Mathematics Middle School


What is the equation for the sum of three consecutive even numbers totaling 198.

Question 4 options:

n+n+1+n+2=198

n+n+2+n+4=198

3n=198

n+3=198

Answers

Answer 1
Let the first number be represented by x.  Then the next is x+2, the next x+4.  Add these 3 expressions together and equate the sum to 198.

Answer 2

Final answer:

Option B: n+n+2+n+4=198

The equation for the sum of three consecutive even numbers totaling 198 can be represented as

n + (n+2) + (n+4) = 198,

where n is the first even number.

Solving the equation, the first even number is 64, and the consecutive even numbers are 66 and 68.

Explanation:

The equation for the sum of three consecutive even numbers can be represented as n + (n+2) + (n+4) = 198, where 'n' is the first even number. Let's solve the equation:

Combine like terms: 3n + 6 = 198Subtract 6 from both sides: 3n = 192Divide both sides by 3: n = 64

So, the first even number is 64, and the consecutive even numbers are 66 and 68.

Related Questions

Elizabeth has two gardens in her yard. The first garden is 8 feet long and 6 feet wide. The second garden is half the length of the first garden. the area of the second garden is twice the area of the first garden. What is the area of the second garden? Ask for details Follow Report by Beatrizsalazar 28.02.2018

Answers

The area of the second garden is 96 square feet.

Let's denote the length of the second garden as l (since it's half the length of the first garden) and the width of the second garden as w.

Given:

Length of the first garden [tex](\(L_1\))[/tex]= 8 feet

Width of the first garden [tex](\(W_1\))[/tex] = 6 feet

Length of the second garden [tex](\(l\)) = \(L_1/2\) = \(8/2 = 4\)[/tex]  feet

Area of the first garden [tex](\(A_1\)) = \(L_1 \times W_1\) = \(8 \times 6 = 48\)[/tex] square feet

We are given that the area of the second garden [tex](\(A_2\))[/tex] is twice the area of the first garden:

[tex]\[A_2 = 2 \times A_1 = 2 \times 48 = 96\][/tex] square feet



Simplify the expression.



2^2 • 2^3




A.
4^5


B.
4^6


C.
2^6


D.
2^5

Answers

When you have like bases, you multiply the exponents together and put it over the base.

[tex] 2^{2} 2^{3} = 2^{2*3} = 2^{6} [/tex]
  Hey there!!

The answer you're looking for is ( D ) because in exponents, the rule is..

║If the bases are the same, add the exponents║

2 ^2 * 2 ^3 = ? (Bases are the same, add the exponents)

Answer: D = 2^5

║Hope that helps :)║

A square garden has an area of 64 square feet. What is the length of the garden?

Answers

Area = Length x Length

Area = Length²

Length² = 64

Length = √64

Length = 8 feet

Answer: 8 feet

The length of the garden will be 8 feet.

It should be noted that the area of a square is gotten by multiplying its lengths together. For example, the area of a square with length of 2cm will be: = 2 × 2 = 4cm²

Therefore, since the square garden has an area of 64 square feet, the length of the garden will be:

= ✓64

= 8 feet

Therefore, the length is 8 feet.

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0.8 x 3.15 it’s multiplying rational numbers

Answers

the answer is 2.52

Let me know if you want me to show my work

3/7÷1/2 how do you graph this

Answers

3/7 divided 1/2 is the same as 3/7 times 2 which is 6/7. 

Not sure what you mean by graphing it though. Like on a number line? There is no x or y in your equation. 
I do not think you can graph that

1)What is the solution to the equation below?
2) How did you get your answer?
x+3 = 8

Answers

Hello there, and thank you for posting your question here on brainly.

