The table below represents a linear function f(x) and the equation represents a function g(x):
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)
Part B: Which function has a greater y-intercept? Justify your answer. (4 points)
Answers
Answer:
Slope of f(x) is greater than slope of g(x)
g(x) has a greater y intercept
Step-by-step explanation:
Given
f(x) table
[tex]g(x) = 2x + 6[/tex]
Solving (a):
First, we determine the slope of f(x).
From the table, we take any two corresponding values of x and f(x).
Represent f(x) with y
[tex](x_1,y_1) = (-1.-12)[/tex]
[tex](x_2,y_2) = (0.-6)[/tex]
The slope (m) is calculated as thus
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{-6 - (-12)}{0 - (-1)}[/tex]
[tex]m = \frac{-6 +12}{0 +1}[/tex]
[tex]m = \frac{6}{1}[/tex]
[tex]m = 6[/tex]
Represent this with m1
[tex]m_1 = 6[/tex]
Calculating the slope of g(x).
The general form of an equation is [tex]y = mx + b[/tex]
Where m represents the slope.
We have that:
[tex]g(x) = 2x + 6[/tex]
By comparing [tex]g(x) = 2x + 6[/tex] with [tex]y = mx + b[/tex]
[tex]m = 2[/tex]
Represent this with m2
[tex]m_2 = 2[/tex]
Comparing both slope, we can say that:
f(x) has a greater than slope of g(x)
Another comparison is that:
Slope of f(x) is 3 times the slope of g(x)
Solving (b): Function with greater y intercept.
The general form of an equation is [tex]y = mx + b[/tex]
Where b represents the y intercept.
First, we need to determine the equation of f(x) using:
[tex]y - y_1 = m(x - x_1)[/tex]
Recall that, from the table of f(x):
[tex](x_1,y_1) = (-1.-12)[/tex]
[tex](x_2,y_2) = (0.-6)[/tex]
[tex]m_1 = 6[/tex]
So:
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - (-12) = 6(x - (-1))[/tex]
[tex]y + 12 = 6(x +1)[/tex]
[tex]y + 12 = 6x +6[/tex]
Solve for y
[tex]y = 6x + 6 - 12[/tex]
[tex]y = 6x - 6[/tex]
By comparing this with [tex]y = mx + b[/tex], the y intercept of f(x) is -6
For g(x), we have:
[tex]g(x) = 2x + 6[/tex]
By comparing this with [tex]y = mx + b[/tex], the y intercept of g(x) is 6
Comparing the y intercepts of both functions, g(x) has a greater y intercept because [tex]6 > -6[/tex]
Related Questions
how many times larger is 0.00000600 than 0.00000008
Answers
Answer:
100
Step-by-step explanation:
A recipe calls for 1/2 cup of ingredient A for every 1 2/5 cups of ingredient B. You use 2 cups of ingredient A. How many cups of ingredient B do you need?
Answers
Answer:
5 3/5 cups of Ingredient B
Step-by-step explanation:
A recipe calls for 1/2 cup of ingredient A for every 1 2/5 cups of ingredient B. You use 2 cups of ingredient A. How many cups of ingredient B do you need?
This is calculated as:
1/2 cups of Ingredient A = 1 2/5 cups of Ingredient B
This means:
1/2 cups of Ingredient A = 7/5 cups of Ingredient B
2 cups of Ingredient A = x
Cross Multiply
2 × 7/5 = 1/2 × x
x = 2 × 7/5/1/2
x = 2 × 7/5 ÷ 1/2
x = 2 × 7/5 × 2/1
x = 28/5
x = 5 3/5 cups of Ingredient B
Hence, For 2 cups of Ingredient A, 5 3/5 cups of Ingredient B is needed
Tom spent $25,167 for a new car. The car will depreciate 11% each year. What will the car
be worth after 1 years? Round your answer to the nearest cent. Do not include the dollar
sign in your answer.
Answers
25,167x11%= 2,768.37
25,167-2,768.37= 22,398.63
whats 1 + 1 plz answer
Answers
Answer:
2
Step-by-step explanation:
Thanks for the points Kiddo
Explain: add one plus the other one and that equals two
Mr. Pao wants to buy a refrigerator that costs $1,232. He can pay the total all at once,
or he can make a one-time payment of $450 plus a $140 payment each month for 6 months.
