Simplify and leave in radical form.
8√x^2 y^6

Step-by-step explanation:

[tex]10 \times 9 \sqrt{72} \\ = 90 \sqrt{36 \times 2} \\ = 90 \times 6 \sqrt{2} \\ = 540\sqrt{2} [/tex]

Final answer:

To find the product of 10 and 9√72, simplify √72 to 6√2, then multiply the outside coefficients (10 and 9) to get 90, and attach the simplified radical. The final answer is 90√2.

Explanation:

The question asks to find the product of 10 and 9√72 in simplest radical form. First, recognize that the square root of 72 can be simplified by factoring out perfect squares. The square root of 72 is equal to the square root of 36 times 2, which simplifies to 6√2. Now, multiply the outside coefficients (10 and 9) and then multiply the result by the simplified radical. The final simplification is 90√2, which is the product of 10 and 9√72 in simplest radical form.

Answer: A

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Genes are our genetic makeup. The way we look, act, talk etc. The way they work is to make protiens for our DNA, as in produce "specific" proteins for ourself.

on expanding polynomial (6x^2−11y^3)(−6x^2−11y^3) or [tex](6x^2-11y^3)(-6x^2-11y^3)[/tex] is [tex]121y^6 -36x^4[/tex] .

Step-by-step explanation:

We have , (6x^2−11y^3)(−6x^2−11y^3):

[tex](6x^2-11y^3)(-6x^2-11y^3)[/tex]

⇒ [tex](6x^2-11y^3)(-6x^2-11y^3)[/tex]

We know that :

[tex](a +b)(c+d) = (ac+ad+ad+bd)[/tex]

⇒ [tex](6x^2(-6x^2) - 11y^3(-6x^2) )+(6x^2(-11y^3) + (-11y^3)(-11y^3))[/tex]

⇒ [tex](-36x^4+66x^2y^3 -66x^2y^3 + 121y^6)[/tex]

⇒ [tex](-36x^4+ 121y^6)[/tex]

⇒ [tex]121y^6 -36x^4[/tex]

Therefore, on expanding polynomial (6x^2−11y^3)(−6x^2−11y^3) or [tex](6x^2-11y^3)(-6x^2-11y^3)[/tex] is [tex]121y^6 -36x^4[/tex] .

Answer:

$81,920

Step-by-step explanation:

money made by january: $40

double that

money made by february: $80

double that

money made by march: $160

double that

money made by april: $320

double that

money made by may: $640

double that

money made by june: $1,280

double that

money made by july: $2,560

double that

money made by august: $5,120

double that

money made by september: $10,240

double that

money made by october: $20,480

double that

money made by november: $40,960

double that

money made by december: $81,920

the total money they made by the end of the year (december) was $81,920

Answer:

$163,800

Step-by-step explanation:

40, 80, 160, 320...

It's a geometric progression

With first term = 40

Common ratio = 80/40 = 2

After 1 year is 12 months

Find S12.

S12 = 40(2¹² - 1)/(2 -1)

= 163800

Step-by-step explanation:

Set up a systems of equations (x = kids, y = adults)

3x+9y=75 --> 15x+45y=375

8x+5y=67 --> 72x+45y=603

Subtract the two equations

57x = 228

x = 4

A KID'S TICKET IS $4

Plug that in for x

4(3)+9y=75

12+9y=75

9y=63

y=7

AN ADULT'S TICKET IS $7

The exponential functions change is represented by decay and the percentage rate of decrease is 1.00619%.

Step-by-step explanation:

Step 1:

To determine if the function represents growth or decay, we substitute values to x.

If the values increase with an increase of x, it represents growth.

If the values decrease with an increase of x, it represents decay.

Step 2:

If [tex]x= 10,[/tex] [tex]y = 1,300 (\frac{1}{2})^{\frac{10}{69} } = 1,300 (0.9044) = 1,175.72.[/tex]

If [tex]x=11,[/tex][tex]y = 1,300 (\frac{1}{2})^{\frac{11}{69} } = 1,300 (0.8953) = 1,163.89.[/tex]

So as x increases the value of y decreases, so it represents decay.

Step 3:

The percentage rate of change is determined by dividing the difference of two consecutive values by the first value.

The percentage rate of change [tex]= \frac{y(x=11) - y(x=10)}{y(x=10)}.[/tex]

Substituting the values, we get

The percentage rate of change [tex]=\frac{1,175.72-1,163.89}{1,175.72}(100) = 1.00619\%[/tex].

As the values of y decrease with an increase in x, it is the percent decrease per unit.

Answer:

The exponential functions change is represented by decay and the percentage rate of decrease is 1.00619%.

Step-by-step explanation:

Because your Beautiful

Answer:

20

Step-by-step explanation:

Answer:

The height is 67 cm

Step-by-step explanation:

Remember that

[tex]1\ in=2.54\ cm[/tex]

we know that

The size of a TV is measured by its diagonal

Convert 60 inches to centimeters

[tex]60\ in=60(2.54)=152.4\ cm[/tex]

Applying the Pythagorean Theorem

[tex]D^2=H^2+W^2[/tex]

where

D is the diagonal

H is the height

W is the width

we have

[tex]D=152.4\ cm\\W=137\ cm[/tex]

substitute

[tex]152.4^2=H^2+137^2[/tex]

solve for H

[tex]H^2=152.4^2-137^2\\H^2=4,456.76\\H=67\ cm[/tex]

Answer:

B) 9/2

Step-by-step explanation:

4½ = 4 + ½

= 8/2 + 1/2 = 9/2

Answer: 9/2

Step-by-step explanation: To write a mixed number as an improper fraction, first multiply the denominator times the whole number, then add the numerator.

