Answers
Division followed by simplification of mentioned rational function gives:
(x + 1)/(x + 4)
What is factorization?Factoring an algebraic expression specifically means writing a given expression as the product of its factors. These factors may be numbers, variables, or algebraic expressions.
1, 2, 6, and 12 are all divisors of 12 because they divide 12 equally. This is an important algebraic operation, which is used to simplify expressions, simplify fractions, and solve equations. This is also called algebraic factorization.
Factorization of x² + 2x - 3
x² + 3x - x - 3
(x² + 3x) - (x + 3)
x(x + 3) - 1(x + 3)
(x + 3)(x - 1)
Factorization of x² + 3x - 4
x² + 4x - x - 4
(x² + 4x) - (x + 4)
x(x + 4) - 1(x + 4)
(x + 4)(x - 1)
Factorization of x² - 2x - 3
x² - 3x + x - 3
(x² - 3x) + (x - 3)
x(x - 3) + 1(x - 3)
(x - 3)(x + 1)
Using identity, a² - b² = (a + b)(a - b)
x² - 9 = x² - 3²
x² - 3² = (x + 3)(x - 3)
Now, for the division:
(x² + 2x - 3)/(x² - 9) ÷ (x² + 3x - 4)/(x² - 2x - 3)
[(x + 3)(x - 1)/(x + 3)(x - 3)] ÷ [(x + 4)(x - 1)/(x - 3)(x + 1)]
By reciprocal of (x + 4)(x - 1)/(x - 3)(x + 1)
[(x + 3)(x - 1)/(x + 3)(x - 3)] × [(x - 3)(x + 1)/(x + 4)(x - 1)]
= (x + 1)/(x + 4)
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Related Questions
Use the figure to complete each sentence. The base of this rectangle is cm. The height of this rectangle is cm. The area of this rectangle is cm2.
Answers
Answer:
Step-by-step explanation:
Use the figure to complete each sentence. The base of this rectangle is cm. The height of this rectangle is cm. The area of this rectangle is cm2.
you have the base and the height in the drawing, the area of the rectangle is found by multiplying the base by the height, 6 x 4 = 24 cm²The base of this rectangle is 4 cm.The height of this rectangle is 6 cmThe Area of this rectangle is 24cm²Answer:
24 cm²
Step-by-step explanation:
Solution Given:
The base of this rectangle is 4 cm. The height of this rectangle is 6 cm
height =6 cm
base = 4cm
Since
Area of Rectangle= base*height
=6*4
=24 cm²
Therefore, the area of this rectangle is 24 cm².
a coin is flipped, and a number cube is rolled. what is the probability of getting heads on the coin and a number less than 3 on the number cube
Answers
The required probability for the given case is obtained as 1/6.
What is probability?Probability is the measurement of the chance for a random event.
It is the ratio of the favorable outcome to the total possible outcome.
It always lies in the interval [0, 1].
The sample space for the given case can be written as follow,
The total number of sample space elements are,
Possible outcomes for coin × Possible outcomes for cube
= 2 × 6 = 12
Now, the number of favorable outcomes for the given event is as below,
Number of head × Number of numbers less than 3
= 1 × 2 = 2
Now, the probability is given as,
P(Head on coin and less than 3 on cube) = 2/12 = 1/6
Hence, the probability of getting heads on the coin and a number less than 3 on the number cube is given as 1/6.
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Joseph is 3 times as old as his son now, if 10 years ago the sum of their ages was 44 ,how old was Joseph when his son was born ?
Answers
Answer:
Step-by-step explanation:
j = 3s
(j-10 + s-10) =44
3s-20 + s =44
4s = 64
s = 16
j=3*16
j=48
currently Joseph is 48, the son is 16, so
16 years ago, when the son was born, Joseph was 32
Answer:
Joseph was 34 years old when his son was born.
The sum of two consecutive mile markers on the interstate is 365. Find the numbers on the markers.
