Answer:
24x - 6y + 21
Step-by-step explanation:
3( 8x - 2y + 7 )
Multiply each term in the bracket by 3
= (3 x 8x) - ( 3 x 2y) + (3 x 7)
= 24x - 6y + 21
3 Mathematical Habit 3 Construct viable arguments
The diagram shows a rectangular prism. The areas of the faces a
6 square centimeters, 10 square centimeters, and 15 square centim
What is the volume of the rectangular prism?
15 cm²
6 cm²
10 cm²
As a result, the rectangular prism has a volume of 1 cubic centimeter.
What is the simple definition of volume?The volume of an object is the area enclosed inside its three-dimensional boundaries. It is referred to as an object's capability on occasion.
We must multiply the rectangular prism's length, width, and height to determine its volume. Although we don't directly know these values, we can use the regions of the faces to locate them.
Let's use the letters l, w, and h to denote the prism's length, breadth, and height, respectively. The area of a top and bottom sides is thus determined to be lw = 10 cm², the front and rear faces are lh = 15 cm², and the left and right sides are wh = 6 cm².
These equations can be used to solve for every variable using the following descriptions of the other variables:
l = 10/w
h = 15/l
w = 6/h
When we add these expressions to the volume formula, we obtain:
V = lwh = (10/w)(6/h)(15/l) = 900/whl = 900/(6×10×15) = 1 cm³
As a result, the rectangular prism has a volume of 1 cubic centimeter.
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Each side of a regular hexagon measures 20 inches. What is the exact area of the hexagon?
Answer:
1039.23 square inches
Step-by-step explanation:
a = 20 inches
[tex]\sf \boxed{\text{\bf Area of regular hexagon = $\dfrac{3\sqrt{3}}{2}a^2$}}[/tex]
[tex]= \dfrac{3\sqrt{3}}{2}*20*20\\\\= 3\sqrt{3}*200\\\\= 1039.23 \ inches^2[/tex]
A merchant mixed 12 lb of a cinnamon tea with 3 lb of spice tea. The 15-pound mixture cost $39. A second mixture included 16 lb of the cinnamon tea and 6 lb of the spice tea. The 22-pound mixture cost $58. Find the
cost per pound of the cinnamon tea and of the spice tea.
cinnamon
spice
Answer:
Step-by-step explanation:
Let x be the cost per pound of the cinnamon tea and y be the cost per pound of the spice tea.
From the first mixture, we have:
12x + 3y = 39
From the second mixture, we have:
16x + 6y = 58
We can solve this system of equations by elimination. Multiplying the first equation by 2 and subtracting it from the second equation gives:
16x + 6y = 58
(24x + 6y = 78)
-8x = -20
Dividing both sides by -8 gives:
x = 2.5
Substituting this value of x into the first equation, we get:
12(2.5) + 3y = 39
Simplifying, we get:
30 + 3y = 39
Subtracting 30 from both sides gives:
3y = 9
Dividing both sides by 3 gives:
y = 3
Therefore, the cost per pound of the cinnamon tea is $2.50 and the cost per pound of the spice tea is $3.
a toy rocket is shot vertically into the air from a 9-foot-tall launching pad with an initial velocity of 144 feet per second. Suppose the height of the rocket in feet t seconds after being modeled by the function h(t)=-16² gthg. where v is the initial velocity of the rocket and he is the initial height of the rocket. How long will it take for the rocket to reach its maximum The rocker will reach its maximum height in second(s) launched can be height what s
Answer:
9 is answer you fool......
answer: Click THANKS if you like my answer. have a good day sir/maam #keep safe
First, we need to find the maximum height that the rocket will reach. To do that, we need to find the vertex of the parabolic function h(t) = -16t^2 + 144t + 9. We can use the formula for the vertex of a parabola, which is given by the formula t = -b/2a, where a = -16 and b = 144.
t = -b/2a = -144/(2*(-16)) = 4.5
So the rocket will reach its maximum height after 4.5 seconds.
