a Show that the sum of any three
consecutive even integers is a multiple of 6.
b) Hence, or otherwise, work out what the
values of three consecutive even integers
must be if their sum is 6000.

Answers

Answer 1

Answer:

Below.

Step-by-step explanation:

a) Let the numbers be n, n + 2 and n + 4

Sum = n + n + 2 + n + 4

= 3n + 6.

As n must be even (2, 4, 6 and so on) , 3n must be divisible by 6  and 3n + 6 is divisible by 6 also.

b) 3n + 6 = 6000

3n =  5994

n = 5994/3 = 1998

So the numbers are 1998, 2000 and 2002.


Related Questions

Paul's car is 16 feet long. He is making a model of his car that is 1/8 the actual size. What is the length of the model?

Answers

The length of the model car is 2 feet

Paul's car is 16 feet long. To create a model of his car that is 1/8 the actual size, we need to determine the length of the scaled-down model.

To find the length of the model, we multiply the length of the actual car by the scaling factor of 1/8.

Length of the model = Length of the actual car * Scaling factor

Length of the model = 16 feet * (1/8)

Length of the model = 16 feet * 1/8

Length of the model = 16/8 feet

Length of the model = 2 feet

Therefore, the length of the model car is 2 feet. The model car is 1/8 the size of the actual car, so it measures 2 feet in length.

This scaled-down model allows Paul to create a representation of his car that is much smaller and more manageable while maintaining the same proportions as the original car.

For more questions on length :

https://brainly.com/question/28322552

#SPJ8  

I’m doing a review but I forgot how to do this can someone help?

Answers

Answer:

-3x+10=5x-8

so basically its like grouping.

so answer is

8x=18?

Step-by-step explanation:

sorry if incorrect

Answer:

x=2.25

Step-by-step explanation:

three -x make -3x and 10 +1s make +10 and 5 xs make 5x and 8 -1s make -8

which makes

-3x+10=5x-8

just solve

18=8x

2.25=x

Two angles form a linear pair. The measure of one angle is 1/3 of the other angle. Find the measure if each angle

Answers

Answer:

The measure of the angles is 45° and 135°

Step-by-step explanation:

When two lines intersect, a linear pair of angles is formed. Two angles are said to be linear if they are adjacent, so a linear pair of angles must add up to 180 degrees.

Let's call x and y the two required angles. Knowing they form a linear pair:

x+y=180

We also know one angle is 1/3 of the other angle, thus:

x=y/3

Or, equivalently:

3x=y

Substituting y into the first equation:

x+3x=180

Simplifying:

4x=180

Solving:

x=180/4=45

The other angle is:

y=3x=3\cdot 45=135

Thus the measure of the angles is 45° and 135°

Mddffffvcfffff ggbtevtrvyrvyr eg rh rhbrybryvr th tu rybry th th ht

Answers

Answer:

Yup, same.

Step-by-step explanation:

Answer:

(keyboard spam, nice)

The original amount borrowed is called the

A.principal
B.Time
C.interest
D.rate

Answers

D. Is the correct answer which is rate

A lab assistant tracked an object’s travel time in hours. However, the lab director wants the time tracked in minutes.

A 2-column table with 4 rows. Column 1 is labeled hours with entries 0.5, 0.75, 1.5, 2.5. Column 2 is labeled Minutes with entries 30, 45, 90, blank.

Help the lab assistant complete the table. How many minutes did the object travel after 2.5 hours?

Answers

Answer:

150

Step-by-step explanation:

Answer: 150!

Step-by-step explanation:

i did the edge test, i got it right. trust me, i dont lie. :)  have a nice day<3

proof:

Which names the longest segment in the figure?
В

Answers

Answer:

PQ

Step-by-step explanation:

Answer: PQ would be the longest segment

Step-by-step explanation:

PQ extend 2 units versus 1

A glass is 1/4
full. Then 70cm3 of orange juice is poured in.
The glass is now 3/5
full. What is the total volume of the glass?
Can you please tell me how to do it as well. Thanks

Answers

749 because it says according to doctor cacarooly

a cookie recipe uses 5/6 cups of sugar lindsey is making 1 1/2 times what the recipe calls for how much sugar is she using

Answers

Answer:

1 1/4 cups of sugar

Step-by-step explanation:

5/6 x 1 1/2 = 1 1/4

Answer:

5/4 cup of sugar.

Step-by-step explanation:

The recipe calls for 5/6 of a cup of sugar, so if you're making 1.5 times what the recipe calls for, you multiply 5/6 by 3/2 (or 1.5 if you prefer decimals) which would give you 15/12. Then simplify down to get 5/4 (or 1.25) cups of sugar.

