Hay dos números naturales consecutivos y la suma del cuadrado de esos números es 221¿cuáles serán esos números?

Answers

Answer 1
Let x and x+1 be the consecutive integers.

The sum of squares is:
(x)² + (x+1)² = 221
Expand second term:
x² + x² + 2x + 1 = 221
Combine like terms:
2x² + 2x + 1 = 221
Subtract 221 from both sides to make quadratic form:
2x² + 2x - 220 = 0
Divide both sides by 2:
x² + x - 110 = 0
Factor:
(x + 11)(x - 10) = 0
x = -11 or x = 10

Answers: 10 and 11 or -10 and -11

Related Questions

Hong needs to memorize words on a vocabulary list for Spanish class. He has memorized 30 of the words, which is five-sixths of the list. How many words are on the list?

Answers

36 words are on the list

The diagram of a living room is shown below. What fraction of the living room is covered by the rug? need done ASAP

Answers

Answer:

[tex] \frac{10}{27} [/tex]

Lauren's vet commented that her puppy gained 10% in weight since the first visit. Write an expression that could be evaluated to show the puppy's current weight. Use a variable to represent the weight of the puppy at the first visit. Write the expression in simplified form. If the puppy gains another 10% in weight from the current visit to a future visit, how much will the puppy weigh? Write an expression that could be evaluated to show the puppy's future weight. Write the expression in simplified form.

Answers

Answer: expression to show puppy's current weight = x+ 0.1x, simplified form = 1.1x

Expression that for puppy's future weight= 1.1x + 0.1(1.1x), simplified form = 1.21 x

Step-by-step explanation:

Let x= Puppy's weight in the first visit.

If it gained 10% in weight from the first visit, then his current weight = (weight in first visit)+10% of (weight in first visit)

= x+ 0.1x

i.e. expression to show puppy's current weight = x+ 0.1x

In simplified form it will be

x+ 0.1x = x(1+0.1)

=x(1.1)

=1.1 x  (simplified form )

If puppy gains another 10% in weight, then its future weight = (current weight)+10% of (current weight)

= 1.1x+10% of 1.1x

= 1.1x + 0.1(1.1x)

Expression that for puppy's future weight= 1.1x + 0.1(1.1x)

= 1.1x(1+0.1)

= 1.1x(1.1)

=(1.1)²x

= 1.21x  (simplified form)

please will give brain

Answers

1)

x=-1 and -3

y=3

2)

x=1 and 4

y=4

3)

x=-3 and 3

y=-9

1. Juliet O'Hara works for a weekly paycheck. Last week she worked 5 days for a total of 39 hours. Her regular rate of pay is $10.95 an hour. In addition to federal income tax, state income tax, Medicare, and social security, Juliet also has insurance of $20 a week withheld and puts 4% of her gross pay into a retirement account. Compute her gross pay, deductions, and net pay. SHOW YOUR WORK!

Answers

Step-by-step explanation:

given data:

hours worked weekly = 39

pay/her = $10.95

insurance withheld weekly = $20

percentage put into Retirement = 4%

Solution:

Gross pay

= hrs worked weekly x pay/hr

= 39 x $10.95

= $427.05.

Deductions

insurance deduction

= $427.05 – $20

= $407.05

Amount put into retirement account

= 4% of $427.05

= 4/100 x $427.05

= $17.082

NET PAY

= $427.05 – $20 –$17.082

= $389.97

Write the slope-intercept form of the equation for the line containing (1,-6) and (−4,4).

Answers

Answer:

-2

Step-by-step explanation:

m = 10 / -5 = 2 / -1 = -2

Graph the linear equation
5x - y = 30 by following these steps:
Step 1: Find the x-intercept. Let y = 0 and solve for x.
=

Answers

Answer:

Step-by-step explanation:

5x-(0)=30

add 0 to both sides to cancel

5x=30

divide by 5 on both sides to cancel

x=6

which expression is equivalent to 0.17w + 0.77 + w? -0.77 + 1.17w
-0.17w + 1.77
-1.94w
-1.6w

Answers

Answer:

113.29w +1.77

Step-by-step explanation:

You were lifting weights with 220,000 and a volume of 1000cm^3. what is the density?

Answers

Answer:

220g/cm³

Step-by-step explanation:

Given parameters:

  Mass of the weight = 220000g

  Volume  = 1000cm³

Unknown:

Density of weight = ?

Solution:

Density is the mass per unit volume of a substance.

Mass is the amount of matter in a substance.

