Tell whether the data represents a linear, an exponential, or a quadratic function. Then, write the function. Picture is attached. I need help!
Answers
SOLUTION:
Case: Equations
Method:
The table:
Plotting the points
Studying the points, could either be quadratic or exponential.
We will proceed to test the points but because the increase of the y values as x increases from left to right is not a fine pattern, it will most likely not be exponential.
Next, we test a quadratic model on the graph
[tex]y=ax^2+bx+c[/tex]Final answer:
Quadratic function
[tex]y=x^2+4x-12[/tex]
To be linear, you'd need a fixed increase in the y-values for a constant increase in the x-values. As x increases by 1 in each new point, your y-values increase by 1, 3, 5, and 7 respectively. That is not the same increase each time. This is not linear.
To be exponential, you need a fixed percent increase in the y-values between the points. From (-2,-16) to (-1,-15), your increase is 1/16 or 6.25%. From (-1,-15) to (0,-12), your increase is 3/15 or 20%. That is not a constant percent increase.
The only option left is quadratic.
To find the function, start with c = -12, based on the point (0,-12).
This gives you f(x) = ax^2 + bx -12
Next plug in (2,0) into f(x): 0 = 4a + 2b - 12
And plug in (1,-7) into f(x): -7 = a + b -12
You now have two equations with two unknowns.
Solve equation 2 for a:
5-b = a
Substitute that into equation 1
0 = 4(5-b) + 2b - 12
0 = 20 -4b + 2b - 12
-8 = -2b
4 = b
Substitute that b-value into 5-b=a
5 - 4 = a
1 = a
You have your three values and have your function:
f(x) = 1x^2 + 4x - 12 or f(x) = x^2 + 4x - 12
You can confirm that the other points also fit with this function.
Related Questions
In which of the following categories do the three families spend about the same dollar amount each month (within $25 of each other)? Select all that apply.HousingFoodChildcareTransportationInsuranceOther NeedsTaxes
Answers
Answer:
Food
Transportation
Explanation:
To find thh correct category, we need to calculate the amount spend on each category for each family, so taking into account the circle graphs, we get:
Family A (income: $5,400)
Housing: 5400 x 19% = 1026
Food: 5400 x 14% = 756
Childcare: 5400 x 18% = 972
Transportation: 5400 x 11% = 594
Insurance: 5400 x 23% = 1242
Other Needs: 5400 x 9% = 486
Taxes: 5400 x 5% = 270
Saving: 5400 x 1% = 54
Family B (income $4675)
Housing: 4675 x 16% = 748
Food: 4675 x 16% = 748
Childcare: 4675 x 18% = 841.5
Transportation: 4675 x 13% = 607.75
Insurance: 4675 x 28% = 1309
Other Needs: 4675 x 7% = 327.25
Taxes: 4675 x 2% = 93.5
Family C (income: $6675):
Housing: 6675 x 14% = 934.5
Food: 6675 x 11% = 734.25
Childcare: 6675 x 30% = 2002.5
Transportation: 6675 x 9% = 600.75
Insurance: 6675 x 20% = 1335
Other Needs: 6675 x 6% = 400.5
Taxes: 6675 x 10% = 667.5
Now, we need to calculate the differences in each categories:
Housing
A - B = 1026 - 748 = 278 > 25
Food
A - B = 756 - 748 = 8
B - C = 748 - 734.5 = 13.5
A - C = 756 - 734.25 = 21.75
Childcare
A - B = 972 - 841.5 = 130.5 > 25
Transportation
A - B = 594 - 607.75 = -13.75
B - C = 607.75 - 600.75 = 7
A - C = 594 - 600.75 = -6.75
Insurance
A - B = 1242 - 1309 = -67 < -25
Other Needs
A - B = 486 - 327.25 = 158.75 < 25
Taxes
A - B = 270 - 93.5 = 176.5 > 25
Therefore, the answers are:
Food
Transportation
if the vertical line test touches the graph more than once, then the graph is a function.
False
True
Answers
The statement is false, the correct one would be:
"if the vertical line test touches the graph more than once, then the graph is not a function."
Is the statement true or false?
A function is a relation that maps inputs x into outputs y, such that each input x can be mapped into only one output.
Remember that the inputs are in the horizontal axis, now, if we draw a vertical line and that line touches the graph twice, this will mean that one input will have two outputs, and thus, that would not be a function.
Then the statement is false
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The function C(x) = 10x +3,000 represents the cost to produce a number of items. How many items should beproduced so that the average cost is less than $30?Provide your answer
Answers
Given:
The cost function is C(x) = 10x + 3000.
Explanation:
The equation for the average cost is,
[tex]\begin{gathered} A(x)=\frac{C(x)}{x} \\ =\frac{10x+3000}{x} \end{gathered}[/tex]The inequality for x is,
[tex]\frac{10x+3000}{x}<30[/tex]Solve the inequality for x.
[tex]\begin{gathered} \frac{10x+3000}{x}\cdot x<30\cdot x \\ 10x+3000-10x<30x-10 \\ \frac{3000}{20}<\frac{20x}{20} \\ 150So the number of items should be more than 150.
- Part A: Is x = 6 a solution of the equation 8x+8 = 56? Explain. Part B: Suppose the solution x = 6 increases to x = 9, and the left side of the equation stays the same. How would the right side need to change if the solution is now x = 9?
Answers
Answers to both subparts are given below:
(A) Yes, x = 6 is the solution of the equation 8x+8 = 56.(B) We need to add 24 on the right side of the equation when x = 9.What do we mean by equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.So, (A) x = 6 is the solution of equation 8x+8 = 56:
Substitute x = 6 in equation 8x+8 = 56 as follows:
8x+8 = 568(6)+8 = 5648 + 8 = 5656 = 56Yes, x = 6 is the solution of the equation 8x+8 = 56.
(B) The change on the right side if x = 9:
Substitute x = 9 in equation 8x+8 = 56 as follows:
8x+8 = 568(9) + 8 = 5672 + 8 = 5680 = 56Now,
80 - 56 = 24So, we need to add 24 on the right side of the equation when x = 9.
The answers to both subparts are given below:
(A) Yes, x = 6 is the solution of the equation 8x+8 = 56.(B) We need to add 24 on the right side of the equation when x = 9.Know more about equations here:
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The ordered pair below is form an inverse variation.find the constant of variation.(8,6)
Answers
We have that an inverse variation can be represented by the following equation:
[tex]\begin{gathered} k=xy \\ or \\ y=\frac{k}{x} \end{gathered}[/tex]In this case we have the ordered pair (8,6), then, we have the following constant of variation:
[tex]\begin{gathered} (x,y)=(8,6) \\ \Rightarrow k=(8)(6)=48 \\ k=48 \end{gathered}[/tex]therefore, the constant of variation is k = 48
I need help solving: c= 8a-3b and solve for a
Answers
hello
[tex]c=8a-3b[/tex]solve for a
step 1
add 3b to both sides of the equation
reason; we're doing this so that we take -3b to the other side of the equation so the we can have a and it's coefficient on one side of the equation
[tex]\begin{gathered} c=8a-3b \\ c+3b=8a-3b+3b \\ c+3b=8a \end{gathered}[/tex]or we can simply say take -3b to the other side of the equation in order to make it easy to equate a
but note that whenever a variable or real number crosses an equality or inequality sign, the sign changes from either positve (+ve) to negative (-ve) or negative (-ve) to positive (+ve).
in this case, -3b
now we have our equation almost set
step 2
divide both sides by 8 to solve for a
[tex]\begin{gathered} 8a=c+3b \\ \frac{8a}{8}=\frac{c+3b}{8} \\ a=\frac{c+3b}{8} \end{gathered}[/tex]pls help thx i don’t know what to do here options are a)0.3125b)2.2c)6.6d)3.2
Answers
Given:
The graph for height and width.
[tex]Height=constant\times width[/tex]Required:
What is the value of the constant in the equation?
Explanation:
From graph, we can evaluate respective values in equation and can get value of constant as:
[tex]\begin{gathered} height=constant\times weight \\ 1.6=constant\times0.5 \\ constant=3.2 \end{gathered}[/tex]Answer:
The value of constant equals 3.2
If this trapezoid is moved through the translation (x+3, y-2), what will the coordinates of B’ be?
Answers
The coordinates of B' in the image of the trapezoid upon translation would be; (-2, 2).
What would be the coordinates of B' after the translation (x+3, y-2) has been done on the trapezoid?It follows from the task content that the coordinates of the point, B' on the trapezoid after the translation (x+3, y-2) has been carried out is to be determined.
On this note, since it follows from the image attached that the coordinates pair of point B, in the trapezoid's pre-image is; (-5, 4).
It simply follows that upon carrying out the transformation; (x+3, y-2) on the trapezoid, the coordinates pair of point B is; (-5+3, 4 -2).
Hence, the required coordinate pair of point B' is; (-2, 2).
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A spherical tank for liquefied petroleum is 8.0 in. In diameter. What is the ratio of the surface area to the volume of tank
Answers
The ratio of the surface area to the volume of the tank is 3 : 4
What is volume?The volume of a shape is the amount of space in it
How to determine the ratio?The given parameter is
Diameter, d = 8.0 inches
Calculate the radius of the above diameter
So, we have
r = d/2
Substitute the known values in the above equation
r = 8/2
Evaluate
r = 4
The surface area of a sphere is
A = 4πr²
Where r represents radius
So, we have
A = 4π(4)²
The volume of a sphere is
V = 4/3πr³
Where r represents radius
So, we have
V = 4/3π(4)³
The ratio is represented as
Ratio = A : V
So, we have
Ratio = 4π(4)² : 4/3π(4)³
Divide by 4³π
Ratio = 1 : 4/3
Multiply the ratio by 3
Ratio = 3 : 4
Hence, the ratio is 3 : 4
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p= principal amount, 0.12= the interest charged; p+0.12p=224 . write a problem based on the given information
Answers
Step 1: Let's review the information given to us to answer the problem correctly:
• p = Principal
,• 0.12 = Interest rate
,• 224 = Future value
Step 2: Let's write a problem based on this information, using the Simple Interest Formula, as follows:
A = P(1 + rt), where:
A = Final amount
P = Principal
r = Annual interest rate
t = Time in years
224 = P (1 + 0.12t)
224 = 1.12Pt
Pt = 224/1.12
Pt = 200
If P = 200, then t = 1
Step 3: Let's interpret the answer and the problem we just wrote.
What is the amount of principal and the time of deposit for a savings account that earns 12% annually, and shows a final balance of $ 224?
Answer: $ 200 and the period of time is 1 year.
How many lines of symmetry does the figure have
○ 8
○ 7
○ 9
○0
Answers
Answer:
7
Step-by-step explanation:
First count the sides and draw a line above the shape and you will it's 7
A rectangular piece of cardboard that is 10 inches by 14 inches has squares of length x inches on a side cut from each corner. (Assume that 0 < x < 5.) If the flaps of the figure are folded up, an open box is formed. Represent the volume of this box in the form of a polynomial function V(x).
Answers
This is an aproximation of the described situation. We are taking 4 squares of side lenght x from each corner.
The dashed lines mark up what would be the base of the box. The blue scrabbled areas will be the sides of the box.
Recall that to calculate the volume of the box, we need to multiply the lenghts of each side of the base and then multiply it by the height of the box. So, to calculate the volume we need to determine the lenght of the dashed lined.
Let us calculate the lenght of the black dashed lines. Notice that the horizontal side has a total lenght of 14. So, since we are taking 2 squares of side x, we have that the lenght of the dashed line plus twice the lenght x, we get the total lenght of the side. That is
[tex]\text{Black dashed line + 2x = 14}[/tex]Then the lenght of the black dashed line is 14-2x.
In the same manner, we can calculate the red dashed lines' lenght. It is 10-2x. Now, our box would be
In the picture, the green line represents the height. Comparing the blue and red lines, we have that the lenght of the green line corresponds to the lenght of the side of the square (x).
So now, we know that the volume of the box is
height * lenght of the base * width of the base = (14-2x)*(10-2x) * (x)
which is a polynomial of the variable x.
A jogger goes 0.8 mi east and then turns south. If the jogger finishes 1.7 mi fromthe starting point, how far south did the jogger go?
Answers
We can use Pythagoras theorem:
[tex]\begin{gathered} H^2=a^2+b^2 \\ \\ \end{gathered}[/tex]Where H=hypotenuse and "a" and "b" are the other sides of the triangule.
In the current problem, we have:
H = 1.7, a = 0.8, b=?
Then:
a(n)=3n-7 what is the sum of the 1st and 5th terms of sequence
Answers
Answer: 4
Step-by-step explanation:
To find the first term you replace n with 1.
a(1) = 3(1) -7
a(1) = -4
Now that you have the first term you must find the fifth term by filling in 5 for n.
a(5) = 3(5) - 7
a(5) = 15 - 7
a(5) = 8
Now that we have both terms simply add them together to find the sum.
-4 + 8 = 4
Identify the digit with the given place value. 116.625 thousandths
Answers
The given number : 116.625
At a lacrosse tournament, students are charged $7 per ticket and adults are charged $10 per ticket. If 450 people attended the tournament, and a total of $4,200 was collected in ticket fees, how many students attended the tournament?
60
100
200
280
Answers
The number of students that attended the tournament is 100.
How many students attended the tournament?The simultaneous equations that would be used to solve this question is:
10a + 7s = 4,200 equation 1
a + s = 450 equation 2
Where:
a = number of adults s = number of studentsThe elimination method would be used to solve the equations.
Multiply equation 2 by 10
10a + 10s = 4500 equation 3
3s = 300
Divide both sides of the equation by 3
s = 300 / 3
s = 100
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Write the equation in point-slope form of the line that passes through the given point with the given slope.
(3, 1); m = 2
Answers
Answer:m = (y – y1)/ (x – x1)
⇒ y – y1 = m(x – x1)….(i)
Step-by-step explanation:
Lookout station A is 12 miles from the fire. Lookout station B is 39 miles from station A. The angle at station A is 52°. Find the distance between Station B and the fire.
Answers
Therefore, in order to find out the distance from station b to the fire, we must use the sine formula, as we know that sine is the opposite side divided by the hypotenuse.
We want to find out the opposite side and we already have the hypotenuse that is 12 miles.
So:
[tex]\begin{gathered} \sin52=\text{ }\frac{x}{12} \\ 12(\sin52)=x \\ 12(0.788)=x \\ 9.456=x \end{gathered}[/tex]Therefore, station B i 09.456 miles from the fire.
A={1,2,6} B= {x | x is an odd whole number less than 8}. Find A∪B.
Answers
The value of set A union set B is A ∪ B = { 1, 2, 3, 5, 6, 7 }.
Consider the set,
A = { 1, 2, 3 }
And, B = { x | x is an odd whole number less than 8 }
An integer's parity determines whether it is even or odd. If an integer is a multiple of two, it is even; otherwise, it is odd.
Therefore, all the numbers less than 8 are:
1, 3, 5, 7
Therefore, the set B will be:
B = { 1, 3, 5, 7 }
In set theory, the set containing every element in a collection is the union of all its sets.
So,
A ∪ B = { 1, 2, 6 } ∪ { 1, 3, 5, 7 }
A ∪ B = { 1, 2, 3, 5, 6, 7 }
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10 candidates are running for president and vice presidentpositions. What is the probability that a particular candidatedoes not win a position?Select one:1/5, 1/20, 1/10, 4/5
Answers
The answer is:
[tex]\frac{4}{5}[/tex]Explanation:
To calculate the probability of an event A occurring, we use the formula:
[tex]P(A)=\frac{favorable\text{ }outcomes}{total\text{ }outcome}[/tex]And, if P(A) is the probability of A occurring, the probability of A not occurring is:
[tex]P(\neg A)=1-P(A)[/tex]In this case, for a particular candidate to win a position, the total outcome is 10 people, and the favorable outcome is 2, for the 2 positions to be elected.
Then:
[tex]P(A)=\frac{2}{10}[/tex][tex]P(A)=\frac{1}{5}[/tex]This is the probability of winning a position. The probability of not winning is:
[tex]\begin{gathered} P(\neg A)=1-\frac{1}{5} \\ p(\neg A)=\frac{4}{5} \end{gathered}[/tex]help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeee
thank you
Answers
The domain can be best described using interval notation. The domain is [-7,8].
The range can be best described using interval notation. The range is [-4,3]
The graph of a function is given. As the graph is a straight line, it is clear that the function is a linear function. Also the function graphed has no breaks or jumps. Hence the function is continuous.
The domain of a function is the x-values for which the function is defined or the function has values.
The values of the function corresponding to the x-values in the domain is called the range. It is also called image and is a subset of the co-domain set.
Now since the graph of the function given is continuous we can better describe the domain and range of the function in the form of intervals.
The x-values for which the function is defined lies form -7 to 8 on the x-axis and hence it is the domain.
The y-values corresponding to the x-values in the domain lies between -4 and 3 on the y-axis and hence it is the range.
That is, The domain is [-7,8] and The range is [-4,3].
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What is the area of the corn field?
Answers
Answer:
23x-3
Step-by-step explanation:
5x+2+8x-11+4x+3+3+2x+4x Got this from adding the area around the field
5x+8x+4x+2x+4x+2-11+3+3 I grouped like-terms
23x+2-11+3+3 I added like-terms
23x-3 Then I got
help fast please!!!!!!
Answers
Answer:
B is correct.
Step-by-step explanation:
[tex] \frac{5.96 \times {10}^{4} }{2.98 \times {10}^{3} } = 2 \times 10 = 20[/tex]
Slope is 1 and (-2,1) is on the line
Answers
Answer:
y = x + 3
Step-by-step explanation:
Write the equation?
Use:
m (slope) = 1
x = -2
y = 1
y=mx + b
1 = 1(-2) +B
1 = -2 + b Add 2 to both sides
3 = b
y = mx + b
y = 1x + 3
y = x + 3
A substance has a mass of 53 grams. Its volume is 12 ml3. What is thedensity? Round to the nearest Tenth. (1 number after decimal) & be sure toinclude the correct label.Your answerThe density of sulfur is 2.1g/cm3. If you have a volume of 6 cm3, what is the poinmass? Round to the nearest Tenth.
Answers
1) Gathering the data
mass = 53 g
V = 12 ml
The density is given using the following formula:
[tex]\begin{gathered} d=\frac{m}{V} \\ d\text{ =}\frac{53}{12\text{ }} \\ d=4.42\text{ g/ml} \end{gathered}[/tex]ONLY (e) questionThe turning points of the graph are ___Type in ordered pair, round each coordinate to two decimal places
Answers
Answer:
[tex]\begin{gathered} (-4.85,-243) \\ (-1.5,136.69) \\ (1.85,-243) \end{gathered}[/tex]Explanation:
Given the function:
[tex]f(x)=3 x\left(x^{2}-9\right)(x+6)[/tex]The graph of f(x) is attached below:
From the graph, the turning points are:
[tex]\begin{gathered} (-4.85,-243) \\ (-1.5,136.69) \\ (1.85,-243) \end{gathered}[/tex]Which of these expressions entered into a graphing calculator willreturn the probability that 45 or fewer heads come up when flipping acoin 100 times?
Answers
Prob P = Heads/ flips
. = (n,p,c)
Here n is number of flips
. p is prob of 1 success
. c number of sucess
Then ANSWER IS
OPTION A) binomcdf (100,0.5, 45)
Farmer Jill needz to ship 9,918 apples if each crate can hold 21 apples how many full crates of apples will jill get how many will be leftover
Answers
The most appropriate choice for division will be given by -
Number of crates = 472 and number of apples remaining = 6
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
Here,
Total number of apples = 9918
Number of apples in one crate = 21
Total number of apples = 9918 ÷ 21
Quotient of 9918 ÷ 21 = 472 and remainder = 6
Number of crates = 472 and number of apples remaining = 6
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7 A total of 340 gallons of oil is divided between two tanks. If at least half of the oil is pumped into the first tank, which number line represents that possible amount of oil in the second tank? (A 400 100 200 300 B 300 400 200 100 tot 200 300 400 100 O HH 300 400 100 200
Answers
Half of 340 gallons is:
[tex]170\text{ gallons.}[/tex]Let x represent the amount of oil in the second tank, we know that at least 170 gallons were pumped into the first tank, therefore, at most the other half is in the second tank:
[tex]x\ge170.[/tex]Answer: The above inequality in the number line is represented as follows:
Your tractor broke down and was in the shop for 4 days.
Mechanics worked on it for 21.4 hours at $48 per hour. They
replaced $1875.42 worth of parts. You lost $18 per hour by not
having the use of the tractor. You work a 15 hour day. How
much did the labor cost? How much did you lose by not having
the use of your tractor?
Answers
The total labor cost for repairing the tractor including the parts replacement is $2902.62 and the loss by not having the use of tractor is $1080.
What is Direct Labor?An individual product, cost center, or work order is assigned to a certain amount of direct labor, which is labor used in production or services. The production team that creates items, such as machine operators, assembly line workers, painters, and so on, is referred to as direct labor when a business generates products.
Total hours of mechanic worked is 21.4Cost for mechanic per hour is $48Cost for replacement of parts = $1875.42Total labor cost = (Total hours of mechanic worked)(Cost for mechanic per hour) = (21.4)(48) = $1027.2Total labor cost including replacement of parts = (Total labor cost)+(Cost for replacement of parts) = $2902.62 Total days the tractor kept in the mechanic shop is 415 hours of work is done with a profit of $18 per hourThe loss by not having the use of tractor= (Total days the tractor kept in the mechanic shop) (hours of work is done in a day) (profit per hour)The loss by not having the use of tractor= (4)(15)(18) = $1080To learn more about Direct labor, refer to:
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