the sum of three numbers is 75 the First number is 9 less than the third the second number is 2 times the third what are the numbers

Answers

Answer 1

The value of the third number is 25.5

What is an algebraic expression?

An algebraic expression can be defined as an expression can be defined as an expression that consists of variables, coefficients, terms, constants and factors.

From the information given as;

First number = x - 9second number = 2(x - 9)third number = x

Now, substitute the values, we get;

x - 9 + 2(x-9) + x = 75

expand the bracket

x - 9 + 2x - 18 + x = 75

collect like terms

x +2x + x = 75 +27

add or subtract the like terms

4x = 102

Make 'x' the subject of formula by dividing both sides by 4

x = 102/4

x = 25.5

Hence, the third number is 25.5

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Complete question

the sum of three numbers is 75 the First number is 9 less than the third the second number is 2 times the third what are the numbers. Find the third number

Answer 2

The three numbers are 19, 28 and 56

What is word problem?

Word problem in mathematics is expressing mathematical problems in words. In other words, a word problem is a verbal description of a problem situation wherein one or more questions are posed, the answers to which can be obtained by the application of mathematical operations to information available in the text.

Represent the three numbers with x, y, z

x = z-9

y = 2z

x+y+z = 75

substitute 2z for y in x+y+z

2z+x+z = 75

substitute z-9 for x

2z+z-9 = 75

3z- 9 = 75

3z = 75+9

3z = 84

z = 28

y = 2z

y = 2× 28

y = 56

to find the value of x;

x = 28-9

x = 19

therefore the value of the three numbers (x,y,z) is 19, 28, 56

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Related Questions

Thomas took 3h to paint a room. Brian could paint the same room in 6h. How long would it take for both of them to finish painting the same room together?

please help !! no algebra please

Answers

Answer:

2 hours

Step-by-step explanation:

If Thomas can paint 1/3 = 2/6 of the room in a hour and Brian can paint 1/6 of the room in an hour. Which means in an hour they can collectively paint 3/6 = 1/2 of the room. Now you need to find how long it would take then to paint 2/2 of the room. Knowing that 1/2+1/2 = 2/2, it would take them 2 hours to paint the room together

Linda is training to be an assistant at the local animal shelter. To become an assistant she needs to complete 48 h of training. Linda keeps a graph of the number of hours of training left to be completed. What is the rate of change of the number of hours remaining with respect to the number of days? Remember to include units.

Answers

The equation between the number of days remaining and number of hours is given as y= -5x+50.

How to illustrate the equation?

Let y be the number of days remaining and x be the no.of hours.

From the graph the slope of the line is given by m.

m=(y2 - y1)/(x2 - x1)

m=(30 - 40)/(4 - 2)

m= -10/2 = -5.

The above slope is in between points 2 and 4. As the line has a constant rate of growth the slope is the same between any points of the line.

Therefore the equation between the no.of days remaining and no.of hours is given by

y=mx +c.

y=-5x+c

Now to find the value of c. This can be determined by substituting the x and y values at a particular instant. For x=0,y=50. Therefore by these values, we get,

50= -5(0)+c

c=50.

Therefore the relation between the number of days remaining and number of hours is given as y= -5x+50.

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You should rotate tires on a car at regular intervals. In how many ways can four tires be arranged on a car?

Answers

The tires can be arranged in 24 ways. Computed using permutation.

The permutation is a way of selecting a smaller set from a larger set when the order of selection is not of concern.

For selecting r number of items, from n number of items, with the order of selection not being a concern, we can calculate the number of ways using permutation:

nPr = n!/(n - r)!.

In the question, we are asked the number of ways in which the four tires can be arranged on a car.

As we need to select 4 tires, from 4 tires, with any order, we will use permutation.

Thus, the number of ways can be calculated as 4P4, which can be calculated using the formula, nPr = n!/(n - r)!.

Thus, 4P4 = 4!/(4 - 4)! = 4!/0! = 24/1 = 24.

Thus, the tires can be arranged in 24 ways. Computed using permutation.

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In which data set is the mean greater than the median?

Answers

One of the basic tenets of statistics that every student learns in about the second week of intro stats is that in a skewed distribution, the mean is closer to the tail in a skewed distribution. So in a right skewed distribution (the tail points right on the number line), the mean is higher than the median.