Volume is the amount of space a substance occupies

        Density  = [tex]\frac{mass}{volume}[/tex]

Input the parameters and solve

        Density  = [tex]\frac{220000}{1000}[/tex]  = 220g/cm³

The following scores represent students' test grades in Ms. Orr's science class. Test Scores 78 81 78 81 78 81 78 81 78 87 91 87 91 87 91 87 91 87 What is the median score for Ms. Orr's science class?

plsss help mee​

Answers

Answer:

Its definitely B 84.5

I took the test

Step-by-step explanation:

Answer:

87

Step-by-step explanation:

The median score is the score that appears in the middle of the graph and the set of numbers. 87 is the median score.

A rock garden is in the shape of a triangle as shown. Which equation could be used to find the area of the rock garden

Answers

Answer1/2(8x15)=60ft2

Step-by-step explanation: hope this helps you

The area of the rock garden will be represented by the equation 1/2 x 15 x 8 = 60. The correct option is D.

What is the area of a triangle?

The entire area filled by a triangle's three sides in a two-dimensional plane is referred to as the triangle's area. The fundamental equation for a triangle's area is A = 1/2 x b x h, where b and h are the product of the triangle's base and height.

The area of the triangle will be calculated as,

Area = 1/2 x 15 x 8

Area = 15 x 4

Area = 60 square feet

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¡¡. PLEASE HELP !!!!

Answers

The answer to question 3 is 4

Determine which quadrant the point is in: (-3,-4)
Quadrant

Answers

the answer is quadrant 3

Answer:

Its in quadrant 3

Step-by-step explanation:

Since they are both negative they go into the third quadrant

plz answer 12 points ​

Answers

Answer:

6+3^3

Step-by-step explanation:

6 plus 3 cubed

which is 6+3^3

Use rounding to estimate the sum.

Estimate the sum.
78.9+71.2

Answers

Answer:

150

Step-by-step explanation:

add 79+ 71 because you rounded to get that number then add :)

150

When estimating you just round off the numbers so, 78.9 becomes 79 and 71.2 becomes 71 so, 79 + 71 = 150.

Please answer quickly!

Answers

Sorry I think the picture is blocked so I can't see it

What is .24 written as a percent?

Answers

Answer:

24%

Step-by-step explanation:

Step 1: Shift the decimal point two places to the right: 0.24 → 2.4→ 24.

Step 2: Add a percent sign: 24%

and that's how you get your answer

The .24 written as a percent is 24%.

To convert .24 to a percent, multiply it by 100.

.24 ×100 = 24

When we express a number as a percent, it represents a proportion out of 100. In this case, .24 as a percent means that .24 is equivalent to 24 out of 100 or 24%. The percent symbol (%) indicates that the number is being represented as a fraction of 100. This can be interpreted as .24 representing 24 parts out of 100, or 24 hundredths.

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If your balance is $90 dollars & you have to pay a $10 deposit fee how much left do you have to pay

Answers

Answer:

90 minus 10 is 80 so $80 left

TIME REMAINING 01:37:16 Absalom states that 0 is a rational number. Which is a correct explanation for this statement? The number 0 is a whole number, which is part of the rational numbers. The number 0 is the center of the number line. The number 0 is a natural number, which is part of the rational numbers. The number 0 cannot be written as a fraction.

Answers

Answer:

The number 0 is a whole number, which is part of the rational numbers, is correct.

Step-by-step explanation:

Absalom states that 0 is a rational number.

As the whole numbers are 0,1,2,3,... which is starting from 0, so the stated number 0 is a part of the whole number.

As all the whole number are rational numbers, so 0 is a rational number

Hence, the explanation (i) which is,

The number 0 is a whole number, which is part of the rational numbers, is correct.

The naturals numbers are 1,2,3,... which starts from 1, so 0 is not a part of the natural number, and the number 0 can be written as a fraction like [tex]0=\frac {0}{1}[/tex].

Hence, statement (ii) The number 0 is a natural number, which is part of the rational numbers as well as the statement (iii) The number 0 cannot be written as a fraction, are wrong.

Answer:

The number 0 is a whole number, which is part of the rational numbers.

Step-by-step explanation:

√2+√2 =
A. 3√2 or B. 2√2
Which one? ​

Answers

Answer:

B

Step-by-step explanation:

Can i plz have brainliest :)

answer with explanation pls​

Answers

Answer:

8.69>8.6

Step-by-step explanation:

Because 8.69 has .09 more than 8.6

Answer:

8.69 > 8.60

Step-by-step explanation:

You need to add a zero to the end to 8.6 so it's easier to compare. Since all the digits in the two numbers are the same except 9 and zero, those are what you need to compare. 9>0, so 8.69 > 8.6

hope this helped! :)

Which number line best shows the position of 13?

