Consider the function f(x) = 3x - 2 and the function g(x), which is represented by the table below. Which of the following statements about f(x) and g(x) is true? Select all that apply.
1. The slope of f(x) is smaller than the slope of g(x)
2. The lines represented by f(x) and g(x) are parallel.
3. The line represented by f(x) crosses the x-axis to the right of the line represented by g(x).
4. The y-intercept of f(x) is smaller than the y-intercept of g(x).
5. The values of f(x) and g(x) are the same at x = 3
Answers
Answer:
4. 5. 3. are correct im pretty sure
Step-by-step explanation:
Statements 1, 2, and 3 about f(x) and g(x) are "true".
What are the functions?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
Consider the function f(x) = 3x - 2 and the function g(x), which is represented by the table below.
x : 1 3 5 7 9
g(x): 3 7 11 15 19
Here the slope of the function g(x) is 2.
This means statements 1 and 2 are false because slopes are different.
To compare the position of the lines at the x-axis, you can evaluate the function at x=0. f(0) = 3×0 - 2 = -2 and g(0) = -1.
Since g(0) is less than f(0), the line represented by g(x) crosses the x-axis to the right of the line represented by f(x). So, statement 3 is true.
The y-intercept of f(x) is -2, while the y-intercept of g(x) is 1. So, statement 4 is true.
To compare the values of f(x) and g(x) at x=3, you can evaluate the functions at x=3. f(3) = 3×3 - 2 = 7 and g(3) = 7. So, the values of f(x) and g(x) are the same at x=3. So, statement 5 is true.
Therefore, the true statements are 2, 3, and 4.
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Related Questions
15. Write the first four terms of the sequence:
a. f(n) = −2[tex]n^{2}[/tex] + 4
b. f (1) = 7, f(n)= −4 ∙ f(n-1) − 1 + 15
Answers
Answer:
16 17
Step-by-step explanation:
A linear function contains the following points. What are the slope and yintercept of this function? O A. O B. O C. O D. 25 The slope is 4. The yintercept is (5, O). The slope is —4. The yintercept is (O, 5). 1 The slope is Tthe yintercept is (O, 5). 1 The slope is . The yintercept is (O, 5).
Answers
Answer:
D
Step-by-step explanation:
points (-4,4) and (0,5)
slope: (y2-y1)/(x2-x1)
(5-4)/(0+4) = 1/4
y intercept given: (0,5)
The rectangle shown
Answers
a^2 + b^2=c^2
please help i’ll do anything and give the brain thing :((
Answers
Answer:
add me on snap kharding1805 and I will add you back
Name the property that the statement illustrates.
Answers
Answer:
Transitive property of segment congruence
Step-by-step explanation:
The reflexive, symmetric, and transitive properties are the criterion for an equivalence relation. In terms of congruence,
The reflexive property states that [tex]\overline{XY} \cong \overline{XY}[/tex] (a segment is congruent to itself)The symmetric property states that if [tex]\overline{AB} \cong \overline{CD}[/tex], then [tex]\overline{CD} \cong \overline{AB}[/tex] (this is essentially commutativity)The transitive property states that if [tex]\overline{AB} \cong \overline{CD}[/tex] and [tex]\ovelrine{CD} \cong \overline{EF}[/tex], then [tex]\overline{AB} \cong \overline{EF}[/tex].In terms of general equivalence relations,
The reflective property states that [tex]a = a[/tex].The symmetric property states that if [tex]a=b[/tex], then [tex]b=a[/tex].The transitive property states that if [tex]a=b[/tex] and [tex]b=c[/tex], then [tex]a=c[/tex].That's the transitive property.
The fact that congruence is transitive means exactly what you have written: if A is congruent to B and B is congruent to C, then you can "bridge" from A to C.
Please help!!!!!!!!!
Answers
Answer:
D
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos CBA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{3}{9}[/tex] , thus
∠ CBA = [tex]cos^{-1}[/tex] ([tex]\frac{3}{9}[/tex] ) ≈ 70.53° ( to 2 dec. places )
Bananas cost $0.79 a pound. Mrs. Huff bought p
pounds of bananas. She paid a total of $7.90.
Write an equation to represent the situation.
Answers
Answer:
p x 0.79 = 7.90 or 0.79 x p =7.90
The mean (average) weight of three dogs is 38 pounds. One of the dogs, Shaggy, weighs
46 pounds. The other two dogs, Eda and Bruno, have the same weight. Find Eda's weight.