To find the maximum height, we need to substitute t = 4.5 into the function h(t):
h(4.5) = -16(4.5)^2 + 144(4.5) + 9 = 324
So the maximum height that the rocket will reach is 324 feet.
Therefore, the rocket will reach its maximum height of 324 feet after 4.5 seconds.
Step-by-step explanation:
hope its help<:
For a given recipe 8 cups of flour are mixed with 12 cups of sugar how many cups of flour should be used if 27 cups of sugar are use
Therefore, if we are using 27 cups of sugar, we also need 18 cups of wheat.
What does an arithmetic ratio mean?An ordered combination of integers a and b, rendered as a / b, is a ratio if b is not equal to 0. A percentage is an expression that sets two numbers at the same value. For instance, you could put the percentage as follows: 1: 3 if it's 1 male and 3 girls. (for every one boy there are 3 girls)
If 8 cups of flour are mixed with 12 cups of sugar, then the ratio of flour to sugar is:
8 : 12
Simplifying this ratio by dividing both numbers by 4, we get:
2 : 3
This means that for every 2 cups of flour, we need 3 cups of sugar.
If we are using 27 cups of sugar, we can set up a proportion to find out how much flour we need:
2/3 = x/27
Multiplying both sides by 27:
2 × 27 / 3 = x
Simplifying:
x = 18
Therefore, we need 18 cups of flour if we are using 27 cups of sugar.
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If the graph of a polynomial function P(x) has -intercepts at x = - 4, x = 0, x * 1 point
= 5, which of the following must be true for P(x)?
• (x + 5) is a factor of the polynomial.
• (x-4) is a factor of the polynomial.
•' The degree of the polynomial is 3.
• The degree of the polynomial is greater than or equal to 3.
(x + 5) is nοt necessarily a factοr οf the pοlynοmial, (x-4) is a factοr οf the pοlynοmial are cοrrect statement.
What is a functiοn ?Functiοn can be define in which it relates an input tο οutput.
If the graph οf a pοlynοmial functiοn P(x) has x-intercepts at x = -4, x = 0, and x = 5, then we knοw that the factοrs οf P(x) are (x + 4), x, and (x - 5). This is because a pοlynοmial has x-intercepts where the value οf P(x) is equal tο zerο, and this οccurs when each factοr is equal tο zerο.
Therefοre, we can cοnclude that (x + 4) and (x - 5) are factοrs οf the pοlynοmial P(x), but x is nοt necessarily a factοr. This is because x is a linear factοr with a zerο intercept, but it cοuld be cancelled οut by anοther factοr in the pοlynοmial.
Thus, the cοrrect statement is:
(x + 5) is nοt necessarily a factοr οf the pοlynοmial.
(x-4) is a factοr οf the pοlynοmial.
The degree οf the pοlynοmial is 3 οr greater since the pοlynοmial has three x-intercepts. Hοwever, we cannοt determine the exact degree οf the pοlynοmial withοut additiοnal infοrmatiοn.
Therefοre, (x + 5) is nοt necessarily a factοr οf the pοlynοmial, (x-4) is a factοr οf the pοlynοmial are cοrrect statement.
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Solve the radical equation √2-√36 - 2x = 6. Check for extraneous solutions.
The solution is |
The extraneous solution is
Enter the real solution first followed by the extarneous solution separated
by a comma.
For example, if real solution is 10 and the extraneous solution is 2.
Enter as 10,2.
Answer:
We have the equation:
√2 - √36 - 2x = 6
Simplifying the radicals we get:
√2 - 6 - 2x = 6
Adding 6 to both sides we get:
√2 - 2x = 12
Subtracting √2 from both sides we get:
-2x = 12 - √2
Dividing by -2 we get:
x = (6 - (1/√2))
Therefore, the real solution is:
x = (6 - (1/√2))
To check for extraneous solutions, we need to substitute this value of x back into the original equation and check if it satisfies the equation.
√2 - √36 - 2(6 - (1/√2)) = 6
Simplifying this we get:
-6 = 6
This is not true, so the solution x = (6 - (1/√2)) is extraneous.
Therefore, there is no real solution to the equation.
