Find four consecutive even integers such that if the sum of the first and the third is multiplied by 5 the result is 12 less than 9 times the fourth

Answers

Answer 1
4 consecutive even integers....x, x + 2, x + 4, x + 6

5(x + x + 4) = 9(x + 6) - 12
5(2x + 4) = 9x + 54 - 12
10x + 20 = 9x + 42
10x - 9x = 42 - 20
x = 22

x + 2 = 22 + 2 = 24
x + 4 = 22 + 4 = 26
x + 6 = 22 + 6 = 28

so ur numbers are : 22,24,26, and 28

Related Questions

Defined by two lines or rays diverging from a common point.
A) arc
B) angle
C) parallel lines
D) perpendicular lines
Defined as bounded by two distinct end points that contain every point on the line between its end points.
A) circle
B) line segment
C) parallel lines
D) perpendicular lines

Answers

Answer:

1. Angle

2. Line Segment

Step-by-step explanation:

Two lines or rays diverging from a common point defines an 'angle', which is a figure forming from two rays starting from the same end-point.

Now, a figure bounded by two distinct end points which contain every point on the line between its end points defines a 'line segment'.

Hence, the answer are: Angle and Line Segment respectively.

Thirty-one books are arranged from left to right in order of increasing prices. The price of each book differs by $2 from that of each adjacent book. The price of the book at the extreme right is equal to the price of the middle book plus a book adjacent to the middle one. Give an expression for the cost of the $n$th book in terms of $n$

Answers

The answer for this problem is 2 since it is not specified whether it is adjacent to the right or adjacent to the left.
If it is adjacent to the right, the answer is:

p (k) = 2 * p(1) + 2 * k

If the is adjacent to the left, the answer is:

P (k) = 2 *p(1) +2 * (k-2)

2 times as many as 8 is 16

Answers

Yes it is it is it's

Answer:

or 16 is the result of doubling 8

Step-by-step explanation:

Write the domain of the function given in the graph in set builder notation.


a. {x|x<=10}
b. {x|x<=0}
c. {x|x>10}
d. {x|x>0}


I can't get a picture of the graph so I'll try to explain. Y axis 0-5, going up by 1's, x axis 0-50, going up by 5's. Line starts at 10 on the x axis, goes up at an angle and stops at 40.

Answers

Based on what I understood, the graph would look something like this (attached as a picture). I don't know what angle it would be but I just assumed simple conditions where in the function is linear. From the given graph, the domain (x-values) would start from 10 to 40.  Thus x would be equal to or greater than 10. The answer would be C.

the current value of a baseball card is 80 times its original value the baseball card is worth $36 write and solve an equation to find the original value of the baseball card

Answers

Final answer:

To find the original value of a baseball card that is now worth 80 times its original value, you divide the current value of $36 by 80, resulting in an original value of $0.45.

Explanation:

The student wants to find the original value of a baseball card that is currently worth 80 times its original value and has a present worth of $36. We set up the equation: original value multiplied by 80 equals current value (80 × original value = $36). To find the original value, we divide the current value by 80.

Write the equation: 80 × original value = $36.Divide both sides of the equation by 80 to isolate the original value. So, original value = $36 ÷ 80.Calculate the result: original value = $0.45.

The original value of the baseball card was $0.45.

The sum of 5 consecutive even numbers is 505 What is the third number in this sequence?

Answers

The answer 101. 99+100+101+102+103 = 505

you can't have 5 even numbers add to 505

even numbers can only add up to an even number.

Prove that a triangle with sides n^2 1, n^2 - 1 and 2n (for n > 1) is a right triangle

Answers

Hello,

You have lost a sign "+".
[tex](n^2-1)^2+(2n)^2\\ =n^4-2n^2+1-4n^2\\ =n^4+2n^2+1\\ =(n^2+1)^2 [/tex]

Theorem of Pythagore is verified in this case: the triangle is a right one

An art student wants to make a model of the classroom. The length of the classroom is 2.4 times its width. The length of the student's model is 42 in. What should the width of the model be?

Answers

Answer:

Width of the model is:

17.5 in

Step-by-step explanation:

The length of the classroom is 2.4 times its width.

Length=2.4×width

The length of the student's model is 42 in.