A Textile Company bought equipment for $40,000. The residual value is $6,000.
The company assumes the equipment will have a useful life of 170,000 units. What
is depreciation expense per unit of production?

$2.00
$1.20
$0.75
$0.20

Answers

The depreciation expense per unit of production for the Textile Company is D. $0.20.

What is the unit-of-production depreciation method?

The unit-of-production depreciation method uses the useful life of an asset based on the units of production and the depreciable amount to estimate the depreciation expense per unit.

For each period, the depreciation expense per unit is multiplied by the units of production to determine the period's total depreciation expense.

Data and Calculations:

Cost of equipment = $40,000

Residual value = $6,000

Depreciable amount = $34,000 ($40,000 - $6,000)

Estimated useful life = 170,000 units

Depreciation expense per unit of production = $0.20 ($34,000/170,000)

Thus, the depreciation expense per unit of production for A Textile Company is D. $0.20.

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A government buys `x`fighter planes at `z` dollars each, and `y` tons of wheat at w dollars each. It spends a total of `B`dollars, where `B=xz+yw`. Write an equation whose solution is the given quantity:

2. The price of a ton of wheat, given that a fighter plane costs 100,000 times as much as a ton of wheat, and that the government bought 20 fighter planes and 15,000 tons of wheat for a total cost of $90 million.

Answers

The equation whose solution is the given quantity is 90,000,000 = 2,000,000w + 15,000w where w = $44.67

Equation

B = xz + yw

Where,

B = Total cost = 90x = number of fighter plane = 20y = tons of wheat = 15,000w = cost of each tons of wheatz = cost of fighter planez = 100,000w

B = xz + yw

90,000,000 = (20 × 100,000w) + (15,000 × w)

90,000,000 = 2,000,000w + 15,000w

90,000,000 = 2,015,000w

w = 90,000,000 / 2,015,000

= 44.6650124069478

Approximately,

w = $44.67

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The following data show the scores of some students in a competition:

13 points

24 points

31 points

24 points

27 points

23 points

11 points

Which box plot represents the data?
A box plot titled "Scores of Participants" and labeled "Score" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 23 to 27 on the number line. A line in the box is at 24. The whiskers end at 11 and 31.
A box plot titled "Scores of Participants" and labeled "Score" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 27 on the number line. A line in the box is at 24. The whiskers end at 11 and 31.
A box plot titled "Scores of Participants" and labeled "Score" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 27 on the number line. A line in the box is at 23. The whiskers end at 11 and 31.
A box plot titled "Scores of Participants" and labeled "Score" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 27 on the number line. A line in the box is at 24. The whiskers end at 10 and 35.

Answers

The box plot that represents the data is a box plot titled "Scores of Participants" and labeled "Score" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 27 on the number line. A line in the box is at 24. The whiskers end at 11 and 31.(second option)

Which box plot represents the data?

A box plot is used to study the distribution and level of a set of scores. The whiskers represent the minimum and maximum values.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. 75% of the scores represents the upper quartile.

The data arranged in ascending order : 11, 13, 23, 24, 24, 27, 31

Median = 24

First quartile = 1/4 x (7 + 1) = 2nd term =13

Third quartile = 3/4 x (7 + 1) = 6th term = 27

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Question 22: 4 pts
Nine cards are numbered from 1 to 9 and placed in a box. One card is selected at random and not replaced.
Another card is randomly selected. What is the probability of selecting two prime numbers?
2/9
O1/12
1/9
1/6

Answers

The probability of selecting two prime numbers is 1/6.

What is the probability?

Probability determines the odds that a random event would happen. The odds that the random event would happen lie between 0 and 1.

The probability of selecting two prime numbers = (number of prime numbers between 1 and 9 / total numbers between 1 and 9) x [(number of prime numbers between 1 and 9 / total numbers between 1 and 9) - 1]

Prime numbers between 1 and 9 = 2, 3, 5, 7

4/9 x 3/8 = 1/6

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A linear function always increases

-true

-false

Answers

Answer: False

Step-by-step explanation:

If the function has a negative slope, then it will decrease.

Consider the following 8 numbers, where one labelled
x
is unknown.

