A possible solution for this case of collinear points is (x, AB, BC, CD, AC, AD) = (0, 18, 14, 10, 32, 42).
What are the lengths of collinear line segments?
In this question we have four points that are collinear, that is, that lie on the same line. Mathematically, speaking we have the following equations representing the geometric system:
BC = 14 + x (1)
AD = 42 + x (2)
AC = x + 32 (3)
By (1) and (3):
AB = (x + 32) - (14 + x)
AB = 18
By (2) and (3):
CD = (42 + x) - (x + 32)
CD = 10
If x = 0, then BC, AD and AC are, respectively:
BC = 14, AD = 42, AC = 32
Then, a possible solution for this case of collinear points is (x, AB, BC, CD, AC, AD) = (0, 18, 14, 10, 32, 42).
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Melatonin is fast-acting and has a half-life of approximately 30 minutes. If you take a 10 milligram tablet, write an exponential equation to model this after t time periods.
The exponential equation to model this after t time periods is:
N(t) = 10 ( 1/2 ) [tex]^\frac{t}{30}[/tex]
Given,
Melatonin is fast-acting and has a half-life of approximately 30 minutes.
10-milligram tablet is taken.
We need to write an exponential equation to model this after t time periods.
What is half-life?Half-life is the time required for a quantity to reduce to half of its initial value.
The formula is given as:
N(t) = [tex]N_{0} ~(\frac{1}{2})~^\frac{t}{t_{1/2}}[/tex]
Where
N(t) = quantity of the substance remaining
[tex]N_{0}[/tex] = initial quantity of the substance
[tex]t_{1/2}[/tex] = half-life of the substance
We have,
Half-life = 30 minutes
[tex]N_{0}[/tex] = 10 mg
The exponential equation to model this after t time periods is:
N(t) = 10 ( 1/2 ) [tex]^\frac{t}{30}[/tex]
Thus the exponential equation to model this after t time periods is:
N(t) = 10 ( 1/2 ) [tex]^\frac{t}{30}[/tex]
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-5/3,-2,-7/3,-8/3 arithmetic
Answer:
Step-by-step explanation:
comment on the comment section with a complete question I will help you there please
help pleaseeeeeeeeeeeeeeeeeeee
Answer:
V(x) = -1600x + 21,000
x (number of years)
Step-by-step explanation:
"advised "
(a). if x = 4 (replace x with 4)
Using the formula above
V(4) = -1600(4) + 21,000
= -6400 + 21,000
= $14600
Value of the car after four years is $14600.
(b). if x = 8 (replace x with 8)
Using the formula
V(8) = -1600(8) + 21000
= -12800 + 21000
= $8200.
Value of the car after eight years is $8200.
(c). V(10) = 5000
This is the value of the car after 10 years
Check.
V(10) = -1600(10) + 21,000
= -16000+21,000
= $5000.
Value of the car after 10 years is $5000.
Hope this helps >>>>
Can someone please break this down for me.
Answer:
length: 343 marea: 6418 m²Step-by-step explanation:
Given an oval track in the shape of a 48 m by 96 m rectangle with semicircular ends, you want the length of the track and the area enclosed.
Track LengthIf you remove the rectangle, you see that what remains is a circle of diameter 48. The length of that circular portion of the track is the circumference of the circle:
C = πd
C = π(48 m) = 48π m ≈ 151 m
Added to that length are the two 96 m sides of the rectangle. So, the total length of the track is ...
track length = curved length + straight length
track length = 151 m + 2×96 m = 343 m
The length of the track is 343 meters.
Enclosed areaThe area enclosed by the track includes the area of the circle we saw above, and the area of the rectangle.
The radius of the circular portion is half the diameter, or 24 m. Then the area is ...
A = πr²
A = π(24 m)² = 576π m² ≈ 1810 m²
The area of the rectangular portion is the product of length and width:
A = LW
A = (96 m)(48 m) = 4608 m²
The enclosed area is the sum of these areas:
enclosed area = area of circle + area of rectangle
enclosed area = 1810 m² +4608 m² = 6418 m²
The area enclosed by the track is 6418 square meters.