How much can he save by paying the total all at once?
Answers
1290-1232 = he can save $58
Simplify
f(x) = x² + 4
g(x)= xº + 5x - 1
find
f(x)- g(x)
Answers
(X^2 + 4) - (x^o + 5x - 1)
X^2 + 4 - x^o - 5x + 1
Then combine like terms
Z1 and Z2 are complementary. The mZ1 = 25°. What is the mZ2?
Answers
Answer:
65°Step-by-step explanation:
Complementary means that the two angles add to 90 degrees. Since we know the measure of one angle, we will subtract 25 from 90 to get 65 degrees for angle 2.
What is the slope of the line that passes through the points (-10, 8) and (-15, -7) Write your answer in simplest form.
Answers
Answer:
-3/5
Step-by-step explanation:
-7-8/-15-10= -15/-25
divide by 5 to get -3/-5 or - 3/5
Write an equation in slope-intercept form for the line with y-intercept 1 and slope 3.
Answers
Answer:
y= 3x + 1
Step-by-step explanation:
Answer:
y=3x+1
Step-by-step explanation:
HELPPP I SUCK AT MATH
Answers
Find the area of the figure
Answers
Answer:
56ft
Step-by-step explanation:
If anyone plays pokemon go put your code in your answer and I will add you
Answers
Answer:
My code issssssss 163759
Step-by-step explanation:
Answer:
go charizard
Step-by-step explanation:
Sara lit a new candle and then recorded its height in inches every hour as (time, height). Her results were Syntax error.
Which statement is true?
The height of the candle decreases by 1.6 inches every hour, and its original height was 20 inches.
The height of the candle decreases by 20 inches every hour, and its original height was 1.6 inches.
The height of the candle decreases by 9.6 inches every hour, and its original height was 20 inches.
The height of the candle decreases by 1.6 inches every hour, and its original height was 18.4 inches.
Answers
Answer:
The height of the candle decreases by 1.6 inches every hour, and its original height was 20 inches.
Step-by-step explanation:
i dont understand please answer seriously will give brainliest
Answers
8. Center
As the location of the center of the circle is (3, 3).
Therefore, the coordinates of the center are (3, 3)9. Endpoints of a diameter
As we know that the diameter is the magnitude (often called the length) of the line through the center.
Please note that the diameter touches two points on the edge of the circle. Diameter is often called the longest possible chord.From the diagram, it is clear that:
The points of the diameter are (6, 3) and (0, 3).Also, observe the length of a diameter is 6 units.
10. A point of Tangency
We know that at the point of Tangency, the tangent to a circle will always be perpendicular to the radius.
From the diagram, it is clear that:
(6, 3) is the point of tangency. Here the tangent is perpendicular to the radius.11. Endpoints of a chord that is not a diameter
A chord is basically a line that touches two points.
From the diagram, it is clear that:
The coordinates of the chord other than the diameter are (3, 0) and (0, 3).12. Endpoints of a radius
We know that a radius is basically a straight line from the center of a circle to the circumference of a circle.
The length of a radius r = diamter length/2
From the diagram, it is clear that:
The coordinates of the endpoints of the radius are (3, 3) and (6, 3)To make a quilt, a quilter is buying fabric in two colors, blue and green.
The quilter needs at least 9.5 yards of fabric in total.
The blue fabric costs $9 a yard.
The green fabric costs $13 a yard.
The quilter can spend up to $110 on fabric.
Let x represent the number of blue yards of fabric purchased and let y represent the number of green yards of fabric purchased.
Please solve the Inequalities.
Answers
Answer:
3.375yards of blue fabric 6.125yards of green fabricStep-by-step explanation:
step one:
given data
blue fabric costs $9 a yard.
green fabric costs $13 a yard.
Let x represent the number of blue yards of fabric purchased and
let y represent the number of green yards of fabric purchased.
Step two:
The quilter needs at least 9.5 yards of fabric in total.
x+y>=9.5--------1
The quilter can spend up to $110 on fabric.