At summer camp, 40 students are divided in two groups for swimming or hiking. Each camper flips a coin, where heads represents swimming and tails represents hiking.
Outcome Frequency
Swimming 12
Hiking 28
Compare the probabilities and determine which statement is true.
The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 28 over 40.
The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40.
The theoretical probability of swimming, P(swimming), is 12 over 28, but the experimental probability is one half.
The theoretical probability of swimming, P(swimming), is 28 over 40, but the experimental probability is one half.
Answer:
Step-by-step explanation:
The theoretical probability of an event is the number of favorable outcomes over the total number of possible outcomes. In this case, the total number of possible outcomes is 2, since each camper can either swim or hike. The number of favorable outcomes for swimming is also 2 (heads on a coin flip). Therefore, the theoretical probability of swimming is 2/2 or 1/2.
The experimental probability of an event is the number of times the event occurred in the experiment divided by the total number of trials. In this case, there were 12 students who chose to swim out of 40 total students. Therefore, the experimental probability of swimming is 12/40 or 3/10.
Comparing the two probabilities, we see that the theoretical probability of swimming is 1/2 while the experimental probability of swimming is 3/10. Therefore, the statement "The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40" is true.
The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40.
The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40. (option b)
The theoretical probability of an event is calculated based on the assumption of equal likelihood for all possible outcomes. In this case, since each student flips a fair coin, there are two equally likely outcomes: heads (swimming) and tails (hiking). Therefore, the theoretical probability of swimming (P(swimming)) is 1/2, and the theoretical probability of hiking is also 1/2.
However, the experimental probability is determined by the actual outcomes observed in the experiment. According to the data provided, out of the 40 students, 12 students got heads (swimming) and 28 students got tails (hiking). To find the experimental probability of swimming, we divide the number of students who swam by the total number of students:
12/40 = 0.3.
The theoretical probability of swimming, P(swimming), is one half (0.5), but the experimental probability is 28 over 40 (0.7).
The theoretical probability of swimming, P(swimming), is one half (0.5), but the experimental probability is 12 over 40 (0.3).
The theoretical probability of swimming, P(swimming), is 12 over 28 (~0.4286), but the experimental probability is one half (0.5).
The theoretical probability of swimming, P(swimming), is 28 over 40 (0.7), but the experimental probability is one half (0.5).
Out of these options, the correct one is the theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40. (option b).
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find the value of x and y
Answer:
Try using the Symbolab calculator.
Step-by-step explanation:
Thats what I usually use and it works
Your take home pay is $3,210 and your federal witholding tax rate is 16%. What was your gross pay? show the math
Answer:
To find your gross pay, we can use the following formula:
Gross Pay = Take Home Pay / (1 - Federal Withholding Tax Rate)
Plugging in the given values, we get:
Gross Pay = 3,210 / (1 - 0.16)
Simplifying the denominator, we get:
Gross Pay = 3,210 / 0.84
Calculating the division, we get:
Gross Pay = 3,821.43
Therefore, your gross pay was $3,821.43.
an athlete ran 200m race in 25 seconds. how fast did he run in meters per second
Answer:
To calculate the speed of the athlete in meters per second (m/s), we can use the formula:
Speed = Distance / Time
Here, the distance is 200 meters and the time is 25 seconds. Substituting these values into the formula, we get:
Speed = 200 meters / 25 seconds
Simplifying, we get:
Speed = 8 meters/second
Therefore, the athlete ran at a speed of 8 meters per second.
100 POINTS + BRAINLIEST!!
Answer:
Taking radius of a semicircle to be 3cm calculate the area using (1/2πr²) and add the area of rectangle calculated by use of formula L×w
Therefore Area=π(1/2×3²)+(12×6)
=76.5π
Answer:
82.27
Step-by-step explanation:
Please see the diagram attached to this solution for measurements
Area of the figure = Area of semi circle + area of rectangle
As per the figure
[tex]l_{rectangle} = 9\\w_{rectangle} = 6\\r_{semi-circle} = 3[/tex]
therefore,
[tex]Area = \dfrac{\pi r^{2}}{2} + l\cdot w[/tex]
substitute values of l, w and r, we get
[tex]Area = 82.27 cm^2[/tex]
Hopefully this answer helped you!!!
how do you do this mathematics?
