Find two consecutive even integers such that the smaller added to three times the larger gives a sum of 54

Answers

Answer 1

Let n be the first even integer, and n+2 will be the second even integer. (Why? Think 2 and 4, 2+2=4. This is the case for every consecutive even integers).

n + 3(n+2) = 54
n + 3n + 6 = 54
4n = 48
n = 12, n+2 = 14

Answer 2

Let's call x the smaller integer and x + 2 the larger one.

[tex]x+3(x+2)=54[/tex]
[tex]x + 3x + 6 = 54[/tex]
[tex]4x = 48[/tex]
[tex]x= \frac{48}{4}=12[/tex]

And [tex]x+2=12+2=14[/tex]

Hope this helps !

Photon

Related Questions

A 10-foot ladder is leaning against a tree. The bottom of the ladder is 4 feet away from the bottom of the tree. Approximately how high up the tree does the top of the ladder reach?
A.2.4
B.6.0
C. 9.2
D. 10.8

Answers

c. 9.2 is your answer

The image of a figure is shown. What are the coordinates of X in the pre-image of the figure if the rule that created the image was T–5.2, 1.4(x, y)? PLEASE ANSWER

X =
a. (-7.2, 3.4)
b. (1.2, 6.6)
c. (3.2, 0.6)
b. (9.2,-0.4)

Answers

The answer is C. The image of X is (-2, 2) according to the graph. The rule of translation is (-5.2, 1.4). Suppose the pre-image of X is (a,b). Then (a,b)+(-5.2,1.4)=(-2,2). a-5.2=-2, a=3.2. b+1.4=2, b=0.6. So (a,b) is (3.2, 0.6), before the translation occurs.

I agree the answer is C)

Hope this somewhat helped! :)

Question 11 options: you take a ride on a ferris wheel which has a diameter of 300 feet. if you ride for four revolutions, what linear distance did you travel? use 3.14 for pi when completing your calculations. round your answer to the nearest whole number, if necessary. the distance traveled is

Answers

is there a slope/graph here?

Ava bought a rectangular rug for her hallway. The rug is 2\3 yards wide and 2 3\4 yards long. What is the area of the rug as a mixed number in simplest form?

Answers

2/3 * 2 3/4 = 1.83 That translated into fraction form is 1 5/6

Answer:

1 5/6

Step-by-step explanation:

Please help me it's homework.

Answers

Left Side
=======
2 faces of 2 * 8 = 32
2 faces of 2 * 7 = 28
2 faces of 7 * 8 = 112
Total = 172

Right Side Prism
=========
2 faces of triangles 1/2 * 7.2 * 4.8 = 34.56
1 bottom face of 7.2 * 10 = 72
2 slanted faces 6 * 10 = 120
Total 34.56 + 72 + 120 = 226.56

I'm in need of Brainlys. If this answer suits you can you award one if it is possible for you to do.

Which graph shows the equation y = x + 2?

Answers

there ya go. your graphs should have this as one of the answers

Select the correct factor from the presentation and calculate how many calories used. (Round to the hundredths.) A person weighing 165 lbs. jogs 1 mile in 8 minutes. How many calories used?
A. 102.30
B. 107.25
C. 253.85
D. 266.13

Answers

Answer:

the answer is 107.25

Step-by-step explanation:

Answer:

B. 107.25

Step-by-step explanation:

Let x be the calories burnt by the man,

Since, when a person runs 1 miles in 8 minutes,

Then,

[tex]\frac{\text{Calories used by him}}{\text{His weight in lb}}=65\%[/tex],

Given,

Weight of the person = 165 lb,

Thus,

[tex]\frac{x}{165}=\frac{65}{100}[/tex],

[tex]x = \frac{165\times 65}{100}[/tex]

[tex]x=\frac{10725}{100}[/tex]

[tex]\implies x=107.25[/tex]

Hence, 107.25 calories will be used.

