The area of a large rectangular rug is 54 square feet. List all the possible pairs of
dimensions for the rug

9514 1404 393

Answer:

  20 . . . . value of last equation

  (A, B, C) = (4, 5, 10) or (3 1/3, 6, 12) . . . . values of symbols

Step-by-step explanation:

If we call the symbols, in order of appearance, A, B, C, then the equations are ...

  2AB = 40   ⇒   AB = 20

  2C/B = 4   ⇒   C/B = 2

Multiplying the second equation by the first, we get ...

  (C/B)(AB) = AC = (2)(20) = 40   ⇒   AC = 40

Then the last equation is ...

  (C-B)A = __

  AC -AB = __ = 40 -20 = 20

The value of the last equation is 20.

_____

Per the above, we have AC = 40. The third equation is ...

  (C +3A) = 22

Using the first relation, we have A = 40/C, so the second becomes ...

  C +3(40/C) = 22

  C² -22C +120 = 0

  (C -10)(C -12) = 0

  C = 10 or 12

As you can see, there are two possible solutions for the values of the symbols. The corresponding values of the other variables are ...

  A = 40/C = 4 or 3 1/3

  B = 20/A = C/2 = 5 or 6

The values of the variables are ...

  (A, B, C) = (4, 5, 10) or (3 1/3, 6, 12)  

Answer:

86 i guess

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

I use the Pythagoras theorem.

[tex]\sqrt{a^{2} +b^{2} } =c^{2}[/tex]

[tex]4^{2}{x}6^{2} = c^{2}[/tex]

16 x 36= 576

[tex]\sqrt{576} = 24[/tex]

Answer:

[tex]y' = 5x + 4[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \frac{1}{5}x - \frac{4}{5}[/tex]

Required

The inverse relation

[tex]f(x) = \frac{1}{5}x - \frac{4}{5}[/tex]

Rewrite as:

[tex]y = \frac{1}{5}x - \frac{4}{5}[/tex]

Swap x and y

[tex]x = \frac{1}{5}y - \frac{4}{5}[/tex]

Multiply through  by 5

[tex]5x = y - 4[/tex]

[tex]y = 5x +4[/tex]

Rewrite the new function as:

[tex]y' = 5x + 4[/tex]

Answer:

10,13 and 16

Step-by-step explanation:

The expression can be simplified as  [tex]7x\sqrt[3]{ 2x} y^7[/tex].

An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)

A phrase in language may contain an action on its own, but it does not constitute a whole sentence.

Given:

The expression = [tex]\sqrt[3]{686x^4} y^7[/tex]

Factorize 686 we get 7³ × 2

= [tex]\sqrt[3]{7^3\times 2x^4} y^7[/tex]

= [tex]7x\sqrt[3]{ 2x} y^7[/tex]

Therefore, the expression can be simplified as  [tex]7x\sqrt[3]{ 2x} y^7[/tex].

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Answer:

Z-score for 34-week baby = 0.643

Z-score for 41-week baby = 1.154

Baby weight of 41-week is more than the baby weight of 34-week in the gestation period.

Step-by-step explanation:

Given - Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 700 grams while babies born after a gestation period of 40 weeks have a mean weight of 3100 grams and a standard deviation of 390 grams. If a 34-week gestation period baby weighs 2950 grams and a 41-week gestation period baby weighs 3550 grams

To find - Find the corresponding z-scores. Which baby weighs more relative to the gestation period.

Proof -

Given that,

In between period of 32 to 35 weeks

Mean = 2500

Standard deviation = 700

In between after a period of 40 weeks

Mean = 3100

Standard deviation = 390

Now,

For a 34-week baby,

X = 2950

For a 41-week baby,

X = 3550

Now,

Z-score = (X - mean) / Standard deviation

Now,

For a 34-week baby,

Z - score = (2950 - 2500) / 700 = 0.643

For a 41-week baby,

Z-score = (3550 - 3100) / 390 = 1.154

∴ we get

Z-score for 34-week baby = 0.643

Z-score for 41-week baby = 1.154

As 1.154 > 0.643

So,

Baby weight of 41-week is more than baby weight of 34-week in the gestation period.

Answer:

First triangle x=9

Second triangle x=20

Step-by-step explanation:

Using Pythagorean theorem

40^2+x=41^2

1600+x^2=1681

-1600        -1600

x^2=81

To find x we do the opposite of powers and find the squared

x=9

Second triangle

21^2+x^2=29^2

441+x^2=841

-441        -441

x^2=400

x=20

Answer:

The surface area is about 267.04 cm^2; the surface area would be divided by 4 if the slant height and diameter were to be cut in half

Answer:

15 boys selected

Step-by-step explanation:

Given

[tex]N =11000[/tex] --- The population

[tex]n = 100[/tex] --- The sample selected

[tex]p =0.152[/tex] -- The proportion of boys

Required

The expected number of boys selected

The expected number is calculated by multiplying the sample size by the proportion of boys.

