Three times the sum of three consecutive integers is 72. What are the integers? a. 4, 5, 6 c. 9, 10, 11 b. 7, 8, 9 d. 6, 7, 8

Answers

Answer 1

Answer:

B

Step-by-step explanation:

7+ 8+ 9= 24

24 x 3= 72

Answer 2

Answer:

The three integers whose three times the sum of three consecutive integers is 72 will be: 7, 8, 9

Step-by-step explanation:

Let x, y, and z be the three consecutive integers

The sum of x, y, and z will be: x+y+z

The three times the sum of three consecutive integers is 72.

so the equation becomes:

3(x+y+z)=72

Now, putting x = 7, y=8 and z=9 in the L.H.S equation to check

3(x+y+z)

⇒ 3(7+8+9)

⇒ 3(24)

⇒ 72

Therefore, it is clear that the three integers whose three times the sum of three consecutive integers is 72 will be: 7, 8, 9


Related Questions

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

An employee at a construction company is ordering interior doors for some new houses that are being built. There are 2 one-story houses and 4 two-story houses on the west side of the street, which require a total of 64 doors. On the east side, there are 5 one-story houses and 4 two-story houses, which require a total of 88 doors. Assuming that the floor plans for the one-story houses are identical and so are the two-story houses, how many doors does each type of house have?

Each one-story house has
doors, and each two-story house has
doors.

Answers

Answer: This is a system of equations, let's set it up.  I set the variable for 1 story houses to x and 2 story houses to y.  Here are the two equations:

6x + 2y = 72

5x + 7y = 124.

Now we multiply the equations so that when we add them together one of the variables will be cancelled out.  I am going to multiply the top equation by 7 and the bottom equation by -2.  This gives us

42x + 14y = 504

-10x -14y = -248

Add the two equations together:

32x = 256

Divide by 32 to get x = 8.  The one story houses have 8 doors.  We can plug this number into one of the original equations and solve for y now.  I'm going to use the first equation.

(6*8) + 2y = 72  

Now we solve for y

y = 12  So, the 1 story houses have 8 doors and the 2 story houses have 12 doors.

For what value of b, would the equation 34(12x−9)+b4=5−3(2−3x) have infinitely many solutions?

Answers

Answer:

Yes.

Step-by-step explanation:

Because.

Answer:

23

Step-by-step explanation:

The length of a rectangle is 3 more than 3 times its width. The perimeter of the rectangle is 174 inches. What is the length of the rectangle?

Answers

Answer:

Sorry I cant help

Step-by-step explanation:

Solve the following expression: (9 x 10) - (30 + 30). Show all steps taken.

Answers

Answer:

First multiply each brackets

90-60

30

Step-by-step explanation:

Answer:

9 x 3= 27 and 30 + 30=  60.. so 60- 27= 33, but if you want to do 27- 30.. it would be -33.

Step-by-step explanation:

Hope that answers your question!

If the graph of f(x) = is translated right 9.5 units and up unit, which function represents the resulting graph? g(x) = – 9.5 g(x) = + 9.5 g(x) = – g(x) = +

Answers

Answer:

the answer is d

Step-by-step explanation:

edenuity2020. also I just did it

Sleep habits of New Yorkers. New York is known as the city that never sleeps". A random sample of 25 New Yorkers were asked how much sleep they get per night. Statistical summaries of these data are shown below. The point estimate suggests New Yorkers sleep less than 8 hours a night on average. Is the result statistically signicant? n x s min max25 7.73 0.77 6.17 9.78(a) Write the hypotheses in symbols and in words.(b) Check conditions, then calculate the test statistic, T, and the associated degrees of freedom.(c) Find and interpret the p-value in this context. Drawing a picture may be helpful.(d) What is the conclusion of the hypothesis test?(e) If you were to construct a 90% condence interval that corresponded to this hypothesis test, would you expect 8 hours to be in the interval?

Answers

Step-by-step explanation:

1.

the null hypothesis:

H0: u = 8 hours ( new Yorkers sleep for 8 hours)

The alternate hypothesis;

H1: u ≠ 8 hours ( new Yorkers sleep less than 8 hours)

b.

test statistic

t = (barX - u)/s/√n

= 7.73-8/0.77/√25

= -1.7532

degree of freedom = n-1

= 25-1 = 24

c.

p(value)

= p(t < -1.7532)

= 0.046

obviously we can see that the p value is less than 0.05 alpha level so we reject the null hypothesis.

d

The data gives strong evidence that new Yorkers sleep less than 8 hours on average every night.

e.

at 90% level of confidence

we have

7.73-0.26334, 7.73+0.26334

= 7.466, 7.993

please check attachment

thank you!

