algebra questions
I don’t need any of the open a textbook answers. I have worked hard to get my algebra done but these last units have turned my mind into mush. I don’t just want answers I need an explanation. Any help would be wonderful
Thank you
2) what is the equation for a line that passes through the points (-4, -4) and (8, 23)?
A. y = 9/4 – 13
B. y = -9/4 + 13
C: Y = -9/4 – 5
B Y = 9/4 + 5
3) The number of entertainment websites in 1995 was 59. By 2004, there were 929 entertainment websites. Approximately what was the rate of change for the number of websites for this period of time?
A: 870 websites per year
B: 97 websites per year
C: 10.34 websites per year
D. 494 websites per year
4) Which of the following function notations corresponds to the equation below?
Y – 5.38x = -3
A: f(y)=5.38y-3
B: f(x)=3x-5.38
C: f(x)=5.38x-3
D f(y)=3y-5.38
5)
(-2,-1)
(0,-5)
(6,31)
(8,59)
What is the domain of the set of ordered pairs above?
A: {-2,0,6,8}
B: {-2,-1}
C: {-1,-5,31,59}
D: {8, 59}
6) If the range of the function
Y = (1/2)x +1
Is {0,2,5}, then what is the corresponding domain?
A: {-3,1,7}
B: {-2,2,8}
C: {-1,3,9}
D: {-2,2,9}
7) A line passes through the point (4,2) and has a slope of 3. Find the equation of the line.
A: y=-3x -10
B: y= 3x-14
C: y=3x-10
D: y=-3x – 14
8) According to the table below, what is the range of the data?
Input output
15 24
16 25
17 26
18 27
19 28
A: 15,16,17,18,19
B: 24,25,26,27,28
C: 15,14,13,12,11
D: 25,27,29,31,33
9) What is the slope of the line given by the linear equation below?
4x+7y=16
A: 4/7
B: 7/4
C: -4/7
D: -7/4
10) A linear equation has a slope of 8/3 and crosses the y-axis at -8. What is the equation of the line?
A: y = -8x – 8/3
B: y = 8/3x – 64/3
C: y = 8/3x -8
D: y = 8/3x + 8
11) What is the slope of the line defined by the table below?
X Y
0 7
7 11
14 15
21 19
A: 4/7
B: -7/4
C: -4/7
D: 7/4
12) A linear function has a y-intercept of -8 and a slope of 9. What is the equation of the line?
A: y = 9x - 8
B: y = 1/9x – 8
C: y = 9x + 8
D: y = 9x + 72
13) Rewrite the following equation as a function of x.
9x+20y-12=0
A: f(x) = -20/9x + 5/3
B: f(x) = 20/9x + 3/5
C: f(x) = -9/20x + 3/5
D: f(x) = 9/20x – 3/5
14: If the domain of the function 4x^2 – 2y = 2 is {-4,0,3}, then what is the corresponding range?
A: {15,-1,8}
B: {31,-1,17}
C: {31,0,18}
D: {33,1,19}
15) In the function f(x) = x^3 + 12x^2 – 14x + 14, what represents the output value?
A: 12x^2
B: x
C: x^3
D: f(x)
16: If f(t) = t^2 + 9, find f(3)
A: 15
B: 3t^2 + 27
C: 9
D: 18
Honestly. If you don't want to open a textbook, get a tutor if you don't understand these varied issues. My experience in teaching tells me you are answer grazing....or you have never opened your texbook. Take 15 for instance, that is pretty basic. as is 16.
Sixteen test problems and you don't know how to do any of them?
There must be a better way to learn this material than asking a bunch of unknown volunteers to explain them all to you.
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Let's go through each of the algebra questions one by one and explain how to solve them:
2) To find the equation for a line that passes through two points (-4, -4) and (8, 23), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is one of the points on the line.
Step 1: Calculate the slope using the formula: slope (m) = (y2 - y1) / (x2 - x1)
m = (23 - (-4)) / (8 - (-4))
m = 27 / 12
m = 9 / 4
Step 2: Choose one of the points, let's use (-4, -4), and substitute the values into the point-slope formula:
y - (-4) = (9/4)(x - (-4))
y + 4 = (9/4)(x + 4)
y + 4 = (9/4)x + 9
y = (9/4)x + 9 - 4
y = (9/4)x + 5
Therefore, the equation for the line that passes through the points (-4, -4) and (8, 23) is y = (9/4)x + 5.
The correct answer is A: y = 9/4 - 13.
3) To find the rate of change, we need to calculate the difference in the number of entertainment websites between 1995 and 2004, and divide it by the number of years.
Step 1: Calculate the difference in the number of websites: 929 - 59 = 870.
Step 2: Calculate the number of years: 2004 - 1995 = 9.
Step 3: Divide the difference in websites by the number of years: 870 / 9 = 97.
Therefore, the approximate rate of change for the number of websites between 1995 and 2004 is B: 97 websites per year.
4) To determine the corresponding function notation for the equation Y - 5.38x = -3, we need to isolate the variable Y.
Step 1: Add 5.38x to both sides of the equation: Y = 5.38x - 3.
Therefore, the corresponding function notation for the equation Y - 5.38x = -3 is C: f(x) = 5.38x - 3.
5) The domain of a set of ordered pairs represents the x-values or the inputs. In this case, the x-values for the given set of ordered pairs are: -2, 0, 6, and 8.
Therefore, the domain of the set of ordered pairs (-2, -1), (0, -5), (6, 31), (8, 59) is A: {-2, 0, 6, 8}.
6) The range represents the y-values or the outputs in a function. In this case, the given range for the function Y = (1/2)x + 1 is {0, 2, 5}.
Therefore, the corresponding domain for the given range is A: {-3, 1, 7}.
7) To find the equation of a line that passes through the point (4, 2) and has a slope of 3, we can use the point-slope form of a linear equation.
Step 1: Substitute the slope (m = 3) and the coordinates of the point (4, 2) into the point-slope formula: y - y1 = m(x - x1)
y - 2 = 3(x - 4)
Step 2: Simplify the equation:
y - 2 = 3x - 12
y = 3x - 10
Therefore, the equation of the line is C: y = 3x - 10.
8) To find the range of the given data, we need to identify the output values.
From the given table:
The output values are: 24, 25, 26, 27, 28.
Therefore, the range of the data is B: {24, 25, 26, 27, 28}.
9) To find the slope of the line given by the linear equation 4x + 7y = 16, we need to rewrite the equation in slope-intercept form (y = mx + b), where m represents the slope.
Step 1: Isolate the y variable:
4x + 7y = 16
7y = -4x + 16
y = (-4/7)x + (16/7)
Step 2: Identify the coefficient of x, which represents the slope.
The slope of the line is -4/7.
Therefore, the answer is C: -4/7.
10) To find the equation of a line with a slope of 8/3 and crosses the y-axis at -8, we can use the slope-intercept form of a linear equation (y = mx + b), where m represents the slope and b represents the y-intercept.
Step 1: Substitute the given values into the slope-intercept form:
y = (8/3)x + (-8)
Step 2: Simplify the equation:
y = (8/3)x - 8
Therefore, the equation of the line is C: y = (8/3)x - 8.
Continue to part 2 for the answers to the remaining questions.