Question

state which metric unit you would probably use to measure each item.

1. length of a computer keyboard
2. mass of a large dog

complete each sentence.

1. 4 ft =? in.
2. 21 ft =? yd
3. 180 g =? kg
4. 3 t =? lb
5. 32 g ≈? oz
6. 3 mi ≈? km
7. 35 yd ≈? m
8. 5.1 l ≈? qt
9. tuna a can of tuna is 6 ounces. about how many grams is it?
10. crackers a box of crackers is 453 grams. about how many pounds is it? round to the nearest pound.

. distance a road sign in canada gives the distance to toronto as 140 kilometers. what is this distance to the nearest mile?
obability a bag contains 3 blue chips, 7 red chips, ellow chips, and 5 green chips. a chip is randomly iwn from the bag. find each probability.
p(yellow)

1. p(green)

p(red or blue)

1. p(not red)

luate each expression if r = 3, q = 1, and w = - 2.
4r + q

1. rw - 6

\frac{r + 3q}{4r}

1. \frac{5w}{3r + q}

|2 - r|+17

1. 8 + |q - 5|

3y=y + 16
3y - 16=y
7x=5
each equation.
: + 3 = 14

1. a - 7 = 9

ic = 20

1. n + 2 = - 11

t - 18 = 30

1. 4x + 7 = - 1

= - 8

1. \frac{3}{5}b = - 2

\frac{w}{2} = - 9

1. 3y - 15 = y + 1

7 - 6d = 7 + 4d

1. 2(m - 16) = 44

solve each inequality.

1. y - 13 < 2
2. t + 8 ≥ 19
3. \frac{n}{4}> - 6
4. 9a ≤ 45
5. x + 12 > - 14
6. - 2w < 24
7. -\frac{n}{7}≥3
8. -\frac{h}{5}≤ - 6

write the ordered pair for each point shown.

1. f
2. h
3. a
4. d

graph and label each point on a coordinate plane.

1. b(4, 1)
2. g(0, - 3)
3. r(- 2, - 4)
4. p(- 3, 3)
5. graph the triangle with vertices j(1, - 4), k(2, 3), and l(- 1, 2).
6. graph four points that satisfy the equation y = 2x - 1.

solve each system of equations.

1. y = 2x

y = - x + 6

1. - 3x - y = 4

4x + 2y = - 8

1. y = 2x + 1

y = 3x

1. \frac{1}{2}x - y = - 1

x - 2y = 5

1. x + y = - 6

2x - y = 3

1. \frac{1}{3}x - 3y = - 4

x - 9y = - 12
simplify.

1. sqrt{18}
2. sqrt{\frac{25}{49}}
3. sqrt{24x^{2}y^{3}}
4. \frac{3}{4-sqrt{3}}

chapter 0 pretest p3

Explanation:

Step1: Consider the size of a keyboard

A keyboard is not very long. Centimeters are a suitable metric unit for measuring its length.
- # Answer: centimeters
- **Mass of a large dog**:
- # Explanation:
## Step1: Think about the weight range of a large dog
Kilograms are commonly used to measure the mass of larger animals like large dogs.
- # Answer: kilograms
2. **Complete each sentence (unit - conversion)**:
- **3. \(4\mathrm{ft}=\underline{?}\mathrm{in}\)**:
- # Explanation:
## Step1: Recall the conversion factor
Since \(1\mathrm{ft} = 12\mathrm{in}\), to convert feet to inches, we multiply by 12.
\(4\times12 = 48\)
- # Answer: 48
- **4. \(21\mathrm{ft}=\underline{?}\mathrm{yd}\)**:
- # Explanation:
## Step1: Recall the conversion factor
Since \(1\mathrm{yd}=3\mathrm{ft}\), to convert feet to yards, we divide by 3.
\(21\div3 = 7\)
- # Answer: 7
- **5. \(180\mathrm{g}=\underline{?}\mathrm{kg}\)**:
- # Explanation:
## Step1: Recall the conversion factor
Since \(1\mathrm{kg} = 1000\mathrm{g}\), to convert grams to kilograms, we divide by 1000.
\(180\div1000=0.18\)
- # Answer: 0.18
- **6. \(3\mathrm{T}=\underline{?}\mathrm{lb}\)**:
- # Explanation:
## Step1: Recall the conversion factor
Since \(1\mathrm{T}=2000\mathrm{lb}\), to convert tons to pounds, we multiply by 2000.
\(3\times2000 = 6000\)
- # Answer: 6000
- **7. \(32\mathrm{g}\approx\underline{?}\mathrm{oz}\)**:
- # Explanation:
## Step1: Recall the conversion factor
Since \(1\mathrm{oz}\approx28.35\mathrm{g}\), to convert grams to ounces, we divide by approximately 28.35.
\(32\div28.35\approx1.13\)
- # Answer: 1.13
- **8. \(3\mathrm{mi}\approx\underline{?}\mathrm{km}\)**:
- # Explanation:
## Step1: Recall the conversion factor
Since \(1\mathrm{mi}\approx1.609\mathrm{km}\), to convert miles to kilometers, we multiply by 1.609.
\(3\times1.609 = 4.827\)
- # Answer: 4.827
- **9. \(35\mathrm{yd}\approx\underline{?}\mathrm{m}\)**:
- # Explanation:
## Step1: Recall the conversion factor
Since \(1\mathrm{yd}\approx0.9144\mathrm{m}\), to convert yards to meters, we multiply by 0.9144.
\(35\times0.9144 = 32.004\)
- # Answer: 32.004
- **10. \(5.1\mathrm{L}\approx\underline{?}\mathrm{qt}\)**:
- # Explanation:
## Step1: Recall the conversion factor
Since \(1\mathrm{L}\approx1.057\mathrm{qt}\), to convert liters to quarts, we multiply by 1.057.
\(5.1\times1.057 = 5.3907\)
- # Answer: 5.3907
3. **Solve each inequality**:
- **36. \(y - 13\lt2\)**:
- # Explanation:
## Step1: Add 13 to both sides
\(y-13 + 13\lt2 + 13\)
\(y\lt15\)
- # Answer: \(y\lt15\)
- **37. \(t + 8\geq19\)**:
- # Explanation:
## Step1: Subtract 8 from both sides
\(t+8 - 8\geq19 - 8\)
\(t\geq11\)
- # Answer: \(t\geq11\)
- **38. \(\frac{n}{4}\gt - 6\)**:
- # Explanation:
## Step1: Multiply both sides by 4
\(\frac{n}{4}\times4\gt - 6\times4\)
\(n\gt - 24\)
- # Answer: \(n\gt - 24\)
- **39. \(9a\leq45\)**:
- # Explanation:
## Step1: Divide both sides by 9
\(\frac{9a}{9}\leq\frac{45}{9}\)
\(a\leq5\)
- # Answer: \(a\leq5\)
- **40. \(x + 12\gt - 14\)**:
- # Explanation:
## Step1: Subtract 12 from both sides
\(x+12 - 12\gt - 14 - 12\)
\(x\gt - 26\)
- # Answer: \(x\gt - 26\)
- **41. \(-2w\lt24\)**:
- # Explanation:
## Step1: Divide both sides by - 2 (and reverse the inequality sign)
\(\frac{-2w}{-2}\gt\frac{24}{-2}\)
\(w\gt - 12\)
- # Answer: \(w\gt - 12\)
- **42. \(-\frac{n}{7}\geq3\)**:
- # Explanation:
## Step1: Multiply both sides by - 7 (and reverse the inequality sign)
\(-\frac{n}{7}\times(-7)\leq3\times(-7)\)
\(n\leq - 21\)
- # Answer: \(n\leq - 21\)
- **43. \(-\frac{h}{5}\leq - 6\)**:
- # Explanation:
## Step1: Multiply both sides by - 5 (and reverse the inequality sign)
\(-\frac{h}{5}\times(-5)\geq - 6\times(-5)\)
\(h\geq30\)
- # Answer: \(h\geq30\)
4. **Write the ordered - pair for each point shown (assuming a standard Cartesian - coordinate system)**:
- Since no graph is provided for points \(F\), \(H\), \(A\), \(D\), we cannot answer this part.
5. **Graph and label each point on a coordinate plane**:
- **48. \(B(4,1)\)**:
- Plot the point 4 units to the right on the x - axis and 1 unit up on the y - axis.
- **49. \(G(0, - 3)\)**:
- Plot the point on the y - axis, 3 units down from the origin (since \(x = 0\)).
- **50. \(R(-2,-4)\)**:
- Plot the point 2 units to the left on the x - axis and 4 units down on the y - axis.
- **51. \(P(-3,3)\)**:
- Plot the point 3 units to the left on the x - axis and 3 units up on the y - axis.
6. **Graph the triangle with vertices \(J(1, - 4)\), \(K(2,3)\), and \(L(-1,2)\)**:
- Plot the points \(J(1, - 4)\), \(K(2,3)\), and \(L(-1,2)\) on the coordinate plane and connect them to form a triangle.
7. **Graph four points that satisfy the equation \(y = 2x-1\)**:
- # Explanation:
## Step1: Choose values for \(x\)
Let \(x = 0\), then \(y=2\times0 - 1=-1\), so the point is \((0, - 1)\)
Let \(x = 1\), then \(y=2\times1 - 1 = 1\), so the point is \((1,1)\)
Let \(x = 2\), then \(y=2\times2 - 1 = 3\), so the point is \((2,3)\)
Let \(x=-1\), then \(y=2\times(-1)-1=-3\), so the point is \((-1, - 3)\)
8. **Solve each system of equations**:
- **54. \(\begin{cases}y = 2x\\y=-x + 6\end{cases}\)**:
- # Explanation:
## Step1: Set the two equations equal to each other
\(2x=-x + 6\)
## Step2: Add \(x\) to both sides
\(2x+x=-x + x+6\), \(3x=6\)
## Step3: Divide both sides by 3
\(x = 2\)
## Step4: Substitute \(x = 2\) into \(y = 2x\)
\(y=2\times2=4\)
- # Answer: \((2,4)\)
- **55. \(\begin{cases}-3x-y = 4\\4x + 2y=-8\end{cases}\)**:
- # Explanation:
## Step1: Multiply the first equation by 2
\(-6x-2y = 8\)
## Step2: Add it to the second equation
\((-6x-2y)+(4x + 2y)=8+( - 8)\)
\(-6x-2y+4x + 2y=0\), \(-2x=0\), \(x = 0\)
## Step3: Substitute \(x = 0\) into \(-3x-y = 4\)
\(-3\times0-y = 4\), \(y=-4\)
- # Answer: \((0,-4)\)
- **Additional systems can be solved in a similar manner using substitution or elimination methods**.
9. **Simplify**:
- **60. \(\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}\)**:
- # Answer: \(3\sqrt{2}\)
- **61. \(\sqrt{\frac{25}{49}}=\frac{\sqrt{25}}{\sqrt{49}}=\frac{5}{7}\)**:
- # Answer: \(\frac{5}{7}\)
- **62. \(\sqrt{24x^{2}y^{3}}=\sqrt{4\times6\times x^{2}\times y^{2}\times y}=2|x|y\sqrt{6y}\)**:
- # Answer: \(2|x|y\sqrt{6y}\)
- **63. \(\frac{3}{4-\sqrt{3}}=\frac{3(4 + \sqrt{3})}{(4-\sqrt{3})(4+\sqrt{3})}=\frac{12 + 3\sqrt{3}}{16-3}=\frac{12 + 3\sqrt{3}}{13}\)**:
- # Answer: \(\frac{12 + 3\sqrt{3}}{13}\)