Answers
Answer:
x is the first mile marker
then, x+%2B+1 the second mile marker
given:
x%2Bx+%2B+1=655
2x+=655-1
2x+=654
x+=654%2F2
x+=327->the first mile marker
and
x+%2B+1=328 the second mile marker
which fraction is equivalent to -4/8
Answers
Answer:
-2/4
Step-by-step explanation:
Caleb is a fashion designer. He designed a jacket with 2 types of fabric. Now Caleb has to make samples. He buys 68 yards of nylon and 94 yards of wool. The nylon is $3 a yard, and a yard of wool is 3 times more expensive. How much did Caleb spend?
Answers
To find out how much the wool costs, we need to multiply the price of a yard of nylon by 3, since the wool is 3 times more expensive. So a yard of wool costs $3 * 3 = $<<3*3=9>>9.
To find out how many yards of wool Caleb bought, we need to divide the total number of yards by the number of fabrics, since he bought the same amount of each fabric. So Caleb bought 68 / 2 = <<68/2=34>>34 yards of wool.
To find out how much Caleb spent on wool, we need to multiply the number of yards of wool by the price of a yard of wool. So Caleb spent 34 * $9 = $<<34*9=306>>306 on wool.
To find out how much Caleb spent on nylon, we need to multiply the number of yards of nylon by the price of a yard of nylon. So Caleb spent 68 * $3 = $<<68*3=204>>204 on nylon.
To find out how much Caleb spent in total, we need to add the amount he spent on wool and the amount he spent on nylon. So Caleb spent $306 + $204 = $<<306+204=510>>510 in total. Answer: \boxed{510}.
A family of bears is going to a movie. The following data points represent the ticket and candy price (in dollars) for each bear. Sort the data from least to greatest. Find the interquartile range (IQR) of the data set.
Answers
The interquartile range (IQR) is a measure of dispersion, which is a measure of how spread out a data set is. The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3).
Q1 = ( n +1 ) / 4th observation
= ( 9 + 1) / 4
= 2.5 th obseravation
That is the average of 2nd and 3rd observations.
Q1 = 2
Q3 = 3 ( n + 1) / 4 th observation
= 3 ( 9 + 1) / 4
= 7.5 th observation
That is the average of the 7th and 8th observation
Q3 = 5.5
Interquartile range = Q3 - Q1 = 5.5 - 2 = 3.5
In this data set, the first quartile is the average of the second and third observations (2), and the third quartile is the average of the seventh and eighth observations (5.5). Subtracting the first quartile from the third quartile gives us an IQR of 3.5. This means that the values in the data set are spread out over a range of 3.5 dollars.
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What tastes juicier?
Mixture A: 2 cups of concentrate and 3 cups of water
Mixture B: 6 cups of concentrate and 8 cups of water
Group of answer choices
Mixture B
Mixture A
They taste the same
Answers
Answer:
Mixture B
Step-by-step explanation:
A) the concentrate per cup is 2/3
B) the concentrate per cup is 6/8 = 3/4
The concentration of B is higher, so it will taste juicier.
it takes Carly 39 minutes to walk 3 miles at that rate how long will it take Carly to walk 7 miles
Answers
The time it takes Carly to walk 7 miles is 91 minutes
How to determine how long will it take Carly to walk 7 milesFrom the question, we have the following parameters that can be used in our computation:
Time = 39 minutes
Distance = 3 miles
The speed can be calculated as
Speed = Distance/Time
Substitute the known values in the above equation, so, we have the following representation
Speed = 3 miles/39 minutes
So, we have
Speed = 1/13 miles per minute
From the question, we have
Distance = 7 miles
Recall that
Speed = Distance/Time
Make time the subject
Time = Distance/Speed
So, we have
Time = 7/(1/13)
Evaluate
Time = 91 minutes
Hence, the time is 91 minutes
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A basketball player makes 70 % of her free throws. When fouled, she gets to take 2 free throws. Let X represent the number of free throws made in two tries. The probability distribution for the number of free throws she makes in two attempts is summarized in the following table:Number of free throws made 0 1 2Probability 0.09 0.42 0.49The probability that she makes at least one free throw isa.0.67b.0.91c.0.95d.1.00
Answers
The probability that she makes at least one free throw is b. 0.91. Probability theory is a branch of mathematics that is used to model and analyze random events.
