the product of two consecutive even positive integers is 10 more than seven times the larger . find the integers?

Answers

Answer 1

2 consecutive even numbers.....x and x + 2

x(x + 2) = 7(x + 2) + 10
x^2 + 2x = 7x + 14 + 10
x^2 + 2x = 7x + 24
x^2 + 2x - 7x - 24 = 0
x^2 - 5x - 24 = 0
(x - 8)(x + 3) = 0

x - 8 = 0
x = 8

x + 3 = 0
x = -3...not this one because it is negative

x = 8
x + 2 = 8 + 2 = 10

so ur 2 consecutive even numbers are 8 and 10

Related Questions

You measure the width of a doorway and find that it is 0.93 m wide. Find the greatest possible error of your measurement

Answers

Answer:

0.5 m

Step-by-step explanation:

The greatest possible error is 1/2 of the unit you are measuring in.

We are measuring in meters; this means the greatest possible error is 0.5 m.

Answer:

The right answer is 0.005m

Step-by-step explanation:

The greatest possible error in a measurement is the half of the measuring unit, it is one hald of the precision unit.

To solve it first you should recognize the measurement unit, in this case meters.

Then, because it is 0.93, you should notice that the last decimal occupies the place of the hundredth, so the GPE might be: 0.01/2 equal to 0.005, your answer.

what is 4.333333333 as a fraction.

I need this answer right now!!

Answers

Answer is : [tex] \frac{4333333333}{1000000000} [/tex]

The correct answer is 13/3.

We draw a random sample of size 36 from a population with the standard deviation 3.5. if the sample mean is 27, what is a 95% confidence interval for the population mean?

Answers

95% refers to 2 standard errors from sample mean (SE)

[tex]SE = \frac{s}{\sqrt{n}} = \frac{3.5}{\sqrt{36}} = \frac{3.5}{6} = 0.583[/tex]

Confidence interval is:
[tex][27 -2(.583), 27+2(.583)][/tex]

heather has 500 dollars in her savings account she withdraws 20 dollars per week for gas write an eqaution heather can use to see how many week it will take her to have a balance of 220 dollars

Answers

500-20x=220
I think this is right

When solving for a system of equations, if you get an answer of 6=0, what does this solution mean regarding the solution to the system ?

Answers

it means the system is inconsistent, which is another way to way, there's no solution, namely, both graphs do not intersect ever, and therefore there's no common point with such x,y pair for both.

It means that graph is inconsistent. Most likely it is a no solution

a spool of ribbon has 18 feet on it. pieces measuring of 8 inches will be cut from the spool of ribbon. how many 8 inch segments will be cut from the spool of ribbon
show work

Answers

1 foot is 12 inches. 18 feet is 18×12=216 inches. each segment is 8 inch measurement, so 18 feet has 216÷8=27 segments. so the correct answer is 27 segments

By dividing the total length by the length of the pieces, we conclude that we can make 2 of these pieces.

How many 8 inch segments will be cut?

To get this, we need to divide the total length by the length of the desired pieces, and then round to the next (lowest) whole number.

Then we get:

N = 18ft/8ft = 2.25

Rounding to the next whole number we get 2, so we conclude that with 18t of ribbon we can make 2 pieces of 8ft each.

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To make lemonade, you used one gallon of water, four quarts of lemon juice, and 32 ounces of honey. How many quarts of lemonade did you make?

Answers

Well, there's 4 quarts in a gallon, so 1 gallon of water would equal 4 quarts of water.

We already know there are 4 quarts of lemon juice.

And there are 32 ounces in a quart, so that would equal 1 quart of honey.

So all you need to do now is add 4 quarts, 4 quarts, and 1 quart to get 9 quarts. You would get 9 quarts of lemonade.

I hope this helped you! :)

Final answer:

To make lemonade, using one gallon of water, four quarts of lemon juice, and 32 ounces of honey, you would make 34 quarts of lemonade.

Explanation:

First, notice that gallons are larger than quarts. You are moving from a larger unit of measure to a smaller unit of measure. This means you will need to multiply. There are 4 quarts in a gallon, so your conversion factor is 4. Now, multiply. Take the given number of gallons and multiply by 4.

