PLEASE HELP, I WILL GIVE BRAINLIEST IF ITS RIGHT :)
(03.03 MC)
The table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −3
0 0
1 3
g(x)
g(x) = 7x + 2
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)
(10 points)
2.
(03.05 HC)
The table below represents the distance of a train from its destination as a function of time:
Time
(hours)
x Distance
(miles)
y
0 665
1 570
2 475
3 380
4 285
Part A: What is the y-intercept of the function, and what does this tell you about the train? (4 points)
Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 4 hours, and tell what the average rate represents. (4 points)
Part C: What would be the domain of the function if the train continued to travel at this rate until it reached its destination? (2 points)
(10 points)
3.
(03.06 MC)
Part A: Billy rented a canoe at $14 for 2 hours. If he rents the same canoe for 5 hours, he has to pay a total rent of $29.
Write an equation in the standard form to represent the total rent (y) that Billy has to pay for renting the canoe for x hours. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
(10 points)
Answers
9514 1404 393
Answer:
(a) Function f is a proportion, so its slope is y/x = 3. The slope of function g is the x-coefficient, 7. The slope of function g is greater. (b) A proportion has a y-intercept of 0; function g has a y-intercept of 2. The y-intercept of function g is greater.(a) The y-intercept is 665, the initial distance to destination. (b) The train's distance to destination is decreasing at 95 miles per hour. (c) The useful domain of the relation is 0 ≤ x ≤ 7.(a) Standard form equation: 5x -y = -4. (We expect that "slope-intercept" form is desired: y=5x+4.) (b) f(x) = 5x +4. (c) The line can be graphed by starting at the y-intercept (0, 4) and drawing a line with slope 5. Axes will be labeled "Rental Time (hours)" (horizontal) and "Rental Cost (dollars)" (vertical). Axes can be numbered in units appropriate to the size of the graph.Step-by-step explanation:
1. (a) The table contains the point (0, 0), and is said to represent a linear function. Consequently, we know that function f is a proportion. Its slope is ...
y/x = 3/1 = 3.
The slope of function g is the x-coefficient, 7. Since 7 > 3, the slope of function g is greater.
(b) As we said, function f has a y-intercept of 0. The y-intercept of function g is the constant in its equation, 2. Since 2 > 0, the y-intercept of function g is greater.
__
2. (a) The y-intercept is the value when x=0, which is 665. That is the train's initial distance to destination.
(b) The average rate of change from x = 1 to x = 4 is ...
m = (285 -570)/(4 -1) = -285/3 = -95 . . . . miles per hour
The train's distance to destination is decreasing at 95 miles per hour.
(c) From part B, we know the train covers 285 miles in 3 hours, so the time to destination will be 3 hours more than 4 hours. (Distance is 285 miles at 4 hours.) The useful domain of the relation is 0 ≤ x ≤ 7.
__
3. We can write the standard form equation using the relation ...
(y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0
(29 -14)(x -2) -(5 -2)(y -14) = 0 . . . . . fill in the given points: (2, 14), (5, 29)
15x -30 -3y +42 = 0 . . . . simpify
5x -y = -4 . . . . . divide by 3 and subtract 4
(We wonder if "slope-intercept" form is desired: y=5x+4.)
(b) The above equation can be solved for y (by adding y+4), and "y" replaced by "f(x)". The result is the "functional form" ...
f(x) = 5x +4
(c) The line can be graphed by starting at the y-intercept (0, 4) and drawing a line with slope 5.
Axes will be labeled "Rental Time (hours)" (horizontal) and "Rental Cost (dollars)" (vertical).
Axes can be numbered in units appropriate to the size of the graph. (That will depend on the graph paper or tool used to create the graph.) An example of a graph is attached.
Related Questions
2. Rachel makes cranberry almond cookies. The number of cups of cranberries and the number of cups of almonds are shown in the table below. What is the ratio of cups of cranberries to cups of almonds?
Answers
Answer:
Step-by-step explanation:
By 2 for the first one. And for 2 they skip counting by 6
What is the simplified base for the function f(x) = 2(7272)?
Answers
Answer:
The simplified base is 9Step-by-step explanation:
The question is not quiet correctly displayed, it should be:
f(x) = 2[tex]\sqrt[3]{27^2^x}[/tex]Simplifying:
f(x) = 2[tex]\sqrt[3]{27^2^x}[/tex] = 2[tex]\sqrt[3]{3^3*^2^x}[/tex] = 2(3²ˣ) = 2(9ˣ)f(x) = 2(9ˣ)The simplified base is 9
The time period, T, of a simple pendulum is directly proportional to the square root of the length, d, of the pendulum.
When d=6, T=5
Find the value of T when d=3
Input note: give your answer correct to 2 decimal place.
Answers
Answer:
[tex]T = 3.54[/tex]
Step-by-step explanation:
Given
Direct Variation of T to [tex]\sqrt d[/tex]
[tex]d =6;\ when\ T = 5[/tex]
Required
Determine T when d = 3
The variation can be represented as:
[tex]T\ \alpha\ \sqrt d[/tex]
Convert to equation
[tex]T = k\sqrt d[/tex]
[tex]d =6;\ when\ T = 5[/tex]; so we have:
[tex]5 = k * \sqrt 6[/tex]
Make k the subject:
[tex]k = \frac{5}{\sqrt 6}[/tex]
To solve for T when d = 3.
Substitute 3 for d and [tex]k = \frac{5}{\sqrt 6}[/tex] in [tex]T = k\sqrt d[/tex]
[tex]T = \frac{5}{\sqrt 6} * \sqrt{3}[/tex]
[tex]T = \frac{5\sqrt{3}}{\sqrt 6}[/tex]
[tex]T = \frac{5 * 1.7321}{2.4495}[/tex]
[tex]T = \frac{8.6605}{2.4495}[/tex]
[tex]T = 3.5356[/tex]
[tex]T = 3.54[/tex] -- approximated
PLEASE HELP!! please do all steps! i’ll mark as brainliest!!!
Answer the following questions using what you've learned from this unit. Write your
responses in the space provided.
1. Factor the polynomial. (2 polnts)
-3x4 - 9x3 + 15x2
2. Use the grouping method to factor the polynomial below completely. (4 points)
10x3 - 35x2 + 6x - 21
Answers
Answer: 1. 3x^2(-x^2-3x+5). 2. (2x-7)(5x^2+3)
Step-by-step explanation:
(1) Find the greatest common factor - 3x^2. Simplify as much as possible.
(2) Split 10x^3 - 35x^2 and 6x-21 into two separate groups. Factor each group separately to get 5x^2(2x-7) and 3(2x-7). The numbers in the parentheses should be the same for each group - (2x-7). Take the numbers outside of the parentheses and put them together to get (5x^2+3). Your final answer will be (2x-7)(5x^2+3).
1. The required factor of the polynomial is
(-3x²)(x²+3x-5).
2. The required factor of the polynomial using grouping method, the answer is (5x²+3)(2x-7).
What is a polynomial?"A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables."
What is factorization of a polynomial?"The factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.
There are six different methods to factorizing polynomials. One of those methods is factorization of a polynomial by grouping method."
1. The given polynomial is
[tex]-3x^{4} - 9x^{3} + 15x^{2} \\= - 3x^{2}(x^{2}+3x-5)\\[/tex]
Therefore, by factorizing the given polynomial, we get:
[tex]- 3x^{2}(x^{2}+3x-5)[/tex].
2. The given polynomial is
[tex]10x^{3}-35x^{2} +6x-21[/tex]
We need to factorize it using grouping method.
Therefore,
[tex]10x^{3}-35x^{2} +6x-21\\= 5x^{2}(2x-7)+3(2x-7)\\= (5x^{2} +3)(2x-7)[/tex]
Hence,
1. The required factor of the polynomial is
(-3x²)(x²+3x-5).
2. The required factor of the polynomial using grouping method, the answer is (5x²+3)(2x-7).
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Which of the following is a vertical line?
1) y = 6
2) x = 6
3) y = 6x - 4
4) y = -x
Answers
Answer:
2) x = 6
Step-by-step explanation:
A vertical line is a line that goes up and down, where x goes not change
It is of the form x=
x =6 is a vertical line
Answer:
It is 2) x=6
Step-by-step explanation:
Since the x axis is the vertical side, it would be vertical. The line would also be vertical, the others are horizantal and are not vertical.
Mr. Floyd, the school librarian, is ordering new keyboards and mice for all of the school's computer labs. Each keyboard costs $13.50, and each mouse costs $6.50. There are 3 computer labs in the school, and each computer lab has s computer stations.
Pick all the expressions that represent how much Mr. Floyd will spend on new keyboards and mice.
Answers
Answer:
13.50 + 6.50 x ( 3 x s) =
Step-by-step explanation:
I don't know what the options are, however that is how I would write it.
a bag contains only red , yellow brown and green marbles
the probabilities of selecting each colour are below
red - 5x
green - 2x
brown - 3x
yellow - 4x
find the probability of selecting a green marble
Answers
Answer:
1/7
Step-by-step explanation:
Probability is the likelihood or chance that an event will occur. this is expressed as;
Probability = Expected outcome/Total outcome
From the question, the total number of marbles is the total outcome
Total outcome = 5x + 2x + 3x + 4x
Total outcome = 14x
Since we are to find the probability of selecting a green marble, the expected outcome will be total number of green marbles which is 2x
Pr(selecting green marbles) = 2x/14x
Pr(selecting green marbles) = 1/7
Hence the probability of selecting a green marble is 1/7
Find the missing y-coordinate that makes the two triangles congruent. Triangle ABC: A(8,4), B(2,6), C(5, 0) Triangle MNO: M(7,4), N(1,2), O(4, y)
Answers
Answer:
negative 2
Step-by-step explanation:
Divide 4a^2 -12ab + 9b^2 by 4a^2 -9b^2
Answers
Answer:
4a(a+b−c)Step-by-step explanation:
4a
2
+4ab−4ca
The common factor =2×2×a
Thus, 4a
2
+4ab−4ca
=4a(a+b−c)
Which equation has infinitely many solutions?
A.
-5(x + 2) = -4x- 12 - X + 2
B.
3x- 4 + 2x = 5(x-4)
c. 5(x + 7) = -5(x-7)
D
6x+ 2 - X=-2x - 2 + 7x
Answers
Answer:
A. -5(x + 2) = -4x - 12 - x + 2
Step-by-step explanation:
The equation that has infinitely many solutions will be the same on both sides.
A is the correct answer.
Simplify the equation by distributing -5 and adding like terms:
-5(x + 2) = -4x - 12 - x + 2
-5x - 10 = -4x - 12 - x + 2
-5x - 10 = -5x - 10
So, this equation is the same on both sides and will have infinitely many solutions.
A is the correct answer.
Answer:
A has infinitely many solutions
Step-by-step explanation:
Once you distribute A you get
-5x-10= -4x-12-x+2
Once you simplfy all that you get
-5x-10= -5x-10
You can check this by putting in a random number and both sides will be equal.
What input is NOT allowed for f(x)
4/-X + 1
Answers
Answer:
x ≠ 1
Step-by-step explanation:
If 1 is used, this will happen:
f(x) = 4/-(1) + 1
f(x) = 4/-1 + 1
f(x) = 4/0 = Undefined
The measures of the angles of a triangle are shown in the figure below. Solve for x.
(4x-6)
73°
57°
Answers
Answer:
14°
Step-by-step explanation:
Sum of angles is 180°
57 + 73 + (4x - 6) = 180
130 + 4x - 6 = 180
4x = 180 - 130 + 6
4x = 56
x = 14°
Would anyone like to help me
Answers
2nd system: 2x = 4 <=> x = 2
23. X=2 Y= -2
If g(x) is the inverse of f(x) and f (x) = 4 x + 12, what is g(x)?
Answers
Answer:
[tex]let \: the \: inverse \: of \: f(x) \: be \: m \\ m = {f(x)}^{ - 1} \\ m = {(4x + 12)}^{ - 1} \\ m = \frac{1}{(4x + 12)} \\ m(4x + 12) = 1 \\ 4x = \frac{1}{m} - 12 \\ x = \frac{1}{4m} - 3 \\ therefore \\ g(x) = \frac{1}{4x} - 3[/tex]
Answer:
g(x) = 1/4 x -3
Step-by-step explanation:
f (x) = 4 x + 12
g(x) = f⁻¹(x)
step 1: re-write as linear equation y = 4x+12
step 2: swap x and y x = 4y + 12
step 3: solve y 4y = x - 12 y = 1/4 x -3
step 4: inverse notation: f⁻¹(x) = 1/4 x - 3 i.e. g(x) = 1/4 x -3
Solve the inequality for u. 7+u>-10
Answers
Answer:
Answer and steps in the pic
Step-by-step explanation:
u > -17
explain:
Move the constant to the right-hand side and change its sign
Calculate the difference
can u pls help me with this question
Answers
Answer:
I cannot see the whole thing
Answer:
Its easy. What grade are you in?
Step-by-step explanation:
{6x+6y=18
{2x-6y=-10
Answers
Answer:
x = 1, y = 2
Step-by-step explanation:
this system is set up nicely to just add because then the y-value will be eliminated and you will have:
8x = 8
x = 1
get y value: 2(1) - 6y = -10
2 - 6y = -10
-6y = -12
y = 2
What is the difference between a fossil and an artifact?
Answers
Answer:
An artifact is an item made by a human being, while a fossil is a preserved remain of a pre-historic animal.
What is the equation of the line that passes through the point (4,7) and has a slope of -1/4
Answers
Answer:
Step-by-step explanation:
since you are given the slope and a point....
use point slope formula y-y1 = m(x-x1)
y - 7 = -1/4 (x - 4)
then get that into the slope intercept form , use the formula y = mx + b as your target
y -7 = -1/4x +1
y = -1/4x +1 +7
y = -1/4x + 8 that's your answer
2(x+3)=x - 4
What is the answer pls
Answers
Answer:
X= -10
Step-by-step explanation:
This is the answer wait I will show u the steps
51) Write the equation of the line passing through (-2, 5) and perpendicular x + 3y = 15.
Answers
Answer: plz mark me brainliest
Step-by-step explanation:
I need points to ask a question
Look at the system of equations graphed below.
What is the solution to the system?
A. X=4, y=-2
68
B. X=4, y=1
5
4
C.x=1, y=-2
3
D D. x=2, y=-1
2
.
2.
4 5 6
-6-5-4 -3 -2 -1 0 1
-1
-3
-4
-5
Answers
Answer: The correct answer to the equation is B.
Hope this helps :)
Not my handwriting sorry if it's sloppy.
Find the quotient of -4 and -9
Answers
Which bag if candy is the better buy and why? (Trents mom shopping)
Answers
Answer:
almond joy
Step-by-step explanation:
its good in my opinion
PLEASE HELP!!!!!
Which of the following is not an exponential function?
Answers
Answer:
g(x)=x3
Step-by-step explanation:
g(x)=x3 is not an exponential function
3. El grupo de Mariana se organizó en seis equipos. Cada equi-
po cumplirá con tres comisiones al mismo tiempo (aseo, pun-
tualidad y orden) durante una semana. Los equipos irán par-
ticipando en orden numérico durante el primer cuatrimestre
del ciclo escolar; los turnos se iniciarán la segunda semana de
clases. Mariana es integrante del equipo 4; ¿en qué periodos
le tocará participar? ¿Todos los equipos participarán el mismo
número de veces? ¿Por qué?
Answers
Answer:
¿en qué periodos le tocará participar?
El equipo cuatro participa en el periodo 5 - 11 - 17
¿Todos los equipos participarán el mismo número de veces?
Todos los equipos los hacen 3 veces . menos 1 equipo que lo hace 2 veces
¿Por qué?
Cuatrimestre. = 120 dias
Numero de semanas = 120/ 7 17,1
17 semanas completas 3 dias
No se trabaja la primera semana. por lo que quedan 16 semana 3 dias.
Son 6 equipos para participar todos serian por lo menos 17 semanas 1 dia.
Step-by-step explanation:
Cuatrimestre. = 120 dias
Numero de semanas = 120/ 7 17,1
17 semanas completas 3 dias
No se trabaja la primera semana. por lo que quedan 16 semana 3 dias.
Son seis equipos. 17 ( 16,3) semanas / 6
Todos los equipos los hacen 3 veces . menos 1 equipo que lo hace 2 veces
Semana 1 2 3 4 5 6
Equipos
1
2 X
3 X
4 X
5 X
6 X
7 X
8 X
9 X
10 X
11 X
12 X
13 X
14 X
15 X
16 X
17 X
18 X
Find x - y subtracted from 0.
a. -x+y
b. -y-x
c. x-y
Answers
need the answer help
Answers
Answer:
Both expression equals 5 when substituting 2 for x, because the expressions are equivalent.
Step-by-step explanation:
Given the expressions:
(1/2)x + 4
x + 6 - (1/2)x - 2
Substituting 2 for x in the equation :
(1/2)x + 4
x = 5
(1/2)2 + 4
2/2 + 4
1 + 4
= 5
x + 6 - (1/2)x - 2
Substituting 2 for x
2 + 6 - (1/2)2 - 2
8 - 2/2 - 2
8 - 1 - 2
= 5
A pyramid has cross-sectional shapes taken parallel to its base that are___ to one another
Answers
Answer:
The fill in the blank is the word similar.
Step-by-step explanation:
A pyramid has a cross-sectional shapes, taken parallel to its base, that are similar to one another.
When we do the cross-section of a pyramid parallel to its base, the cross-section formed will be in the same shape like the base.
Whenever a cross section is done parallel to the base of any pyramid, the resulting shape will be same like the base. As we move up in the pyramid and cross section it, the shape formed will be like the base but with smaller dimensions. But the shape will be the same as the base.
Answer: Similar
Step-by-step explanation:
Triangle A B C is cut by line segment M N. Line segment M N goes from side A B to side B C and cuts both sides into equal parts. The lengths of A M and M B are 88 centimeters, the lengths of C N and N B are 75 centimeters, and the length of A C is 116 centimeters. What is the length of Line segment M N? 58 cm 75 cm 88 cm 116 cm
Answers
Answer:
A
Step-by-step explanation:
Edge
The measure of MN is equal to 58cm, the correct option is A.
What is a Triangle?A triangle is a polygon with three sides, vertices and angle.
Triangle A B C is cut by line segment M N.
such that,
A M = M B = 88 centimeter
CN =NB = 75 centimeter
AC = 116 centimeter
If a line segment joins the mid-points of two sides of a triangle, then the line segment is parallel to the third side of the triangle and the measure is equal to half of its length.
MN = (1/2) AC
MN = (1/2) * 116
MN = 58 centimeter
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