Probability can be used to predict the likelihood of different outcomes in a wide range of situations, from games of chance to scientific experiments to everyday events. Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
To find the probability that the player makes at least one free throw in two attempts, you can subtract the probability that she misses both free throws from 1. The probability that she misses both free throws is 0.09, so the probability that she makes at least one free throw is:
1 - 0.09 = 0.91.
Therefore, the correct answer is 0.91, or choice (b).
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b) If the marginal revenue function for output x is given by MR = C, where a, b, c, m and n are constant. mn (ax+b)² Prove that the demand function is p mn b(ax+b) C.
Answers
The demand function is given by the expression -
D{x} = mn(a²x + 2b + b²)
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is the revenue function as follows -
f(x) = mn (ax + b)²
The revenue function is simply [x] multiplied by the demand function.
R{x} = x (D{x})
The revenue function is -
f(x) = mn (ax + b)²
So, the demand function can be written as -
mn(ax + b)² = x (D{x})
D{x} = {mn(ax + b)²}/x
D{x} = {mn(a²x² + b² + 2abx)}/x
D{x} = {a²x²mn + mnb² + 2bmnx}/x
D{x} = a²xmn + 2bmn + mnb²
D{x} = mn(a²x + 2b + b²)
Therefore, the demand function is given by the expression -
D{x} = mn(a²x + 2b + b²).
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Two parallel lines are cut by transverse as shown suppose
Answers
Find the y-intercept from the line of best fit y = 6 + 2x.
Answers
Answer:
y - intercept = 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 6 + 2x , that is
y = 2x + 6 ← is in slope- intercept form
with y- intercept c = 6
24 divided by 4•2 - 2
Answers
Answer:
the answer is 10
Step-by-step explanation:
The value of the numerical expression 24 / (4 × 2 - 2) will be 4.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ 24 / (4 × 2 - 2)
Simplify the expression, then we have
⇒ 24 / (4 × 2 - 2)
⇒ 24 / (8 - 2)
⇒ 24 / 6
⇒ 4
The value of the numerical expression 24 / (4 × 2 - 2) will be 4.
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26
Select the correct answer.
The height (cm) of an object oscillating up and down at the end of a spring is s(t) = 100 + cos t. Find the eceleration at time t.
O A.
100-cos t
OB.
-sin t
O C.
-cos t
O D. 100-sin t
Reset
Next
Answers
-sint is the acceleration at time t.
What is Acceleration?Acceleration is the rate of change of the velocity of an object with respect to time.
Given, the height (cm) of an object oscillating up and down at the end of a spring is s(t) = 100 + cos t.
We need to find the acceleration at time t.
s(t) = 100 + cos t.
To find the acceleration we have to differentiate the above equation.
d/dt=d/dt(100+cost)
=d/dt(100)+d/dt(cost)
=0+(-sint)
s'(t) = -sint.
Hence, the acceleration at time t is -sint.
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tia equally shares 8 cookies among herself and 4 friends which fraction shows how many cookies each person gets?
answers:
8/4
8/5
5/8
4/8
Answers
Answer: The answer is 8/5
Answer:
Each person gets 8/5 part of cookie
write the equation in slope intercept form and graph using a table
X = 5
Answers
Answer:
y=5x+0
Step-by-step explanation:
wouldn't the equation be something like y=5x+0? If x=5 then x would be the slope. So then if the slope is 5 you'd start off your equation y=5x but there might not be a y-int for this equation because the equation only has an x and there is no y.
(Not sure if you understand it, but if it were to me I'd do something like this because there is only one number in the equation, hope this helps in some way....)
determine the area (in units2) of the region between the two curves by integrating over the y-axis. x
Answers
The area of the region between the two curves by integrating over the y-axis, x = y² and x = 9 is 18 square units.