The length (perimeter) of the track is approximately equal to 342.796 meters and the area enclosed by the track is approximately equal to 6417.557 square meters.
What is the perimeter and the area enclosed by the track?In this problem we have a composite figure generated by a rectangle and two semicircles, of which we must determine its perimeter and area. The perimeter is the sum of the contour lengths of the semicircles and the rectangle and the enclosed area is the sum of areas of the two semicircles and a rectangle.
The perimeter of the composite figure is:
p = 2π · r + 2 · l
p = 2π · (24 m) + 2 · (96 m)
p ≈ 342.796 m
A = π · r² + l · (2 · r)
A = π · (24 m)² + (96 m) · (48 m)
A ≈ 6417.557 m²
The length (perimeter) of the track is approximately equal to 342.796 meters and the area enclosed by the track is approximately equal to 6417.557 square meters.
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The table shows the relationship between x-values and y-values. Which of the following statements is true?
Answer:
When faced with this question as multiple choice, you can either try to verify that one of the answers is true, or you can try to solve for the answer and compare to the choices. Your challenge during a multiple choice test is to identify the fastest possibility so that you can go on to the next problem.
In this case neither choice takes any significant amount of time. You can verify which equation is satisfied by any two points in the table very quickly.
Or you can notice that the equations are all linear and then take two points and solve for the equation of the line between them.
In either case, answer C quickly reveals itself as correct.
Step-by-step explanation:
A city places street lights at equal intervals along a city street beginning 3/8 mile from one end of the street. If the street is 7/8 mile long, how many street lights will the city use? Explain.
The number of street lights that will be needed is 3 street lights.
How to calculate the fraction?From the information, it was stated that the city places street lights at equal intervals along a city street beginning 3/8 mile from one end of the street. If the street is 7/8 mile long,
The number of street lights needed will be:
= 7/8 ÷ 3/8
= 7/8 × 8/3
= 7/3
= 3 street lights.
Therefore, the number of street lights that will be needed is 3 street lights.
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Christa had a music lesson every week for one year.
Each of the 52 lessons lasted for 45 minutes.
Calculate the total time that Christa spent in music lessons.
Give your time in hours.
Answer:
39 hours
Step-by-step explanation:
52 × 45 = 2340
2340 mins into hours = 39 hours
hope this helps :)
Miles has a square garden in his backyard. He decides to decrease the size of the garden by 1 foot on each side in order to make a gravel border. After he completes his gravel border, the area of the new garden is 25 feet2. In the equation (x - 1)2 = 25, x represents the side measure of the original garden.
The length of each side of the original garden was
feet.
The area of the original garden was
feet2.
The original garden was 6 feet long on each side. The original garden's footprint measured 36 feet.
How would you define Area?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.
Using the information provided,
(x-1)²=25
(x-1)=5
x=6
6x6=36 feet²
The original garden had six sides that were the same length.
The original garden covered 36 feet of space.
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Answer:
6 ft & 36ft
Step-by-step explanation:
This is a question from Algebra 1, relating to symbolic representation. Please add an explanation to your answer. Thank you! I will mark you brainliest if you answer & explain!
What the given equation m = ((C + 200y) - 8000))/12y represents is as follows;
m is the amount of each monthly payment
C is the cost of the car
y is the length of loan in years
(C + 200y) - 8000) is the total amount she will repay
12y is the number of payments that she will make
How to interpret Compound Interest formula?
We know that the formula to get the compound interest is;
A = P(1 + r/100)ⁿ
Where;
A is Amount.
P is Principal
r is Rate of interest
n is time in years
Now, when we compare that to our formula given as;
m = ((C + 200y) - 8000))/12y
we can say that;
m is the amount of each monthly payment
C is the cost of the car
y is the length of loan in years
(C + 200y) - 8000) is the total amount she will repay
12y is the number of payments that she will make
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A party planner is making gift bags for an event. He has 96 pencils,
36 erasers, and 24 pencil toppers. Each bag needs to have the same number
of each object. What is the greatest number of gift bags that the party
planner can make? How many of each item are in each bag?
