A positive real number is 1 more than another. When -2 times the smaller is added to the square of the larger, the result is 33. Find the numbers.

Answers

Answer 1

Answer:

The smaller number is 4√2 and the larger number is (4√2 + 1).

Step-by-step explanation:

Let the two numbers be x and y, where y is the larger of the two numbers.

Since y is the larger number, it is one more than the smaller number. So:

[tex]y=x+1[/tex]

When negative two times the smaller is added to the square of the larger, the result is 33. In other words:

[tex]-2x+y^2=33[/tex]

Substitute:

[tex]-2x+(x+1)^2=33[/tex]

Solve for x. Square:

[tex]-2x+(x^2+2x+1)=33[/tex]

Simplify:

[tex]x^2+1=33[/tex]

Subtract one from both sides:

[tex]x^2=32[/tex]

And take the square root of both sides:

[tex]x=\pm\sqrt{32}=\pm 4\sqrt{2}[/tex]

Since y is positive, we can ignore the negative case. So, the smaller number is:

[tex]x=4\sqrt{2}\approx5.66[/tex]

And the larger number is:

[tex]y = 4\sqrt{2} + 1 \approx6.66[/tex]


Related Questions

What is the length of the diagonal of a rectangle that is 12 inches long and 6 inches wide?​

Answers

To find the diagonal of the rectangle we have to use Pythagorean theorem!

Pythagorean theorem is used to find the length of a missing angle such as the hypotenuse or the sides a and b.

Steps to solve:

1. 12 in is the length or the base of the right triangle, and 6 in is the wide or the side a.
2. Now use the formula: a^2+b^2=c^2, and plug in the numbers!
3. 6^2+12^2=c^2, now just solve the squared numbers.
4. 36+144=c^2
5. 180=c^2
6. Find the square root of 180.

And that is you answer!
If helped mark me the brainiest!!

If f(x) = 2x – 6 and g(x) = 3x + 9, find (f+ g)(x).

Answers

Answer:

(f + g)(x) = 5x + 3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Terms/CoefficientsFunctionsFunction Notation

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 2x - 6

g(x) = 3x + 9

(f + g)(x) is f(x) + g(x)

Step 2: Find

Substitute in function values:                                                                          (f + g)(x) = 2x - 6 + 3x + 9Combine like terms:                                                                                         (f + g)(x) = 5x + 3

Fill in the table of values so that this is a proportional relationship with k=3/2 X. Y. *blank*. 0 2. *blank*. *blank*. 6. -2. *blank*

Answers

Answer:

x => y

0 => 0

2 => 3

4 => 6

-2 => -3

Step-by-step explanation:

The equation of a proportional relationship is represented as y = kx,

where, k = y/x

We are given that k = ³/2

This means that, equation of the relationship therefore would be:

y = ³/2x

Use this equation to solve for each missing value on the table given:

✔️Where, y = 0, substitute y = 0 into y = ³/2x to find x:

0 = ³/2x

0 * 2 = 3x

0 = 3x

0/3 = x

x = 0

✔️Where, x = 2, substitute x = 2 into y = ³/2x to find y:

y = ³/2(2)

y = 3

✔️Where, y = 6, substitute y = 6 into y = ³/2x to find x:

6 = ³/2x

6 * 2 = 3x

12 = 3x

12/3 = x

x = 4

✔️Where, x = -2, substitute x = -2 into y = ³/2x to find y:

y = ³/2(-2)

y = -3

who is the president of Uganda​

Answers

Who is the president of Uganda?