Answer:

1. State which metric unit you would probably use to measure each item:

• Length of a computer - keyboard:
• # Explanation:

Step1: Consider the size of a keyboard

A keyboard is not very long. Centimeters are a suitable metric unit for measuring its length.

• # Answer: centimeters
• Mass of a large dog:
• # Explanation:

Step1: Think about the weight range of a large dog

Kilograms are commonly used to measure the mass of larger animals like large dogs.

• # Answer: kilograms

1. Complete each sentence (unit - conversion):

• 3. \(4\mathrm{ft}=\underline{?}\mathrm{in}\):
• # Explanation:

Step1: Recall the conversion factor

Since \(1\mathrm{ft} = 12\mathrm{in}\), to convert feet to inches, we multiply by 12.
\(4\times12 = 48\)

• # Answer: 48
• 4. \(21\mathrm{ft}=\underline{?}\mathrm{yd}\):
• # Explanation:

Step1: Recall the conversion factor

Since \(1\mathrm{yd}=3\mathrm{ft}\), to convert feet to yards, we divide by 3.
\(21\div3 = 7\)

• # Answer: 7
• 5. \(180\mathrm{g}=\underline{?}\mathrm{kg}\):
• # Explanation:

Step1: Recall the conversion factor

Since \(1\mathrm{kg} = 1000\mathrm{g}\), to convert grams to kilograms, we divide by 1000.
\(180\div1000=0.18\)

• # Answer: 0.18
• 6. \(3\mathrm{T}=\underline{?}\mathrm{lb}\):
• # Explanation:

Step1: Recall the conversion factor

Since \(1\mathrm{T}=2000\mathrm{lb}\), to convert tons to pounds, we multiply by 2000.
\(3\times2000 = 6000\)

• # Answer: 6000
• 7. \(32\mathrm{g}\approx\underline{?}\mathrm{oz}\):
• # Explanation:

Step1: Recall the conversion factor

Since \(1\mathrm{oz}\approx28.35\mathrm{g}\), to convert grams to ounces, we divide by approximately 28.35.
\(32\div28.35\approx1.13\)

• # Answer: 1.13
• 8. \(3\mathrm{mi}\approx\underline{?}\mathrm{km}\):
• # Explanation:

Step1: Recall the conversion factor

Since \(1\mathrm{mi}\approx1.609\mathrm{km}\), to convert miles to kilometers, we multiply by 1.609.
\(3\times1.609 = 4.827\)

• # Answer: 4.827
• 9. \(35\mathrm{yd}\approx\underline{?}\mathrm{m}\):
• # Explanation:

Step1: Recall the conversion factor

Since \(1\mathrm{yd}\approx0.9144\mathrm{m}\), to convert yards to meters, we multiply by 0.9144.
\(35\times0.9144 = 32.004\)

• # Answer: 32.004
• 10. \(5.1\mathrm{L}\approx\underline{?}\mathrm{qt}\):
• # Explanation:

Step1: Recall the conversion factor

Since \(1\mathrm{L}\approx1.057\mathrm{qt}\), to convert liters to quarts, we multiply by 1.057.
\(5.1\times1.057 = 5.3907\)

• # Answer: 5.3907

1. Solve each inequality:

• 36. \(y - 13\lt2\):
• # Explanation:

Step1: Add 13 to both sides

\(y-13 + 13\lt2 + 13\)
\(y\lt15\)

• # Answer: \(y\lt15\)
• 37. \(t + 8\geq19\):
• # Explanation:

Step1: Subtract 8 from both sides

\(t+8 - 8\geq19 - 8\)
\(t\geq11\)

• # Answer: \(t\geq11\)
• 38. \(\frac{n}{4}\gt - 6\):
• # Explanation:

Step1: Multiply both sides by 4

\(\frac{n}{4}\times4\gt - 6\times4\)
\(n\gt - 24\)

• # Answer: \(n\gt - 24\)
• 39. \(9a\leq45\):
• # Explanation:

Step1: Divide both sides by 9

\(\frac{9a}{9}\leq\frac{45}{9}\)
\(a\leq5\)

• # Answer: \(a\leq5\)
• 40. \(x + 12\gt - 14\):
• # Explanation:

Step1: Subtract 12 from both sides

\(x+12 - 12\gt - 14 - 12\)
\(x\gt - 26\)

• # Answer: \(x\gt - 26\)
• 41. \(-2w\lt24\):
• # Explanation:

Step1: Divide both sides by - 2 (and reverse the inequality sign)

\(\frac{-2w}{-2}\gt\frac{24}{-2}\)
\(w\gt - 12\)

• # Answer: \(w\gt - 12\)
• 42. \(-\frac{n}{7}\geq3\):
• # Explanation:

Step1: Multiply both sides by - 7 (and reverse the inequality sign)