Considering the greatest common divisor, you obtain:
the greatest number of gift bags that the party planner can make is 12.the number of each item present in each bag is 8 pencils, 3 erasers and 2 pencil toppers.Greatest common divisorThe greatest common divisor is the largest number that exactly divides two or more numbers at the same time. That is, it is the largest number by which two or more numbers can be divided, resulting in a whole number.
A method to calculate the greatest common factor must follow the following steps:
Decompose or separate each number into prime factors.Common factors are noted.In each of the commons, the factor with the smallest exponent is chosen.Multiply the chosen factors.This caseTo find the greatest number of gift bags the party planner can make, you find the greatest common divisor.
To do this, decompose the numbers 96, 36 and 24:
96= 2⁵×336= 2²×3²24= 2³×3The common factors with the smallest exponent are: 2² and 3
So, the greatest common divisor between 96, 26 and 24 is calculated as: 2²×3= 4×3= 12
This means that the greatest number of gift bags that the party planner can make is 12.
To calculate the number of each item present in each bag, you divide the quantity of each item by the quantity of gift bags:
96 pencils÷ 12= 8 pencils36 erasers÷ 12= 3 erasers24 pencil toppers÷ 12= 2 pencil toppersFinally, the number of each item present in each bag is 8 pencils, 3 erasers and 2 pencil toppers.
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The weight of an organ in adult males has a bell-shaped distribution with a mean of 340 grams and a standard
deviation of 35 grams. Use the empirical rule to determine the following.
(a) About 68% of organs will be between what weights?
(b) What percentage of organs weighs between 235 grams and 445 grams?
(c) What percentage of organs weighs less than 235 grams or more than 445 grams?
(d) What percentage of organs weighs between 270 grams and 375 grams?
According to the empirical rule, there are a answers of the given statement.
According to the statement
We have to find that the answers of the given statement.
So, For this purpose, we know that the
The empirical rule is a statistical rule which states that for a normal distribution, almost all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).
From the given information:
The mean of 340 grams and a standard deviation of 35 grams.
Then
a) About 68% of organs weight between:
According to the empirical rule:
68% of the information values lie within 1 variance of the mean
95% of the info values lie within 2 variance of the mean
99.7% of the information values lie within 3 variance of the mean
Thus, 68% of the information values consist the range: Mean - 1 variance to Mean + 1 variance.
Using the values of Mean and variance, we get:
Mean - 1 variance = 320 - 20 = 300 grams
Mean + 1 variance = 320 + 20 = 340 grams
This means 68% of the organs will weigh between 300 and 340 grams.
And
b) In order to search out what percentage of organs weight between the given range, we'd like to seek out what proportion far these values are from the mean.
Since, mean is 320 and 280 is 40 but mean, we will write:
280 = 320 - 40
280 = 320 - 2(2)
280 = 320 - 2 Standard Deviations
Similarly,
360 = 320 + 40
360 = 320 + 2 Standard Deviations
So, we've got to inform what percentage of values lie within 2 variance of the mean. in step with the empirical law, this amount is 95%.
So, 95% of the organs weigh between 280 grams and 360 grams.
And
c) From the previous part we all know that 95% of the organs weight between 280 grams and 360 grams.
It is on condition that the distribution is bell shaped. the full percentage under a bell shaped distribution is 100%. So so as to calculate what proportion percentage of values are below 280 and above 360, we'd like to subtract the proportion of values that are between 280 and 360 from 100% i.e.
Percentage valuable outside the range = 100% - Percentage of values inside the range
So,
Percentage of organs weighs but 280 grams or over 360 grams = 100 - Percentage of organs that weigh between 280 grams and 360 grams
Percentage of organs weighs but 280 grams or quite 360 grams = 100% - 95% = 5%
So, 5% of the organs weigh but 280 grams or over 360 grams.
And
D) 300 is 1 variance below the mean and 360 is 2 standard deviations above the mean.
