Respuesta :
Answer:
#1) (4, 3); #2) g = 30; #3) The x-coordinates will increase; #4) three places to the right; #5) 5 - (-9); #6) -24; #7) [tex]a_n=2\times 3^{n-1}[/tex]; #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
[tex]a_n=a_1\times r^{n-1}[/tex], 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
[tex]a_n=2\times 3^{n-1}[/tex]
#8) To find the slope of a line we use the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
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.
#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.