34
,

31
,

15
,

x
,

17
,

4
,

20
,

25

Given that the range of the numbers is 69, work out 2 values of
x
.
x
=

x
=

Answers

Answer:

x = 73

x = -35

Step-by-step explanation:

Here are the 8 numbers:

34, 31, 15, x, 17, 4, 20, 25

Here are the 8 numbers in ascending order with x as the greatest number:

4, 15, 17, 20, 25, 31, 34, x

x - 4 = 69

x = 73

Here are the 8 numbers in ascending order with x as the smallest number:

x, 4, 15, 17, 20, 25, 31, 34

34 - x = 69

-x = 69 - 34

-x = -35

x = -35

Answer:

x = 73

x = -35

Question 4 of 10
What should you substitute for y in the second equation (bottom equation) in
order to solve the system by the substitution method?
5x+y=10
3x-2y =6
A. -0.2y+2
B. -5x+10
C. 5x-10
D. 1.5x+3

Answers

Answer:

Step-by-step explanation:

5x+y=10

-5x -5x

y= -5x+10

Write the expression as a polynomial:
(a-2)(4a³-3a²)

Answers

Answer:

[tex]4a^{4} -11a^{3} + 6a^{2}[/tex]

2. State two (2) values of θ (theta) to the nearest degree for
sin θ = − 0. 966

Answers

Using equivalent angles, the solutions to the equation are given as follows:

[tex]\theta = 255^\circ, \theta = 285^\circ[/tex]

What are equivalent angles?

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

In this problem, the equation is:

[tex]\sin{\theta} = -0.966[/tex]

Applying the inverse relation:

[tex]\theta = \arcsin{-0.966} = 255^\circ[/tex]

Which is on the third quadrant. The equivalent angle on the fourth quadrant is given as follows:

[tex]270^\circ + (270^\circ - 255^\circ) = 285^\circ[/tex]

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A group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the trip. Each small car can hold 5 people and each large car can hold 7 people. A total of 10 cars were rented which can hold 66 people altogether. Write a system of equations that could be used to determine the number of small cars rented and the number of large cars rented. Define the variables that you use to write the system.

Answers

The system of equations that could be used to determine the number of small cars rented and the number of large cars rented is;

x + y = 10

x + y = 105x + 7y = 66

Simultaneous equation

Small car = 5 peopleLarge car = 7 peopleTotal cars = 10Total number of people = 66

Let

Number of small cars rented = x

Number of large cars rented = y

x + y = 10

x + y = 105x + 7y = 66

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Use the drawing tool(s) to form the correct answer on the provided graph.

Graph the solution to this system of inequalities in the coordinate plane.

3y 2x+122x + y ≤5

Answers

The plotting of the inequalities was done using geogebra online graphing calculator. The graph is attached.

What are inequalities?

Inequalities are the mathematical expressions in which both sides are not equal. It should be noted that in inequality, unlike in equations, we compare two values.

The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign. Inequality is an expression used to show the nonequal comparison of numbers and variables.

Given the system of inequalities:

3y > 2x + 12

3y - 2x > 12 (1)

2x + y < -5 (2)

Plotting the inequalities using GeoGebra online graphing calculator. The graph is attached

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PLEASE HELP!!!!
Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 400 minus quantity y minus 110 end quantity squared over 2304 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number.

100 meters
50 meters
48 meters
40 meters

Answers

Answer:

(a) 100 meters

Step-by-step explanation:

You want the width at the base of a cooling tower whose walls are modeled by the equation (x/20)² -((y-110)/48)² = 1.

Base

The width at the base will be the difference in the values of x when y=0.

(x/20)² -((0 -110)/48)² = 1

(x/20)² = 1 +3025/576

x = ±20/24√3601 ≈ ±50.01

The width will be 50.01 -(-50.01) ≈ 100 meters.

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Which expression is it equivalent too help a brother out

Answers

The expression which is equivalent to the given expression in the task content is; 1/x²⁴.

Which expression is equivalent to the given expression?

It follows from the task content that the given expression is; ((x)^-6/x²)³.

Hence, it follows from the laws of indices that the expression can be evaluated as follows;

= (x^-8)³

= x^-²⁴

= (1/x²⁴).

Answers

In order to define the quantity of which of the two website produces a larger amount of content per single writer, Charlotte thought of:

A Average number of posts per writer C Average number of words per writer

How can Charlotte define the quantity?

Charlotte wants to know which website has more content per writer which means that she wants to know which website is more productive with writing.

One way she can do this is to check the average number of posts per writer per website. This would show her which website has a writer that writes more content on average.