Short answer: #1; 5 #2; Explained below

So, we know the answer is 5, so how did I get that? Well, to find that, you have to subtract the two known numbers, 8 and 3. What is 8 - 3? 5. ((8 - 3 = 5))

Hope this helped you! ♥

the first computer is usually regarded as one called ROACH completed in 1945. Email was invited in 1971. how many years after the computer was email invented

Answers

hello,

the first computer is usually regarded as one called ROACH completed in 1945. Email was invited in 1971. how many years after the computer was email invented

in this vase we will use soustraction

1971-1945=26

email was invented 26 years after computers

hopes this helped you well
may i please have the brainliest
have a wonderful day or night

Final answer:

Email was invented 26 years after the completion of the first recognized computer in 1945.

Explanation:

The first computer is often attributed to the work carried out during World War II, with machines like ENIAC, completed in 1945, incorporating vacuum tubes and filling entire rooms. However, the question references a machine called ROACH, which seems to be a typo or a misunderstanding; we usually refer to ENIAC as one of the first computers. Email, on the other hand, was invented in 1971 by Ray Tomlinson. Calculating the difference between the years when the first computer was completed and when email was invented gives us the number of years it took for email to be developed after the advent of the computer.

To find this, we subtract the year the first computer was completed, 1945, from the year email was invented, 1971:

1971 (the year email was invited) - 1945 (the year the computer was completed) = 26 years.

Email was invented 26 years after the completion of the first computer.

Evaluate the expression. If necessary, round to the nearest hundredth. lne

Answers

lne equals 1 because they cancel each other out. e is the base of ln. 
For example: log has a base of 10, log10 = 1
We are to find the value of ln(e) 

ln stands for Natural Log. The Base of the natural log is e. So we can also write the given expression as:

[tex]ln(e)= log_{e}(e) [/tex]

When the base of log is equal to the value for which you are finding the log, the answer is always equal to 1.

So the answer to this question is 1.

Please find perimeter and area. also show work plz. It's really easy. I will mark as brainliest.

Answers

Perimeter: 115.472 ft

The perimeter of an enclosure is the length around the enclosure, or the sum of all the outer sides added up (red+blue lines in picture).

1) We are told that the two vertical sides of the enclosure (shown in blue) are each 20ft, making it 20 + 20 = 40ft total. All we need to find is the sum of the lengths of the four sides of the triangles (shown in red).

2) We are given the height of the triangle, 16ft, and the length of the base of the triangle, 20ft. To find the length of the edge we're looking for, we need to find the hypotenuse of the right triangle shaded in green. One of the legs of the triangle is 10ft (half of the base of the larger triangle) and the other leg is 16ft (same as height of the larger triangle).

Use the pythagorean theorem, which says [tex] a^{2} + b^{2} = c^{2} [/tex].
a and b are the length of your legs, 10ft and 16ft, and c is the length of the hypotenuse, or the side we're looking for. Plug your numbers in and find c:
[tex]10^{2} + 16^{2} = c^{2} \\ c^{2} = 356\\ c = 18.868 ft[/tex]

3) Now you know each red side is 18.868 ft. There are 4 red sides, so 4 x 18.868ft = 75.472ft. Add this number to the length of your two blue sides to get the perimeter:
75.472ft + 40ft = 115.472ft.

--------------

Area: [tex]720ft^2[/tex]

The area of the enclosure is shaded in yellow. To find the area of the enclosure, you want to find the sum of the areas of all the shapes. Break the enclosure down into one square (in the middle) with two triangles on the top and bottom, find the area of those three shapes, and add those areas together.

1) The equation for the area of the square is [tex]A=s^2[/tex], where s = length of the side. 
You're told that the length, s = 20ft. Plug that in and solve for the area of the square:
[tex]A=s^2\\ A=20^2\\ A = 400 ft^2[/tex]

2) The equation for the area of a triangle is [tex]A = \frac{1}{2} bh[/tex], where b = length of base and h = height of triangle.
You're told that the length of the base, b = 20ft and the height of the triangle, h = 16ft. Plug these values in and solve for area of one of the triangles:
[tex]A = \frac{1}{2} bh\\ A = \frac{1}{2} (20)(16)\\ A = 160 ft^2[/tex]