Let w be the width of student's model.

By using the equation Length=2.4×width , we get

   42=2.4×w

⇒ [tex]w=\dfrac{42}{2.4}[/tex]

w=17.5

Hence, width of the model is:

17.5 in

Answer:answer is actually 17.5 in

Step-by-step explanation:

Which property is illustrated by the following equation?
- 10 + 8 = 8 + ( - 10 )

Answers

I believe it is commutative property cause the numbers didn't change instead they just switched places in the equation.

You are going to order some of your favorite cookies. If you order two boxes it will cost you $14. If you place an order for eight boxes it will cost you $26. Write an equation that represents the cost of ordering your favorite cookies.

Step 1: Decide what information represents your two points.
Hint: The points are in the format (number of boxes of cookies, cost) as these are your two variables.

Point 1: Point 2:


Step 2: Use your two points to write an equation.

Answers

this is alittle confusing but im guessing youre suppose to put 14 and 26 oin a numberline? so that would be why theres a point one and point two correct?
so im just gonna try and guess what the  equation might be ^-^

14 devided by 2=?
26 devided by 8=?
 then multiply the two answers to get the final answer.


(note im not trying to take points im just trying to help out a friend so im sorry if its wrong chika)
There are a multitude of ways to solve this, but to help you visualize it, we can use a graph to plot these points, and then form a line. Once we have a line, we can simply get the equation of the line to answer our question.

How do we plot the points?

We should obviously start out with a graph. We only need Quadrant I. We will let our x-axis (the horizontal axis) contain the number of boxes of cookies, and our y-axis (the vertical one) contain our prices.

We put our number of boxes on the x-axis because it is the independent variable, while the price per box goes on the y-axis because it is the dependent variable.

At this "point," we should be able to plot our numbers at the proper points. We can simply line up our "dot" (point) with the information given, so that Point 1 is (2 , 14) and Point 2 is (8 , 26). We know that information from the prompt.

Now, we simply need to draw a line that connects these 2 points.

Once we have done that, we need to remember the equation for a line. This is "y=mx+b" where "m" is our slope and "b" is our y-intercept. Our slope is going to be in a fraction with the format  [tex] \frac{rise}{run}[/tex], or the change in the y-value over the change in the x-value. 

When we work this out, we will find that the equation for this is y=2x+10.

Below, I have attached an image of the graph that we should make while doing this. Note that this graph "goes by 2s." The red point represents 2 boxes for 14 dollars. The blue point represents 8 boxes for 26 dollars. The green line represents the relationship between them.

juan drives to work. Due to traffic, he averages 22 miles per hour. He returns home averaging 32 per hour. The total time is 22.5 hours. Write and solve an equation to find the time juan spends driving to work.

Answers

32(22*22.5)

Hope I helped out

Students received these scores: 70, 75, 80, 90, 95, 95, and 100. the score of 95 is what?

Answers

95 is the mode because there is the largest quantity of it

Mr. rancher wants to build a pen for his horse. he wants the pen to be 40 yards long and 50 yards wide. if the fencing comes in 5 foot pieces, how many pieces does mr. rancher need to buy?

Answers

(50 x 2) + (40 x 2) = 180 yards x 3 = 540 feet of fence needed. 540 / 5 = 108. He will need 108 pieces of fencing 

There are 36 pieces need to buy by Mr. rancher.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The length of pen for his horse = 40 yards

The width of pen for his horse = 50 yards

And, The fencing comes in 5 foot pieces,

Now,

The perimeter of the pen for his horse = 2 (50 + 40)

                                                            = 2 x 90

                                                            = 180 yards

Since, The fencing comes in 5 foot pieces,

Hence, Number of pieces to buy by Mr. rancher = 180 / 5

                                                                          = 36

Thus, There are 36 pieces need to buy by Mr. rancher.

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The formula for the area of a triangle is a = 1 2 bh, in which b represents the length of the base and h represents the height. if a triangle has an area of 192 mm2 and the height is 16 mm, what is the measure of the base?

Answers

so first what you would do is take 192(2)=384 and then take 384/16=24 hope this help ;)

The measure of an angle and the measure of its supplement are equal. find the measure of each of the supplementary angles

Answers

each angle is 90° because 90°=90°. 90°+90°=180°

Answer:

Step-by-step explanation:

Sorry, here are the problems:

160: 20 degrees

90: 90 degrees

X: ____

Alan drove 756 miles in 12 hours. at the same rate, how many miles would he drive in 8 hours?

Answers

First find the unit rate, or how many miles he drives per hr.
756 mi/12 hrs= 63 mph

Multiply the speed by time to get distance.
63 mph* 8 hrs= 504 mi

Final answer: 504 mi

Final answer:

Alan would drive 504 miles in 8 hours.

Explanation:

To find out how many miles Alan would drive in 8 hours, we can set up a proportion using the information given. Since Alan drove 756 miles in 12 hours, we can write the proportion as:

12 hours / 756 miles = 8 hours / x miles.



To solve for x, we can cross-multiply and then divide:



12 * x = 8 * 756



x = (8 * 756) / 12



x = 504



Therefore, Alan would drive 504 miles in 8 hours.

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Kim estimates that the faucet in her kitchen drips at a rate of 1 drop every 2 seconds. Erik wants to know how many times the faucet drios in a week

Answers

302400. the amount of seconds in a week divided by 2

What is the answer for 7-2n=n-14

Answers

the answer is as such: n=7
Hey! Hope that I can help.

Kaitlin drove 260 miles using 12 gallons of gas. at this rate, how many gallons of gas would she need to drive 286 miles?

Answers

260 miles/12 gallons ≈21.7 miles per gallon
286 miles ÷ 21.7 ≈ 13.2 gallons needed

The real number -16 belongs to which sets of numbers?

Answers

counting numbers or natural numbes are like 1,2,3,4,5,6, etc

whole numbers include counting numbers, but with 0, so 0,1,2,3,4, 5, etc

integers include the negatives, so -4,-3,-2,-1,0,1,2,3,4, etc

rational numbers are numbers that can be written in form a/b where a and b are integers and b≠0


irrational numbers can't be written as a rational numer



so -16 is an integer and ratinoal number

-16 is an integer and rational number.

What are natural numbers, rational numbers, integers and irrational numbers?

Natural numbers are: 1, 2, 3, ....

Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )

Irrational numbers are those real numbers which are not rational numbers.

Know that all natural numbers are integers, all integers are rational numbers. That means natural numbers are not irrational.

The counting numbers or natural numbers are like 1,2,3,4,5,6, etc

Note that whole numbers include counting numbers, but with 0, so 0,1,2,3,4, 5, etc

Also rational numbers are numbers that can be written in form a/b where a and b are integers and b≠0

so -16 is an integer and rational number

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confused how do i create this?

Answers

Here's one way to construct the second triangle. See the attached image. 

Give an example of an open equation

Answers

an example would be x+4=8
one example would be x - 7 = -3 or 2x = 28

I need math help. Look at the attachment. No multiple choice.

Answers

there are 4 quarters per year

 if annual rate = 8%

 quarterly rate would be 8%/4 = 2%

 so the (1+r) beomes (1+0.02) = 1.02

Write an equation for the line through p that is parallel to l and perpendicular to l

Answers

well the equation can't be paralle and perpendicular to I at the same tjme

Need help! Please. It could be a integer or a decimal

Answers

It could be a integer

if a 40-foot tree casts a 12-foot shadow,find the length of a shadow cast by a 23-foot tree

Answers

ratio and proportion

shadow:length=12:40=3:10

if length is 23 then
3:10=?:23
3/10=?/23
multiply both sides by 23
69/10=?
6.9=?

6.9ft is the shadow length

The length of the shadow cast by the 23 feet tree is 6.9 feet

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

Given data ,

Let the height of the tree A = 40 feet

The height of the shadow of the tree A = 12 feet

Now ,

The height of the tree B = 23 feet

Let the height of the shadow of the tree B = x

So , the proportion equation is

height of the shadow of the tree A  / height of the tree A = height of the shadow of the tree B / height of the tree B

And the proportion will be ,

12 / 40 = x / 23

Multiply by 23 on both sides , we get

x = ( 12 × 23 ) / 40

x = ( 3 × 23 ) / 10

x = 69 / 10

x = 6.9 feet

Therefore , the value of x is 6.9 feet

Hence , The length of the shadow cast by the 23 feet tree is 6.9 feet

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Which ordered pairs are solutions to the inequality 4x+y>−6?

Select each correct answer.



(2, 0)

(−3, 6)

(4, −20)

(0, −9)

(−1, −1)

Answers

Answer:

(2,0) , (4,-20) and (-1,-1)

Step-by-step explanation:

[tex]4x+y>-6[/tex]

WE need to select an ordered pair that is solution to our inequality

Lets check with each option

(2,0) , plug in 2 for x  and 0 for y

[tex]4x+y>-6[/tex]

[tex]4(2)+0>-6[/tex]

[tex]8>-6[/tex] True

(−3, 6), plug in -3 for x  and 6 for y

[tex]4x+y>-6[/tex]

[tex]4(-3)+6>-6[/tex]

[tex]-6>-6[/tex] False

(4, −20) , plug in 4 for x  and -20 for y

[tex]4x+y>-6[/tex]

[tex]4(4)-20>-6[/tex]

[tex]-4>-6[/tex] True

(0, −9) , plug in 0 for x  and -9 for y

[tex]4x+y>-6[/tex]

[tex]4(0)-9>-6[/tex]

[tex]-9>-6[/tex] False

(-1, −1) , plug in -1 for x  and -1 for y

[tex]4x+y>-6[/tex]

[tex]4(-1)-1>-6[/tex]

[tex]-5>-6[/tex] True

Final answer:

The ordered pairs that are solutions to the inequality 4x+y>-6 are (2, 0), (4, -20), and (-1, -1) as they satisfy the condition when substituted into the inequality.

Explanation:

To determine which ordered pairs are solutions to the inequality 4x+y>-6, we need to plug the x and y values from each ordered pair into the inequality.

For the pair (2, 0), we substitute x = 2 and y = 0 into the inequality: 4(2) + 0 > -6, which simplifies to 8 > -6. This is true, so (2, 0) is a solution.For the pair (-3, 6), we substitute x = -3 and y = 6: 4(-3) + 6 > -6, which simplifies to -12 + 6 > -6. This gives -6 > -6, which is not true, so (-3, 6) is not a solution.For the pair (4, -20), we substitute x = 4 and y = -20: 4(4) - 20 > -6, which simplifies to 16 - 20 > -6. This gives -4 > -6, which is true, so (4, -20) is a solution.For the pair (0, -9), we substitute x = 0 and y = -9: 4(0) - 9 > -6, which simplifies to -9 > -6. This is not true, so (0, -9) is not a solution.For the pair (-1, -1), we substitute x = -1 and y = -1: 4(-1) - 1 > -6, which simplifies to -4 - 1 > -6. This gives -5 > -6, which is true, so (-1, -1) is a solution.

The correct solutions to the inequality are the ordered pairs (2, 0), (4, -20), and (-1, -1).

If a polygon has eight sides then it is an octagon. True or False

Answers

This is true because octa- means 8

The clean up hitter on a baseball tean batted 1/3 of the runs the team scored. The hitter batted in 3 runs. Select the equation that represents the number of n of runs the team scored. Then solve the equation:

A.1/3n=3
B.n/3=1/3
C.3n=1/3
D.3n=9

Answers

The number of runs the team scored is n. The clean up hitter batted in 1/3 of the runs. The clean up hitter batted in 3 runs. We can use this information to set up an equation. 1/3 (number of runs) = 3 1/3 (n) = 3 n = 9 The team scored 9 runs. The correct answer is A. 1/3 (n) = 3

What can you infer about elements that are in the same group?
a. they will have the same atomic mass
b. they will display similar chemical and physical properties
c. they will contain the same number of protons
d. they will emit x rays of similar frequency

Answers

b.

Elements of the same group in the Periodic Table will have similar chemical and physical properties.

Answer:

b.They will display similar chemical and physical properties.

Step-by-step explanation:

We have to find about the elements that are in the same group.

In modern periodic table

Elements are arranged in group according to similar properties.

The elements which have same properties are placed in the same group and mass of different elements are different in the group.

The outer electronic configuration of every element in the same group are same.

Therefore, the physical and chemical properties of the elements are same in the group.

Hence, option B is true.

Answer:b.They will display similar chemical and physical properties.

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