Answer: Yoweri Museveni

☆彡Hanna
Yoweri Museveni is the president of Uganda

27 exponent x divided by 3 is equal to one divided by 81.​

Answers

27 exponent x/3 = 1/81

we can say exponent as power also

(27 power x) × (3 power -1) = 81 power -1

(3 power 3x) × ( 3 power -1) = 3 power -4

IN MULTIPLICATION WHEN BASES ARE SAME THEN POWERS ARE ADDED

3 power 3x + (-1) = 3 power -4

IN AN EQUATION WHEN BASES ARE EQUAL POWERS ALSO EQUAL

3x +(-1) = -4

3x - 1 = -4

3x = -4 + 1

3x = -3

x = -3/3

x = -1

Answer:

x = -1

Step-by-step explanation:

27 exponent x =  [tex]27^x[/tex]

Divided by 3 =   [tex]\frac{27^x}{3}[/tex]

Is equal to : [tex]\frac{1}{81}[/tex]

Therefore,

         [tex]\frac{27^x}{3} = \frac{1}{81}[/tex]

Cross multiplying :

       [tex]27^x \times 81 = 1 \times 3[/tex]

       [tex]27^x = \frac{3}{81}[/tex]

       [tex]27^x = \frac{1}{27}[/tex]

       [tex]27^x = 27^{-1}[/tex]

         [tex]x = -1[/tex]                     [tex][a^x = a^y => x = y][/tex]

describe the pattern in words ​

Answers

What pattern? Include the pattern please. Thank you.

Words used to describe patterns and arrangements - thesaurus

broken. adjective. a broken pattern or sound has

spaces in it.

candy-striped. adjective. ...

checked. adjective. ...

checkered. adjective. ...

chequered. adjective. ...

chronological. adjective. ...

criss-cross. adjective. ...

dappled. adjective.

Hope my answer helps uh ✌️

witch value of x makes this eqation true -12x-2(x+9)=5(x+4)​

Answers

Answer:

x = -2

Step-by-step explanation:

A poll is given, showing 60% are in favor of a new building project.

If 7 people are chosen at random, what is the probability that exactly 5 of them favor the new building project?

Answers

Answer:  0.2612736

Round this value however you need to.

==================================================

Explanation:

n = 7 = sample sizep = 0.60 = probability of someone being in favork = 5 = number of people in favor

We use the binomial distribution here. The formula for that is

P(k) = (n C k)*(p)^k*(1-p)^(n-k)

where the n C k refers to the nCr combination formula

[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]

simply replace r with k.

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

So,

P(k) = (n C k)*(p)^k*(1-p)^(n-k)

P(5) = (7 C 5)*(0.6)^5*(1-0.6)^(7-5)

P(5) = 21*(0.6)^5*(0.4)^(2)

P(5) = 21*0.07776*0.16

P(5) = 0.2612736

This decimal value is exact (meaning there aren't any other digits after that last '6'). Round this value however you need to.

There's roughly a 26.1% chance of getting exactly 5 people to be in favor of the project.

Which of the following best descifrar the graph shown below?

Answers

Answer: It's B

Step-by-step explanation:

Which statement is true?

Answers

Answer:

second 1

Step-by-step explanation:

i literally just had that question

If 14 people are shorter than Alice, 12 people are taller than Bob, and 4 people are shorter than Alice and taller than Bob, how many people are there?

Answers

Answer:

THERE IS A LOT OF PEOPLE

ᴘʟs ʜᴇʟᴘᴘᴘᴘ ᴍᴇᴇᴇᴇᴇᴇ!!

ɴᴏɴsᴇɴsᴇ = ʀᴇᴘᴏʀᴛ ​

Answers

216 in²

Step-by-step explanation:

The above diagram is a rectangular prism, a three-dimensional shape, having six faces, where all the faces (top, bottom, and lateral faces) of the prism are rectangles such that every two opposite side faces are identical.

Hence we can calculate the surface area of the diagram by multiplying the surface areas of the three faces by 2, and adding them together.

= 2(5 x 4.5) + 2(5 x 9) + 2(4.5 x 9)

= 45 + 90 + 81

= 216 in²

Problem:-

What is the approximate surface area of the figure?

A. 101.3 in²

B. 108 in²

C. 202.5 in²

D. 216 in²

Solution:-

Since the base of the prism is a rectangle, the perimeter P of the base is 2(9+4.5) or 27 inches. The area of the base is 9•4.5 or 40.5 square inches. The height is 5 cinches.

