The ordered pair given are not inverse to each other because:
Substituting a value say 5/2 into f(x)=2x+5 gives 10Substituting 10 into g(x)= x-5/2 does not return 5/2How to know inverse functionsWhen two functions are inverse to each other substituting a value A in function say AA will give answer say X, substituting the answer X to the the other function say BB returns the value A.
Instance
say function AA, plug in A gives X
the inverse will be:
say function BB plug in X gives A
So, we have f(x)=2x+5 and g(x)= x-5/2
plugging in say 5/2 in f(x) will give
f(x) = 2 * 5/2 + 5
f(x) = 5 + 5
f(x) = 10
We plug in 10 to g(x)= x-5/2
g(x) = 10 - 5/2
g(x)= 7/2
since 7/2 ≠ 5/2 the pair of functions are not inverse to each other
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Need help with this please
Answer:
Step-by-step explanation:
185miles / 75mph = 2.5 hours
The triangle shown has an area of 32.5 square centimeters. Find the measure of the base (segment XY).
Answer:
XY = 13 cm
Step-by-step explanation:
Area of a triangle formula:
area = base × height / 2
a = bh / 2
Plug numbers into equation:
32.5 = b × 5 / 2
Multiply both sides by 2 to isolate the variable
65 = b × 5
Divide both sides by 5 to isolate the variable
13 = b
Check your work:
32.5 = 13 × 5 / 2
32.5 = 65 / 2
32.5 = 32.5
Correct
Which expression is represented by the following area model?
A. 3/5(2/5 + 1/3)
B. 3/5 x 2/5 + 1/3
C. 3/5 + 2/5 + 1/3
D. 3/5 x 2/5 x 1/3
From the fig the Area model is, = 3/5(2/5 + 1/3)
Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area. Now, imagine your square is made up of smaller unit squares.
Area of rectangle = l x b
given that, lets consider the fig as rectangle with one side 2/5+1/3 as breadth and another side 3/5
As we know , Area of rectangle = l x b
l=3/5
b=2/5+1/3
Area model= 3/5(2/5 + 1/3)
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Answer:
The Area model for the fig. is, = 3/5(2/5 + 1/3).
Step-by-step explanation:
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.
Rectangle area = l x b
Given that, let's imagine the fig as a rectangle with a width of 2/5+1/3 and a length of 3/5.
As we know , Area of rectangle = l x b
l=3/5
b=2/5+1/3
Area model= 3/5(2/5 + 1/3)
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 8^x and y = 2^x + 2 intersect are the solutions of the equation 8^x = 2^x + 2. (4 points)
Part B: Make tables to find the solution to 8^x = 2^x + 2. Take the integer values of x between −3 and 3. (4 points)
Part C: How can you solve the equation 8^x = 2^x + 2 graphically? (2 points)
Answer + Step-by-step explanation:
Part A :
Let M(a , b) be a point where the graphs
of the equations y = 8ˣ and y = 2ˣ⁺² intersect.
M lies on both graphs
Then
the coordinates of M verify both equations (equation of graph1 and equation of graph 2)
Then
[tex]b=8^{a}\ \text{on the other hand} \ b=2^{a+2}[/tex]
Then
[tex]8^{a}=2^{a+2}[/tex]
Therefore ‘a’ (the x-coordinates of the points M where the two graphs intersect) is a solution to the equation :
[tex]8^{x}=2^{x+2}[/tex]
Part B : check the attached table.
Part C :
Graphically, we try to spot the points of intersection of the two graphs ,the x-coordinates of those points are the solution to our equation.
In our case , obviously the two graphs intersect at only one point M(1 ,8)
Therefore 1 is the only solution to 8ˣ = 2ˣ⁺².
Also ,Check the attached graph.
In the diagram below, AD || EH, m/ABF
m/CGH = 80°. Find m/I.
Step
1
2
try
Angle
m/ABF = 138°
m/CGH 80°
m/
-
D
H
O
80°
G
I
C
= 138° and
Select a Reason
F
Reason
Given
Given
B
138⁰
E
Answer:
Step-by-step explanation:for the triangle GIF, angle g = 80
angle f = 42 since angle FBA = 138
so angle i = 180 - 42 - 80
= 58
The sum of four and eight times a number is -76.
Answer: x = -10
▬▬▬▬▬▬▬▬▬▬
Given problem,[tex]4 + 8 \times x = -76[/tex]
Find x▬▬▬▬▬▬▬▬▬▬
[tex]4+8(x)-4=-76-4\\8(x)=-80\\\frac{8(x)}{8}=\frac{-80}{8}\\= -10\\x = -10[/tex]
▬▬▬▬▬▬▬▬▬▬
Answer Explained:
Given the keywords sum(add), times(multiply), as well as a number(variable), we can make an equation out of this, which was 4 + 8 * x = -76. We subtracted the sides by 4, then divided both of the sides by the next factor, 8, to get -10.
Thus,
4 + 8 × -10 = -76
Hope this helped you. :)
The distance between Lon
Cardiff is 150 miles.
) What is this distance in k
I
kilo
Answer:
241.5 km
Step-by-step explanation:
The distance between London and Cardiff in kilometres is 241.5 km
en Vision Algebra 2
1-1 Reteach to Build Understanding
Key Features of Functions
Linear, quadratic, and absolute-value functions can be graphed using key features
that the equation identifies. Key features can be labeled using either set builder
notation or interval notation. Interval notation represents a set of real numbers by
a pair of values. Parentheses are used when the points are not included. Brackets
are used for when a boundary point is included.
1. Use the function f(x) = x2 – 16 and identify the key features that are listed in
the table for the graph. Label the graph with the key features.
Key Feature
Domain
Range
Minimum Value
Function is Function is
x-intercept
decreasing increasing
10
y-intercept
LEAD) 14.0VA
Function is Positive
-2 O
Function is Negative
TO
Interval Increasing
Domain:
Interval Decreasing
Range:
-20160-16)
The value of
Domain(- ∞,∞), Range(- 16, ∞), Minimum Value = -16
Function is a quadratic function. x-intercepts are -4 and 4.
The function decreasing before vertex = (-∞,0)
The function increasing after vertex = (0, ∞)
y-intercept is -16.
Function is Positive(- ∞, - 4) ∪ (4, ∞) : , Function is negative : (- 4, 4)
Interval Increasing Domain(0,∞),
Interval Decreasing Range(- ∞, -16)
According to the data, equation f(x) = [tex]x^{2}[/tex] – 16
It is an upward parabola because coefficient of is positive.
The vertex form of a parabola is
f(x) = a[tex](x - h)^{2}[/tex] . . . (2)
where, a is constant and (h , k) is vertex.
From (1) and (2), we get
a = 1, h = 0, k = - 16
So, vertex of the parabola is (0,-16).
The given function is defined for all values of x. So,
Domain : (- ∞,∞)
The value of a function which is an upward parabola cannot be less than the y-coordinate of its vertex. So
Range : (- 16, ∞)
Minimum Value = y-coordinate of vertex = -16
Function is a quadratic function.
For f(x)=0
⇒ 0 = [tex]x^{2}[/tex] - 16
⇒ 16 = [tex]x^{2}[/tex]
⇒ x = ± 4
So, x-intercepts are -4 and 4.
The function decreasing before vertex = (-∞,0)
The function increasing after vertex = (0, ∞)
For x=0,
f(0) = [tex](0)^{2}[/tex] - 16
⇒ - 16
So, y-intercept is -16.
Function is Positive : (- ∞, - 4) ∪ (4, ∞)
Function is negative : (- 4, 4)
Interval Increasing Domain: (0,∞)
Interval Decreasing Range: (- ∞, -16)
Following are the key features of functions
1. Domain and Range
2. x-intercept and y-intercept
3. Positive and Negative intervals
4. Intervals of increasing, decreasing and constant behavior
5. Parent Functions
6. Maxima and Minima
Domain and Range
Domain : The domain is the set of all possible inputs or x-values. To find the domain of a function, we have to look at the x-axis of the graph.
Determining Domain :
1. Start at the origin.
2. Move along the x-axis until you find the lowest possible x-value. This is your lower bound.
3. Return to the origin.
4. Move along the x-axis until you find your highest possible x-value. This is your upper bound.
Range :The range is the set of all possible outputs or y-values. To find the range of the graph, we have to look at the y-axis of the graph.
Determining Range :
For the range, do the same thing but move along the y-axis.
x-intercepts and y-intercepts
x-intercept :
1. This is where the graph crosses the x-axis.
2. To find it algebraically, set y = 0.
3. Have many names :
x-intercept
-Roots
-Zeros
-y-intercept :
1. This is where the graph crosses the y-axis.
2. To find it algebraically, set x = 0.
Positive Interval :
In the diagram below, the graph of the function is above the x-axis in the following intervals.
(-3, -1) and (2, 4)
More precisely, y is positive when x ∈ (-3, -1) and (2, 4).
So, the positive intervals for the above graph are
(-3, -1) and (2, 4)
Negative Interval :
In the diagram above, the graph of the function is below the x-axis in the following intervals.
(-∞, -3), (-1, 2) and (4, +∞)
More precisely, y is negative when x ∈ (-∞, -3), (-1, 2) and (4, +∞).
So, the negative intervals for the above graph are
(-∞, -3), (-1, 2) and (4, +∞)
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5.Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets of cardboard from which she cuts out - squares from each corner. The length of the original piece of cardboard is more than the width. If the volume of the box is , determine the dimensions of the original piece of cardboard.
The dimensions of the original piece of cardboard are 24 inches by 12 inches
How to determine the dimensions of the original piece of cardboard?The given parameters are:
Length (l)= Width (w) + 12
Length of the square cut out = 6
Volume of box, V = 1728
The volume of the box is then calculated as
V = Length of squares * Length * Width
This gives
V = 6 * (w + 12) * w
So, we have:
6 * (w + 12) * w = 1728
Divide both sides by 6
(w + 12) * w = 288
Expand
w^2 + 12w - 288 = 0
Using a graphing calculator, we have:
w = 12
Substitute w = 12 in l = w + 12
Evaluate
l = 12 + 12
l = 24
Hence, the dimensions of the original piece of cardboard are 24 inches by 12 inches
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Complete question
Lorene plans to make a box from rectangular sheets of cardboard from which she cuts out 6 inches squares from each corner. The length of the original piece of cardboard is 12 inches more than the width. If the box is 1728 inches cubed, determine the dimensions of the original piece of cardboard.
Lines a & m are parallel. Using the diagram below, solve for x.
Enter the numerical answer only. Do NOT type x =
Answer:
Angle 2 is 36 degrees because of Alternate Exterior Angle Theorem being that both of the angle outside and are alternate are Congruent.
The answer is X=11 because 2x+14=36, 2x=22, x=11. 2(11)+14=36
The longest river in Africa is the Nile it is 2455 KM longer than the Congo river also in Africa the sum of the lengths of these rivers is 11,195 KM what is the length of each river 
The length of river Nile is 6825 KM and the length of river Congo is 4370 KM
Calculating lengthsFrom the question, we are to determine the lengths of the each river
From the given information,
"The longest river in Africa is the Nile it is 2455 KM longer than the Congo river"
Let the length of river Nile be N
and the length of river Conge be C
Thus,
N = C + 2455
Also,
"the sum of the lengths of these rivers is 11,195 KM"
That is ,
N + C = 11195
Substitute the first equation into the second equation
N + C = 11195
C + 2455 + C = 11195
2C + 2455 = 11195
2C = 11195 - 2455
2C = 8740
C = 8740/2
C = 4370
Substitute the value of C into the first equation
N = C + 2455
N = 4370 + 2455
N = 6825
Hence, the length of river Nile is 6825 KM and the length of river Congo is 4370 KM
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You are the owner of four Taco Bell restaurant locations. You have a business loan with Citizens Bank taken out 60 days ago that is due in 90 days. The amount of the loan is $50,000, and the rate is 9.5% using ordinary interest.
You currently have some excess cash: $35,000. Due to situations beyond your control, you, as the owner, must make an immediate business decision now to pursue only one of these two choices:
1) sending all of the $35,000 to Citizens Bank as a partial payment on your loan, or
2) using the $35,000 to purchase serving supplies such as food containers, cups, and plastic dinnerware for your inventory. This is the last day to take advantage of the opportunity to save some money due to a special discount price that is "10% off" the normal cost of $35,000 for these items.
Consider these calculations:
(a)
How much interest (in $) will you save on this loan if you make the partial payment and don't purchase the additional serving supplies? (Round your answer to two decimal places.)
$
Incorrect: Your answer is incorrect.
(b)
How much money (in $) will you save if you purchase the serving supplies with the discount and don't make a partial payment on the loan? (Round your answer to two decimal places.)
$
(c)
How much (in $) will you save by purchasing the discounted serving supplies rather than making the partial payment? (Hint: Find the difference between the savings on the supplies found in part (b) and the savings on the loan interest found in part (a). Round your answer to two decimal places.)
$
(d)
What other factors should you consider before making this decision?
The amount saved by repaying the loan early is $831.25
The amount of discount received by purchasing supplies is $3,500
The net amount saved by purchasing supplies rather than repaying loan is $2,668.75
What is ordinary interest?
Ordinary interest is the interest computation that is based on 360-day a year count rather than 365-day year count, hence, in determining the amount saved by paying $35,000 out of the amount due to Citizens Bank, we time-apportion the interest for 90 days with respect to 360 days not 365 days.
Amount saved in interest=$35,000*9.5%*90/360
Amount saved in interest=$831.25
Using the $35,000 to purchase serving supplies, 10% discount is given off the normal cost of $35,000
Amount saved with discount=10%*$35,000
Amount saved with discount=$3,500
The difference between discount on supplies and interest saved=$3,500-$831.25
The difference between discount on supplies and interest saved=$ 2,668.75
The other factors to consider before making the final decisions include, the fact the loan is more important than the supplies because the loan relates to the firm's financing rather than operational needs of supplies
Secondly, the amount saved in interest may be more if another loan of $35,000 can be borrowed elsewhere with significant lower interest rates
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What is the area of the figure shown below?
Answer with a numeric value only. That is, do not include "square centimeters" with your response.
Answer:
96cm²
Step-by-step explanation:
1.) You can split the shape into 2: a rectangle and a triangle.
2.) The formula to find the area of the rectangle is:
length × width.
10 (length) × 8 (width) = 80cm²
3.) Then you can find the area of the triangle. The formula for finding the area of a triangle is:
½ × base × height.
½ × 4 (base) × 8 (height) = 16cm²
3.) Add the two answers together to give you the combined and total area of the shape.
80cm² + 16cm² = 96cm²
Help please I’ll mark brainly
Hello,
[tex]4 = - 8 - \boxed{(-12)}[/tex]
Perform the following mathematical operation, and report the answer to the correct number of significant figures. 0.34 x 0.568 = [ ? ]
The multiplication of 0.34 by 0.568 will be 0.19312 and the number of significant figures is five.
How to illustrate the information?In positional notation, significant figures are the digits in a number that are trustworthy and required to denote the amount of something. Significant figures are the number of digits that add to the correctness of a value, frequently a measurement.
It should be noted that significant figures are the numbers that are reliable and are usually non zero digits.
In this case, the multiplication of 0.34 by 0.568 will be 0.19312.
Therefore, the number of significant figures is five.
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The graph of f(x) = x³ has been reflected about the y-axis and vertically shifted up 4 units. Which equations is correct for these transformations ?(choose only one)
a. g(x) = -x³-4
b. g(x) = (-x)³ – 4
c. g(x) = -(x +4)³
d. g(x) = (-x)³ + 4
The transformation of the equation will be f(x) = (-x)³ + 4.
Then the correct option is D.
What is a function?A function is a statement, tenet, or rule that establishes a connection between two variables. Mathematics is replete with functions, which are necessary for the construction of intricate connections.
The collection of all the values that the function may input while it is defined is known as the domain. The whole set of values that the function's output can produce is referred to as the range. The set of values that might be a function's outputs is known as the co-domain.
The function's graph is provided below.
f(x) = x³
If the graph crosses the y-axis, substitute a negative value for x.
The function will then be f(x) = (-x) ³
Add 4 if the graph has been raised by 4 units.
The equation will then be transformed to f(x) = (-x)³ + 4
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HEEEEEEEEEEEEEEEEEEEEEELP
pls
Which point on the number line could represent Negative 2 and one-fourth? A number line going from negative 5 to positive 5. Point A is between negative 4 and negative 3, point B is between negative 3 and negative 2, point C is between negative 2 and negative 1, point D is between negative 1 and 0. Group of answer choices A B D C
Answer:
point A and point B
Step-by-step explanation:
Answer:
B.
Step-by-step explanation:
I think it’s B. because it has negative 3 and negative 2 but for C., it is between negative 2 and negative 1 which can’t be correct since it would end at negative 2 and this is why it is b.
Which funcation has an inverse that is a function b(x)=x^2 +3 d(x)=-9
Functions b(x) is not one-to-one functions as the domain of there inverse is not the range of function then you can't find an inverse function. Function d(x) doesn't include x, then you can't also find an inverse function.
What is Mathematical function ?
Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.
Steps of Finding the inverse of a function f(x):
1. First, replace f(x) with y. This is done to make the rest of the process easier.
2. Replace every x with a y and replace every y with an x.
3. Solve the equation from Step 2 for y. This is the step where mistakes are most often made so be careful with this step.
4. Replace y with In other words, you’ve managed to find the inverse.
5. Remember: the domain of f is the range of and the range of f is the domain of [tex]f^{-1}(x)[/tex].
Using this algorithm, you can find the inverse of non.
for f(x) = x^2 +3
y = x^2 + 3
x = y^2 + 3
y = √x-3
[tex]f^{-1}(x)[/tex] = √x-3
The domain and the range of f'(x) :
domain : [3,∞]
Range : [3,∞]
The domain and the range of f(x) :
Domain: x ∈ R (all real number)
Range: y ≥ 3
Functions b(x) is not one-to-one functions as the domain of there inverse is not the range of function then you can't find an inverse function. Function d(x) doesn't include x, then you can't also find an inverse function.
Therefore, for both the given function we cannot find the inverse.
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Write the following in terms of cos0 only? Csc0
Answer:on the given cushion. We want to represent cost like 30 in terms of cost. Rita. Now by the identity sector tragical toe one by scientists. Now we know that science can't theta plus Costco Arteta is equal to one. So they get signed. Tetteh is equal to plus minus quite a tough one. Minus cause squared theta. So this will be a photo one by plus minus square wrote off one minus y squared theta.
Step-by-step explanation:
Use Table 12-2 to solve.
Ron Sample is the grand prize winner in a college tuition essay contest awarded through a local organization's scholarship fund. The winner receives $8,000 at the beginning of each year for the next 5 years. How much (in $) should be invested at 6% interest compounded annually to award the prize? (Round your answer to the nearest cent.)
$
Based on the amount that Ron Sample gets at the beginning of each year, the number of years, and the interest compounded annually, the amount that should be invested to award the price is $35,720.80.
How to find the invested amount?The value of $8,000 is constant which makes it an annuity. However, it comes at the beginning of each year which makes it an annuity due.
The amount to be invested to gain this $8,000 every year is therefore the present value of this annuity due based on the interest rate.
Present value of annuity due = Annuity due x (Present value interest factor of annuity due, 6%, 5 years)
= 8,000 x 4.4651
= $35,720.80
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How much of an alloy that is 40% copper should be mixed with 500 ounces of an alloy that is 70% copper in order to
get an alloy that is 60% copper?
☐ounces
Answer:
250 ounces of 40% percent copper alloy
Step-by-step explanation:
Let a be the number of ounces of 40% copper alloy.
[tex].4a + .7(500) = .6(500 + a)[/tex]
[tex].4a + 350 = 300 + .6a[/tex]
[tex].2a = 50[/tex]
[tex]2a = 500[/tex]
[tex]a = 250[/tex]
250 ounces of 40% copper alloy.
What is greater .0048 km or 4800 da m (decimeters)
Answer: 4800 decimeter
Step-by-step explanation:
0.0048 km = 48 dm
4800 dm = 0.48 km
M (-3,4) is the midpoint of segment RS. The coordinates of S are (2,-3). What is the x-coordinate of R?
The x-coordinate of point R from the given coordinates is -8
Midpoint of a coordinateThe formula for calculating the midpoint of coordinates is expressed according to the formula:
M(x, y) = {(x₁+x₂)/2, (y₁+y₂)/2}
Given the coordinate points M (-3,4) and S (2, -3)
Substitute
-3 = (x₁+x₂)/2
-3 = 2+x₂/2
-6 = 2 + x₂
x₂ = -8
Similarly;
Substitute
4 = (-3+y₂)/2
4 = -3+x₂/2
8 = -3 + y₂
y₂ = 11
Hence the x-coordinate of point R from the given coordinates is -8
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Which type of sampling is being used in this scenario: a school
administrator gets the alphabetical list of students and chooses every
third one to survey.
A:Cluster
B:Convenience
C:Stratified
D:Systematic
The given scenario, "A school administrator gets the alphabetical list of students and chooses every third one to survey", is Systematic Sampling.
In the question, we are asked to identify the type of sampling used in the scenario: "a school administrator gets the alphabetical list of students and chooses every third one to survey", among cluster, convenience, stratified, and systematic.
First, we will understand all these types of sampling:-
Cluster Sampling: By segmenting the population into clusters, usually, geographically, cluster sampling is performed. These units are referred to as blocks or clusters. The clusters are chosen at random, and each component in the chosen clusters is used.Convenience Sampling: Convenience sampling is the most straightforward method, but it should never be used. Convenient data are utilized in convenience sampling. These are the first individuals the surveyor encounters.Stratified Sampling: The population is also divided into groups known as strata via stratified sampling. This time, though, it is based on a characteristic rather than a location.Systematic Sampling: In systematic sampling, the elements are "counted off" from the list. Every kth element is thus taken. Comparable to having everyone in a line and counting off "1,2,3,4; 1,2,3,4; etc." All those numbered 4 would be used once the list had been completed.In the given scenario, the school administrator is getting the list of students in alphabetical order, similar to taking everyone in a line and counting off "1,2,3,4; 1,2,3,4; etc. And then he is choosing every third student, similar to choosing all those numbered 4.
Thus, the given scenario, "A school administrator gets the alphabetical list of students and chooses every third one to survey", is Systematic Sampling.
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How to do this picture 8th grande math
Answer:
4.61x10^5
Step-by-step explanation:
You want the first number to be between 0 and 10, not equaling either. So you move the decimal place to the left. Then, you write the second half, which is that you multiply it by ten to the power of however many digits you moved to the left for, which is 5.
Algebraic fraction equations
Solving question
Answer:
10x-11 over 4
Step-by-step explanation:
step1:find common denominator
step 2:apply the distributive property
step3: remove the parentheses for addition or subtraction
step4: reorder and gather like terms
step5: collect co-efficients of the like terms
step6: calculate the sum or difference
Write the equation of the line with a slope of 2/7 that passes through the point (3, -4). Write solution in slope intercept form.
The equation of the line with a slope of 2/7 that passes through the point (3, -4) is:
y = (2/7)*x - 34/7
How to write the linear equation?Here we know that the linear equation has a slope of 2/7, so we can start by writing it as:
y = (2/7)*x + b
Now we need to find the value of b, which is the y-intercept.
To find the value of b, we can use the values on the given point, which is (3, -4), This means that when the value of x is 3, the value of y is -4, then we can replace that in the above linear equation, so we will get:
-4 = (2/7)*3 + b
-4 - 6/7 = b
-28/7 - 6/7 = b
-34/7 = b
Then we can conclude that the linear equation is:
y = (2/7)*x - 34/7
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help me pls asap ill give u 21 points'
Answer:
I think the answer is A
Step-by-step explanation:
I'm not sure if it's correct or not but I chose the option because the atoms in substance are not chemically combined
Which of the following represents an EFFICIENT point of production?
A. Point B
b. Point A
c. Point D
d. None
Answer:
d none
Step-by-step explanation:
because they are sloping down
An inchworm moved 1/2 foot in 10 seconds. An earthworm moved 12 inches in 60 seconds. (12 inches = 1 foot)
Determine if the situation represents a proportional relationship.
Answer:hi
Step-by-step explanation:hello