Answers

The 3rd number line because the square root of 13 is 3.6!

is 77.65488319 rational or irrational

Answers

Answer:

rationale

Step-by-step explanation:

step by step instructions

Answer:

Irrational

Step-by-step explanation:

The decimal doesn't terminate.

√294
A. 7√6
B. 8√3
Which one?

Answers

Answer:

√294 = A. 7√6

Explanation:

Factor  49  out of  294 . √

49 ( 6 ) Rewrite  

49  as  7 ² . √ 7 ² ⋅ 6

Pull terms out from under the radical.

7 √ 6

Which is true about x, the quotient of the division problem shown below? х 81 918 O The quotient contains a repeating decimal. O The quotient contains a terminating decimal. O The quotient is a whole number less than 11. O The quotient is a whole number greater than 11

Answers

Answer:

The answer is choice 2 and 3, that is "The quotient has a final decimal and the whole number is less than 11".

Step-by-step explanation:

The product of a ratio: amount (r) over other(s) (variance from 0) becomes mandatory to note this quotient and in the following case Thus q is = 0.0882352941.

[tex]\to \frac{81}{918}= 0.0882352941[/tex]

It wasn't a repeating decimal, however a final decimal, so it's got an end.

Its quotient may be less than 11 in total.

Numbers of W = {0,1,2, ...} and 0 < 11 are provided for this entire series of data therefore It's real .

Answer:

a

Step-by-step explanation:

Gemma makes a conjecture that the sum of an odd integer and itself is always an even integer. Which choice is the best proof of her conjecture?

A) Look at these different examples: 7 + 7 = 14, 13 + 13 = 26, 23 + 23 = 46. So the sum of an odd number and itself must be even
B) Let 2n + 1 be an odd number; (2n + 1) + (2n + 1) = 4n + 2. Because 4(n + 2) is divisible by 2, the sum of 2n + 1 and itself is even.
C) Let n represent an odd number, and let n + n be an even number. Therefore, n + n = n + n, which shows that the sum of an odd number and itself is even.
D) Every time you add an odd number and itself, the sum is an even number.Every time you add an odd number and itself, the sum is an even number.

Answers

Answer:

Let 2n + 1 be an odd number......  B/2nd option

Step-by-step explanation:

The best choice is

Let 2n + 1 be an odd number; (2n + 1) + (2n + 1) = 4n + 2.

Because 4(n + 2) is divisible by 2, the sum of 2n + 1 and itself is even.

What is Conjecture?

A hypothesis in mathematics is a conclusion or a proposition made tentatively without supporting evidence. Some conjectures, like the Fermat's Last Theorem or the Riemann hypothesis, have significantly influenced the development of new branches of mathematics.

First, Only three examples are given which is not appropriate at all.

Second, This is the best proof is

Let 2n + 1 be an odd number; (2n + 1) + (2n + 1) = 4n + 2. Because 4(n + 2) is divisible by 2, the sum of 2n + 1 and itself is even.

Fourth, State the meaning of Title without proof.

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HELP PLEASE!!

Select the equation of the line parallel to y=-4x-6 the
equation and that passes through the point (1, 2).
O y=-4x+6
O y=4x-4
O y=-4x-4
O y = 4x+6

Answers

Answer:

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

Step-by-step explanation:

If you are looking for a parallel line with just the equation then look for an equation with the same slope and different Y intercept. After you find that just check and see if it passes the coordinate.

[tex]2=-4(1)+6[/tex]

[tex]2=-4+6[/tex]

[tex]2=2[/tex]

If it works you have your answer!

The equation of the line parallel to y = -4x - 6 and passing through (1, 2) is

y = -4x + 6.

The slope of y = -4x - 6 is -4.

passing through the point (1, 2)

the new line is parallel to the original line, it will have the same slope (-4).

Use the point-slope form of a linear equation to write the equation of the new line. The point-slope form is y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the given point.

substituting values,

y - 2 = -4(x - 1)

y - 2 = -4x + 4

y = -4x + 6

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Name the property that the statement illustrates.

Answers

Answer:

Symmetric property of angle congruence

symmetric property of angle congruence

Simplify 6.9y+2.4y please help me

Answers

Answer:

6.9y+2.4y

= 9.3y

Hope it helps u,

pls put thanks and pls mark as the brainliest

Which fraction is in simplest form?

​2-10​

​5-12​

​3-6​

​4-8

Answers

Answer:

5/12

Step-by-step explanation:

All of the other answers share at least one factor they can be divided by (the numerator in all cases). 5/12 however shares no factors and cannot be simplified anymore.

5/12 is in simplest form because you can not divide 5 into a half.
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