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
3×_5=16 and 3×=21
the first equation is a true statement for a certain value of x.
can you explain why the second equation must also be true for the same value of x?
Answers
Understanding:
First, let's try simplifying the first equation as much as we can. As you know, you can add, subtract, multiply, divide, etc on both sides of the equation and it will remain the same value. To simplify [tex]3x-5=16[/tex] we can simply add 5 to both sides to cancel the -5 on the left-hand side. That will give us [tex]3x-5 +5=16+5[/tex], notice we added the 5 to both sides. The +5 cancels -5 and 16+5 is 21, which evaluates to [tex]3x=21[/tex]. And this equation looks familiar, it's our second equation actually. That's why both equations are the same, and in that x value that makes the first equation true, it will also do the same for the second equation. If you want to actually find the value of x which makes the equation true, you can simply divide the 21 on the right-side by 3 to make x coefficient equal to 1, [tex]\frac{3x}{3} =\frac{21}{3}[/tex], and that gives us, [tex]x=7[/tex]. When x is 7 both equations are true.
Answer:
We conclude that the second equation must also be true for the same value of x because the value x = 7 satisfies the 2nd equation too.
Step-by-step explanation:
Given the first equation
[tex]3x-5=16[/tex]
Add 5 to both sides
[tex]3x-5+5=16+5[/tex]
simplify
[tex]3x=21[/tex]
Divide both sides by 3
[tex]\frac{3x}{3}=\frac{21}{3}[/tex]
simplify
[tex]x=7[/tex]
Thus, x = 7 is a value that satisfies the first equation.
Now, put x = 7 in the 2nd question to check whether x = 7 satisfies the equation or not.
3x = 21
3(7) = 21 ∵ x = 7
21 = 21
Thus, x = 7 also satisfies the 2nd equation.
Therefore, we conclude that the second equation must also be true for the same value of x because the value x = 7 satisfies the 2nd equation too.
Solve the system of equations x + y = 12 and x + 7y = -20 by combining the
equations.
Answers
Answer:
this will be 12
Step-by-step explanation:
since you said =12
When hitting the ski slopes, which location do skiers have the most potential energy
Answers
Answer:
at the top of the mountain or hill
Step-by-step explanation:
potential energy is stored energy so therefore the higjestpoint will have the most potential energy.
The skier begins at an elevated position, thus possessing a large quantity of potential energy (i.e., energy of vertical position).
What is Kinetic Energy?The energy an object has as a result of motion is known as kinetic energy. A force must be applied to an object in order to accelerate it. We must put in effort in order to apply a force. After the work is finished, energy is transferred to the item, which then moves at a new, constant speed.
The skier has a lot of potential energy because they are starting from an elevated position (i.e., energy of vertical position).
If the skier is starting from rest, all of their mechanical energy is potential energy.
and, Potential energy is lost and kinetic energy, or the energy of motion, is acquired as the skier starts the ascent down the hill.
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Need help!!!!!! ASAP
Answers
Answer:
og
Step-by-step explanation:
In the diagram below
Please help I’ll give brainliest
Answers
Answer:
m<GFA = 110
Step-by-step explanation:
1. ABCD - parallelogram Definition of a parallelogram
(AB ll CD) (AD ll BC)
2. m<B + m<C = 180 Consectuive angles in a
110 + m<C = 180 parallelogram are supplementary
m<C = 70
3. m<GCB = 1/2 m<C Definition of angles bisector
m<GCB = 70
4. m<B = m<D = 110 Opposite angles in a
parrallelogram are congruent
5. m<CDG = 1/2 m<D Defintion of an angle bisector
m<CDG = 55
6. m<GCB+m<CDG+m<CGD=180 Sum of anlges in a triangle (ΔCDG)
70 + 55 + m<CGD = 180
125 + m<CGD = 180
m<CGD = 55
7. m<CGD + m<DGF = 180 Linear pair, supplmentary angles
55 + m<DGF = 180
m<DGF = 125
8. m<C = m<A = 70 Opposite angles in a paralellogram
are congruent
9. m<ADG = 1/2m<D Definiton of an angle bisector
m<ADG = 55
10.m<ADG+m<DFG+m<GFA+m<A=360 Sum of angles in quadrilateral
55 + 125 + m<GFA + 70 = 360 DGFA
m<GFA + 250 = 360
m<GFA = 110
PLS someone help me im trying to get a 80% so i can finish this!
You roll a 6-sided die. What is P(less than 3)? Write your answer as a fraction or whole number.
Answers
Answer:
any number less than 3
Step-by-step explanation:
Let f(x) = −2x 2 − 7 and g(x) = √x + 3. Find (f ∘ g)(25)
Answers
Answer:
(f О g)(25) is -135
Step-by-step explanation:
The composite function (f О g)(x) means substitute x in f by g
∵ f(x) = -2x² - 7
∵ g(x) = √3 + 3
→ To find (f О g)(25), find g(25) first, then substitute x in f by the value of g(25)
∵ x = 25
∴ g(25) = √25 + 3
∵ √25 = 5
∴ g(25) = 5 + 3
∴ g(25) = 8
→ Now substitute x in f by 8
∵ x = 8
∴ f(8) = -2(8)² - 7
∴ f(8) = -2(64) - 7
∴ f(8) = -128 - 7
∴ f(8) = -135
∴ (f О g)(25) = -135
PLSSSS HELP ASAP!! GIVING BRAINLIEST!! Pls Explain :)
At the store, meat was $73.70 for 5 pounds. If you bought 15 pounds, how much would it cost?
Answers
Answer: 221.10
Step-by-step explanation:
Plzz help meeee quickkk!!!
Answers
Answer:
[tex]D.x=35[/tex]
Step-by-step explanation:
[tex]As\ we\ observe\ that,\ all\ sides\ of\ the\ triangle\ are\ marked\ equal,\ the\ triangle\\ provided\ is\ equilateral.\\This\ implies\ that\ all\ the\ angles\ of\ an\ equilateral\ triangle\ are\ equal\ and\\ measure\ 60\ degree.[Through\ Angle\ Sum\ Property]\\Hence,\\(2x-10)=60\\2x-10+10=60+10[Adding\ 10\ to\ both\ the\ sides]\\2x=70[Simplifying]\\x=\frac{70}{2}[Dividing]\\x=35[Finding\ the\ value\ of\ x]\\[/tex]
Damien deposited $100 into his savings account. He then deposits $15 three times per month. Write an equation that shows the amount in Damien's savings account after t months
Answers
Answer: 100 + 45t
Step-by-step explanation:
From the question, we are informed that Damien deposited $100 into his savings account and that he then deposits $15 three times per month.
The equation that shows the amount in Damien's savings account after t months will then be:
= $100 + [($15 × 3) × t months]
= $100 + $45t
= 100 + 45t
SGA is doing a fundraiser to sell candles for project graduation. Small candles cost $4.00 and large candles cost $6.00. They have at most 50 candles, and want to make at least $100. Which system of linear inequalities represents the situation? x: The number of small candles y: The number of large candles
Answers
Given:
Cost of small candles = $4.00
Cost of large candles = $6.00
They have at most 50 candles, and want to make at least $100.
To find:
The system of linear inequalities represents the situation.
Solution:
Let x be the number of small candles and y be the number of large candles.
At most 50 candles means total candles must be less than or equal to 50.
[tex]x+y\leq 50[/tex]
Want to make at least $100. It means, the total sales must be greater than or equal to $100.
[tex]4x+6y\geq 100[/tex]
Therefore, the inequalities in the system of linear inequalities are [tex]x+y\leq 50[/tex] and [tex]4x+6y\geq 100[/tex].
y= 2x +3
y= 4x-3
Is(3,9) a solution of the system?
Choose 1 answer:
A: yes
B: no
Answers
B:yes
Explanation:
Label the point 3 would be x and 9 would be y. Substitute these points into the equation were it corresponds.
Y= 2x+3
9=2(3)+3
9=6+3
9=9
Y=4x-3
9=4(3)-3
9=12-3
9=9
Hope this helps!!
Answer:
A: yes :)
Step-by-step explanation:
6) Jesse is buying a home for $450,000 at 7.8% interest and Jesse is putting 30% down? He wishes to buy 3 points what is the cost of the points?
Answers
Answer:
$9450
Step-by-step explanation:
Given that:
The price of the home = $450000
The interest = 7.8%
Down payment = 30% of price of the home
i.e 0.3 × 450000 = 135000
The principal outstanding balance = 450000 - 135000
= 315000
Finally, the cost of 3 points will be;
[tex]= 315000 \times \dfrac{3}{100}[/tex]
= $9450
m is the midpoint of pq. pm= 9x+3 and mq= 11x-17, find x and pq
Answers
3=2x-7
10=2x
x=5
pq=20x-14
pq=20*5-14
pq=86
The values of x = 5 and pq = 86.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
Operators which let do a basic mathematical calculation
+ Addition operation: Adds values on either side of the operator.
For example 12 + 2 = 14
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 12 -2 = 10
* Multiplication operation: Multiplies values on either side of the operator
For example 12*2 = 24
Given that m is the midpoint of pq,
pm= 9x+3 and mq= 11x-17
⇒ 9x + 3 = 11x - 7
⇒ 3 = 11x - 9x -7
Rearrange the likewise terms and apply the arithmetic operations,
⇒ 3 = 2x - 7
⇒ 10=2x
⇒ x = 10/2
Divided by 2
⇒ x = 5
⇒ pq = 20x-14
⇒ pq = 20*5-14
⇒ pq = 86
Hence, the value of pq is 86.
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Damian's teacher told him that the standardized score (z-score) for his science exam, as compared to the exam scores of other students in the course, is 1.50. Which of the following is the best interpretation of this standardized score?
Damian's test score is 150.
Damian's test score is 1.50 standard deviations above the average test score of students in the course.
Damian's test score is 1.50 above the average test score of students in the course.
Damian's test score is 1.50 times the average test score of students in the course.
None of the above gives the correct interpretation.
Answers
Answer:
Damian's test score is 1.50 standard deviations above the average test score of students in the course.
Step-by-step explanation:
Took the test
This area model shows the quotient of 1/5÷4.
Answers
Answer: 4/5
Step-by-step explanation: 1/5 times 5/1=4/5
Determine the solution of the equation 4y - 5= 7.
A) 4
B) 3
C)
Answers
Answer:
B) 3
Step-by-step explanation:
add 5 to both sides, 4x=12
divide both sides by 4, x=3
Answer:
The answer is B) 3
Step-by-step explanation:
You add 5 to 7 to move it from one side to the other
You should then have 4y=12
Then to solve for why you divide 12 by 4
You will get y=3
So your answer is 3
which calculation and answer show how to convert 9/16 to a decimal
Answers
Answer: 0.5625
Step-by-step explanation:
A is ur answer
h ope it helps!
Construct an equilateral triangle of side 7cm and construct circumcircle.
Can anyone help me with this , I have to sumbit my PROJECT.
THanks
Answers
Answer:
To do this, all you need is to draw triangle with each side being 7 cm, and a circle that intersects all three of its corners.
Step-by-step explanation:
With a ruler and a pencil, draw a 7cm line.With a compass set to a radius of 7cm draw an arc centered around the right end of the line.With the same compass, still at 7cm, draw an arc centered around the left end of the line.These two arcs will intersect on either side of the line (you only need one side, so you only need a small arc in the right place, roughly where you think the third point if the triangle is.Where those arcs intersect is the third point on your triangle. Mark that, and then trace two lines from that point to either end of the line segment you started with.You now have an equilateral triangle with 7cm sides. Next you need to draw the circle
Measure the halfway point on two of your three lines.Draw a line from that each of those halfway points to the opposite corner. The new lines you're drawing will be perpendicular to the edge your measuring against.You have now drawn two line segments, and they intersect in the center of the circle. Now take your compass and set its radius to the distance from that center point to one of the three corner points.Centered on that middle point, trace a circle with the selected radius.And you're done!
What is the equation of the following line written in slope-intercept form?
y = 5x
y = -5x
y =
Answers
Answer:
_+5 is the best way to get the best way answer
Solve these two by using factor the polynomial by grouping
Answers
Answer:
15. (8x^3 + 27)(x + 1)
17. (x^2 + 3)(x + 2)
Step-by-step explanation:
8x^3(x + 1) + 27(x + 1)
x^2(x + 2) + 3(x + 2)
WILL GIVE BRAINLIEST AND 100 POINTS FOR FIRST CORRECT ANSWER
MP _____ PK
Choose the relationship symbol to make a true statement.
Answers
Answer:
give the person above brainliest
Step-by-step explanation:
A number y minus 12 is no more than −32.
The inequality is
Answers
Answer:
y-12<-32
Step-by-step explanation:
just remember to underline the less than sign
helpppppppppppppppppp
Answers
Answer:
addition
Step-by-step explanation:
if you add the 4 to the -2 you will get x=2 therefore isolating the variable
plsss help no spam.
.....................
Answers
Answer:
Third one.
x=6 y=12
Ok!
Answer:
fourth option
Step-by-step explanation:
Given the 2 equations
y = 2x - 3 → (1)
x + y = 18 → (2)
Substitute y = 2x - 3 into (2)
x + 2x - 3 = 18
3x - 3 = 18 ( add 3 to both sides )
3x = 21 ( divide both sides by 3 )
x = 7
Substitute x = 7 into (1) for corresponding value of y
y = 2(7) - 3 = 14 - 3 = 11
Solution is x = 7, y = 11
Plz, Help me with this question.
Answers
Answer:
first option
Step-by-step explanation:
Given
area = 15x - 9 ← factor out 3 from each term
= 3(5x - 3)
Thus the dimensions are 3 by (5x - 3)
Help!!!! I will give brainliest.
Answers
Answer:
Step-by-step explanation:
Well lets try to simplify this.
-3y= -4x +17
y=4/3 x - 17/3
Thus y-int is (0, -17/3)
To solve for x-int, y=0
y=4/3 x - 17/3
0=4/3 x - 17/3
4/3 x = 17/3
x=17/4
Thus x-int is (17/4, 0)
can someone please help me
Answers
Answer:
x=1
Step-by-step explanation:
If BC = 3x, CD = 7x, and BD = 10, what is BC?
Answers
Answer:
BC= 3
Step-by-step explanation:
Suppose a line BD is 10 and it has a point C somewhere on the line. It is given that BC is 3times and CD is 7 times or algebraically if we take x as a variable then according to the given information
BC+ CD= BD
3x+ 7x= 10
10x= 10
x= 10/10
x= 1
3x would give 3 (1)= 3
Hence the Line BC = 3
and the line CD= 7
What would be the equivalent discount for this item be?
Answers
Answer:
it's almost $100 and there's $17 off. so 99.99-17 would make the exact cost 82.99
82.99/99.99= 0.8299 so you payed 83% and that would make it so you got a 17% discount.
but if you didn't want to do all the math, you could've just rounded the 99.99 up to 100, and $17 would make it a 17% discount.