8(1/2) x 4 = (17/2) x (4/1) = 68/2 = 34

The answer is 8(1/2) gallons - 34 quarts.

5 (9/12 - 1/4) + 0.5

Answers

5 (9/12 - 1/4) + 0.5
5 (9/12 - 3/12) + 0.5
5 (6/12) + 0.5
5(2.5) + 0.5
12.5 + 0.5
13

First we want to simplify the fraction 9/12 so it can be 3/4
next we want to subtract 3/4 - 1/4 and we get 2/4
next we want to multiply 5 * 2/4 and we get 10/4
and lastly we want to add 5/2 + 0.5 to get our answer

Answer: 3

Joy organized a wedding.
Guests had to choose their meal from beef, chicken or vegetarian.
1/3 of the guests chose beef
5/12 of the guests chose chicken
23 of the guests chose vegetarian
How many guests were at the wedding?

Answers

23 is one fourth
so 23 times 4 is 92

The only way to sober up after drinking is

Answers

What is the only way to sober up?stuff like cold showers, fresh air, or chewing gum works but time is the only

Final answer:

The body metabolizes and eliminates alcohol at a fixed rate, which can only be sped up with time. Hydrating and eating food may make you feel better, but they do not speed up the process of becoming sober.

Explanation:

The only way to sober up after drinking is to allow time for your body to metabolize and eliminate the alcohol. No amount of coffee, water, or food can speed up this process. The liver processes alcohol at a fixed rate, and it takes about one hour to metabolize one standard drink. Other factors such as sex, weight, and age can affect this rate, but ultimately, getting sober just takes time. While waiting to sober up, hydrating and eating food can make you feel better, but doesn't actually speed up the sobriety process.

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Joe tapped his maple tree to get syrup. The tree filled 3/4 of a cup in 1/2 hour.At what rate does syrup flow from the tree?

Answers

Okay. 3/4 of a cup of maple syrup is filled in 1/2 an hour. We can divide fractions to find the rate that the tree runs out syrup. To divide fractions, keep the first fraction the same, change multiplication into division, and flip the second fraction over. It would look like this: 3/4 * 2/1. 3/4 * 2/1 is 6/4 or 1 1/2 in mixed number form. Syrup flows from the tree at 1 1/2 cups per hour.

The rate of flow of syrup from the tree will be in mixed fraction form, equal to 1 1/2.

What are arithmetic Operations?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the data mentioned in the question,

The amount of syrup obtained from the tree = 3/4 cup

The time is taken to fill 3/4 cup = 1/2 hour

Then, the rate of flow of syrup will be,

(3/4) ÷ (1/2)

3/4 × 2/1

= 6/4 = 3/2

It can also be written in mixed fraction form,

= 1 1/2

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one integer is 30 more than another integer if the difference between the larger and twice the smaller is 8 find the integers

Answers

x = larger int
y = smaller int
---
x - y = 30
x - 2y = 8
---
put the system of linear equations into standard form
---
x - y = 30
x - 2y = 8

---
solution:
x = larger int = 52
y = smaller int = 22
---

How can i use decimal models to add decimals?

Answers

I don’t know. Quite honest here. You didn’t give enough info. What type of decimal problems. Addition, Subtraction, Multiplication, Division. Be more specific.

Which of the binomials below is a factor of this trinomial? x^2-7x-44

Answers

x-11
because
(x-11)(x+4)
when you multiply that you get x^2 - 7x -44

Answer:

C. (x -11)

Step-by-step explanation:

The given trinomial is [tex]x^2 - 7x - 44[/tex]

Let's factor it. To find factor, we need to find the factors of -44 such that when you add them, we have to get -7

-44 = -11*4

- 7 = -11 + 4

so the correct factors are -11 and 4

Now we can write the middle term - 7x = -11x + 4x

[tex]x^2 - 7x - 44 = x^2 - 11x + 4x - 44[/tex]

Now let's group the first two terms and second two terms and factor it.

= x(x - 11) + 4(x - 11)

Here (x-11) is common factor, so we can take outside and rewrite.

= (x - 11)(x + 4)

So the factors are (x - 11) and (x + 4)

Answer is C. (x -11)

What would you do isolate the variable in the equation below,using only one step?

X-3=7

Select the correct answer below.

