Question

HELP PLEASE!

A function has the rule y = -2x + 11. Which of the following ordered pairs represents an input of 4 and its output?

(4, 3.5)
(4, 3)
(3, 4)
(3.5, 4)

Solve g + (-11) = 19 for g.


A figure on the coordinate plane is translated to the right. What will happen to its coordinates?

The x-coordinates will increase.
The y-coordinates will increase.
The x-coordinates' signs will change.
The y-coordinates' signs will change.


To multiply a decimal number by 1,000, move the decimal point _____.

three places to the left
three places to the right
four places to the left
four places to the right


All of the following expressions simplify to -4, except _____.

-1 - 3
5 - (-9)
2(-2)
-8 + 4

Use the order of operations to simplify the following expression.

-23 + |7| - 4 · 2

-10
-38
-9
-23

Which formula describes the following geometric sequence? Remember that n represents the term number.

2, 6, 18, 54, ...

an = 2 · 3n - 1
an = 3 · 2n - 1
an = 2 + 3(n - 1)
an = 3 + 2(n - 1)


What is the slope of a line that goes through the points (1, -5) and (-3, 2)?

-4/7
-7/4
-3/4
-4/3

Let a = -4.82 and b = 4.35. All of the following statements are true except

The sum of a and b is negative.
The distance between a and b on the number line is 0.47 units.
The product of a and -b is positive.
The quotient of a and -b is the same as the quotient of -a and b.

Which type of graph would be most appropriate to help you organize a set of data in numerical order?

box-and-whisker plot
bar graph
stem-and-leaf plot
line graph

Answer 1

#1) (4, 3); #2) g = 30; #3) The x-coordinates will increase; #4) three places to the right; #5) 5 - (-9); #6) -24; #7)
`a_n=2* 3^(n-1)`; #8) -7/4; #9) The distance between a and b on the number line is 0.47 units; #10) line graph

Explanation:

#1) Using 4 as the input means we replace x in the equation with 4:

y = -2(4) + 11 = -8+11 = 3

This gives us (4, 3).

#2) To solve the equation, we must isolate the variable, g. To do this we cancel the -11; to cancel the addition of a negative number we will add a positive:

g+(-11)+11 = 19+11 (remember, what you do to one side you must do to the other)

g = 19+11 = 30

#3) As a graph is slid to the right, the x-coordinates change. Since we are going to the right, which is the positive axis, the x-coordinates increase.

We are not moving the figure up or down, so the y-coordinates do not change.

#4) Each time we multiply by 10, we move the decimal point 1 place to the right.

Multiplying by 100 is multiplying by two 10's; this moves it 2 places to the right.

Multiplying by 1000 is multiplying by three 10's; this moves the decimal 3 places to the right.

#5) When subtracting, we can add the opposite:

-1 - 3 = -1 + -3 = -4

5 - (-9) = 5 + (+9) = 14

Multiplying a positive and a negative number means we multiply the digits and make the answer negative:

2(-2) = -(2(2)) = -4

Adding two integers of different signs means we must subtract the digits and take the sign of the larger digit:

-8 + 4 = -(8-4) = -4

The only answer that did not equal -4 was 5 - (-9).

#6) -23 + |7| - 4*2

The order of operations says we perform any operation in parentheses first. We have no parentheses, but we can treat the absolute value as parentheses: |7| = 7; this gives us

-23 + 7 - 4*2

We are then to move on to exponents; we have no exponents.

Next we perform any multiplication and division, from left to right. The only multiplication we have is 4*2, which is 8:

-23 + 7 - 8

Lastly we add or subtract from left to right:

-16 - 8 = -24

#7) A geometric sequence is written as

`a_n=a_1* r^(n-1)`, where a₁ is the first term and r is the common ratio.

In this sequence, the first term is 2 and the common ratio is 3; this gives us

`a_n=2* 3^(n-1)`

#8) To find the slope of a line we use the formula

`m=(y_2-y_1)/(x_2-x_1)`

Using our points, we have

m = (2--5)/(-3-1) = (2+5)/-4 = 7/-4 = -7/4

#9) Adding these two numbers, we have

-4.82 + 4.35 = -0.47.

The distance between these two will be the sum of their absolute values:

4.82+4.35 = 9.17. This is not -0.47.

The number -b will be -4.35; this means the product of a and -b will be the product of two negative numbers, which will be a positive.

The quotient of a and -b will be the same as the quotient of a and b. The number -a will be 4.82, which means the quotient of -a and b will be the same as the quotient of a and b, which is the same as the quotient of a and -b.

#10) A box-and-whisker plot shows the spread of data. A bar graph displays the frequency of data, as does a stem and leaf plot. a line graph, however, will help you organize the data in numerical order.

Answer 2

#1) (4, 3); #2) g = 30; #3) The x-coordinates will increase; #4) three places to the right; #5) 5 - (-9); #6) -24; #7) ; #8) -7/4; #9) The distance between a and b on the number line is 0.47 units; #10) line graph

Explanation:

#1) Using 4 as the input means we replace x in the equation with 4:

y = -2(4) + 11 = -8+11 = 3

This gives us (4, 3).

#2) To solve the equation, we must isolate the variable, g. To do this we cancel the -11; to cancel the addition of a negative number we will add a positive:

g+(-11)+11 = 19+11 (remember, what you do to one side you must do to the other)

g = 19+11 = 30

#3) As a graph is slid to the right, the x-coordinates change. Since we are going to the right, which is the positive axis, the x-coordinates increase.

We are not moving the figure up or down, so the y-coordinates do not change.

#4) Each time we multiply by 10, we move the decimal point 1 place to the right.

Multiplying by 100 is multiplying by two 10's; this moves it 2 places to the right.

Multiplying by 1000 is multiplying by three 10's; this moves the decimal 3 places to the right.

#5) When subtracting, we can add the opposite:

-1 - 3 = -1 + -3 = -4

5 - (-9) = 5 + (+9) = 14

Multiplying a positive and a negative number means we multiply the digits and make the answer negative:

2(-2) = -(2(2)) = -4

Adding two integers of different signs means we must subtract the digits and take the sign of the larger digit:

-8 + 4 = -(8-4) = -4

The only answer that did not equal -4 was 5 - (-9).

#6) -23 + |7| - 4*2

The order of operations says we perform any operation in parentheses first. We have no parentheses, but we can treat the absolute value as parentheses: |7| = 7; this gives us

-23 + 7 - 4*2

We are then to move on to exponents; we have no exponents.

Next we perform any multiplication and division, from left to right. The only multiplication we have is 4*2, which is 8:

-23 + 7 - 8

Lastly we add or subtract from left to right:

-16 - 8 = -24

#7) A geometric sequence is written as

, where a₁ is the first term and r is the common ratio.

In this sequence, the first term is 2 and the common ratio is 3; this gives us

#8) To find the slope of a line we use the formula

Using our points, we have

m = (2--5)/(-3-1) = (2+5)/-4 = 7/-4 = -7/4

#9) Adding these two numbers, we have

-4.82 + 4.35 = -0.47.

The distance between these two will be the sum of their absolute values:

4.82+4.35 = 9.17. This is not -0.47.

The number -b will be -4.35; this means the product of a and -b will be the product of two negative numbers, which will be a positive.

The quotient of a and -b will be the same as the quotient of a and b. The number -a will be 4.82, which means the quotient of -a and b will be the same as the quotient of a and b, which is the same as the quotient of a and -b.

#10) A box-and-whisker plot shows the spread of data. A bar graph displays the frequency of data, as does a stem and leaf plot. a line graph, however, will help you organize the data in numerical order.