Answers
Pleaseeeee helpppp !!!!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answers
Answer:
x = 6
Step-by-step explanation:
This means that they are equivalent to each other.
10 = 30 *Multiply by 3
2 = x
Since we multiplied by 3 to get 30, x is just 2 mulitplied by 3.
x = 6
Answer:
Hi
the answer would be:
10/40 = 2/2+x => if you solve the equation, it'll be equal to : x = 6
I hope that it's correct.
Step-by-step explanation:
I’ll mark as BRANLIEST!!!
45 POINTS!!!
I need help with both questions plz help god loves you all.
Answers
Answer:
43
-161
Step-by-step explanation:
-161
you’re welcome:))
The proportional relationship between the number of inches a candle has burned away, b, at any time in hours, t, can be represented by the equation b = 0.25tb=0.25t. What is the constant of proportionality from the time in hours to the inches of candle that has burned away?
Answers
Answer:
k = 0.25t^2
Step-by-step explanation:
Given the equation :
b = 0.25t
b = number of inches that has burned away
t = time
From our knowledge of variation;
Since candle length will decrease with time ;
b α 1/ t
b = k/t
Where k is the proportionality constant
Comparing the equation :
b = 0.25t
k/t = 0.25t
k = 0.25t^2
A chrome book cost 249.99 at target on Black Friday it is on sale for 15 % off what is the price of the computer on Black Friday
Answers
Answer:
The price is 212.49
Step-by-step explanation:
sorry if wrong.
Help Pls Fast! (55 POINTS!)
Answers
Answer:
Close to 6 miles. Exact is between 5.7 and 6
Step-by-step explanation:
Answer:
no
Step-by-step explanation:
Pls help really fast I don't know this!!!!!
Answers
I think it's (3,4) but I am not confident so please be understanding
Answer:
(3, 1 )
Step-by-step explanation:
The centre of the circle is at the midpoint of the diameter.
Given endpoint (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
Here (x₁, y₁ ) = (9, 7) and (x₂, y₂ ) = (- 3, - 5 ) , then
midpoint = ( [tex]\frac{9-3}{2}[/tex], [tex]\frac{7-5}{2}[/tex] ) = ( [tex]\frac{6}{2}[/tex], [tex]\frac{2}{2}[/tex] ) = (3, 1 )
Thus centre of circle = (3, 1 )
Factor the following 36k^2-1
Answers
answer
[tex] {36k}^{2} - 1[/tex]
using identity
[tex](a + b)(a - b) = {a}^{2} - {b}^{2} [/tex]
let a=6k and b=1
we get
[tex](6k + 1)(6k - 1)[/tex]
hope you are satisfied
PLEASE HELP ASAP!!!
Find the values of the variables and round to the nearest hundredth if necessary.
Answers
Answer:
x = 1.73
y = 2.45
z = 1.41
Step-by-step explanation:
1/z = z/2
z^2 = 2
z = sqrt(2)
1^2 + z^2 = x^2
1 + 2 = x^2
x^2 = 3
x = sqrt(3)
z^2 + 2^2 = y^2
2 + 4 = y^2
y^2 = 6
y = sqrt(6)
x = 1.73
y = 2.45
z = 1.41
How many different ways can you write a ratio?
Answers
Answer:
3 different ways
Step-by-step explanation:
Answer:
3 different ways
Step-by-step explanation:
hope this helps
example of the diffrent way to write a ratio :
5 to 10
5 : 10
[tex]\frac{5}{10}[/tex]
Write an equation in slope-intercept form that represents the data. Show ALL work.
1.)
0
1
2
Sales per
day(x)
Daily pay ($), y
100
105
110
115
11212
I
Equation
Answers
Answer:
y = 5x + 100
Step-by-step explanation:
Using the x and corresponding y values from the given table.
Let's use the coordinate (0, 100) and (1, 105)
The equation in slope intercept form is expressed as y = mx+c
m is the slope
c is the y-intercept
Slope m = y2-y1/x2-x1
m = 105-100/1-0
m = 5/1
m =5
Get the y intercept
Substitute the slope m = 5 and any point say (0, 100) into the equation
y = mx+c
100 = 5(0) + c
100 = c
c = 100
Get the required equation;
y = mx+c
y = 5x + 100
Hence the equation in slope-intercept form that represents the data is expressed as y = 5x + 100
What is the slope of the line?