9x+13y<=110----2
from equation
x+y>=9.5
x=9.5-y
put x=9.5-y in equation 2 we have
9(9.5-y)+13y<=110----2
85.5-9y+13y=110
4y=110-85.5
4y=24.5
y=24.5/4
y=6.125
put y=6.125 in x=9.5-y to find x
x=9.5-6.125
x=3.375
Hence the quilt can purchase
3.375yards of blue fabric
6.125yards of green fabric
3.375 yards of blue fabric and 6.125 yards of green fabric was purchased.
Let x represent the number of blue yards of fabric purchased and let y represent the number of green yards of fabric purchased.
Hence:
x + y ≥ 9.5 (1)
The quilter can spend up to $110 on fabric. Hence:
9x + 13y ≤ 110 (2)
The solution to the inequality is:
x = 3.375, y = 6.125
3.375 yards of blue fabric and 6.125 yards of green fabric was purchased.
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Round 621.97 to tens place. What is It?
Answers
Answer:
622
Step-by-step explanation:
The 7 rounds up the .9, adding 1 to the ones place, making it 622
Answer:
620
Step-by-step explanation:
As they said TENS ( and not TENTHS ) place, the 1 ( in ones position) determines the answer hence 620.
THere are 7 people on the bus, and the bus picks up 4 additional people at each stop. How many stops will it take to have 31 people on the bus?
Answers
Answer:
6 stops.
Step-by-step explanation:
The answer is 6 stops, because 4 times 6 is 24 and 24 plus 7 is 31.
Which of the following expressions is equal to -2 · -2 · -2 · -2 · -2 · -2? 6(-2) (-2)6 -26
Answers
Answer:
-2
Step-by-step explanation:
2x6= - 2
Answer:
(-2)6
Step-by-step explanation:
IF THE SUM OF THREE CONSECUTIVE ODD NUMBERS IS 45, FIND THEM. (STEP BY STEP PLZ)
Answers
Please help me!
Simplify each ratio. Write the simplified version in the same form of the ratio.
3 to 6
5:20
18 to 22
1820
2555
6 to 42
18 to 10
12 to 4
16:8
24 to 16
18 to 36
54 to 9
81:27
72 to 9
1812
Answers
Answer:
1 to 2
1:4
9 to 11
?
?
1 to 7
9 to 5
3 to 1
2:1
3 to 2
1 to 2
6 to 1
3:1
8 to 1
?
1:4
9:11
9:10
5:11
1:7
9:5
3:1
2:1
3:2
1:2
7:1
3:1
8:1
3:2
help please idk what to do
Answers
Step-by-step explanation:
solve the ineq first then plot on the number line so,
-2(4x + 5) ≤ 30
-8x - 10 ≤ 30
-8x ≤ 40
x ≥ -5
therefore, option A is correct.
Topic: Inequalities
If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!
can some help me on these questions please!
Answers
Answer:
let y=the inner missing angle
y+x+31=180
y+(2x-8)=180
and combine the two
2x-8-x-31=0
x=39
Step-by-step explanation:
The top answer is right!
IV. Describe the following rotations
PLS HELP ASAP
Answers
Answer:
90 degree rotation counterclockwise, or a 270 degree rotation clockwise.