How do you solve this inequality: 7 ≤ x+11

Answers

solve the inequality like an equation
7 ≤ x + 11
subtract 11 from both sides
-4 ≤ x

From there on, any number greater than or equal to -4 will be a solution to the inequality

Hope this helps

How do you solve this inequality: 7 ≤ x+11

[tex] 7 \leq x+11 \\ \\ 7 -11\leq x \\ \\ -4 \leq x\qquad\to\qquad x\in \left[-4; +\infty) [/tex]

Given that ∆MTW ≅ ∆CAD, which angles are corresponding parts of the congruent triangles?

∠M ≅ ∠A

∠M ≅ ∠D

∠M ≅ ∠C

Answers

Answer:

It is M = C

Step-by-step explanation:

The measure of the angle ∠WMT is congruent to the measure of the angle ∠DCA. Then the correct option is C.

What is the triangle?

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangle ∆MTW is congruent to the triangle ∆CAD. Then we have

∠MTW ≅ ∠CAD

∠TWM ≅ ∠ADC

∠WMT ≅ ∠DCA

The proportion of the point ∠WMT is harmonious with the proportion of the point ∠DCA. Then, at that point, the right choice is C.

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What is the denominator of the fraction 1/9?

Answers

The denominator is the bottom number it will be 9

9

any number below the bar is the denominator, any number above the bar is the numerator

Can someone please help me with 4?? I’m really struggling.

Answers

4) given is that
m<DAC=y
m<BAC=3x

ABCD is a square so m<DAB = 90° because each angle in a square is a right angle so 3x+y=90° (1) ;
AC is a diagonal in the square so m<DAC=m<BAC so 3x=y (2);

Find x by substituting y to 3x from (2) into (1)
3x+3x=90
6x=90
x=90/6=15°

Answer x=15°

How could the relationship of the data be classified? (1 point)

scatter plot with points loosely scattered going down to the right

Answers

Scatterplots are a useful way of visualizing statistical data and to draw some quick conclusions from the data. Each scatterplot is unique but there are some common trends about association of the 2 variables that can be applied. In a scatterplot with an upward trend, we would say that the variables have a positive association or that they have a positive correlation. When one variable increases, the other increases too (in general). If the plot has a downward trend, we talk of a negative association. Finally, there could also be no association, with plot points scattered all around. Thus, in this case, we have negative correlation. If there is anything else you need regarding this answer, comment.

Solve the following system of equations using matrices.
4x – 2y = -6
3x – 6y = -18

(40, 90)

(3, 0)

(0, 3)

(-6, 18)

Answers

It is convenient to let a calculator do the math.
.. (x, y) = (0, 3) . . . . . your 3rd selection

_____
I prefer using the RREF function to put the augmented matrix into reduced row-echelon form. If the equations are dependent or inconsistent, using that method tells you so without giving a matrix inversion error.

Find the smallest value of k if 264k is a perfect square

Answers

Try factoring this first.
264k = 132*2k = 11*12*k = 11*3*2*2*k
To get a perfect square, you are going to have to have an even number of prime factors.
You have one 11 and one 3. You are going to have to do something about those two.
k = 11 * 3 <<<<< ======= answer.

Now put that into 264k and you get 11 * 3 * 2 * 2 * 11 * 3 which is a perfect square. 11^2 * 3^2 * 2^2 = 4356

The square root of 4356 = 66
4356 is a perfect square when 33 = k.

Which equivalent expression would you set up to verify the associative property of addition for (3x + 4) + ((5x2 – 1) + (2x + 6))

(3x + 4) + (5x2 – 1)

(5x2 – 1) + ((3x + 4) + (2x + 6))

((3x + 4) + (5x2 – 1)) + (2x + 6)

(3x + 4) + (5x2 – 1) + (2x + 6)

Answers

Associative Property of Addition
(3x + 4) + [(5x2 - 1) + (2x + 6)]

As given in the definition below, to make it an associative property, we can change the bracket

[(3x + 4) + (5x2 - 1)] + (2x +6)

Your answer will be the third option :)

It's C.