Answers
What is the solution set of (x-2)(x-3) = 2?
O (1.4)
O (2, 3)
O [4,5)
Answers
(1,4)
Answer:
I think A but i'm not sure
Step-by-step explanation:
Given g(x)=2x+3, solve for x when g(x)=3
Answers
Answer:
-3/2
Step-by-step explanation:
Ants have 6 legs. Elena and Andre write equations showing the proportional relationship between the number of ants, , to the number of ant legs . Elena writes a= 6L and Andre writes l=1/6a . Do you agree with either of the equations? Explain your reasoning.
Answers
Answer: Elena would be the correct answer
Step-by-step explanation: since ants have 6 legs and have 1 body we know that there are 6 legs for every 1 ant. hope this helps
helpppppppppppppppppp
Answers
Answer:
hmmmmmmmmmm i think its inverse operation
A bird goes from a higher location to a lower location at a rate of 3 meters per second. Which equation models the change in the bird's position at 120 seconds?
a. 120(-3) = -360
b. 120 x 3 = 360
c. (-120)(-3) = -360
d. 120(-3) = 360
Answers
Answer:
D
Step-by-step explanation:
We know that every second the bird's position lowers by 3(-3) so the equation for it is option D
Answer:
its A i got got right on my test
Step-by-step explanation:
A.P.E.X.
The air pressure P is inversely proportional to the altitude h. write the related variation equation
Answers
Step-by-step explanation:
P * h = k, where k is a real constant.
The terminal side of Ø is in quadrant II and sin ø = 5/13 What is cos ø?
A. 5/12
B. -12/13
C. -5/12
D. 12/13
Answers
Step-by-step explanation:
In Quadrant II, cosine is negative.
We know that sin²x + cos²x = 1, so:
cosx = sqrt[1 - sin²x]
= sqrt[1 - (5/13)²]
= sqrt(144/169)
= -12/13 (since cosx is negative here)
The answer is -12/13. (B)
Option B is correct.
Quadrants and the "cast" Rule:In the first quadrant, the values for sin, cos, and tan are positive.In the second quadrant, the values for sin are positive only.In the third quadrant, the values for tan are positive only.In the fourth quadrant, the values for cos are positive only.
According to the given question
We have, sin ∅ = 5/13
From the trigonometric identities we know that
[tex]sin^{2}[/tex]∅ + [tex]cos^{2}[/tex]∅ =1
substitute the value of sin∅ in the above identity
[tex](\frac{5}{13} )^{2} + cos^{2}[/tex]∅ =1
⇒ [tex]\frac{25}{69} +cos^{2}[/tex]∅ =1
⇒ [tex]cos^{2}[/tex]∅ = 1 - [tex]\frac{25}{169}[/tex]
⇒ [tex]cos^{2}[/tex]∅ = [tex]\frac{169-25}{69} =\frac{144}{169}[/tex]
⇒[tex]cos[/tex]∅ = [tex]\sqrt{\frac{144}{169} }[/tex]
⇒cos∅ = ±[tex]\frac{12}{13}[/tex]
Since, ∅ is in quadrant II, then cos<0
⇒ cos∅ = -[tex]\frac{12}{13}[/tex]
Hence, option B is correct.
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write and equation of the line below
Answers
Answer:
y = 1/4x + 0 or just y = 1/4x
Step-by-step explanation:
First I need the slope so I look at the dots and see how much boxes it goes up and then to the side. So it’s up 2 to the side 8. The slope would be 2/8 but you can simply it by 2 and you get 1/4. And the y intercept is given its zero.
what is the slope intercept form of a linear function
Answers
Answer:
In the slope-intercept form you use the slope of the line and the y-intercept to express the linear function. ... y=mx+b. Where m is the slope and b is the y-intercept.
Step-by-step explanation: I hope this helps
Answer:
y=mx + b
Step-by-step explanation:
16an - 19an +8b +9an +12 b
Answers
Answer:
16an - 19an + 9an + 8b + 12b
6an + 20b
Answer:
6an+20b I believe
Step-by-step explanation:
Jennifer claims that her bank account is growing at a greater rate of change than William’s bank account. Determine if Jennifer is correct and justify your reasoning.
Answers
Answer:
Jennifer is wrongStep-by-step explanation:
Jennifer's bank account is growing at a rate of change 10 as per the given function
William’s bank account is growing at a rate of change 14 as per the table
Jennifer is wrong because 10 < 14