\(-\frac{n}{7}\times(-7)\leq3\times(-7)\)
\(n\leq - 21\)

• # Answer: \(n\leq - 21\)
• 43. \(-\frac{h}{5}\leq - 6\):
• # Explanation:

Step1: Multiply both sides by - 5 (and reverse the inequality sign)

\(-\frac{h}{5}\times(-5)\geq - 6\times(-5)\)
\(h\geq30\)

• # Answer: \(h\geq30\)

1. Write the ordered - pair for each point shown (assuming a standard Cartesian - coordinate system):

• Since no graph is provided for points \(F\), \(H\), \(A\), \(D\), we cannot answer this part.

1. Graph and label each point on a coordinate plane:

• 48. \(B(4,1)\):
• Plot the point 4 units to the right on the x - axis and 1 unit up on the y - axis.
• 49. \(G(0, - 3)\):
• Plot the point on the y - axis, 3 units down from the origin (since \(x = 0\)).
• 50. \(R(-2,-4)\):
• Plot the point 2 units to the left on the x - axis and 4 units down on the y - axis.
• 51. \(P(-3,3)\):
• Plot the point 3 units to the left on the x - axis and 3 units up on the y - axis.

1. Graph the triangle with vertices \(J(1, - 4)\), \(K(2,3)\), and \(L(-1,2)\):

• Plot the points \(J(1, - 4)\), \(K(2,3)\), and \(L(-1,2)\) on the coordinate plane and connect them to form a triangle.

1. Graph four points that satisfy the equation \(y = 2x-1\):

• # Explanation:

Step1: Choose values for \(x\)

Let \(x = 0\), then \(y=2\times0 - 1=-1\), so the point is \((0, - 1)\)
Let \(x = 1\), then \(y=2\times1 - 1 = 1\), so the point is \((1,1)\)
Let \(x = 2\), then \(y=2\times2 - 1 = 3\), so the point is \((2,3)\)
Let \(x=-1\), then \(y=2\times(-1)-1=-3\), so the point is \((-1, - 3)\)

1. Solve each system of equations:

• **54. \(

$$\begin{cases}y = 2x\\y=-x + 6\end{cases}$$

\)**:

• # Explanation:

Step1: Set the two equations equal to each other

\(2x=-x + 6\)

Step2: Add \(x\) to both sides

\(2x+x=-x + x+6\), \(3x=6\)

Step3: Divide both sides by 3

\(x = 2\)

Step4: Substitute \(x = 2\) into \(y = 2x\)

\(y=2\times2=4\)

• # Answer: \((2,4)\)
• **55. \(

$$\begin{cases}-3x-y = 4\\4x + 2y=-8\end{cases}$$

\)**:

• # Explanation:

Step1: Multiply the first equation by 2

\(-6x-2y = 8\)

Step2: Add it to the second equation

\((-6x-2y)+(4x + 2y)=8+( - 8)\)
\(-6x-2y+4x + 2y=0\), \(-2x=0\), \(x = 0\)

Step3: Substitute \(x = 0\) into \(-3x-y = 4\)

\(-3\times0-y = 4\), \(y=-4\)

• # Answer: \((0,-4)\)
• Additional systems can be solved in a similar manner using substitution or elimination methods.

1. Simplify:

• 60. \(\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}\):
• # Answer: \(3\sqrt{2}\)
• 61. \(\sqrt{\frac{25}{49}}=\frac{\sqrt{25}}{\sqrt{49}}=\frac{5}{7}\):
• # Answer: \(\frac{5}{7}\)
• 62. \(\sqrt{24x^{2}y^{3}}=\sqrt{4\times6\times x^{2}\times y^{2}\times y}=2|x|y\sqrt{6y}\):
• # Answer: \(2|x|y\sqrt{6y}\)
• 63. \(\frac{3}{4-\sqrt{3}}=\frac{3(4 + \sqrt{3})}{(4-\sqrt{3})(4+\sqrt{3})}=\frac{12 + 3\sqrt{3}}{16-3}=\frac{12 + 3\sqrt{3}}{13}\):
• # Answer: \(\frac{12 + 3\sqrt{3}}{13}\)