Previously it's been established that, 68% of the info values lie within 1 variance of the mean i.e
From 1 variance below the mean to 1 variance above the mean, the share of values is 68%. Since the distribution is bell shaped and bell shaped distribution is symmetric about the mean, therefore the percentage of values below the mean and above the mean must be the identical.
So, from 68% of the information values that are within 1 variance from the mean, 1/2 them i.e. 34% are 1 variance below the mean and 34% are 1 variance above the mean. Thus, percentage of values from 300 to 320 is 34%
Likewise, data within 2 standard deviations of the mean is 95%. From this half the information i.e. 47.5% is 2 standard deviations below the mean and 47.5% is 2 standard deviations above the mean. Thus, percentage of values between 320 and 360 grams is 47.5%
So,The total percentage of values from 300 grams to 360 grams = 34% + 47.5% = 81.5%
Therefore, 81.5% of organs weigh between 300 grams and 360 grams.
So, According to the empirical rule, there are a answers of the given statement.
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Explain why it is not reasonable to say that 6.32 is less than 6.235 because 6.32 has
fewer digits after the decimal point than 6.235.( Use the process of comparing
numbers to help you with your explanation
The number of digits attached to the number is irrelevant as long as we considering the first non-identical integer. For example:
[tex]6.32215 > 6.32214 \\ since \: 5 > 4[/tex]
Additionally some numbers are written with two decimals only, implying that there an infinite amount of unnecessary zeros attached at the end. For example:
[tex]6.32 = 6.320000000000000000...[/tex]
Now a more clear approach would be to compare these two numbers after attaching these zeros.
[tex]6.3200000000... \\ 6.2350000000...[/tex]
Comparing the first three digits,
[tex]320 > 235 \\ 6.32 > 6.235[/tex]
what ratio is equivalint to 3:1
Answer:
3:1 = 6:2 = 12:4
Hope this helps :)
Answer:
3.1=12.4
Step-by-step explanation:
12.4
12/12+4=12/16=3/4.
so 3.1=12.4
If JK = 8, IL =31, and JL = 25, what is IK?
Answer: IK=14
Step-by-step explanation:
IK=IJ+JK
IL=IJ+JL
IL-JL=IJ+JL-JL
IJ=IL-JL
IK=IL-JL+JK
IK=31-25+8
IK=6+8
IK=14
The position of a body moving along the x-axis is given by s = t³ - 12t2+36t, with s in meters and t in seconds.
Find the total distance traveled by the body from t = 0 tot = 4.
Total distance =
The total distance travelled by the body is 48 meters
According to the question we have been given an equation of the position of a body moving along x-axis as
s = t³ - 12t² + 36t
where, s = distance in meters
t = time in seconds
We need to find the total distance traveled by the body from t=0s to t=4s
The formula for the total distance is given as :
S = |s(1) - s(0)| + |s(2) - s(1)| + |s(3) - s(2)| + |s(4) - s(3)|
Now we will find out the distance travelled in time 0s to 4s
when t = 0s , s = (0)³ - 12(0)² + 36*0
= 0m
t = 1s , s = (1)³ - 12(1)² + 36*1
= 25m
t = 2s , s = (2)³ - 12(2)² + 36*2
= 32m
t = 3s , s = (3)³ - 12(3)² + 36*3
= 27m
t = 4s , s = (4)³ - 12(4)² + 36*4
= 16m
Putting the required values in the above formula we get ,
S = |25-0|+|32-25|+|27-32|+|16-27|
S = 25 + 7 + 5 + 11 meters
S = 48 meters
Hence the total distance travelled by the body is 48 meters
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For each of the following, evaluate or solve, assuming that the function is one-to-one.
Carlos’ pay stub is shown. What is his net pay? Round to the nearest cent. Gross Pay-$1,800.00
Medicare-$26.10
Social Security (6.2%)-?
Federal Withholding Income Tax (19%)-?