Charlotte could also use average number of words per writer. This shows just how much writing the writers in each websites are doing, in terms of words. The website with the higher average words per writer is therefore providing more content.

Options for this question include:

A Average number of posts per writerB Total number of wordsC Average number of words per writerD Average number of likes per word

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which of the following functions is graphed below?

Answers

The function that's illustrated in the graph is function D.

How to explain the function?

First, you look at the left side of the graph. You can tell by the shape that it is an x³ function.

Also, the filled-in circle means inclusive. so we know that when x is less than or equal to a number.

The answer that illustrates the information explained is D.

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Answer:

Step-by-step explanation:

An open circle means to exclude the point.

A closed circle means to include the point.

In this graph we see a part of a parabola with an open circle above. The parabola starts at x = 1, but does not include x = 1, and the x values of the parabola increase.

A parabola has an x squared in the equation.

The solution has to have an equation with an x² as its greatest exponent, and also must include x > 1.

The lower part of the graph is a third degree polynomial, so it must have an x cube term, x³. Also, the greatest x value for the x³ function is x = 1, but x = 1 is included. Then all x values tot he left of x = 1 are also included, so for the cubic polynomial, the domain (x values) must be x ≤ 1.

The answer is B.

Complete the statements. If both expressions have the same value after substituting and simplifying two different values for the variable, then they are . The value of both expressions when k = 3 is and when k = 5 is 45, so the expressions are .

Answers

When both expressions have the same value, then they are equal to each other.

What is an equivalent expression?

The equivalent is the expressions that are in different forms but are equal to the same value.

Consider the expressions 5 + 8k and 8k + 5.

Using k = 3

5 + 8k = 8k + 5

5 + 8(3) = 8(3) + 5

5 + 24 = 24 + 5

29 = 29

Using k = 5

5 + 8k = 8k + 5

5 + 8(5)= 8(5) + 5

5 + 40 = 40 + 5

45 = 45

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Complete question:

Consider the expressions 5 + 8k and 8k + 5. Determine why the expressions are equivalent.

Using k = 3 5 + 8k 8k + 5 5 + 8(3) 8(3) + 5 5 + 24 = 29 24 + 5 = 29

Using k = 5 5 + 8k 8k + 5 5 + 8(5) 8(5) + 5 5 + 40 = 45 40 + 5 = 45

Complete the statements.

If both expressions have the same value after substituting and simplifying two different values for the variable, then they are.

The value of both expressions when k = 3 is and when k = 5 is 45, so the expressions are.

A matrix A has x rows and x+5 columns. B has y rows and 11−y columns. Both AB and BA exist. Find x and y.

Answers

Answer:

x = 3

y = 8

Step-by-step explanation:

A matrix product exists if and only if the number of columns in the left matrix is equal to the number of rows in the right matrix.

Setup

For AB to exist, we must have ...

columns of A = rows of B

x +5 = y

For BA to exist, we must have ...

columns of B = rows of A

11 -y = x

Solution

Using the second equation to substitute for x in the first equation, we have ...

(11 -y) +5 = y

16 = 2y

8 = y

Then the value of x is ...

11 -8 = x = 3

The values of x and y are ...

x = 3y = 8

Additional comment

The dimensions are A = 3×8; B = 8×3.

Which of the following is a true proportion of the figure based on the triangle
proportionality theorem?

Answers

Based on the triangle proportionality theorem, the true proportion is h/j=k/i

How to solve for the true proportion

In the diagram that we have here, we have TU to be parallel to QR.

We have following

ST is equal to h, TQ is equal to j, SU is equal to k and UR is equal to i.

This can then be used to form the equation

ST/TQ = SU/UR

When we h/j = k/i

Answers

Answer:

ΔABC ≅ ΔEDF

Step-by-step explanation:

Triangle ABC is congruent to triangle EDF because they're the same size.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex] \sf\triangle ABC \cong \triangle DEF[/tex]

For checking congruency, we need to follow a proper order when choosing the triangle. because each triangle name is unique in itself.

So, According to Triangle ABC, we need to find the triangle with first two letters That resembles AB, that is :

AB = DE

and next should be :

BC = EF

[tex] \qquad \large \sf {Conclusion} : [/tex]

so, now we got the sense for naming, therefore the answer will be :

[tex] \sf\triangle ABC \cong \triangle DEF[/tex]

An American roulette wheel contains 38 slots. Eighteen of the slots are colored red and eighteen are colored
black. The remaining two slots are colored green. A ball is spun on the wheel and comes to rest in one of the
38 slots. If you bet $1 on the the number 32 and win, the house pays you $36.
What is the expected value of betting on 32?
$1
O-$1
4
O-$5.30
O-$0.053

Answers

The expected value of betting 32 is -$0.053, making the 4th option the right choice.

In the question, we are asked for the expected value of betting on 32, given that if we bet $1 on the number 32 and win, the house pays $36, and there are 38 slots.

The probability distribution can be shown as:

x $35 -$1

p(x) 1/38 37/38

as, if we get 32, which has the probability of 1/38, the winning number, we gain $35, and for the rest, having a probability of 37/38, the losing number, we lose -$1.

Thus, the expected value can be calculated as E(x) = ∑x.p(x).

Thus, the expected value = $35(1/38) + (-$1)(37/38) = -$2/38 = -$0.05263 ≈ -40.053.

Hence, the expected value of betting 32 is -$0.053, making the 4th option the right choice.

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A person draws a card from a hat. Each card is one color, with the following probabilities of being drawn: 1/5 for pink, 1/25 for blue, 1/10 for yellow, and 1/15 for black. What is the probability of pulling a blue or yellow card,

Answers

The probability of pulling a blue or yellow card, written as a reduced fraction is 7/50

How to determine the probability of pulling a blue or yellow card, written as a reduced fraction?

From the question, we have the following probabilities:

P(Pink) = 1/5

P(Blue) = 1/25

P(Yellow) = 1/10

P(Black) = 1/15

The probability of pulling a blue or yellow card, written as a reduced fraction is the calculated as:

P(Blue or yellow card) = P(Blue card) + P(Yellow card)

Substitute the known values in the above equation

P(Blue or yellow card) = 1/25 + 1/10

Express 1/25 as 2/50 and 1/10 as 5/10

P(Blue or yellow card) = 2/50 + 5/50

Take the LCM

P(Blue or yellow card) = (2+ 5)/50

Evaluate the sum

P(Blue or yellow card) = 7/50

Hence, the probability of pulling a blue or yellow card, written as a reduced fraction is 7/50

Answers

Answer: D

Step-by-step explanation:

There are vertical asymptotes at x=7 and x=-3, so the denominator should have factors of (x-7) and (x+3).

This eliminates everything except for D.

Write the equation of the line that is perpendicular to the graph of

2x-3y=-3

and passes through (–3, 0).

Answers

Answer:

Step-by-step explanation:

eq. of line is 2x-3y=-3

its slope=(-co-efficient of x/co-efficient of y)=-2/-3=2/3

slope of line perpendicular to given line=-3/2

eq. of line through (-3,0) is

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

2y=-3x-9

3x+2y=-9

any eq. perpendicular to given line is

3x+2y=c where c is a constant.

it passes through (-3,0)

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

c=-9

reqd. eq. is

3x+2y=-9

Two sides of a triangle have lengths 18m and 23m. Describe the possible length of the thired side

Answers

The possible length of the third side will be values that are less than 41 and greater than 5

Triangular theorem

For three sides to be the sides of a triangle, the sum of any two sides of the triangle must be greater than the third.

Given the two sides of a triangle have lengths 18m and 23m, the sum of the sides is given as:

sum = 18 + 23

Sum = 41

Let the third side be x, such that;

x + 18 >23

23 + x > 18

x > 23 - 18

x > 5

Similarly

x > -5

Hence the possible length of the third side will be values that are less than 41 and greater than 5

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Let f(x) = √3x and g(x) = x + 3. What's the smallest number that is in the domain of
fºg?

Answers

Answer:

-3

Step-by-step explanation:

[tex]f\left( x\right) =\sqrt{3x} \ \ \text{and} \ \ g\left( x\right) =x+3[/tex]

it’s clear that :

f is defined if and only if x ≥ 0

Therefore ,

fºg is defined if and only if x + 3 ≥ 0

x + 3 ≥ 0

⇔ x ≥ -3

Then ,the smallest number that is in the domain of fºg is -3

Drag a statement or reason to each blank in the table to complete the proof that <1 is congruent to <7.

Answers

Step-by-step explanation:

<1 congruent to <5.

<5 congruent to <7.

<1 congruent to <7.

Answer:

don't know but i need thee points

Step-by-step explanation:

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