A.add 7 to both sides

B. Subtract 3 from both sides of the equation

C.add 3 to the left, 7 to the right.

D.add 3 to both sides

Answers

The answer would be D) Add 3 to both sides or the fourth option because if we add three to both sides and then add seven and three together then we get our answer which is x = 10 since 10 - 3 = 7.

Which expression represents the distance between −14.6 and −5.2 on the number line?

Answers

Hello! To answer this question, all you have to do is subtract both numbers from each other. 14.6 - 5.2 is 9.4. The numbers are 9.4 units away from each other on a number line. An expression that would represent a distance between them are 14.6 - 5.2 = x. Just make the negative numbers positive to make it easier to solve.

Answer:

9.4

Step-by-step explanation:

We are given that two integers -14.6 and -5.2

We have to find distance between -14.6 and -5.2.

Difference between =-5.2-(14.6)

Difference=-5.2+14.6=9.4

Distance is the absolute value of 9.4

Therefore,

[tex]\mid 9.4\mid =9.4[/tex]

Distance between -14.6 and -5.2 is 9.4

Naomi has 50 red beads and white beads. The number of red beads is 1 more than 6 times the number of white beads. How many red beads does Noami have?

Answers

Let the number of red beads be r.
Let the number of white beads be w.

r + w = 50
r = 6w + 1

Substitute 6w + 1 in for r in the first equation.

6w + 1 + w = 50

7w + 1 = 50

7w = 49

w = 7

She has 7 white beads.

Now we use the first equation to find the number of red beads.

r + w = 50

r + 7 = 50

r = 43

She has 43 red beads.

The sum of two numbers is 43 . The smaller number is 19 less than the larger number. What are the numbers?

Answers

Let the smaller number be x and the larger number be y.
We can calculate this by using simultaneous equation, aka listing 2 equations out.
From given,
X + y = 43
Let this be equation no. 1
X + 19 = y
Let this number be equation 2.
We can do simultaneous equations either by substitute method or elimination. In this case I'm using substitute.
We can already obtain the value of y (in terms of x) in euqation no. 2, so all we gonna do is to put y into equation 1.
X + x + 19 = 43
Solve this by algebra.
2x = 43 - 19
X = 12
Now we know the exact value of x
Now substitute x = 12 into equation no. 2
12 + 19 = y
Y = 31
So the answer is 12 and 31

Final answer:

By setting up a system of equations, we find that the larger and smaller numbers in question are 31 and 12, respectively. We solve for the larger number first and then use it to find the smaller number.

Explanation:

To solve this problem, we can use variables to represent the two unknown numbers. Let's call the larger number x and the smaller number y. We have two pieces of information that can be turned into mathematical equations:

Now we can substitute the second equation into the first one to solve for x:

x + (x - 19) = 43

Simplifying the equation, we get:

2x - 19 = 43

Adding 19 to both sides gives us:

2x = 62

Dividing both sides by 2 gives us:

x = 31

Now that we have the value of x, we can find y:

y = 31 - 19

This gives us:

y = 12

Therefore, the larger number is 31 and the smaller number is 12.

All but two of the here amid’s built by the ancient Egyptians have faces inclined at 52° angles. Suppose an archaeologist discovers the ruins of a pyramid. Most of the pyramid has eroded, but the length of a side of the square base is 82 m. How tall was the pyramid, assuming it’s faces were inclined at 52°? Round your answer to the nearest meter.
A) 25m
B) 32m
C)52m
D) 105m

Answers

Consider the cross-sectional right triangle shown in the figure.

One of its sides is the height of the pyramid, with length H. The other side is half of the square base, so its length is 81 m. The hypotenuse of this triangle is the height of one of the faces.

By right triangle trigonometry,

[tex]\displaystyle{ \tan52^o= \frac{H}{41 \ m } [/tex],

thus,

[tex]H=\tan52^o\cdot41 \ m=1.28 \cdot41 \ m=52 \ m[/tex].

Answer: C) 52 m

if 152 divided by x equals 36 what would x be?