Trust me, I had trouble figuring out this answer...

what do all similar circles have in common
a) congruent circumference value
b) congruent diameters
c) π

Answers

All the similar circles have π in common.

Thus, option (c) is correct.

When two circles are similar, it means they have the same shape but possibly different sizes.

However, the ratio of their corresponding lengths, including the circumference, remains constant.

Second, the ratio of the diameter will be constant but not congruent.

Third, the value of π is the universal constant whose value is 22/7 or 3.14.....

which is the same for every similar circle.

Thus, π has a common value.

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Which linear function has the greatest y-intercept?

A) x + 6y = 36

B) y = 15x + 5

C) 3x + 8y = 24

D) y = 4x + 7

Answers

I believe the answer is D).

Answer:

the answer is y=4x+7

Step-by-step explanation:

Find the exact value of sin ( 2
a. if cos a = 3 /5 . assume a is a quadrant i angle in standard position.

Answers

In a right angled triangle 'efg' cos a = 3/5
From Pythagoras theorem the third side will be 4
cos a =3/5
sin a =4/5
sin 2a =2 x 4/5
sin 2a= 8/5

.can you please help me thank you you will be given brainley

Answers

They aren't marked so that you can't tell. If I had to guess, I'd say it's SSS but it just a guess. Without markings of some kind we can't do much. SSS is based on appearance alone.

Mr Savage used 3 gallons of paint to cover 1,350 square feet of wall space. At this rate, how much paint will be needed to cover 1,800 square feet

Answers

This problem is solved using a rule of three

we know that
Mr Savage used 3 gallons of paint to cover--------------> 1,350 square feet
X--------------------------------------------------------------------> 1,800 square feet
X=1800*3/1350=4 gallons

the answer is 4 gallons

What is value of x?
https://static.k12.com/nextgen_media/assets/8093716-NG_GMT_SemB_08_UT_12.png

Answers

check the picture below.

The calculated measure of the angle x is 76 degrees

How to determine the measure of the angle x

From the question, we have the following parameters that can be used in our computation:

The figure

Also, we have

Angle with a measure of 76 degrees

By the theorem of corresponding angles, we have

x = 76

Hence, the measure of the angle x is 76 degrees

Answers

In addition, from the response shown, using a graphical calculator brings the following benefits:
1) You can write the system of linear equations as big as you want. This is: systems 3 * 3, 4 * 4, 5 * 5.
2) The response to systems of equations greater than 2 * 2 can be complicated when you graph the solution, therefore, the graphing calculator can be much more efficient in these cases.
3) You can write the linear equations in any way. Resolving by hand you should probably rewrite the system of equations to find the solution.

HELP! ASAP!
What is the measure of ∠A?

What is the measure of ∠B?

Answers

The opposite angles of a parallelogram are equal.
Therefore
m∠A = m∠C, so that
5y - 3 = 3y + 27
Subtract 3y from each side.
5y - 3y - 3 = 3y - 3y + 27
2y - 3 = 27
Add 3 to each side.
2y - 3 + 3 = 27 + 3
2y = 30
y = 30/2 = 15

Therefore
m∠A = 5*15 - 3 = 72°
m∠C = 72°

Let x = m∠B
Then x = , m∠B = m∠C
Because the sum of the angles in the parallelogram is 360°, therefore
x + x + 72 + 72 = 360
2x = 360-144 = 216
x = 216/2 = 108

Answer:
m∠A = 72°
m∠B = 108°

Answer:

What is the measure of ∠A?

72°

What is the measure of ∠B?

108°

Step-by-step explanation:

I literally copied and pasted from edge

Debra is on the swim team. Each week she swims a total of 7000 meters. How many kilometers does she swim each week?

Answers

Hm 7 meters is it kilometers...7 kilometers

Number of security staff = a over 100 if a audience, is 10500, how many security staff are needed for the event

Answers

Substituting for "a" in the formula, we have
.. Number of security staff = 10500/100 = 105

You are preparing to tile the floor of a rectangular room that is 15.5 feet by 18 feet in size. The tiles you plan to use are squares, measure 12 inches on each side, and are sold in boxes that contain enough tiles to cover 25 square feet. Each box costs $30.

To determine the cost of materials you multiply 15.5 by 18, divide by 25, round up to the next whole number, and multiply by 30. Is this correct?
A) Yes.
B) No, you need to round down and then multiply by 30.
C) No, you need to round down and then multiply by 144.
D) No, you need to divide by 144, round up, and then multiply by 30.
E) No, you need to divide by 144, round down, and then multiply by 30.

Answers

Final answer:

To find the cost of tiling the room, you have to calculate the area in square feet, convert tile size to the same units, calculate how many boxes needed and round up, then multiply by the cost per box. The correct answer is D).

Explanation:

The correct answer is D). The process to determine the cost of the tiles needed to cover the room starts with calculating the area of the room in square feet. This is done by multiplying the room's length and width, so 15.5 feet * 18 feet which equals 279 square feet.

The tiles are 12 inches in size on each side, but the dimensions of the room are in feet. Therefore, we need to convert the tile size to square feet. Since 1 foot = 12 inches, 1 square foot = 144 square inches. Our tile is 12 inches * 12 inches = 144 square inches, which equals 1 square foot.

However, the tiles are sold in boxes that cover 25 square feet. So, we will divide the total room area by the area covered by one box of tiles. 279 square feet / 25 = 11.16 boxes needed, approximately.

It's important to round up at this stage, as you can't buy a fraction of a box. So, you'd need 12 boxes.

The last step is to calculate the total cost, which is done by multiplying the number of boxes by the cost of each box. So, 12 * $30 equals $360.

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Match the corresponding function formula with each function when h(x) = 3x + 2 and g(x) = 2 x .

1. k(x) = 2x + 3x + 2    k(x) = g(x) ∘ h(x)

2. k(x) = 2x - 3x - 2     k(x) = g(x) + h(x)

3. k(x) = (3x)2-x + 2-x + 1   k(x) = h(x) ÷ g(x)

4. k(x) = 23x + 2      k(x) = g(x) - h(x)

5. k(x) = 2x(3x + 2) k(x) = g(x) × h(x)

6. k(x) = 3(2x) + 2 k(x) = h(x) ∘ g(x)

Answers

the correct functions are
h(x) = 3x + 2
g(x) = 2^x

I proceed to calculate the different values of K (x)
case 1) k(x) = g(x) ∘ h(x)
g(x) ∘ h(x)=g(h(x))
k(x) = [2]^[3x + 2]-----------> is the option 4. k(x) = 2^(3x + 2 )

case 2) k(x) = g(x) + h(x)
k(x) = [2^x]+[3x + 2]=2^x+3x+2--------> is the option 1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)
k(x) = [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)
is the option 3.) k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)
k(x) = [2^x]-[3x + 2]=2^x-3x-2--------> is the option 2.) k(x) = 2^x - 3x - 2

case 5) k(x) = g(x) × h(x)
k(x) = [2^x]*[3x + 2]-----------> is the option 5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)
h(x) ∘ g(x)=h(g(x))
k(x)=3*[2^x]+2---------------> is the option 6. k(x) = 3(2^x) + 2

To simplify the other user's answer (which is correct):

1 = B

2 = D

3 = C

4 = A

5 = E

6 = F

Alternatively, your right boxes should look like:

A employer, who started a new business, has promised his employees a minimum starting wage of $3, with an increase of $2 every 4 years. Sketch a graph of wage as a function of time for 16 years. Assume the wages take effect at the beginning of the year where the change is made. (HINT: use a step function to represent the function.)

Answers

This is a step function because it increases in "steps". The wage stays constant for a 4 year period, then jumps by $2 instead of a steady increase.

Final answer:

To sketch the graph, use a step function to represent the wage as a function of time over 16 years. The minimum starting wage is $3, and it increases by $2 every 4 years.