[tex]\sf{S=Ph+2B}[/tex]

[tex]\sf{ \: \: \: \: =(27•5)+2(4.5)}[/tex]

[tex]\sf{ \: \: \: \: =135+81}[/tex]

[tex]\sf{ \: \: \: \: =\:}{\color{magenta}{216}}[/tex]

Answers:-

The surface area of the figure is 216 square inches. So, the correct option is D.

========================

#Hope it helps!

(ノ^_^)ノ

A baseball is "popped" straight up by a batter with an initial velocity of 32 ft/sec. The height of the ball above ground is given by a function where t is time in seconds after the ball leaves the bat and h(t) is the height in feet above the ground. The batter hit the ball at an original height of 4 feet off of the ground, and the acceleration due to gravity is -16ft/se2

Answers

Answer:

The ball reaches the maximum height after 1 seconds

Step-by-step explanation:

Given

[tex]y = -16t^2 + 32t + 4[/tex] --- the function missing from the question

Required

Time to reach maximum height

The time (t) to reach maximum height is calculated using:

[tex]t = -\frac{b}{2a}[/tex]

Where

[tex]y =at^2 + bx + c[/tex]

So, by comparison:

[tex]a = -16[/tex]

[tex]b = 32[/tex]

[tex]c = 4[/tex]

So, we have:

[tex]t = -\frac{b}{2a}[/tex]

[tex]t = -\frac{32}{2*-16}[/tex]

[tex]t = -\frac{32}{-32}[/tex]

[tex]t = \frac{32}{32}[/tex]

[tex]t = 1[/tex]

Chang knows one
sides of this
side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two
triangle?
• 5 cm and 8 cm 8

6 cm and 7 cm

7 cm and 2 cm
®
8 cm and 9 cm

Answers

9514 1404 393

Answer:

  (d)  8 cm and 9 cm

Step-by-step explanation:

The sum of the other two side lengths must exceed 13 cm for a triangle to be possible.

  8 cm and 9 cm

the answer is that last one 8cm and 9cm

the data below shows the number of car thefts in a city for a period of 20 days. complete parts (a) and (b) below.

51, 64, 71, 56, 53, 68, 53, 49, 70, 33
64, 53, 79, 65, 55, 46, 80, 76, 73, 74

a. Draw an ordered stem and leaf plot for the data. ​

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

The oederd data :

33, 46, 49, 51, 53, 53, 53, 55, 56, 64, 64, 65, 68, 70, 71, 73, 74, 76, 79, 80

Stem Leaf

3 | 3

4 | 6 9

5 | 1 3 3 3 5 6

6 | 4 4 5 8

7 | 0 1 3 4 6 9

8 | 0

Key :

3 | 3 = 33

use the diagram below to find all the missing angles

Answers

Answer: M<1=135     M<2=45      M<3=135      M<4=45

Step-by-step explanation:

Every spring the grade four students play the grade five students in softball. The graph shows their scores.
Softball Scores
5
4
Score
2
1
grade 4
grade 5
year 1 year 2 year 3
Year
year 4 year 5
In which year was the difference between the grade four score and the grade five score the greatest?
O A year 1
O B. year 2
Oc. year 3
D. year 4
O E years

Answers

Answer:

B

Step-by-step explanation:

Write the numbers in a standard form:

57,900,000

227,900,000

1,427,000,000

Answers

Answer:

madarchud

bhag loudeye bsdk

HELPP PLEASEE!!! FIRST ONE TO ANSWER GETS BRAINLEST!!!!
A square pyramid is shown. What is the surface area of the pyramid? Enter your answer in the box.
4 cm
3 cm
3 cm
cm2

Answers

Answer:

33cm squared

Step-by-step explanation:

Answer:

33cm

Step-by-step explanation:

4. Temperature graphs from two cities on July 1 are shown below. Which statement is true?

O A. City A experienced a bigger temperature change than City B.
O B. City B experienced a bigger temperature change than City A.
O C. The low temperature in City B was lower than the low temperature in City A.
O D. Both B and C are true.