Answer:
What Mathematics
Step-by-step explanation:
100 Points!!! Algebra question, multiple choice. Only looking for an answer to #8. Find the maximum value of f(x,y)=3x+y for the feasible region. Photo attached. Thank you!
Answer:
+4
Step-by-step explanation:
F(x,y) = 3x+y and y <= -2x+ 4 sub in for 'y'
= 3x + (-2x+4)
= x + 4
If you look at the graph for y <= - 2x+4 ( see below)
you will see that the domain (x values ) can only go from 0 to 4 and the max value is +4 ( rememeber too that y is restricted to >= 0 as is x )
what is the angle measurement of 1
I'm sorry, but your question is not clear. Did you mean "What is the angle measurement of a unit circle when radius equals 1?" If so, the answer is that the angle measurement is 360 degrees or 2π radians.
As shown in the figure below, Kaitlin is standing 93 feet from the base of a leaning tree. The tree is growing at an angle of
88° with respect to the ground. The angle of elevation from where Kaitlin is standing to the top of the tree is 35°. Find the
length, x, of the tree. Round your answer to the nearest tenth of a foot.
35°
-93 ft-
H
88°
feet
X
5
Answer:The measure of Ф = 75.7° :)
Step-by-step explanation:the measure of Ф = 75.7°,We will use the rule sin to find the measure of Ф
At first we will find the angle opposite to the side of length 31
∵ 180° - 73° = 107°
hope this helps:)(:
Danny is opening a savings account with an initial deposit of 45$. He saves $3 per day
The equation of the line is slope intercept form is y = 3x + 45.
What is a graph?
The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, Danny is opening a savings account with an initial deposit of $45 and he saves $3 per day.
Let y be the total amount he saves and x is the no. of days.
As he starts with $45 deposit it'll be added as a constant.
∴ The equation of the required line is y = 3x + 45.
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What is 17 + 8 x (2.7 ÷ 6) - 3
using
P
E
M
D
A
S
Answer:
17.6
Step-by-step explanation:
2.7÷6= 0.45
0.45×8= 3.6
17+3.6 - 3=17.6
Can someone help me, please?
PLEASE HELP ASAP DUE IN A HOUR
Answer:
51
Step-by-step explanation:
3x+4y^2
3(5)+4(3)^2
3(5)+4(9)
15+36
51
Answer: 51
Step-by-step explanation:
Anna has one dollar she buy some candy for $.83 which shows how much change and I should get
Answer:
Anna should receive $0.17 (17 cents) in change
Step-by-step explanation:
Anna has $1, she spends $.83 on candy
To find how much change she will get, we must subtract
1 - 0.83
$0.17
Answer:$0.17
Step-by-step explanation:
A dollar is 100 cents just subtract 83 from 100 to get 17.
The ratio of boys to girls in a class is 4:5 a)What fraction of the class are boys b) what a fraction of the class are boys!
the fraction of the class that are boys is 4/9. And the fraction of the class that are girls is 5/9.
What is ratio?
A ratio is a comparison of two or more quantities that are related in some way. It expresses the relationship between these quantities in terms of the number of times one quantity contains another. Ratios are usually expressed as a fraction, where the numerator represents the first quantity and the denominator represents the second quantity. For example, the ratio of boys to girls in a class of 40 students may be expressed as 2:3 or 2/3, meaning there are 2 boys for every 3 girls. Ratios can also be expressed in other forms, such as percentages or decimals. Ratios are commonly used in mathematics, science, engineering, and everyday life to compare quantities and make predictions or decisions.
A fraction is a number that represents a part of a whole or a ratio of two quantities. It consists of two numbers, a numerator and a denominator, separated by a line. The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole or in the comparison. Fractions are used in many areas, such as mathematics, science, engineering, cooking, and everyday life. They can be added, subtracted, multiplied, and divided, and can be converted to decimals or percentages.
a) The total ratio of boys to girls in the class is 4+5 = 9. Therefore, the fraction of the class that are boys is 4/9.
b) The question is unclear as it seems to be asking for the same answer as in part (a). If you meant to ask for the fraction of the class that are girls, you can use the same approach: the fraction of the class that are girls is 5/9.