Total Area inclosed between line and Curve:The area where the "area under the curve" is common to both the straight line and the given curve is called the bounding area. Therefore, the area common to both can be found by subtracting the area under line T from the area under curve C. The x constraint for computing the area under the curve can be found by solving the system of equations for the coordinates of the intersection of the line and the curve.
We have given the curve , x = y² and line x = 9 and bounded region is A in above graph of x = y² and line x = 9.
Now, we determine the intersection points of curve and line,
put x = 9 in curve equation we get,
y² = 9 => y = +-√9
= + 3 or -3
Total area bounded by curve and line, A = integration of curve over y from y = -3 to y= 3
= ₋₃∫³x dy = ₋₃∫³y² dy = ₋₃[ y³/3]³
= [ (3)³/3 - (-3)³/3]
= 9 + 9 = 18
Hence, the required area is 18 square unit.
Complete question:
determine the area (in units2) of the region between the two curves by integrating over the y-axis. x = y² , x = 9
Factors 3x^4-5x^3+6x^2-15x completely over the set of integers
Answers
The Factors of 3x^4-5x^3+6x^2-15x completely over the set of integers will give 5(1-3x).
How can this be calculated?In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller
The expression can be broken down after the other as
[2x4 = 8] + [5x3=15] + [6x2=12]
= [8-15+12-15x]
=5-15x
then we can factorize as
5(1-3x)
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Solve the equation for x.
−0.28x − 8.4 = 8.26
x = 59.5
x = −59.5
x = 50.5
x = −50.5
Answers
The value of x after solving −0.28x − 8.4 = 8.26 is x = −59.5 .
What is linear equation in one variable ?
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it.
To solve linear equation in one variable:
Step 1: Simplify each side, if needed.
Step 2: Use Add./Sub. Properties to move the variable term to one side and all other terms to the other side.
Step 3: Use Mult./Div. Properties to remove any values that are in front of the variable.
Given :
-0.28x - 8.4 = 8.26
Adding 8.4 both the sides , we get
-0.28x + (-8.4 + 8.4) = 8.26 + 8.4
-0.28x = 16.66
x = - (16.66/0.28)
x = -59.5
Hence , the value of x after solving −0.28x − 8.4 = 8.26 is x = −59.5 .
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The total weight of a giraffe and her calf is 904 kilograms. How much does the calf weigh? Use a tape
diagram to model your thinking.
Answers
The Calf weigh about 75 kg.
How is weight calculated ?The force of gravity acting on an item is known as its weight, and it can be determined using the formula w = mg, which equals the mass times the acceleration of gravity. The newton is the SI unit for weight since it is a force.The gravitational force that pulls a body toward the earth or another celestial body; it is equal to the mass times the acceleration due to local gravity.We treat our weight as mass and use the unit kg to measure weight by presuming that the gravitational field is the same everywhere.The fundamental mass unit in the metric system is the kilogramme (kg). The mass of 1,000 cubic centimeters of water is extremely close to (and was originally meant to be exactly) one kilogram. The actual weight of a pound is 0.45359237 kg.Given data :
The total weight of a giraffe and her calf is 904 kilograms.
Weight of the giraffe is 829 kg
So the weight of the calf = Total weight - weight of giraffe
= 904 - 829 = 75
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1-9 Enrichment Worksheet
Geometry Crossword Puzzle
12
NAME
16
13
19
3
18
10
ACROSS
3. Points on the same line
are -
4. A point on a line and all
points of the line to one
side of it.
9. An angle whose measure
is greater than 90.
10. Two endpoints and all
points between them.
16. A flat figure with no
thickness that extends
indefinitely in all
directions.
1
17. Segments of equal length
segments.
are -
18. Two noncollinear rays
with a common endpoint.
19. If m ZA+ m ZB = 180,
then ZA and ZB are -
angles.
17
2
15
9
4
8
14
18
DATE
DOWN
1. The set of all points collinear to two points
is a.