Explanation:

To sketch a graph of wage as a function of time for 16 years, we can use a step function to represent the function.

The minimum starting wage is $3 and it increases by $2 every 4 years. For the first 4 years, the wage will be $3. At the start of the 5th year, the wage will increase to $5. This pattern continues, with the wage increasing by $2 every 4 years.

So, the graph will have flat lines representing each 4-year interval, with a step up at the start of each interval.

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Find all real values of $v$ that satisfy the equation $(v+6)^2 = 324$. If you find more than one, then list your values in increasing order, separated by commas.

Answers

we have that

(v+6)^2 = 324-----> I raise to 1/2 both members----> [(v+6)^2]^(1/2)=(324)^(1/2)[(v+6)]=(324)^(1/2)-------------> v+6=√324
v=√324-6---------> 18-6=12
v=12

the answer is v=12

Answer:

The values of v in increasing order are, -24, 12

Step-by-step explanation:

Given equation is,

[tex](v+6)^2=324[/tex]

[tex]v+6=\pm 18[/tex]

[tex]v=-6\pm 18[/tex]

[tex]\implies v=-6-18\text{ or }v=-6+18[/tex]

[tex]\implies v = -24\text{ or }v=12[/tex]

Since, -24 < 12

Thus, the values of v in increasing order are,

-24, 12

X divides into the line PQ in the ratio 2:3 P is (2,1) and Q is (12.5,7.5) work out the coordinates of point X

Answers

According to ratio theorem;
x = 2/5(Q) + 3/5(P)
= 2/5(12.5,7.5) + 3/5(2,1)
= 2( 2.5, 1.5) + 3( 0.4, 0.2)
= (5,3) + (1.2,0.6)
= (6.2, 3.6)
The Coordinates of X will be;
=(6.2, 3.6)

Answer: (6.2, 3.6)

Step-by-step explanation:

We know that if a point M (x,y) divide a line segment having endpoints [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in ratio m:n , then the coordiantes of M is given by :-

[tex]x=\dfrac{mx_2+nx_1}{m+n}\ ;\ y=\dfrac{my_2+ny_1}{m+n}[/tex]

Given : X divides into the line PQ in the ratio 2:3 P is (2,1) and Q is (12.5,7.5).

Then, coordinate of X is given by :-

[tex]x=\dfrac{2(12.5)+3(2)}{2+3}\ ;\ y=\dfrac{2(7.5)+3(1)}{2+3}\\\\\Rightarrow\ x=\dfrac{31}{5}\ ;\ y=\dfrac{18}{5}\\\\\Rightarrow\ x=6.2\ ;\ y=3.6[/tex]

Hence, the coordinate of X = (6.2, 3.6)

Other Questions

I have attached a picture of a question I am stuck on. It is about Riemann sums. I have attempted the question but did not get the correct answer :( Here is my work:I see that this graph has the same area repeating 12 times.I did (b - a)/n, or (12 - 0)/36, and found that the width of each rectangle should be 1/3. Because we are asked to find the area using "circumscribed angles," I will use right-endpoint rectangles on the first part of the graph that shows a decreasing interval from 0 to 1:t = 1/3, r(t) = 2.01745506t = 2/3, r(t) = 2t = 1, r(t) = 1.45369751These values for r(t) represent heights of the rectangles. I can add them and multiply by the width of each rectangle:1/3(2.01745506 + 2 + 1.45369751) = 1/3(5.47115257) = 1.823717523I can multiply the area by 12 to find the area under the entire function:1.823717523 * 12 = 21.88461028This is not an answer choice, so I clearly did something wrong! Can someone help me find my mistake? Lately, Ive been giving more thought to the kind of English my mother speaks. Like others, I have described it to people as broken or fractured English. But I wince when I say that. It has always bothered me that I can think of no other way to describe it other than broken, as if it were damaged and needed to be fixed, as if it lacked a certain wholeness and soundness. How does Tan build a central idea of her story in the excerpt? Tan discusses her thoughts about language to build the idea that the English language does not have words to match some Chinese terms. Tan discusses her relationship with her mother to build the idea that mothers and daughters in all cultures often have misunderstandings. Tan discusses her mothers use of English to build the idea that a form of language can be purposeful and meaningful even if it is nonstandard. Tan discusses the English language to build the idea that there is a lack of appropriate synonyms for the word broken. 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Thanks to an aggressive bald eagle protection program, bald eagle numbers in the wild have soared as seen in the population graph above. The bald eagle's population very nearly reached extinction. Why did the bald eagle's declining population make it more vulnerable to extinction? A)As populations decline, reproduction stops B)As populations decline, less resources are available C)As populations decline, there is less genetic diversity D)As populations decline, birds migrate farther away from other populations Compare the viscosity of n-hexane, ch3ch2ch2ch2ch2ch3, to the viscosity of n-heptane, ch3ch2ch2ch2ch2ch2ch3. A borrower with bad credit is likely to be charged.... a low interest rate. a high interest rate. no interest rate. higher property taxes. please help!!!!!The author, Virginia Driving Hawk Sneve, uses many details to paint an image of Grandpa. 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Was there a man dismay'd? 10Not tho' the soldier knew Some one had blunder'd: Theirs not to make reply, Theirs not to reason why, Theirs but to do and die: 15Into the valley of Death Rode the six hundred. Cannon to right of them, Cannon to left of them, Cannon in front of them 20 Volley'd and thunder'd; Storm'd at with shot and shell, Boldly they rode and well, Into the jaws of Death, Into the mouth of Hell 25 Rode the six hundred. Flash'd all their sabres bare, Flash'd as they turn'd in air Sabring the gunners there, Charging an army, while 30 All the world wonder'd: Plunged in the battery-smoke Right thro' the line they broke; Cossack and Russian Reel'd from the sabre-stroke 35 Shatter'd and sunder'd. Then they rode back, but not Not the six hundred. Cannon to right of them, Cannon to left of them, 40Cannon behind them Volley'd and thunder'd; Storm'd at with shot and shell, While horse and hero fell, They that had fought so well 45Came thro' the jaws of Death, Back from the mouth of Hell, All that was left of them, Left of six hundred. When can their glory fade? 50O the wild charge they made! All the world wonder'd. Honor the charge they made! Honor the Light Brigade, Noble six hundred! 55Which lines imply the theme or message of the poem?A. "Theirs not to make reply,/Theirs not to reason why./Theirs by to do and die."B. "Into the jaws of Death,/Into the mouth of Hell/Rode the six hundred."C. "Flash'd as they turn'd in air/Sab'ring the gunners there"D. "When can their glory fade?"E. "Half a league, half a league,/Half a league onward," Kim paycheck was $257.20. She put 1/4 of her paycheck into a savings account and used 1/3 of what was left to pay bills. How much money does she have remaining from her paycheck Francisca purchased 425 shares of Kellogg Company stock at $14.15 apiece. She earns $374.00 in dividends every year. What is the yield on Francisca's Kellogg Company stock? Identify the vertical asymptote(s) of each function. Check all of the boxes that apply. f(x)=x-8/x^2-3x+2x = -8x = -2x = -1x = 1x = 2x = 8Nevermind the answer was x=1 and x=2. If anyone is wondering how to do it you can put the denominator in desmos and where the 2 points hit the x axis is your answer. PLEASE HELP!!!! NEED NOW!!! 20 ptsExplain how the Quotient of Powers was used to simplify this expression. 2 to the 5th power, over 8 = 2 to the 2nd power By finding the quotient of the bases to be one fourth, and cancelling common factors By finding the quotient of the bases to be one fourth, and simplifying the expression By simplifying 8 to 2^3 to make both powers base two, and subtracting the exponents By simplifying 8 to 2^3 to make both powers base two, and adding the exponents