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Question 4
What are the coordinates of point C on the directed segment
from A(-8,4) to B(10,-2) that partitions the segment such that
AC:CB is 2:1?
We may conclude after answering the presented question that Therefore, the coordinates of point C are (-6, 0).
what are coordinate ?In mathematics, a coordinate is a number or combination of numbers that represents the location of a point or object in space. Coordinates are frequently used to define a point or object's position in a certain coordinate system, such as the Cartesian or polar coordinate systems. In the Cartesian coordinate system, a point is found by its distance from the origin along the x-axis and its distance from the origin along the y-axis. These distances are represented by two integers, the x-coordinate and the y-coordinate. The point's location in the plane is specified by the two coordinates.
Using the distance formula, we can find the distances AC and CB:
[tex]AC = \sqrt((x - (-8))^2 + (y - 4)^2)\\CB = \sqrt((10 - x)^2 + (-2 - y)^2)\\[/tex]
Since AC:CB = 2:1, we have:
[tex]AC/CB = 2/1\sqrt((x - (-8))^2 + (y - 4)^2) / \sqrt((10 - x)^2 + (-2 - y)^2) = 2/1\\(x - (-8))^2 + (y - 4)^2 / ((10 - x)^2 + (-2 - y)^2) = 4\\(x - (-8))^2 + (y - 4)^2 = 4((10 - x)^2 + (-2 - y)^2)\\5x^2 + 5y^2 - 116x + 20y + 340 = 0\\(x - (-8))^2 + (y - 4)^2 = r^2\\(x - (-8))^2 + (y - 4)^2 / ((10 - x)^2 + (-2 - y)^2) = 4\\[/tex]
where r is the radius of the circle.
Solving this system of equations, we get:
x = -6
y = 0
Therefore, the coordinates of point C are (-6, 0).
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9. If the figure below is made of cubes with 2 cm side lengths, what is its volume? 14 cu. cm. 42 cu. cm. 144 cu.cm 280 cu. cm.
is this correct??
Total volume of shape is =144cu.cm
Formula for Cube VolumeBy knowing the length of the cube's edges, we can quickly determine its volume (V). Assume that "a" is the cube's edge length. The product of length, height, and breadth will then be the V. The cube's volume formula is as follows:
Cube Volume = Length× Width× Height
Volume equals= a× a× a =a³
where "a" denotes the cube's side or edges' length.
GivenLength of each cube = 2cm
Volume of each cube=a³
=2³
=8cm³
Total number of cubes=18
Total volume of shape=18×8
=144 cu.cm
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Find The surface area of tHe triangle prism 3,4,4,5
To find the surface area of a triangular prism with side lengths 3, 4, 4, and 5, we can use the formula:
Surface Area = 2(Area of the base) + (Perimeter of the base) x (Height of the prism)
First, let's find the area of the base. Since the base is a triangle, we can use the formula for the area of a triangle:
Area of base = (1/2) x base x height
The base of the triangle is the side with length 5, and the height can be found using the Pythagorean theorem:
height^2 = 4^2 - (3/2)^2
height^2 = 16 - 2.25
height^2 = 13.75
height = sqrt(13.75)
So the area of the base is:
Area of base = (1/2) x 5 x sqrt(13.75)
Area of base = 10.825
Next, let's find the perimeter of the base. Since the base is a triangle with side lengths 3, 4, and 5, the perimeter is:
Perimeter of base = 3 + 4 + 5
Perimeter of base = 12
Finally, let's find the height of the prism. We can use the Pythagorean theorem again:
height^2 = 4^2 - (3/2)^2
height^2 = 16 - 2.25
height^2 = 13.75
height = sqrt(13.75)
So the height of the prism is also sqrt(13.75).