3) Since you have two identical triangles, multiply the area of one triangle by two to get the total area of the two triangles:
[tex]160 ft^2 \times 2 = 320 ft^2[/tex]

4) Add up the areas of the square and the two triangles to get the total area of the enclosure:
[tex]400 ft ^2 + 320 ft^2 = 720ft^2[/tex]

A box containing 3 small bags of flour weighs 950 grams. Each bag of flour weighs 300 grams. How much does the empty box weigh

Answers

the box would weight 50 grams since 3 bags of flour contained 300 grams each would add up 900 grams now subtract 900 from 950 like this 950-900=50 and that's your answer. hope this helped :)
the empty box weights 50 grams. as the total weight is 950, and you have 3 bags that weight 300.
3x300=900
950-900=50
50 is the total weight that is left fi you were to take the 3 bags out of the box

a furnace is rated 4000 BTU per hour. How many foot pounds of energy are released in one hour?

- 5.1 foot pounds

- 2,456,000 foot pounds

- 0.2 foot pounds

- 3,112,000 foot pounds

Answers

To solve this we are going to use a conversion factor. We know that 1 BTU per hour is approximately 778 foot-pounds of energy per hour, so our conversion factor will be: [tex] \frac{778foot-pound}{1BTU} [/tex].

Now we just need to multiply 4000 BTU by our conversion factor:
[tex]4000BTU*\frac{778foot-pound}{1BTU}=3112000foot-pound[/tex]

We can conclude that the furnace released 3,112,000 foot pounds of energy in one hour.

Write each mixed numbers as a product of a whole number and a unit fraction

1 1/2

1 3/5

3 3/4

Answers

1. 1/2 x 3
2. 1/5 x 8
3. 1/4 x 15

Solve the system of equations algebraically.
3x-3y=6
6x-7y=5
a. (8,8)
b. (9,7)
c. many solutions
d. no solution

Answers

The answer is (9,7).

The system of equations has a solution at (9, 7), which is an option (b).

What are Systems of equations?

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

The given equations are:

3x-3y=6

6x-7y=5

Multiply the first equation by 2 to get rid of the coefficient of x in the second equation:

6x - 6y = 12

6x - 7y = 5

Subtract the first equation from the second equation to eliminate x:

0x - y = -7

y = 7

Substitute y = 7 into one of the original equations and solve for x:

3x - 3y = 6

3x - 3(7) = 6

3x - 21 = 6

3x = 27

x = 9

Therefore, the solution to the system of equations is (9, 7), which corresponds to option (b).

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please please someone help me and show me how you got the answer super super thanks in advance

Answers

18 liters of 100 is 18 percent. So the chemist would need 40 liters of acid to make a 40% acid solution.

18/100
=0.18
Convert it to a percent by moving the decimal point two places to the right.

So 40/100
=.40
Move the decimal point over two and add the percent sign.
40%

PLX HELP! Need this ASAP! Thx

One of the same side angles of two parallel lines is 20° smaller than the other one. Find all angles.

Answers

Same side angles together form angle with measure 180^{0}. Let x be a measure of smaller angle, then x+20^{0} is measure of bigger angle.
x+x+20^{0}=180^{0}
2x=160^{0}
x=80^{0}.
So measure of smaller angle is 80^{0} and measure of bigger angle is x+20^{0}=80^{0}+20^{0}=100^{0}.

Answer:

80° and 100 °

Step-by-step explanation:

The total of the two angles is 180°, and one angle is 20° smaller than the other, so the equation would be x+x-20°=180°, then all you need to do is find x, and x-20°.

DONT FORGET TO WRITE THE DEGREE SYMBOL OR IT WILL BE COUNTED AS INCORRECT!!!

-Char-

Keisha has one penny, one nickel, and one dime in her pocket. She randomly takes on coin out of her pocket. Without putting it back, she randomly takes out another coin. If Keisha lists all the possible outcomes of picking the two coins one at a time, how many outcomes are there?

Answers

There are 12 different ways she could take a penny, a nickle, and a dime out of here pocket and only pick 2. What i did was i took 2 and 3 and multiplied them. because i can pick 2 coins, and there are 3 coins in total. After i multiplied them i got 6, then i got 2 and multiplied it by 6 and came out with 12. The reason why i did that is because there are 6 outcomes so far then you have to multiply them by 2 to get all of your complete outcomes. I hope i could help!!! Please give me brainliest!!! Have a great day =D!!!

given the equation (x+a)^2(x-2)=x^3+bx^2+12x-72 find a and b

Answers

Isolate the variable by dividing each side by factors that don't contain the variable.

[tex]a=- \frac{ x^{2}- \sqrt{( x^{3} + x^{2} b+12x-72(x-2)-2x} }{x-2} ,- \frac{ x^{2}+ \sqrt{( x^{3} + x^{2} b+12x-72(x-2)-2x} }{x-2} [/tex]

Solve for b by simplifying both sides of the equation then isolating the variabel.

[tex]b= \frac{12}{x}+ \frac{72}{ x^{2} }-2+2a- \frac{4a}{x}+ \frac{ a^{2} }{x}- \frac{2a^{z} }{ x^{2} } [/tex]

Hopefully i helped ^.^ Mark brainly if possible 
 

The following data shows the low temperature in Vancouver, in degrees Celsius, for two weeks in January one year. 8.90, 8.35, 8.50, 8.65, 8.55, 8.20, 8.50, 8.32, 8.50, 8.60, 8.60, 8.30, 8.10, 8.65 Which box plot best represents this data?

Answers

To create the dot plot you will list the data in order and use the given numbers to create the box plot.

8.10, 8.20, 8.30, 8.32, 8.34, 8.50, 8.50, 8.50, 8.55, 8.60, 8.60, 8.65, 8.65, 8.90

Lower extreme: 8.10
Upper extreme: 8.90
Median: 8.50
1st/lower quartile: 8.32
3rd/upper quartile: 8.60

Please see the attached picture for the boxplot.

Kathy is baking cakes each cake requires 1/12 of a teaspoon of vanilla and she has 9/12 of a teaspoon how many cakes can she bake?

Answers

Kathy can make 9 cakes
9 cakes•••• If 1 teaspoon = 1 cake, then 9 teaspoons must = 9 cakes.

use the given graph to determine the period of the function. 1 & 2 plz

Answers

The period of the function is that distance where the function becomes equal again.
 We have then:
 Part 1:
 The period of the function is:
 T = 3
 Part 2:
 The period of the function is:
 T = 4
 Answer:
 The period of functions 1 and 2 respectively are:
 T = 3
 T = 4

which numbers are rational numbers 2, -4.0, 8.1, 3/4, 0, -8

Answers

All of them except,for 8.1


need urgent help Which sets of numbers are closed under addition?



Choose all answers that are correct.









A.

whole numbers








B.

natural numbers








C.

negative integers








D.

integers

Answers

Hello!

Whole numbers are closed under addition and multiplication

Integers are closed under addition, subtraction, and multiplication

natural numbers are positive whole integers so they are also closed under addition

The answers are A, B and D

Hope this helps!

which of the following is equal to the rational expression.......

Answers

The expression equal to the rational expression is 3/(x + 6)


Calculating the value of the rational expression

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

3(x + 2)/(x + 6)(x + 2)

Divide the fraction by x + 2

So, we have

3(x + 2)/(x + 6)(x + 2) = 3/(x + 6)

Hence, the value of the rational expression is 3/(x + 6)

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Leo has 100 coins in his piggy bank. All coins are either nickels, or dimes, or quarters. There are as many nickels as dimes and quarters together. How much money are nickels in Leo's piggy bank worth? will mark brainliest!!! PLEASE HELP

Answers

Alisa I'm rayna from ms tatiana's class is that you

Total money nickles are worth of = $2.5


Let number of nickles coins be 'x'

Let number of dime coins be 'y'

Let number of quarter coins be 'z'

we have,

x + y + z = 100      and x = y +z

on solving the two equations, we get x = 50

1 nickle = 5 cents

50 nickles = 250 cents = $2.5


if the circumference of the base=126 cm and h=10 cm, find the volume

Answers

126 times 10 and whatever that answer is is the volume

Which expression gives the distance between the points (5, 1) and (9, -6)?

Answers

Answer:

[tex]d = \sqrt{65}\text{ units}[/tex]

Step-by-step explanation:

Let [tex](x_1,x_2)[/tex] and [tex](y_1, y_2)[/tex] be the two points.

We have to find the distance between the two points.

The distance Formula:

[tex]d = \sqrt{(x_1 - y_1)^2 + (x_2 - y_2)^2}[/tex]

Here, we are given [tex](x_1,x_2)[/tex] = (5,1) and  [tex](y_1, y_2)[/tex]  = (9,-6)

Then, the distance between these two points is given by:

[tex]d = \sqrt{(5 - 9)^2 + (1- (-6))^2}[/tex]

[tex]d = \sqrt{(-4)^2 + (7)^2}[/tex]

[tex]d = \sqrt{16 + 49}[/tex]

[tex]d = \sqrt{65}[/tex]

Thus, the distance between the given point is [tex]\sqrt{65}\text{ units}[/tex].

In a large apartment building, 35 of the apartments have a balcony and 55 do not. An apartment us randomly selected as part of a survey. What is the probably it has a balcony?

Answers

11/18 probability

90 apartments total

35/90=

11/18

Answer:

Thanks

Step-by-step explanation:

This person is correct peeps :DD

In the diagram,CD is tangent to the circle, AB = 6 in, and BD = 10 in. Find AD.

Answers

the complete question in the attached figure

we know that
AB=6 in-----> this is the radius of circle
BC=AB-----> 6 in
AC=12 in-------> is the diameter of circle
BD=10 in

in the right triangle BCD
Applying the Pythagoras theorem

BD²=BC²+CD² --------> CD²=BD²-BC²-----> CD²=10²-6²----> CD²=66
CD=√66 in

in the right triangle ACD
AD²=AC²+CD²-----> AD²=12²+(√66)²----> AD²=144+66----> AD²=210
AD=√210 in-----> AD=14.49 in

the answer is
AD is 14.49 in


Your answer is B. 14 in.

A cylinder has a circular base with a diameter of 12ft. The height of cylinder is 4 ft. What is the volume of the cylinder rounded to the nearest whole number? Use 3.14 for pi.

Answers

Is it like 12×4=48 rounded
Volume of a cylinder = πr² h

Volume = (3.14)(12÷2)²(4) = 452 ft³ (nearest whole number)

Answer: 452 ft³

Parker was able to pay for 44% of his college tuition with his scholarship.
The remaining $10,054.52 he paid for with a student loan.
What was the total cost of Parker's college tuition?
Round your answer to the nearest dollar.
Tuition cost = $_

Answers

The total cost is $17,955.

Let x be the total amount of his tuition.  He paid for 44% of it, or 0.44, with his scholarship. This leaves 100%-44% = 56% = 0.56 of it to be taken care of with loans.  We know he took out 10054.52 in loans:

0.56x = 10054.52

Divide both sides by 0.56:
0.56x/0.56 = 10054.52/0.56
x = 17954.50 ≈ 17955
Final answer:

The total cost of Parker's college tuition, rounded to the nearest dollar, is $17,952.

Explanation:

If Parker was able to pay for 44% of his total college tuition with his scholarship, this means that the $10,054.52, which he paid using his student loan, represents the remaining 56% of his tuition cost. Therefore, to find the total cost of tuition, we need to divide the amount he paid with a loan by 0.56. Performing this calculation gives us:

$10,054.52 / 0.56 = $17,952.00

Therefore, the total cost of Parker's tuition rounded to the nearest dollar is $17,952.

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