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 you organize a set of data in numerical order?

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

#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

Step-by-step 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.

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2