Please help me. Thanks! :)
Answers
Answer:
Required Answer:-R (-1,5)S (-3,1)T (-7,3)V (-5,7)[tex]{:}\leadsto[/tex][tex]\sf RS=\sqrt {(-3-1)^2+(1-5)^2}[/tex]
[tex]{:}\leadsto[/tex][tex]\sf \sqrt {(-4)^2+(-4)^2}[/tex]
[tex]{:}\leadsto[/tex][tex]\sf \sqrt {16+16}[/tex]
[tex]{:}\leadsto[/tex][tex]\sf \sqrt {32}[/tex]
[tex]{:}\leadsto[/tex][tex]\sf RS=\sqrt{32}[/tex]
____________________[tex]{:}\leadsto[/tex][tex]\sf ST=\sqrt {(-7-3)^2+(3-1)^2}[/tex]
[tex]{:}\leadsto[/tex][tex]\sf \sqrt {(-10)^2+(2)^2}[/tex]
[tex]{:}\leadsto[/tex][tex]\sf \sqrt {100+4}[/tex]
[tex]{:}\leadsto[/tex][tex]\sf ST={\sqrt{104}}[/tex]
___________________[tex]{:}\leadsto[/tex][tex]\sf TV=\sqrt {(-5-7)^2+(7-3)^2}[/tex]
[tex]{:}\leadsto[/tex][tex]\sf \sqrt{(-12)^2+(4)^2}[/tex]
[tex]{:}\leadsto[/tex][tex]\sf \sqrt {144+16}[/tex]
[tex]{:}\leadsto[/tex][tex]\sf TV=\sqrt {150}[/tex]
____________________[tex]{:}\leadsto[/tex][tex]\sf RV=\sqrt {(-5-1)^2+(7-5)^2}[/tex]
[tex]{:}\leadsto[/tex][tex]\sf \sqrt{(-6)^2+(2)^2}[/tex]
[tex]{:}\leadsto[/tex][tex]\sf \sqrt {36+4}[/tex]
[tex]{:}\leadsto[/tex][tex]\sf RV=\sqrt {40}[/tex]
______________________Perimeter =RS+ST+TV+RV
[tex]{:}\leadsto[/tex][tex]\sf \sqrt{32}+\sqrt {104}+\sqrt {150}+\sqrt {40}[/tex]
[tex]{:}\leadsto[/tex][tex]\sf Perimeter =4\sqrt{20}[/tex]
Audrie's mom gave her $20.00 to buy school supplies. Audrie needs to buy 4 packs of index cards and some notebooks. If each pack of index cards costs $1.95 and each notebook costs $1.99, how many notebooks can Audrie buy using only the money her mom gave her?
Answers
Step-by-step explanation:
20=4*1.95+1.99n
n=6
Audrie can buy 6 notebooks
help me of i die so pls help me
Answers
Answer:
10
100
1000
Step-by-step explanation:
I had a quiz on that the other day got 100%
Write the equation of a line that is perpendicular to y = -1 and that passes through the point (8,-4)
Answers
Last year Beth's annual salary was $38,350. This year she received a promotion and now earns $46,462 annually. She is paid biweekly.
a.) What was her biweekly salary last year?
b.) What is Beth’s biweekly salary this year?
c.) On a biweekly basis, how much more does Beth earn as a result of her promotion?
Answers
Answer:
Quite simple. There are 52 weeks in a year. She gets paid 26 times, every other week.
38,350 / 26 = her salary from last year per check.
46,462 / 26 = her new salary per check
(46,462 - 38,350) / 26 = the difference per week
a. last year Beth's biweekly salary was 1597.91 dollars.
b. This year Beth's biweekly salary is 1935.91 dollars.
c. On a biweekly basis she earns 338 dollars more now as a result of her promotion.
How to convert months into bi-weeks ?One months contains 2 bi-weeks therefore to convert months into bi-weeks we have to multiply the given months by 2.
According to the given question
Last year Beth's annual salary was 38350 dollars.
∴ Her monthly salary was (38350/12) dollars.
= 3195.83 dollars.
She is being paid biweekly meaning twice a month in every two weeks interval.
∴ Her biweekly amount is
=(3195.83/2) dollars
= 1597.91 dollars. (a).
So, her salary last year was 1597.91 dollars biweekly.
This year she received a promotion and now earns 46462 dollars per year.
∴ Her biweekly salary is
= (46462/2×12) dollars. ( as there is 2 bi-weeks in every months)
= 1935.91 dollars. (b).
As a result of her promotion she earns (1935.91 - 1597.91) dollars more as a result of her promotion.
= 338 dollars.
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Please Help Me With This Please!
Answers
Answer:
d:113 sq in
Step-by-step explanation:
Enter the equation of the line in slope-intercept form.
The line parallel to y =
5
4
x + 8 that passes through (−8, 0).
The equation of the line that passes through (−8, 0) is y = ???
Answers
Answer:
typing this answer to get points hope u get ur answer soon :)
Step-by-step explanation: