Two trains leave Cleveland at the same time. One train travels east and the other travels west. The speed of the westbound train is 3mph
greater than the speed of the eastbound train. After 4
hours, they are 648
miles apart. Find the rate of each train. Assume that the trains travel in a straight line in directly opposite directions.

Answers

Answer 1

Answer: Let x be the speed of the eastbound train.

Then the speed of the westbound train is x+3 mph.

We can set up the following equation using the distance formula (rate x time = distance)

x*4 = 648/2 + (x+3)*4

Solving for x,

x= 42

So the speed of the eastbound train is 42 mph and the speed of the westbound train is 45 mph.

Step-by-step explanation:


Related Questions

Josh drank 70 ounces of water yesterday.how many cups of water did he drink

Answers

Answer:

8.75

Step-by-step explanation:

Use your formula 1/2(a+b)h, to determine the height of a trapezoid with an area of
24 cubic centimeters and base lengths of 9 cm and 7 cm

Answers

The height of the trapezoid that has an area of 24 cubic cm is: 3 cm.

How to Calculate the Height of a Trapezoid?

The formula for the area of a trapezoid is 1/2(a+b)h, where a and b are the lengths of the bases and h is the height.

Given that the area of the trapezoid is 24 cubic centimeters and the base lengths are 9 cm and 7 cm, we can plug in those values to the formula and solve for h:

24 = 1/2(9+7)h

24 = 1/2(16)h

24 = 8h

To find h, we divide both sides of the equation by 8:

h = 24/8

h = 3

So the height of the trapezoid is 3 cm.

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The points on this graph represent a relationship between x
- and y
-values. Which statement about the relationship is true?

Answers

Since the points on this graph represent a relationship between x- and y-values, a statement about the relationship which is true is that: A. it cannot be proportional because a straight line through the point does not go through the origin.

What is a proportional relationship?

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

x and y represents the variables or data points.k represents the constant of proportionality.

Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.

In conclusion, the relationship between the x-value and y-value isn't proportional because the straight line does not pass through the origin (0, 0).

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0.75 * ( x+4)=9. what does x equal?

Answers

Answer:

x = 8

Step-by-step explanation:

0.75 * ( x+4) = 9

0.75x + 3 = 9

0.75x = 9 - 3

0.75x = 6

x = 6 / 0.75

x = 8

PLEASE ANSWER DUE TOMORROW

Answers

The measurement of angles formed by intersecting line segments UT and WV are -

∠TXV = 25°

∠UXW = 25°

∠TXW = 155°

∠UXV = 155°

What is a line segment?

A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.

Two line segments UT and WV are given.

The line segment UT and WV are intersecting each other at a point X.

Due to the intersection many angles are formed.

To find the measure of the angles, use the protractor.

The first angle is ∠TXV.

Keep the protractor's midpoint at point X.

Then turn the protractor so that it aligns with line UT.

The measure of ∠TXV is approximately 25°.

The second angle is ∠UXW.

Keep the protractor's midpoint at point X.

Then turn the protractor so that it aligns with line WV.

The measure of ∠UXW is approximately 25°.

The third angle is ∠TXW.

Keep the protractor's midpoint at point X.

Then turn the protractor so that it aligns with line WV.

The measure of ∠TXW is approximately 155°.

The fourth angle is ∠UXV.

Keep the protractor's midpoint at point X.

Then turn the protractor so that it aligns with line UV.

The measure of ∠UXV is approximately 155°.

Therefore, all the four angles are obtained.

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A form of nickel has a half life of 91 years. How much of a 90 gram sample is left after 290 years? 

Answers

The amount of the 90gram-sample that will remain after 290 years is 9.88 grams

How to determine the number of half-lives?

We'll begin by obtaining the number of half lives that has elapsed. This can be obtained as follow:

Step1

Half-life (t½) = 91yearsTime (t) = 290 yearsNumber of half-lives (n) =?

n = t / t½

n = 290 / 91

n = 3.1868

Step 2

determine the amount remaining:

Original amount (N₀) = 90 gramsNumber of half-lives (n) = 3.1868Amount remaining (N) =?

The amount remain can be obtained as follow:

N = N₀ / 2^n

N = 90 / 2^3.1868

=9.88

N=9.88 grams

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U.S. inflation is intentionally kept at a steady 5%, for a variety of economic reasons. Because of this, the cost
of most things is expected to increase by 5% per year, with few exceptions.
In 2009, minimum wage was set to 7.25, and has not changed since. If it had risen to meet the intended
inflation, what would minimum wage be now in 2023?
A$21.16
B $14.35
C$15.05
D$2,116,.49

Answers

Its….C $15.05. Bedbehdhhsdhdhdhdhdhdhdbsbs

complete the description of the piecewise function graphed below

Answers

The supplied input should simply be replaced in the function definition for that precise interval.

What best describes a piecewise function?

An equation or set of equations, rather than a single equation, defines a piecewise-defined function. For a specific interval, each equation is valid.

Find out to which of the above intervals (or inequalities) the supplied input belongs before evaluating a piecewise function at any given input. The function definition for that specific interval should therefore just have the specified input replaced.

When a rule or relationship changes as an input value passes specific "boundaries," we refer to these instances as piecewise functions. For instance, scenarios where the price per piece of a specific item is decreased once the quantity requested exceeds a given amount are frequent in business.

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Solve for c

a(c + b)=d

Answers

Answer:

[tex]c = \frac{d}{a} - b[/tex]

Step-by-step explanation:

Isolate the variable, c. Note the equal sign, what you do to one side, you do to the other.

Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, divide a from both sides of the equation:

[tex]a(c + b) = d\\\frac{a(c + b)}{a} = \frac{d}{a} \\c + b = \frac{d}{a}[/tex]

Next, isolate the variable, c, by subtracting b from both sides of the equation:

[tex]c + b = \frac{d}{a} \\c + b (-b) = \frac{d}{a} (-b)\\c = \frac{d}{a} - b[/tex]

[tex]c = \frac{d}{a} - b[/tex] is your answer.

~

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Answer:

c = (d/a) - b

Step-by-step explanation:

Now we have to,

→ Find the required value of c.

The equation is,

→ a(c + b) = d

This can be distributed as,

→ a(c + b) = d

→ a(b) + a(c) = d

→ ab + ac = d

Then the value of c will be,

→ a(c + b) = d

→ a × (c + b) = d

→ c + b = d/a

→ c = -b + (d/a)

→ [ c = (d/a) - b ]

Hence, value of c is (d/a) - b.

What is the solution to 9|x + 8| > 45?

x < –3 or x > 13
–3 < x < 13
x < –13 or x > –3
–13 < x < –3

Answers

The inequality model of the question will be -13 > x > -3

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

9|x + 8| > 45

now when we remove the modulus there will be two terms.

|x + 8| > 45/9

|x + 8| > 5

-5>x + 8>5

-5-8>x >5-8

-13 > x > -3

Hence, the inequality model will be -13 > x > -3

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Analysis A question on a test asks students to find the speed at which a car
travels. The graph shows a proportional relationship between the distance traveled
in miles and time in hours. Anna incorrectly says that the speed of the car is 59
mile per hour. What is the speed of the car? What error might Anna have made?

Answers

The speed of the car is 59 miles per hour. Anna might have made an error by using change in y-coordinates/change in x-coordinates to find a unit rate, instead of change in x-coordinates/change in y-coordinates.

What is defined as speed?Speed is a measure of how quickly something is moving, or how quickly something can be done. It is usually measured in terms of distance traveled per unit of time, such as miles per hour or kilometers per hour. The unit of speed is Miles per hour (mph).Speed can also be measured in terms of the rate of change of a certain quantity. For example, speed can be used to measure acceleration, which is the rate of change in velocity. Speed can also be used to describe the rate of flow of a certain quantity, such as the rate of water flow in a river. Speed is also used to measure the rate at which a certain process is taking place, such as the rate at which a person is typing words. In many cases, speed is used to describe how quickly something is happening relative to something else, such as the speed of light relative to the speed of sound. Speed is an important concept in many fields, including physics, engineering, and sports.

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what is the measure of arc BC?
130 degrees
180 degrees
65 degrees
32.5 degrees

Answers

The angle subtended by arc BC on center of circle is of 2 times 65 = 130

What is Area of circle ?

Area of circle can be defined as the product of pi and the square of radius of a circle.

Using the property that angle subtended by an arc on center is double than on circumference, you can find measure of arc BC.

The angle subtended by arc BC on center of circle is of 2 times 65 = 130

Given,

The angle subtended by arc BC on circumference is 65 degrees.

We have to find  Length of arc BC

Relation between angle at center and angle at circumference by an arc:

"Angle subtended by an arc of a circle on its center is double than angle subtended by it on circumference"

Therefore , angle subtended by arc BC on center of circle is of 2 times 65 = 130 .

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Jude types 1,281 characters in 7 minutes. What is her typing rate in characters per minute?

Answers

Answer:

183 charters

7 goes into 12 1 time so 12-7=5

bring down the 8 so 7x8=56 so 58-56=2

being down the 1 and you have 21. 7 goes into 21 three times.

Answer:

183 characters per minute

Step-by-step explanation:

1281 divided by 7

Kim will choose 1 type of meat and 1 type of cheese for her sandwich. The meats offered are ham, turkey, or roast beef. The cheeses offered are American, Swiss, cheddar, or provolone. Kim dislikes roast beef and Swiss cheese. How many different possible sandwiches does that leave Kim?


5


6


8


12

_______________________________________________________

Show your work!

Answers

The number of possible sandwiches does is 6.

What is combination ?

In arithmetic, a combination is a way of choosing gadgets from a set where the order of selection does no longer count. suppose we've got a hard and fast of 3 numbers P, Q and R. Then in what number of methods we can select two numbers from every set, is described via combination.

Given ,

Kim will choose 1 type of meat and 1 type of cheese for her sandwich. The meats offered are ham, turkey, or roast beef.

The cheeses offered are American, Swiss, cheddar, or provolone. Kim dislikes roast beef and Swiss cheese.

factorial of n! = n*(n-1) !

The number of possible sandwiches does  =  3!

=3*2 = 6.

Therefore, The number of possible sandwiches does is 6.

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16 x 6 equals 92 How do I find 6?!?

Answers

The area of the rectangle would be 96 square inches.

Option (D) is correct.

What is the area of the rectangle?

The formula for the area of a rectangle is:

Area = length x width

where length is the distance along the longer side of the rectangle and width is the distance along the shorter side of the rectangle.

In the given figure,

The length of the rectangle = 8 + 8 = 16 inches.

Now by using the Pythagoras theorem, we can find the height

  [tex]Height= \sqrt{(10)^2-(8)^2} \\\\=\sqrt{100-64}\\\\=\sqrt{36}\\\\=6[/tex]

So the base would be 6 inches.

Now we can find the area of the rectangle

Area = 16 * 6

Area = 96 square inches.

Hence, the area of the rectangle would be 96 square inches.

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Eagle Airlines flies charter planes all over the world. Susan, one of the airlines' top pilo
routes in Europe and North Africa. Susan's plane uses 2 kilograms of fuel for every kil
she flies.
There is a proportional relationship between the distance Susan flies (in kilometers), x
the amount of fuel her plane uses (in kilograms), y.
Graph this relationship. Select two points to draw a line.


What is the slope of the line?

Answers

The proportional relationship that models this situation is given as follows:

y = 2x.

The graph is given by the image presented at the end of the answer.

How to model the proportional relationship?

A proportional relationship is modeled as follows:

y = kx.

In which k is the constant of proportionality.

Susan's plane uses 2 kilograms of fuel for every unit she flies, hence the constant is given as follows:

k = 2.

The relationship is:

y = 2x.

The domain is:

x >= 0, as the number of units flied cannot be negative.

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2. How many points
of intersection are there
on the graph
of
y=x² + 3x-2
y -x=4

Answers

There is one point of intersection on the graph of y = x² + 3x - 2 and y - x = 4

To find the point of intersection, we need to set the two equations equal to each other and solve for x and y.

y = x² + 3x - 2

y - x = 4

x² + 3x - 2 - x = 4

x² + 2x - 6 = 0

(x-3)(x+2)=0

x =3 or x=-2

When x = 3, we substitute it into the first equation y = x² + 3x - 2

y = 3² + 3(3) - 2

y = 9 + 9 - 2

y = 16

When x = -2, we substitute it into the first equation y = x² + 3x - 2

y = -2² + 3(-2) - 2

y = 4 -6 -2

y = -4

So the point of intersection is (3,16) or (-2,-4)

Hence there is only one point of intersection on the graph of y = x² + 3x - 2 and y - x = 4

A movie club surveyed 200 high school students. The students were asked how often they go to the movies and whether they prefer action movies or dramas. Their responses are summarized in the following table

Answers

The percentage of students that prefer drama is 52%.

The percentage of students that go to the movies three times or more is 34%.

What are the percentages?

Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %. In order to change a number to percentage, multiply the number by 100.

The percentage of students that prefer drama = (total number of students that prefer drama / total number of students surveyed) x 100

= [(70 + 34) / 200] x 100

= (104 / 200) x 100 = 52%

The percentage of students that go to the movies three times or more = (total number of students that go to the movies three times or more / total number of students surveyed) x 100

[(34 + 34) / 200] x 100

(68 / 200) x 100 = 34%

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Students will present a play in an
auditorium that has 550 seats. Each
student performing in the play must
sell 12 tickets to the performance.
The remaining 370 tickets will be
sold by other students in the school.
Which equation could be used
to
find x, the number of students
performing in the play?

Answers

Answer:

550 - 12x = 370

At the nearest wholesale store, 3 bags of cereal cost $21.75. Which equation represents the proportional relationship?
please help

Answers

The equation that represents the proportional relationship is: k = 7.25.

What is a Proportional Relationship Equation?

A proportional relationship is a relationship between two variables such that one variable is a constant multiple of the other. A proportional relationship can be represented by an equation of the form y = kx where y and x are the variables, and k is the constant of proportionality. This equation can also be written as y/x = k.

From the given information, we have:

Constant of proportionality (k) = 21.75 / 3

k = 7.25

To write the equation, substitute k = 7.25 into y = kx:

y = 7.25x

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The explicit rule for an arithmetic sequence is an = 8. 7 + (-1. 4)(n-1). What is the value of the 47th term? round to the nearest tenth, if necessary.


answer: A) -55. 7

Answers

The value of the 47th term of the given arithmetic sequence is -55.7

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is always the same.

We are given the explicit rule for an arithmetic sequence as follows -

[tex]a_n[/tex] = 8.7 - 1.4(n-1)

We have to find the value of the 47th term in the series.

So, we have the value of n = 47

The equation will become -

[tex]a_{47}[/tex] = 8.7 - 1.4(47-1)

[tex]a_{47}[/tex] = 8.7 - 1.4(46)

[tex]a_{47}[/tex] = 8.7 - 64.4

[tex]a_{47}[/tex] = -55.7

Thus, the value of the 47th term of the given arithmetic sequence is -55.7

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The same type of dinner plate is sold in two different packs. Small pack contents 3 plates £5. 25. Large pack contents 12 plates £21. 24 which size packet is the better value for money?​

Answers

Large pack with 12 plates has better value of money with $1.77 for each plate comparison to smaller pack with $1.75 for each plate.

Number of plates in smaller pack is equal to 3 .

Cost of smaller pack with three plates = $5.25

Cost of each plate in smaller pack = $5.25 / 3

                                                         = $1.75

Number of plates in larger pack is equal to 12 .

Cost of larger pack with twelve plates = $21.24

Cost of each plate in larger pack = $21.24 / 12

                                                         = $1.77

$1.77 is greater than $1.75.

Larger pack of plates have better value of money for each plate comparing the smaller pack.

Therefore, the larger pack has better value of money than the smaller pack .

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Translate the phrase into a variable expression. Use the letter g to name the variable. If necessary, use the asterisk (*) for multiplication and the slash (/) for division.

The total number of seagulls standing on the pier and the 51 gulls in the air

Answers

The expression that represents the ratio between the total number of seagulls standing on the pier and the 51 gulls in the air is given as follows:

g/51.

How to obtain the ratio?

The ratio between two amounts a and b is found applying a proportion, which is the division between them.

The amounts for this problem are given as follows:

g is the number of seagulls standing on the pier.51 is the number in the air.

Hence the ratio is given as follows:

g/51.

Missing Information

The problem asks for the expression for the ratio the total number of seagulls standing on the pier and the 51 gulls in the air.

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three people ann, bob and colin have a total of $1.80 between them, each having a different amount. does ann have the most money? (1) ann has $0.6 (2) bob has $0.5

Answers

Compared to Ann and Bob, Colin has more. Thus, Ann is not have most money.

In the given question, we have to find Ann have the most money or not.

Three people Ann, Bob and Colin have a total of $1.80 between them, each having a different amount.

Ann has $0.6 amount and Bob has $0.5 amount.

Ann + Bob + Colin = 1.80

0.6 + 0.5 + Colin = 1.80

1.1 + Colin = 1.80

Subtract 1.1 on both side, we get

Colin = 0.70

So Colin has $0.70.

So, Colin has more amount than Ann and Bob. So Ann does not have most money.

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Find two numbers that the quotient is between.
4,096 divided by 61
The quotient is between _ and _

Answers

Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

see image

The quotient from 4,096 divided by 61  is between 66 and 67.

Sandra Williams bought a home with a 10. 25% adjustable rate mortgage for 25 years. She paid $9. 27 monthly per thousand on her original loan. At the end of 3 years she owes the bank $50,000. Since then interest rates have increased to 12. 75%. The bank will renew the mortgage at this rate, or Sandra can pay the bank $50,000. She decides to renew and will now pay $11. 10 monthly per thousand on her loan. You can ignore the small amount of principal paid during the 3 years. What was the old monthly payment? $ a0 What is the new monthly payment? $ a1 What is the percent increase in her monthly payment (to the nearest tenth)? a2 %

Answers

a) The old monthly payment was =  9.27 × 50 = 463.5

b) The new monthly payment is = 11.10 × 50 = 555

c) The percent increase in his monthly payment is 1.947 %

With a 25-year, 10.25% adjustable rate mortgage, Sandra Williams purchased a property. She made monthly payments of $9.27 per thousand on his initial debt.

According to the question,

The per thousand value of $65000 is, 50000/1000 = 50

Now, the old monthly payment was =  9.27 × 50 = 463.5

She makes the decision to renew and will now make monthly loan payments of $11.10 per thousand.

So, the new monthly payment is = 11.10 × 50 = 555

The percent increase in his monthly payment is = 11.10 /9.27 - 1 × 100

⇒ 19.7411 %

And to nearest tenth it is 1.947%

Hence, the old monthly payment was =  9.27 × 50 = 463.5

The new monthly payment is = 11.10 × 50 = 555

Thus, the percent increase in his monthly payment is 1.947%.

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the value of philipine peso is less than the value of one US dollar

Answers

The mathematical statement that accurately depicts how value of philipine peso is less than the value of one US dollar is: p < d. The Option C is correct.

What is Less than Symbol all about?

The Less-than symbol is used to compare two values where the first number is less than the second number, for example, in ascending order. The opening angle bracket is approximated by the less than symbol.

"<" is the symbol used to represent the less than inequality. The less than sign is a universally recognized math symbol composed of two equal measure strokes intersecting in an acute angle at the left.

For example: If given 2< 5: 2 is less than 5

Missing options "Which of the following mathematical statement represents the given situation? a. d = p b. p>d c. p <d d. none of these​

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Here is some information about the goals scored in some hockey games.

Each game has four quarters.

Goals in hockey games

9

8

7

Number

6

of goals 5

4

3

2

1

The mean number of home

goals scored is 2. 5

The mean number of away

goals scored is 1. 8

How many home and away

games have been played

in total?

0

1st

3rd

4th

+

2nd

Quarter

Away goals

Key:

Home goals

Answers

If the mean number of home goals is 2.5 and away goals is 1.88 , then the number of home and away games have been played in total is 32 games .

From the histogram , we get that ,

the total number of home goals is = 9 + 6 + 8 + 7 = 30 goals ;

the total number of away goals is = 2 + 7 + 4 + 5 = 18 goals ;

the mean number of home goals is = 2.5 ;

the mean number of away goals is = 1.8  ;

we know formula that⇒ Mean Goal = (total goals)/(number of games) ;

For Home goals :

⇒ 2.5 = 30/n ⇒ n = 30/2.5 = 22 games .

For Away goals :

⇒ 1.8 = 18/n ⇒ n = 18/1.8 = 10 games .

So , total number of games is = 10 + 22 = 32 games ,

Therefore , In total the total number of home and away games played is 32 games .

The given question is incomplete , the complete question is

Here is some information about the goals scored in some hockey games. Each game has four quarters. the histogram is given below :

The mean number of home goals scored is 2.5  ;

The mean number of away goals scored is 1.8  ;

How many home and away games have been played in total ?

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Two triangular sculptures are similar. The leg of the first sculpture is 4.5 feet and the base is 7.2 feet. The leg of the second sculpture is 6 feet. What is the length of the base for the second sculpture? Show your work.

Answers

For two similar triangular sculptures having leg l1 = 4.5 ft, l2 = 6 ft, and base b1 = 7.2 ft, the measurement of b2 is 9.6 ft.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

Two triangles are similar.

Let the two similar triangles sculptures be ΔABC and ΔDEF.

The length of the leg ΔABC, AB = 4.5 feet

The length of the base of ΔABC, BC = 7.2 feet

The length of the leg ΔDEF, DE = 6 feet

The length of the base of ΔDEF, EF = x feet

To find the measure of base of ΔDEF, use the formula for indirect measurement.

According to indirect measurement the formula will be -

AB/DE = BC/EF

Substitute the values in the equation -

4.5/6 = 7.2/x

4.5 × x = 7.2 × 6

4.5x = 43.2

x = 43.2/4.5

x = 9.6

Therefore, the value for x is obtained as 9.6 feet.

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Does someone mind helping me with this problem? Thank you!

Answers

Answer:

x=71; y=19

Step-by-step explanation:

x+y = 90 so x =90-y = 14+3y

so  90=14+4y

90-14 = 4y

76=4y

y=19

x=71

Answer:

x = 71

y = 19

Step-by-step explanation:

I solved by graphing and got (71,19) as included in the image. A more mathematical way to solve is by substitution. You try to find x with one of the equations, plug in x and then solve for y.

x + y = 90

x = 90 - y

90 - y = 14 + 3y

90 - y + y= 14 + 3y + y

90 = 14 + 4y

90 - 14= 14 + 4y - 14

76= 4y

19 = y

x + y = 90

x + (19) = 90

x + 19 - 19= 90- 19

x = 71

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