By subtracting the taxes from the gross pay we can see that Carlos' net pay is $1,500.30
How to find Carlos' net pay?We know that the gross pay is $1,800, now we need to subtract the social security and taxes.
First, there is a 6.2% and 19% in taxes, adding that we get:
6.2% + 9% = 15.2%
Then we need to subtract a 15.2% of the gross pay, this will give:
P = $1,800*(1 - 15.2%/100%) = $1,800*(0.848) = $1,526.40
And now we also need to subtract the Medicare, which is $26.10, it gives:
$1,526.40 - $26.10 = $1,500.30
We conclude that Carlos' net pay is $1,500.30
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If KL = 3, KM = 8, and MN = 24, what is LN?
Answer: LN=29
Step-by-step explanation:
LN=LM+MN
KM=KL+LM
KM-KL=KL-KL+LM
LM=KM-KL
LN=KM-KL+MN
LN=8-3+24
LN=5+24
LN=29
Please help me with this question
Answer:
Step-by-step explanation:
f(x) = 1/x
Compute ⌈x⌉ and ⌊x⌋ for the following value of x. 71.999
The floor and ceiling functions of 71.999 returns ⌈x⌉ = 71 and ⌊x⌋ = 72.
What is the Floor and Ceiling Functions?By definition, the ceiling function returns the smallest nearest integer which is greater than or equal to the specified number whereas the floor function returns the largest nearest integer which is less than or equal to a specified value.
Thus, the Floor function ⌊x⌋ of 71.999 returns 71 which is less than 71.999. Meanwhile, the ceiling function ⌈x⌉ of 71.999 returns 72 which is greater than 71.999.
Thus, we conclude that the floor and ceiling functions of 71.999 returns ⌈x⌉ = 71 and ⌊x⌋ = 72.
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Express as a simplified fraction 5y - 20 = 0
Answer:
[tex]5y - 20 = 0 \\ 5y = 20 \\ y = \frac{20}{5} = 4[/tex]
your answer is 4Henry and Emma want to buy a total of 2.5 yards of fabric. The fabric costs $6.44 per yard. How much will each pay if they want to split the cost evenly?
$16.10
$14.10
$8.05
$4.03
Write the quadratic function in standard form. f(x) = x^2 − 6x
The standard form of the given equation f(x) = 6x² − x + 1 is:
[tex]f(x)=6\left(x-\frac{1}{12}\right)^2-\frac{23}{24}[/tex]
What are quadratic functions?A quadratic function is one of the following: f(x) = ax² + bx + c, where a, b, and c are positive integers and an is not equal to zero. A parabola is a curve that represents the graph of a quadratic function. Parabolas can open up or down, and their "width" or "steepness" can vary, but they all have the same basic "U" shape.So, f(x) = 6x² − x + 1:
We must convert this to standard form, which is provided by:
[tex]f(x)=a(x-h)^2+k[/tex]Where x² is the co-efficient of the leading term and (h, k) is the curve's vertex (minimum and maximum point).
The formula h = -b/2a can be used to calculate h.
a = 6 and b = -1[tex]h=\frac{-(-1)}{2(6)}=\frac{1}{12}[/tex]We can find k by determining f(h), as k=f (h).
[tex]\begin{aligned}&k=f\left(\frac{1}{12}\right)=6\left(\frac{1}{12}\right)^2-\frac{1}{12}+1 \\&k=\left(6 \times \frac{1}{141}\right)-\frac{1}{12}+1 \\&k=\frac{1}{24}-\frac{1}{12}+1 \\&k=\frac{1-2+24}{24}=\frac{23}{24}\end{aligned}[/tex]
Therefore, the standard form of the given equation f(x) = 6x² − x + 1 is:
[tex]f(x)=6\left(x-\frac{1}{12}\right)^2-\frac{23}{24}[/tex]
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The correct question is given below:
Write the quadratic function in standard form.
f(x) = 6x² − x + 1
The lowest form of this fraction 75/100
In the figure, m ∠ 7 = 100 ° . Find the measure of ∠ 8 .