So, we have:

[tex]Boys = p * n[/tex]

[tex]Boys = 0.152 * 100[/tex]

[tex]Boys = 15.2[/tex]

[tex]Boys = 15[/tex] --- approximated

Answer:

1: A. 448 2: 209 pi cm^2 3: D. 351 m^2 4. B 240 cm^2 C. 561.1 cm^2

Step-by-step explanation:

just took the test!!!

Answer:

y=1/7x

Step-by-step explanation:

55-48= 7, 2-1=1, 1/7= slope

Answer:

how can i answer?

Step-by-step explanation:

Answer:

Chapter Three: Calculate Total Countertop Square Footage

To calculate the total square footage (after placing seams) you will need to follow this formula: “L” x “W” / 144 = s.f. (Length times width divided by 144 = square feet).

Answer:

Answer option c is correct.

Step-by-step explanation:

385.50 is adding to the amount because it his paycheck. 16.35 is subtracted because it is bing deducted. Then there is the adding amount of 28.75 and 37.35 because of his commission and overtime. When you add it all up, you get 435.25. This whole thing would look like this in equation format:

385.50 +(-16.35) + 28.75 + 37.35 = 435.25.

Answer:

The 3rd option

Step-by-step explanation:

If we find X then this would become a Mult. problem

Answer:

280,000

Step-by-step explanation:

Solve

Given: 100,000 subscribers increases by 2.4% per month

To find: After a year, how much will that be?

First step:

Find the increase of the subscribers per month

100,000 of 2.4%

Set up an equation

2.4/100 × 100,000/1

Cross multiply, cancel zeros in both 100,000 and 100. Which is equal to:

2.4/1 x 1,000/1 =

2,400

Second step: If it increases per month,

then to find the year, find out how many months is in a year:

12 months = 1 year

Now that has been figured out, multiply the result by the result in the first step:

12 × 2400 = 28.800

Therefore, the number of subscribers will be after a year

Answer:x=2,5

Step-by-step explanation:

sqrtx-1=x-3. Sqrt5-1=5-3

sqrt2-1=2-3. Sqrt4=

sqrt1=1. 2=2

1=1

Answer:

1/8

Step-by-step explanation:

its easy just count backwards by 2/8 each time

Answer:

h=-7

Step-by-step explanation:

-4(-6h - 7) = 9h + 10h - 7

24h+28=19h-7

Both side -28

24h+28-28=19h-7-29

24h=19h-35

Both side -19h

24h-19h=19h-19h-35

5h=-35

h=-7

Answer:

h = -7

Step-by-step explanation:

-4(-6h-7)= 9h+ 10h-7

24h+ 28=19h-7

-19. -28. -19 -28

5h -35

h= -7

The volume of Larry’s picture is approximately 653in³

The volume of Sandra’s pitcher is approximately 905in³

The formula for calculating the volume of a cylinder is expressed as;

V = πr²h

Such that the parameters are;

Now, substitute the values, we have;

Larry's cylinder

Volume = 3.14 × 4² × 13

Find the square value and multiply the expression

Volume = 653in³

Sandra's cylinder

Volume = 3.14 × 6² × 8

Find the square value and multiply the expression

Volume = 905in³

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Answer:

A change from 55 to 77 represents a positive change (increase) of 40%.

Hope this helps!

Answer:

Increase

Step-by-step explanation:

55 videos to 77 videos is equal to 140% increase

so how we find the result?

multiply 77 with 100 and divide it by 55

77*100/55 = 140

Answer: Answer= -23

Step-by-step explanation: plug in -5 for v. THen multiply 4 and -5 which should give you -20. then subtract -3 from -20 which will give you -23. :)

Try this option:

1. to calculate the difference of the final sequence:

the difference between two terms of the sequence A is 4 (7-3=11-7=...=4) and the difference between two terms of the sequence B is 7 (9-2=16-9=...-7). It means, in the final sequence the difference should be 7*4=28;

2. to calculate the first term of the final sequence:

A={3;7;11;15;19;23;27;31;...;407} and B{2;9;16;23;30;...;709}. It means, the first term of the final sequence is 23.

3. to calculate the last term of the final sequence:

if 407<709, it means the last term is less than 407, then it is possible to make up the equation 23+28*n<407, where 23 - the 1st term of the final sequence, 28 - the difference of the final sequence, (n+1) - number of the last term of the final sequence and n∈Z.

n<(407-23)/28; n<13.71. If n∈Z, then n=13.

So, the last term of the final sequence is 23+28*13=387.

4. if the first term is 23, the last one is 387 and the difference of the final sequence is 28, then the final sequence is consists of 14 terms:

{23; 51; 79; 107; 135; 163; 191; 219; 247; 275; 303; 331; 359; 387}

Answer:

4.10.99

Step-by-step explanation:

3.14 * 3.5