Note: 5/4 also equals 1 1/4, they are both correct, it just depends on which way you choose to write it, or how your teacher wants you to write it.

A circle measures _____.

Answers

Answer:

360 degress

Step-by-step explanation:

the circumference of a circle is its perimeter or distance around it. it is denoted by c in math formulas and has units of distance, such as milimeters, centimeters, meters, or inches. the circumference of a circle is the easured total length around a circle, which when measured in degrees in equal to 360 degress.

Please help!! Thanks

Answers

Answer:

the x-intercept is 3 and the y-intercept is -4

Step-by-step explanation:

Answer:

x-intercept: (3,0)

y-intercept: (0,-4)

Given the speeds of each runner below, determine who runs the fastest. Emily runs 15 feet per second. Noah runs 358 feet in 36 seconds. Liz runs 1 mile in 405 seconds. Zach runs 768 feet in 1 minute.

Answers

Brooke
Step-by-step explanation:
Since the first is already given in terms of rate (10 feet per second), we need to find the other rates. Remember, to convert to feet/sec rates.
Noah:
10 ft/sec
Brooke:
489 feet in 36 seconds means:
489/36 = 13.58 ft/sec
Stephanie:
1 mile is 5280 feet, so we can say:
5280 feet is 557 seconds, so rate is:
5280/557 = 9.48 ft/sec
Liz:
732 feet in 1 minutes. We know 1 minute is 60 seconds, so we can say:
732 feet in 60 seconds, so rate is:
732/60 = 12.2 ft/sec
Comparing all the rates (in ft/sec), we can say that "Brooke" is the fastest.

Solve for x2:

y2 − y1 = m(x2 − x1)


this is literal equations btw

Answers

Answer:

x2 = y2/m - y1/m + x1

Step-by-step explanation:

Expand

y2 - y1 = mx2 - mx1

Rearrange

y2 - y1 + mx1 = mx2

Divide both sides by m to make x2 on its own

y2/m - y1/m + x1 (m's cancel out) = x2

Hence:

x2 = y2/m - y1/m + x1

Answer:

x2 = x1 +  (y2 - y1)/m

Step-by-step explanation:

Given equation

y2 − y1 = m(x2 − x1)

Solving for x2

y2 − y1 = m(x2 − x1)  ⇒ divide both sides by m(y2 - y1)/m = x2 - x1  ⇒ add x1 to both sidesx2 = x1 +  (y2 - y1)/m

or

x2 = x1 + y2/m - y1/m

Here’s an algebra problem given 20 points and brainliest if correct

Answers

Answer:

12/7

Step-by-step explanation:

Hello,

C is  the point (0,0)

D is the point (7,12)

So

[tex]\text{slope} =\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{12-0}{7-0}=\dfrac{12}{7}[/tex]

thanks

Answer:

12/7 possibly.

Step-by-step explanation:

Point C is (0,0) and point D is (7,12). Using the formula given, You should have something that looks like this:

[tex]\frac{(12-0)}{(7-0)}[/tex]

Then you solve:

[tex]\frac{12}{7}[/tex]

That would be your answer I believe.

I hope it helps.

Kk someone explain this i feel so dumb thanks

Answers

Answer:

Yes

Step-by-step explanation:

The reason is all u do is 12 +1=13 aka 1pm then 30 +50=80 making the time 2:20

help me !!!!!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

The MAD is 2.

The answer would be 2 because of the fact it is talking about the snow days

The length of a rectangular field is 7 m less than 4 times the width. The perimeter is 136 m. Find the width and length

Answers

Answer:

Width: 15 Length: 53

Step-by-step explanation:

Find the distance between the points (5, 8) and (-1, 3). Round to the nearest tenth.

Answers

Answer:

7.81

Step-by-step explanation:

Solve for t in the scientific formula C =Wtc1,000.

Answers

t=C/(1000Wc). Divide both sides of the equation to isolate the variable t.

At Wal Mart a 32 ounce gatorade cost $ 1.99 and at Target a 24 ounce gatorade costs $1.09. Which store has the better buy?

Answers

I believe target has the better deal.

Lines LaTeX: CEC E and LaTeX: ADA D intersect at LaTeX: BB. Lines C E and A D intersect at the point B. Angle A B C is labeled 37 degrees. Select all the true statements. Group of answer choices The measure of angle LaTeX: CBA C B A is equal to the measure of angle LaTeX: DBE D B E . The sum of the measures of angles LaTeX: CBA C B A and LaTeX: DBE D B E is 180 degrees. The measure of angle LaTeX: CBD C B D is equal to the measure of angle LaTeX: ABE A B E . The sum of the measures of angles LaTeX: CBD C B D and LaTeX: CBA C B A is 180 degrees. The sum of the measures of angles LaTeX: CBA C B A and LaTeX: DBE D B E is 90 degrees.

Answers

*see attachment below for the figure referred to

Answer:

*The measure of angle <CBA is equal to the measure of angle <DBE.

*The measure of angle CBD is equal to the measure of angle ABE.

*The sum of the measures of angles CBD and CBA is 180 degrees.

Step-by-step explanation:

Since lines CE and AD bisects at D, they form two pairs of vertical angles that are congruent to each other. The vertical angle pairs formed are:

<CBD and <ABE;

<CBA and <DBE

Thus:

m<CBD = m<ABE;

m<CBA = <DBE = 37°

Also, m<CBA + m<CBD = 180° (supplementary linear pair)

m<ABE + m<DBE = 180° (supplementary linear pair)

Therefore, the following statements are TRUE:

*The measure of angle <CBA is equal to the measure of angle <DBE.

*The measure of angle CBD is equal to the measure of angle ABE.

*The sum of the measures of angles CBD and CBA is 180 degrees.

A snail traveled 2 feet in 90. How far will it travel in 6 hours?

Answers

Answer:

it will travel 8 minutes

Step-by-step explanation:

Answer:

[tex]\frac{2}{15}[/tex] feet

Step-by-step explanation:

Set up a proportion: [tex]\frac{2}{90} = \frac{x}{6}[/tex]  Cross multiply, then divide: 2 × 6 = 12, 12 ÷ 90 = [tex]\frac{2}{15}[/tex]  

I hope this helps!

I WILL GIVE YOU BRAINLIEST IF YOU CAN ANSWER PLEASE !?

Its propertys i have yo find which property it is please help?.

Answers

Answer:

Given

distributive property

Subtraction property of equality

Addition property of equality

Division property of equality

Solution

Step-by-step explanation:

Distributive Property!! Lmk if that isn’t right

A box of 200 baseball cards included 10 cards that featured the Los Angeles Dodgers.

1. What fraction of the cards featured the LA Dodgers. Use simplest form.

2. What is the amount as a decimal?

3. What percent of the cards featured the LA Dodgers?

Answers

Answer:

1. 1/20

2. 0.05

3. 5%

Step-by-step explanation:

Hope it helps :)

Have a good day/night

Brainliest pls?

Like I said I’m horrible at math so I’m just gonna keep posting these.

Answers

Answer:

slope is -2/1

Step-by-step explanation:

when you find slope of a line, its rise over run

so when ever the line hits a point, it goes 2 down and 1 right (if you explain this simply)

Answer:

m= -2

Step-by-step explanation:

The two points are 0,2 and 1,0 and the equation used between them spits out -2

The diagram shows TUV. Which term describes point W?

Answers

Answer:

centroid

Step-by-step explanation:

a centroid is the point of intersection of it's medians (center of the sides and the vortexes)

1
Amber ran 1
miles over a period of
1
of an hour. How fast in miles per hour is Amber running?

Answers

Answer: 1mph

Step-by-step explanation:

She s running 1 mile per hour because that's what it says in the problem.

Find the value of f(-5).

Answers

Answer:

-5f

Step-by-step explanation:

move -5 to the left of f

use the slope to determine if lines AB and CD are parallel, perpendicular, or neither. (please help asap!!)

Answers

Answer:

It’s perpendicular

Step-by-step explanation:

If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.

lines AB and CD are perpendicular to each other

This is all about getting the slope of a line between two coordinates.

The formula for the slope in this case is;

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

We are given coordinates of A and B as;

A(9, 2) and B(-1, 8)

Thus;

m = (8 - 2)/(-1 - 9)

m = 6/-10

m_ab = -6/10 = -3/5

For coordinates of C and D, we have;

C(-5, 16) and D(-8, 11)

Thus;

m_cd = (11 - 16)/(-8 - (-5))

m_cd = -5/-3 = 5/3

For the slopes to be parallel, they have to be equal but for the slopes to be perpendicular, one of them would have to be negative inverse of the other.

We see that; m_cd = 5/3 is same as -1/(m_ab) = -1/(-3/5) = 5/3

Thus, lines AB and CD are perpendicular to each other.

Read more at; brainly.com/question/4853862

Are the triangles similar?

Answers

No the side’s are different
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