Glencoe Division, Macmillan/McGraw-Hill
7
2. The point where the x- and y-axis meet.
5. An angle whose measure is less than 90.
6. If m ZA+ m ZD = 90, then ZA and ZB are
angles.
7. Lines that meet at a 90° angle are
8. Two angles with a common side but no
common interior points are
10. An "angle" formed by opposite rays is a
_________ angle.
11. The middle point of a line.segment.
12. Points that lie in the same plane are -
13. The four parts of a coordinate plane.
14. Two nonadjacent angles formed by two
intersecting lines are - angles.
15. In angle ABC, point B is the
Answers
Answer:
Look at the image I attached to this answer for the answers.
This is a crossword puzzle on geometry terms and concepts, including lines, angles, and planes.
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A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:
Likes hamburgers Does not like hamburgers Total
Likes burritos 29 41
Does not like burritos 54 135
Total 110 205
Part A: What percentage of the survey respondents liked neither hamburgers nor burritos? Show all work. (3 points)
Part B: What is the marginal relative frequency of all customers who like hamburgers? Show all work. (3 points)
Part C: Which category has the lowest joint relative frequency? Show all work. (4 points)
Answers
A: 16.09 % of the survey respondents liked neither hamburgers nor burritos
B) 0.65 is the marginal relative frequency.
C) The lowest joint relative frequency of those who like Hamburgers but not burritos.
What is Marginal Frequency?The ratio of a row total's or column total's frequency to the overall frequency of the data is known as marginal relative frequency. It is frequently used to examine broad trends in a single type of data.
Given:
Like Hamburgers Does Not Like Hamburgers Total
Likes burritos 39 38 77
Does not like burritos 95 33 128
Total 134 71 205
A) There are 33 such respondents.
So, percentage is
= 33/205 x 100
= 16.095
B) It will be the ratio of the sum of the customers that like hamburgers to the total number of respondents
So, the ratio is
= 134/205
= 0.65 :1
Part C: For this, we need to find the ratio of all the four data with the total.
Those who like Hamburgers and burritos
= 39/134
Those who like Hamburgers but not burritos
= 95/134
Those who like burritos but not Hamburgers
=38/71
Those who do not like burritos or Hamburgers = 33/71
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The diagram shows the lengths of corresponding sides of similar triangles A'B'C' and ABC. Which expression gives the perimeter of A'B'C'?
Answers
The expression that gives the perimeter of the A'B'C is 2 (a + b + c).
Option B is the correct answer.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
The side length of triangle A'B'C' is twice the length of the corresponding side length of triangle ABC.
The perimeter of a triangle.
= Sum of all the three sides
Now,
The perimeter of the triangle ABC.
= a + b + c
Thus,
The perimeter of the triangle A'B'C'.
= 2 (a + b + c)
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Michael pays $34.65 for eleven 18-count boxes of granola bars. How much does 1 box of granola bars cost?
One box of granola bars costs $
Answers
Answer:−cnotu+53.65
Step-by-step explanation: I don't really know how I got it. But it was quite easy.
(x+1)=(7x-5) how do i solve this
Answers
Step-by-step explanation:
You start with x+1=7x-5
Basically you want all the x's on one side and all the constants on the other
(x+1)+5=(7x-5)+5, to get rid of the 5 on the right side
(x+6)-x=7x-x, to get rid of the x on the left side
We are now left with 6x=6
No we simplify, 6x/6=6/6
Now we have x=1, which is the answer
I hope this made sense.
x= 1.
Step-by-step explanation:1. Write the expression.[tex](x+1)=(7x-5)\\ \\x+1=7x-5[/tex]
2. Subtract "1" from both sides of the equation.[tex]x+1-1=7x-5-1\\ \\x=7x-6[/tex]
3. Subtract "7x" from both sides of the equation.[tex]x-7x=7x-6-7x\\ \\-6x=-6[/tex]
4. Divide both sides by "-6".[tex]\frac{-6x}{-6} =\frac{-6}{-6} \\ \\x=1[/tex]
5. Verify.[tex](1)+1=7(1)-5\\ \\2=7-5\\ \\2=2[/tex]
That's correct!