Answers

152/x = 36

x[(152/x)] = 36x

152 = 36x

152/36 = x

38/9 = x

Find all the real cube roots of 1000/27

10/3
10/9
-10/9
-10/3

Answers

Can you do prime factoriztion

1000
100 * 10
10 * 10 * 10

27
9 * 3
3 * 3 * 3

cube root (1000/27) = 10/3

Answer:

10/3

Step-by-step explanation:

Price Tax Rate Tax
$199 5%
$4,750 6%
$99.50 4.7%
$19.88 6.9%
$8.95 7.2%
$14.27 6.8%
$544.38 4.2%
$7.49 8.1%
$28.56 7.5%
$14.98 4.9%

Answers

199 *0.05 = 9.95

4750 * 0.06 = 285

99.50 * 0.047 = 4.68

19.88 * 0.069 = 1.37

8.95 * 0.072 = 0.64

14.27 * 0.068 = 0.97

544.38 * 0.042 = 22.86

7.49 * 0.081 = 0.61

28.56 * 0.075 = 2.14

14.98 * 0.049 = 0.73

Simone is in a bike a thon for a fundraiser. she recives 15 dollars. for each mile she bikes if she wants to raise 510 dollars how many miles does she need to bring ke

Answers

Simone would have to bike for at least 34 miles to reach $510

About thirty-four times because 15 x 30 equals 510 all you had to do was find the common multiples of 15

What does X equal?

15= x/6 - 1

Answers

x=96

first add the one to the 15 then multiply it by 6 and you get 96

Ok, you have your equation 15=x/6-1.
First, add 1 to both sides, get 16=x/6.
Then, multiply both sides by 6.
Get your answer of x=96
Hope this helps

how do you read this number. 7,654,321?

Answers

seven million, six hundred fifty four thousand, three hundred twenty one

What is the value of 2 in 0.812

Answers

Hello There!

It is equal to two thousandths.
The first number after the decimal point is tenths.
The second number after the decimal point is hundredths
The third number after the decimal point is thousandths.

Hope This Helps You!
Good Luck :)

- Hannah ❤

The place of the digit 2 in the decimal number will be hundredths place.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The decimal number is the sum of a whole number and part of a fraction number. The fraction number is greater than zero but less than one.

The decimal number is given below.

⇒ 0.812

The place after the decimal starts from the tenths, hundredths, thousandths, and so on.

The place of the digit 2 in the decimal number will be hundredths place.

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What is difference between 164 and 220

Answers

56 is the difference

The difference between 164 and 220 is 56.

The difference between 164 and 220 is 56. In mathematical terms, you calculate the difference by subtracting the smaller number from the larger one:

220 - 164 = 56.

If f(x) = 2x2 + 1 and g(x) = x2 – 7, find (f + g)(x).
A. 3x2 + 8
B. 3x2 – 6
C. x2 – 6
D. x2 + 8

Answers

Remember that, although it may look intimidating, (f+g)(x) is simply f(x) + g(x)
Therefore:
(f+g)(x) = f(x) + g(x) Substitute the functions for f(x) and g(x)
(f+g)(x) = (2x² + 1 )+ (x² - 7)
Notice that we first want to write the functions in as parenthesis before we add them. This helps us keep from getting confused on what signs to give each term.
(f+ g)(x) = 2x² + x² + 1 - 7 Collect like terms
(f + g) (x) = 3x² - 6
Answer is B

convert 220 from degrees to radians

Answers

220 degrees = 3.83972

to convert degrees to radians, multiply by π180°, since a full circle is 360° or 2π radians.220°⋅π180° radians Cancel the common factor of 20 111⋅π9 radians Multiply 111and π9 to get 11π911π9 radians

I hope this helps.

The conversion of the given degrees 220° is equal to 11π/9 radians approximately.

To convert degrees to radians, use the following formula:

radians = degrees × (π / 180)

Let's apply this formula to convert 220 degrees to radians:

radians = 220 × (π / 180)

radians = 220π / 180

Now, to simplify the fraction, you can divide both the numerator and denominator by their greatest common divisor, which is 20:

radians = (220/20)π / (180/20)

radians = 11π / 9

Therefore, 220 degrees is equal to approximately 11π/9 radians.

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Cookies are sold singly or in packages of 10

or 30
.
With this packaging, how many ways can you buy 60

cookies?

Answers

10 + 10 + 10+ 30
30+30
10+10+10+10+10+10

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