=2000,$ $b=-\frac{1}{5}$

Find the value of each expression

$\frac{17\left(2+26\right)}{4}$

MEDICINE 

Suppose a patient must take a blood pressure medication that is dispensed in 125-milligram tablets. The dosage is 15 milligrams per kilo gram of body weight and is given every 8 hours. If the patient weighs 25 kilograms, how many tablets would be needed for a 30-day supply? Use the formula $n=24d÷\left[8\left(b\times 15÷125\right)\right]$, where $n$ is the number of tablets, $d$ is the number of days the supply should last, and $b$ is the body weight of the patient in kilograms. 

In 1950, the average price of a car was about $\backslash (2000$. This may sound inexpensive, but the average income in 1950 was much less than it is now. To compare dollar amounts over time, use the formula $V=\frac{A}{S}C$, where A is the old dollar amount, S is the starting year’s Consumer price index (CPI), C is the converting year’s CPI, and V is the current value of the old dollar amount. Buying a car for $\backslash )2000$ in 1950 was like buying a car for how much money in 2000?

FIREWORKS 

Suppose you are about a mile from a firework display. You count 5 seconds between seeing the light and hearing the sound of the firework display. You estimate the viewing angle is about $4°$. Using the information at the left, estimate the width of the firework display.

Information at the left

To estimate the width $w$ in feet of a firework burst, use the formula $w=20At$. In this formula, $A$ is the estimated viewing angle of the firework display and $t$ is the time in seconds from the instant you see the light until you hear the sound.

Write expressions having values from one to ten using exactly four 4s. You may use any combination of the operation symbols $+,-,\times ,÷,$ and/or grouping symbols, but no other numbers are allowed. An example of such an expression with a value of zero is $\left(4+4\right)-\left(4+4\right)$

Answer the question that was posed at the beginning of the lesson.

How are formulas used by nurses?

Include the following in your answer:

• an explanation of why a formula for the flow rate of an IV is more useful than a table of specific IV flow rates, and
• a description of the impact of using a formula, such as the one for IV flow rate, incorrectly.

Find the value of $1+3\left(5-17\right)÷2\times 6$

$\begin{array}{cc}\left(A\right)-4& \left(B\right)109\\ \left(C\right)-107& \left(D\right)-144\end{array}$

The following are the dimensions of four rectangles. Which rectangle has the same area as the triangle at the right?

$\begin{array}{cc}\left(A\right)1.6\text{ ft by }25\text{ ft}& \left(B\right)5\text{ ft by }16\text{ ft }\\ \left(C\right)3.5\text{ ft by }4\text{ ft }& \left(D\right)0.4\text{ ft by }50\text{ ft}\end{array}$

Evaluate each expression 

59. $\sqrt{9}$

Evaluate each expression 

$\sqrt{16}$

Evaluate each expression 

61. $\sqrt{100}$

Evaluate each expression 

 $\sqrt{169}$

Evaluate each expression 

63. $-\sqrt{4}$

Evaluate each expression 

$-\sqrt{25}$

Evaluate each expression 

65. $\sqrt{\frac{4}{9}}$

Evaluate each expression 

$\sqrt{\frac{36}{49}}$

OPEN ENDED

Give an example of each type of number.

1. Natural
2. Whole
3. Integer
4. Rational
5. Irrational
6. Real

Explain why $\frac{\sqrt{3}}{2}$ is not a rational number. 

Disprove the following statement by giving a counterexample. A counterexample is a specific case that shows a statement is false. Explain.

Every real number has a multiplicative inverse. 

Find the value of each expression.

$18-12÷3$ 

Name the sets of numbers to which each number belongs.

 $-4$

Name the sets of numbers to which each number belongs.

5. 45

Name the sets of numbers to which each number belongs.

6. $6.\overline{23}$

Name the property illustrated by each equation. 

$\frac{2}{3}·\frac{3}{2}=1$

Name the property illustrated by each equation. 

$\left(a+4\right)+2=a+\left(4+2\right)$

Name the property illustrated by each equation. 

$4x+0=4x$

Identify the additive inverse and multiplicative inverse for each number 

10. $-8$

Identify the additive inverse and multiplicative inverse for each number 

11. $\frac{1}{3}$

Identify the additive inverse and multiplicative inverse for each number 

$1.5$

Simplify each expression

$3x+4y-5x$

Simplify each expression

14. $9p-2n+4p+2n$

Simplify each expression

$3\left(5c+4d\right)+6\left(d-2c\right)$

Simplify each expression

 $\frac{1}{2}\left(16-4a\right)-\frac{3}{4}\left(12+20a\right)$

BAND BOOSTERS

Use the information below and in the table.

Ashley is selling chocolate bars for $\$1.50$ each to raise money for the band.

17. Write an expression to represent the total amount of money Ashley raised during this week.

Use the information below and in the table.

Ashley is selling chocolate bars for $\$1.50$ each to raise money for the band.

Evaluate the expression from exercise 17 by using the distributive property.

Name the sets of numbers to which each number belongs.

0

Name the sets of numbers to which each number belongs.

$-\frac{2}{9}$

Name the sets of numbers to which each number belongs.

21. $\sqrt{121}$

Name the sets of numbers to which each number belongs.

$-4.55$

Name the sets of numbers to which each number belongs.

$\sqrt{10}$

Name the sets of numbers to which each number belongs.

24. $-31$

Name the sets of numbers to which each number belongs.

25. $\frac{12}{2}$

Name the sets of numbers to which each number belongs.

$\frac{3\pi }{2}$

Name the sets of numbers to which all of the following numbers belong. Then arrange the numbers in order from least to greatest.

$2.\overline{49}, 2.4\overline{9}, 2.4, 2.49, 2.\overline{9}$

Name the property illustrated by each equation. 

28. $5a+\left(-5a\right)=0$

Name the property illustrated by each equation. 

$\left(3·4\right)·25=3·\left(4·25\right)$

Name the property illustrated by each equation. 

$-6xy+0=-6xy$

Name the property illustrated by each equation. 

31. $\left[5+\left(-2\right)\right]+\left(-4\right)=5+\left[-2+\left(-4\right)\right]$