Now we can plug these values into the formula for the surface area:
Surface Area = 2(Area of the base) + (Perimeter of the base) x (Height of the prism)
Surface Area = 2(10.825) + 12 x sqrt(13.75)
Surface Area = 21.65 + 41.4
Surface Area = 63.05
Therefore, the surface area of the triangular prism with side lengths 3, 4, 4, and 5 is 63.05 square units.
If the diameter of a circle is
30
30 centimeters, what is the radius of the circle?
Answer:
15 centimeters
Step-by-step explanation:
radius is half of the circles diameter
Lyla invests $2,500 into a savings account
which earns 5% per year. In 15 years, how
much will Lyla's investment be worth if interest
is compounded semiannually (twice a year)?
Round to the nearest dollar.
Answer:
We can use the formula for compound interest to find the future value of Lyla's investment:
A = P(1 + r/n)^(nt)
where A is the future value, P is the principal (initial investment), r is the annual interest rate as a decimal, n is the number of times interest is compounded per year, and t is the time in years.
Substituting the given values, we get:
A = $2,500(1 + 0.05/2)^(2*15)
Simplifying, we get:
A = $2,500(1.025)^30
Using a calculator, we get:
A ≈ $5,016.35
Therefore, Lyla's investment will be worth approximately $5,016.35 in 15 years if interest is compounded semiannually. Rounded to the nearest dollar, the answer is $5,016.
In a land far away, green goo varies jointly with blue goo and red goo. There are pounds of green goo when pounds of blue goo and pounds of red goo are present. Therefore, there will be blank pounds of green goo when pounds of blue goo and pounds of red goo are present.
So, when 14 pounds of blue goo as well as 16 pounds of red goo are present, there are 2688 pounds of green goo.
Explain about the direct variation?Simply generate ratios from a table of values to see whether it reflects a direct variation. A direct variation exists if every one of the ratios are the same.Any time one quantity directly affects the other, such as when one quantity rises in relation to the other and vice versa, there is a direct variation between the two variables. When one of the variables is still a constant multiple of another one, there is a link between the two variables.Let the green goo be G.
Let the blue goo be B.
Let the red goo be R.
G ∝ B*R
G = k*B*R (k is the constant of proportionality)
Put the values:
G = 288 = k*B*R
288 = k*8*3
288 = k*24,
k = 288/24 = 12
Now, for the second case:
G = k*B*R
Put the value of k.
G = 12*14*16 = 2688.
So, when 14 pounds of blue goo as well as 16 pounds of red goo are present, there are 2688 pounds of green goo.
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Answer:
Step-by-step explanation:
ut it A
Can someone help me!!!!!
Answer:
c
Step-by-step explanation:
because I did it in my book ️
June is driving from Brookline, Massachusetts, to Brooklyn, New York. The cities are 200 miles apart. Pretend June lives in a world in which she encounters no traffic jams and can drive at a constant speed of 50 mph the entire way. The distance June has traveled, c, is a function of her driving time, t Write a formula that describes this function.
This function's definition is given by the formula [tex]c = 50t + 200[/tex].
What pace is it moving at?Consider how many individuals and gadgets will be utilizing the network at once as well as how it will be utilized before choosing the "optimal" speed for your home. As a general rule, anything that can connect many devices simultaneously and is above 200 Mbps is regarded as "fast" internet.
What would you define speed as?Speed, which is a scalar number, is the "speed at which an item is moving." The pace at which an item travels a distance may be referred of as its speed. A fast-moving item travels at a great velocity and completes a significant distance in a brief period of time.
[tex]y = mx + b[/tex]
Where [tex]y,x[/tex] are variables, m is the rate of change and [tex]b[/tex] is the y intercept.
Let [tex]c[/tex] represent the distance June has traveled after time [tex]t[/tex].
Since the cities are [tex]200[/tex]miles apart, hence [tex]b = 200[/tex]. Also the speed is [tex]50[/tex]mph, hence [tex]m = 50[/tex]:
[tex]c = 50t + 200[/tex]
The formula that describes this function is [tex]c = 50t + 200[/tex]
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