You have a garden row of 20 watermelon plants that produce an average of 30 watermelons apiece. For any additional watermelon plants planted, the output per watermelon plant drops by one watermelon. How many extra watermelon plants should you plant?

Answers

Answer: You should plant another 25 watermelons.

Step-by-step explanation:

The total number of watermelons can be calculated as:

W = (20 + x)*(30 - x)

x is the number of plants that we add, for each plant that we add, the output per watermelon plants drops by one watermelon, then if we add x plants, each plant will give (30 - x) watermelons.

We want to maximize this equation, so let's distribute the product.

W = 600 + 30*x + 20*x - x^2

W = 600 + 50*x - x^2

Notice that this is a quadratic equation with a negative leading coefficient, this means that the maximum is at the vertex, and the arms of the equation will open down.

To find the maximum, we can just derive with respect to x, and find the value of x that makes that equal to zero, this is:

W'(x) = dW/dx = 50  - 2*x

W'(x) = 0 = 50 - 2*x

           2*x = 50

          x = 50/2 = 25.

Then the maximum output will be if you plant 25 more watermelon plants.

And this will be:

W(25) = 600 + 50*25 - 25^2 = 1,225 watermelons

You should plant 5 extra watermelon plants to maximize production.

Since you have a garden row of 20 watermelon plants that produce an average of 30 watermelons a piece, and for any additional watermelon plants planted, the output per watermelon plant drops by one watermelon, to determine how many extra watermelon plants should you plant you must perform the following calculation:

20 x 30 = 600 24 x 26 = 624 25 x 25 = 625 26 x 24 = 624

Therefore, you should plant 5 extra watermelon plants to maximize production.

Learn more in https://brainly.com/question/2173344

I WILL GIVE BRAINLIEST ONLY IF YOU ANSWER WELL
Which expression uses the commutative property to make it easier to evaluate 3/5·1/4·25
A.25·4·3/5
B.5/3·25·1/4
C.3\5·25·1\4
D.3/5·1/25·1/4​

Answers

Answer:

I dont know im in middle school can you please giva me one i have to get my grades up

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

3

5

(1)

4

(25)

=

3

5

4

(25)

=

3

20

(25)

=

15

4

What is the probability that a normal random variable will take a value that is less than 1.05 standard deviations above its mean?

Answers

Complete Question

What is the probability that a normal random variable will take a value that is less than 1.05 standard deviations above its mean? In other words, what is P(Z < 1.05)

A 0.8531

B 0.1468

C 0.9332

D 0.0668

Answer:

The correct option is  A

Step-by-step explanation:

Generally from the z table  the area under the normal curve to the left corresponding to  1.05 is

     [tex]P(Z < 1.05) = 0.8531[/tex]

-3a - 4(a - 6) = 24 - 7a

Solve the equation

Thanks

Answers

-3a-4(a-6)=24-7a

-3a-4a+24=24-7a

-7a+24=24-7a

-7a+24=-7a+24

-7a+24-24=-7a+24-24

Simplify

Subtract the numbers

Subtract the numbers

−7a=-7a

Add 7a to both sides of the equation

-7a+7a =-7a+7a

Simplify

Combine like terms

Combine like terms

0=0

answer is 0=0

Let a function y represent the water level in a harbor measured in meters, and let x represent the number of hours since high tide. At time x = 0, the water level is 19.5 meters (a maximum). At time x = 6.26 hours, the water level is 10.5 meters (a minimum). The period of the function is 12.5 hours.


After how many hours is the water expected to reach a depth of 17 meters for the first time? Round to the nearest tenth of an hour.


A 2.2 hours

B 6.3 hours

C 12.1 hours

D 12.5 hours

Answers

Answer:

A 2.2

Step-by-step explanation:

a gardener uses a grow light to grow vegetables indoors. if m<1 = (8x) and m<2 = (7x-4), what is m<1?

Answers

Answer:

64

Step-by-step explanation:

5(x+2) - 3 = 2x + 7 + 3x *
One Solution
No Solution
Infinitely Many Solutions

5x + 27x - 10 = 8(4x +10)
One Solution
No Solution
Infinitely Many Solutions

Answers

Answer:

First we must solve them both to determine,

5(x+2)-3=2x+7+3x
5x+10-3=5x+7
5x+7=5x+7

The statement is True or has Infinitely Many Solutions.

5x+27x-10=8(4x+10)
32x-10=32x+80
-10=80

The statement is False or has No Solution.

PLEASE HELP!!!!!
What is the result when the number 59 is decreased by 7%?

Answers

Answer:

= 59 - (59*0.07)

= 59 - 4.13

= 54.87

Answer:

The result would be 54.87

For which value of p will the equation 6x – 5 = 6x + p have an infinite number of solutions?
A. 5
B. 0
C. -10
D. -5

Answers

Answer:

the answer is b

Step-by-step explanation:

Can anyone help me with this i need help quick

Answers

Answer:

C

Step-by-step explanation:

y=mx+n m is slope if slopes are perpendicular m1.m2=-1

(2/3) . (-3/2) = -1

m1=2/3

m2=-3/2

y=(2/3)x-3 m=2/3 n= -3

y=(-3/2)x+2   m = -3/2 n = 2

The graph shows the rate at which water is leaking from a tank. The slope of the line gives the leaking rate in gallons per minute.

Answers

Answer:

the rise is 6 and the run is 7.  the rate of leaking per minunte is about .8  gallons per minute

Step-by-step explanation:

i think its right this time

A linear function contains the following points. (-2,8) (0,6) What are the slope and y-intercept of this function?​

Answers

Answer:

slope= -1

y-intercept is 6

Step-by-step explanation:

slope = y2-y1/ x2-x1

slope = 6-8/ 0-(-2) = -1

y-intercept is 6 because of (0,6), where the points cross y-axis

Use the equation m=y2-y1/x2-x1 to find the slope
6-8/0-(-2)
-2/2
M=-1
Plug inyour slope one set of coordinates into y=mx+b. I’ll use the ordered pair (0,6)
6=-1(0)+b
6=b
Equation: y=-x+6

(39×5) to siplifiy please help

Answers

Answer:

195

Step-by-step explanation:

you just muliply

Answer:

The answer is 175! :)

I recommend searching or creating a times table for yourself, they are incredibly handy! Easy to print off or write down. :))

Step-by-step explanation:


What is the value of 15/2+I?

Answers

Answer:

First, make the denominators

15/2+2/2

Then, add

17/2

If you want it in decimal points

8.5

Step-by-step explanation:

I hope I explained well, please give me brainliest

First divide 15/2= 7.5 and then add 7.5 with the 1 = 8.5
If you want a fraction just remove the point like this
85 and divide by 10
85= 17/2.
10
Hope that helps :D

C(5,-5),D(5,3) what is the distance between the points

Answers

Here is my answer 8.

Maurice made a model of the steel tabletop his model measures 7 inches by 13 inches is the model simular to the original

Answers

The first example has students building upon the previous lesson by applying the scale factor to find missing dimensions. This leads into a discussion of whether this method is the most efficient and whether they could find another approach that would be simpler, as demonstrated in Example 2. Guide students to record responses and additional work in their student materials.
§ How can we use the scale factor to write an equation relating the scale drawing lengths to the actual lengths?
!
ú Thescalefactoristheconstantofproportionality,ortheintheequation=or=!oreven=
MP.2 ! whereistheactuallength,isthescaledrawinglength,andisthevalueoftheratioofthe drawing length to the corresponding actual length.
§ How can we use the scale factor to determine the actual measurements?
ú Divideeachdrawinglength,,bythescalefactor,,tofindtheactualmeasurement,x.Thisis
! illustrated by the equation = !.
§ How can we reconsider finding an actual length without dividing?
ú We can let the scale drawing be the first image and the actual picture be the second image. We can calculate the scale factor that relates the given scale drawing length, , to the actual length,. If the actual picture is an enlargement from the scale drawing, then the scale factor is greater than one or
> 1. If the actual picture is a reduction from the scale drawing, then the scale factor is less than one or < 1.
Scaffolding:
A reduction has a scale factor less than 1, and an enlargement has a scale factor greater than 1.
Lesson 18: Computing Actual Lengths from a Scale Drawing.

A rectangular pool has a length of 200 ft. You're building a model. Using a scale
factor of 1725, what is the scale length of your model? *

Answers

Answer:

1.4 inches.

Step-by-step explanation:

Given that the length of the pool = 200 ft.

Scale factor = 1725.

As,

[tex]\text{Scale factor }=\frac{\text{Original length}}{\text{Scaled length}}[/tex]

So,

[tex]\text{Scaled length} = \frac{\text{Original length}}{\text{Scale factor}}[/tex]

By using the given values, we have

{Scaled length} [tex]= \frac{200}{1725} ft.=0.116 ft.[/tex]

As 1 foot = 12 inch,

So, scaled length = 0.116 x 12 = 1.4 inches.

Hence, the scale length of the model = 1.4 inches.

Steps for solving rational equations

Answers

Answer:

1. Find the common denominator.

2. Multiply everything by the common denominator.

3. Simplify.

4. Check the answer(s) to make sure there isn't an extraneous solution.

Step-by-step explanation:

Hope this helps!

The steps for solving rational equations will be to take common factors and simplify the equation.

What are the steps for solving rational equations?

A rational equation, abbreviated as P(x) / Q(x), is one that has at least a single fraction with polynomials as the numerator and denominator. Q(x) / P(x). These integers might be on either end of the equation or sometimes both.

The steps are given below.

Discover the common factor.Divide everything by the lowest common factor.Simplify the equation.Verify the response(s) to verify sure there isn't a redundant response.

The steps for solving rational equations will be to take common factors and simplify the equation.

More about the steps for solving rational equations link is given below.

https://brainly.com/question/27230278

#SPJ6

Find (fog)(x).
f(x) = 6x
g(x) = x + 3
Write your answer as a polynomial in simplest form.
(fog)(x) = ????

Answers

Answer:

[tex](fog)(x)=6x+18[/tex]

Step-by-step explanation:

We are given:

f(x)=6x

and g(x)=x+3

We need to find (fog)(x)

(fog)(x) =f(g(x)) i.e we will put value of g(x) into f(x) i.e

[tex](fog)(x)=f(g(x))\\f(g(x))=6(x+3)\\f(g(x))=6x+18[/tex]

So, [tex](fog)(x)=6x+18[/tex]

Plz help me answer this, Marked brainlest, Marry and Julie both have a goal of raising $1000 for charity. Mary raises $12 every 4 days. Julie raises $19 every 6 days. Will Mary or Julie reach her goal first? Explain​

Answers

Answer:

Julie

Step-by-step explanation:

Mary would have a rise of 12 and a run of 4, making her slope, or rate of change, $3 a day. Julie would have a rise of 19 and a slope of 6, making her slope, or rate of change, $3.17 a day. Since Julie is raising money at a faster rate, she would get to the goal of $1000 first.

Answer:

Mary has a rise of 12 and a run of 4.  Mary has a slope of 3. Mary would have a rise of 12 and a run of 4, making her slope, or rate of change, $3 a day. Julie would have a rise of 19 and a slope of 6, making her slope, or rate of change, $3.17 a day. Since Julie is raising money at a faster rate, she would get to the goal of $1000 first. Julie has a rise of 19 and a run of 6.  Julie has a slope of 19/6 or 3 and 1/6.  Julie will reach her goal first, as she has the greater slope.

Hope this Helps!

Please help & thank you.

Answers

Answer:

2). 79°; 3). 65°; 4). 45°; 5) 73°

Step-by-step explanation:

m∠4 = 180° - (70° + 65°) = 45°

m∠3 = 180° - (45° + 70°) = 65°

m∠2 + m∠3 = 180° - 36° = 144°

m∠2 = 144° - 65° = 79°

m∠5 = 118° - m∠4 = 118° - 45° = 73°

Reduce the fraction and find the domain.
[tex]\frac{a(x-2y)}{b(2y-x)}[/tex]

Thanks!

Answers

Answer:

-a/b

Step-by-step explanation:

a(x - 2y)/b(2y - x) =            ⇒ consider x - 2y = - (2y - x)-a(2y - x)/b(2y - x) =-a/b

Which numbers should go in the shaded overlap?
Factors of 30
Factors of 20

Answers

Both of these numbers have 2 and 5 as their factors

What is the inequality of y-2x<=-3

Answers

y>= 2x-3
In inequalities when you are moving a negative, you flip the sign.
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