6. Conclude.x= 1.
Write and equation of a circle that has a diameter that passes through the points (3,0) and (7,6)
Answers
The equation of a circle that has a diameter that passes through the points (3,0) and (7,6) is x² + y² - 10*x - 6*y +21 =0
Given that, the points (3,0) and (7,6)
(x1, y1) = (3,0) and (x2, y2) = (7,6)
We know that the formula for the equation of circle whose points of diameter are given is equal to :
(x - x1) * (x - x2) + (y - y1) * (y - y2)
So now,
(x - 3) * (x - 7) + (y - 0) * (y - 6) = x² + y² - 10*x - 6*y +21 =0
so the equation of a circle that has a diameter that passes through the points (3,0) and (7,6) is x² + y² - 10*x - 6*y +21 =0
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Chau sells beaded necklaces.Each large necklace sells for $6.30 and each small necklace sells for $4.80.How much will he earn from selling 4 large necklaces and 5 small necklaces?
Answers
Marta conducts emissions inspections on cars. She finds that 8 % 8%8, percent of the cars fail the inspection. Let X XX be the number of cars Marta inspects until a car fails an inspection. Assume that the results of each inspection are independent. Find the mean and standard deviation of X XX. Round your answers to one decimal place.
Answers
There are X automobiles, with a mean of 12.5 cars. The standard deviation for X is also SD = 12.0.
What connection exists between the mean and the standard deviation?First, a data set's mean and standard deviation convey distinct information. The average (center) of a data collection is provided by mean (it is a measure of central tendency). You may learn about the range (dispersion) of data around the mean by looking at the standard deviation. We may investigate a data set's characteristics and characterize it using both the mean and standard deviation. To provide confidence intervals for data that has a normal distribution, they are frequently combined. If two or more data sets need to be compared:
The mean reveals whether data set is, on average, greater or lower (or better or worse). We can determine whether data set has a wider dispersion using the standard deviation (higher standard deviation means data is more spread out from the mean). Second, there are variations in how each metric is calculated. In particular, we utilize squaring to get the standard deviation but not the mean. We completely avoid using squaring when determining the mean of a data collection. Simply multiplying the total number of data points in the set by the sum of all the values in the data set yields the answer.
What is the standard deviation and mean formula?The mean is calculated as follows:
Mean = (all data values added together) / (number of data values)
However, when calculating standard deviation, we do employ squaring. We take the square of the deviation between each data point and the mean in particular.
The standard deviation equation is as follows:
Finally, when we add the identical value to each data point in the data set, the mean and standard deviation "respond" differently. If we multiply every value in a data collection by the constant "K":
No of the size of the data collection, the mean rises by precisely K.
No matter how many observations are in the data collection, the standard deviation does not vary. The identical value is then added.
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A train traveled 300 miles. How long did the trip take if the train was traveling at a rate of: Note * Use the d=rt formula (distance = rate * time). NOTE: You may not be able to solve for the variable. If you do not have enough information to solve for the variable then write the equation. 1) 50 mph 2) 70 mph 3) x mph 4) (x+10)mph 5) (x-5)mph
Answers
If a train traveled 300 miles. The time is, 6 hours, 4.29 hours, 300/x hours, 300/(x+10) hours,300/(x+5) hours.
How to find the time?Distance = Rate × Time
Time =Distance/Rate
1. 50 mph
Time = 300/50
Time = 6 hours
2. 70 mph
Time = 300/70
Time = 4.29 hours
3. x mph
Time = 300/x
Time = 300/x hours
4. (x+10)mph
300/(x+10) hours
5. (x-5)mph
300/(x-5) hours
Therefore the time is, 6 hours, 4.29 hours, 300/x hours, 300/(x+10) hours,300/(x+5) hours.
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