In the figure, m ∠ 7 = 100 °. The measure of angle 8 is 80°
What do you mean by an angle?An angle is a figure in the Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by the two rays are in the plane where the rays are located. The meeting of the two planes also creates angles. We refer to these as the dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of the intersecting curves.
Angle can also refer to length of a rotation or an angle. This metric represents relationship between a circular arc's length and radius. The arc is centered at the vertex and defined by sides in the case of a geometric angle. When there is a rotation, the arc is defined by any other point and rotation's image, and it is centered at the rotation's center.
Given,
∠7 = 100°
According to the given figure,
∠7+∠8= 180°
100°+ ∠8= 180°
∠8= 180°- 100° = 80°
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A lifeguard walks around the perimeter of the lazy river ride. How far does the lifeguard walk?
The lifeguard walks around the perimeter which is 637.50 feet.
Perimeter is defined as the measure of sum all sides of a 2 dimensional figure. To calculate the perimeter we add all the individual sides of a polygon. The perimeter of a square is the sum of all four sides.
Since a triangle has three sides, the perimeter of a triangle is calculated by adding the sum of all the three sides of the triangle.
In the given figure we can see that the triangle is isosceles and the measure of the sides of the triangle are 216.75 feet , 216.75 feet and 204 feet.
Now the lifeguard walks around the perimeter of the triangular lazy-river ride.
Therefore perimeter = 216.75 +216.75 + 204 = 637.50 feet
Hence the lifeguard walks the perimeter which is 637.50 feet.
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Find the distance between the points. Give an exact answer and an approximation
to three decimal places.
(-1,-9) and (6, - 16)
The distance between the two points are-9.87 units.
What is referred as the distance formula?In coordinate geometry, we have a list of distance formulas that can be used to obtain the distance between two points, the distance between a point and a line, the distances between two vertical lines, this same distance between these two parallel planes, and so on.The Euclidean distance formula is another name for the distance formula used to calculate the distance between 2 points in a two-dimensional plane. Acknowledge two points in the 2D plane, A(x₁, y₁) and B, to derive the formula (x₂, y₂). Assume 'd' represents the distance from A to B.The distance formula is;
d² = (y₂ - y₁)² + (x₂ - x₁)²
Let the two given points be;
A(x₁, y₁) = (-1,-9)
B(x₂, y₂) = (6, - 16)
Put the values in the formula;
d² = (-16 + 9)² + (6 + 1)²
d² = (-7)² + (7)²
d² =2 (7)²
d = 7√2
d = 7×1.41
d = 9.87
Therefore, the distance between the two points is found as 9.87 units.
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3. If m/E+mZF = 120°, which expression is equivalent to mZG?
A (7x)°
C (7x+4)°
B (8x)°
D (8x + 4)º
(7x + 2)°
(8x-2)
In a triangle of EFG we have ∠E+∠F = 120°,E=(8x-2)° and F=(7x+2)°.
Option B is true and angle of G is 60°.
Given that,
∠E+∠F = 120°
In the figure we have a triangle with EFG.
E=(8x-2)°
F=(7x+2)°
We know
∠E+∠F = 120°
8x-2+7x+2=120
15x=120
x=120/15
x=8
We got x =8
∠E=8[tex]\times[/tex]8-2=62°
∠F=7[tex]\times[/tex]8+2=58°
Now, we know in a triangle all angles are equal to 180°.
∠E+∠F+∠G=180°
62°+58°+G=180°
120°+G=180°
G=180°-120°
G=60°
We have 4 option
a) (7x)° which is false
b) (7x+4)° which is true (7[tex]\times[/tex]8+4=60°)
c)(8x)° which is false
d) (8x+4)° which is false
Therefore, option B is true and angle of G is 60°.
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Sean mixes coconut oil with several other ingredients to make homemade toothpaste for his dog Rocky. He uses 1/2 cup of coconut oil to make 2/3 cup of toothpaste.
Using the graph, find the following values of the function.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer:
f(1) = 1
f(4) = -2
f(0) = 2
Step-by-step explanation:
y = f(x)