Answers

Answer:

City B experienced a bigger temperature change than City A.

Step-by-step explanation:

From the graph of the temperature given, using visual inspection, we can see how the graph of both cuties change, for city A, the change in temperature, very low as the highest temperature is about 80 and the lowest temperature value is about 76 ;

However. For city B, the highest temperature value is about 100 and the lowest is about 76

Hence, City B experienced a bigger temperature change than A.

For low temperature, the low temperature in city A and B are the same with a value of about 76°

Trapezoid A B C D is shifted down and to the left to form trapezoid A prime B prime C prime D prime. Trapezoid A prime B prime C prime D prime is rotated 270 degrees about point B.
What is the final transformation in the composition of transformations that maps pre-image ABCD to image A"B'C"D"?

a translation down and to the right
a translation up and to the right
a 270° rotation about point B'
a 180° rotation about point B'

Answers

Answer:

a 270° rotation about point B'

Answer:

C is correct 270°

Step-by-step explanation:

yuh

The average daily balance of a credit card for the month of November was $700, and the unpaid balance at the end of the month was $1400. If the monthly interest rate is 1.3% of the average daily balance, what is the total balance on the next billing date December 1? Round your answer to the nearest cent. Do not use commas to separate numbers or dollar signs. For example, $5,678.00 should be entered as 5678.00.

Answers

9514 1404 393

Answer:

  $1409.10

Step-by-step explanation:

The interest is added to the unpaid balance to obtain the total balance.

  $700×1.3% + 1400 = $9.10 +1400 = $1409.10

HELLLLLLLPPPPPPPPPPPP

Answers

Answer:

250

5:15

true

i already helped you

Answer:

9- 4 hours 30 minutes

10- 250

11- False

Help me please if you can't don't touch it

Answers

Answer:

The correct answer is A

Step-by-step explanation:

A vault contains 3000 worth of nickels.
How many nickels are in the vault

Answers

Answer:

600 nickels

Step-by-step explanation:

60,000 nickels are in the vault

$3,000 divided by 0.05 (value of 1 nickel) = 60,000 nickels

Sherrie travels 120 miles in 3 hours. Find the unit rate of speed missing number.

Answers

Answer:

The unit rate of speed is 40 miles per hour.

Step-by-step explanation:

Since Sherrie travels 120 miles in 3 hours, to find the unit rate of speed the following calculation must be performed:

3 = 120

1 = X

(1 x 120) / 3 = X

120/3 = X

40 = X

Therefore, the unit rate of speed is 40 miles per hour.

aman şego şego...... ....​

Answers

sego........ ... sego segó

Question
The angles in
triangle are such that one angle is 100 degrees more than the smallest angle, while the third angle is 2 times
as large as the smallest angle. Find the measures of all three angles.

Answers

9514 1404 393

Answer:

  20°, 120°, 40°

Step-by-step explanation:

Let s represent the smallest angle. Then the largest is (100+s) and the third angle is (2s). The sum of angles in a triangle is 180 degrees, so we have ...

  s + (100+s) +(2s) = 180

  4s = 80 . . . . . . . . . . subtract 100

  s = 20 . . . the smallest angle

  100+s = 120 . . . the largest angle

  2s = 40 . . . the third angle

The angle measures are 20°, 120°, and 40°.  

Write an equation of a line that is parallel to 6x - 2y = -3 and passes through the point (1, 3).

Answers

Answer:

Step-by-step explanation:

hope this video link be helpfull to you

answer please answer

Answers

Answer:

4 liters

Step-by-step explanation:

8/2 8 divided by 2 is 4 how do I know this, because if its per apple juice then we have to find out what can get me per apple juice, you just basically had to divde it by its own number

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