So here, we multiply the denominator, 2, times the whole number, 4, then we add the numerator, 1. So we have (2 × 4) + 1 of 8 + 1 which is 9.

Finally, we put our new number over our old denominator and we have our answer, 9/2. There is also an image provided showing my work.

So 4 and 1/2 can be rewritten as the improper fraction 9/2.

Answer:

33 1/5

Step-by-step explanation:

Turn 92/4 into a mixed number to make this problem easier, which equals 23. So the equation will look like: 23 + 10 + 4/10. Now add them all together and you will get 23 + 10 + 4/10 = 33 4/10. Now simplify 33 4/10 and you will get 33 1/5

Answer:

Step-by-step explanation:

92 /4 +10+4/10

=23+10+ 4/10

=33+4/10

=33+2/5

=167/5

Answer:

I = 2.04.

Step-by-step explanation:

From the question we are asked that what is the simple interest ,

$ 850 , 4% , 6 months

using the formula

simple interest = prt/100

I = interest

P= principal

R = rate.

our P = $850

R = 4% = 4/100 = 0.04

T = 6months

I = (850 × 0.04 × 6)/ 100

I = 204/100

I = 2.04.

Answer: Warming up and drinking enough water

Step-by-step explanation:

You should really ask yourself this, but you can talk about your perserverance, and not being afraid to try something new.

Answer:

the distribute property is basically taking the number outside the parenthesis and multiplying with the numbers inside each by each.

Step-by-step explanation:

20(30-15)

20×30= 600, and 20×15=300

finally you just use the new numbers and solve the solution which is 600-300. The answer is 300

Answer: 300

Step-by-step explanation: The distributive property tells us that when there's a number outside a set of parentheses, you can multiply it times each of the terms that are inside the set of parentheses and then add those products together.

So in this problem, we can multiply 20 (30) - 20 (15) which simplifies to 600 - 300 which is 300.

Step-by-step explanation:

The Mathematical transformation of the given statement would be:

[tex]2x - 3 = y[/tex]

Answer:

Length:15 cm

Width: 12 cm

Step-by-step explanation:

The complete question is

Amanda uses a rectangular canvas for a painting. The length is 6x - 3 centimeters. The width is 2x + 6 centimeters, and is 4/5 of the length. What are the dimensions of the canvas?

Let

L ----> the length of the rectangular canvas

W ---> the width of the rectangular canvas

we know that

The width is 4/5 of the length

so

[tex]W=\frac{4}{5}L[/tex] ----> equation A

substitute the given values in equation A

[tex](2x+6)=\frac{4}{5}(6x-3)[/tex]

solve for x

[tex]10x+30=24x-12\\24x-10x=30+12\\14x=42\\x=3[/tex]

Find the dimensions of the canvas

substitute the value of x

[tex]L=6(3)-3=15\ cm[/tex]

[tex]W=2(3)+6=12\ cm[/tex]

Answer:

see the explanation

Step-by-step explanation:

Let

x ----> the number of males on the elevator

y ----> the number of females on the elevator

we know that

The inequality that represent this situation is

[tex]180x+150y\leq 2,700[/tex]

The solution of the inequality is the shaded area below the solid line [tex]180x+150y=2,700[/tex]

The slope of the solid line is negative

The y-intercept of the solid line is (0,18)

The x-intercept of the solid line is (15,0)

see the attached figure

The solution is the triangular shaded area

The maximum number of females is 18 (when the number of males is zero)

The maximum number of males is 15 (when the number of females is zero)

[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&\$70000\\ P=\textit{original amount deposited}\\ r=rate\to 5.46\%\to \frac{5.46}{100}\dotfill &0.0546\\ t=years\dotfill &20 \end{cases} \\\\\\ 70000=Pe^{0.0546\cdot 20}\implies 70000=Pe^{1.092}\implies \cfrac{7000}{e^{1.092}}=P \\\\\\ 23488.13 \approx P~\hfill \stackrel{~\hfill \textit{the earned interest will be}}{70000-23488.13\implies 46511.87}[/tex]

Answer:

(x+11)(x-11)

Step-by-step explanation:

A ^2 - B ^2 =(A+B) (A-B).. (*)

x^2 - 121=

x^2 - 11^2=(*)

(x+11)(x-11)

Answer:15

Step-by-step explanation:

You have to divide the fractions so it 3/4÷1/10 then you can do keep change flip so the new equation is 3/4×10/1 or 3/4×10 then cross simply then get 3/2×5/1 to get 15/2 then use division to get 7 1/2

Amira's cat food will last 7.5 weeks, considering the cat eats 1/10 of a bag per week.

To find out how many weeks the cat food will last, you can divide the amount of food Amira has by the amount her cat eats per week.

First, let's calculate how much her cat eats per week:

1/10 of a bag per week.

Now, let's calculate how many weeks the food will last:

(3/4) / (1/10)

To divide fractions, you can multiply by the reciprocal of the divisor:

(3/4) * (10/1) = (3/4) * 10 = (3 * 10) / 4 = 30/4

Now, let's simplify 30/4:

30 divided by 4 equals 7 with a remainder of 2, so 30/4 = 7 + 2/4

Since 2/4 simplifies to 1/2, we get:

7 + 1/2 = 7.5

So, the cat food will last approximately 7.5 weeks.

Answer:

The scale factor is 1.25 and this represents an enlargement.

Step-by-step explanation:

As shown at the figure

The side length of the first hexagon = 5

The side length of the second hexagon  = 6.25

So, the scale factor = 6.25/5 = 1.25

and the second hexagon is larger than the first hexagon.

So,

The scale factor is 1.25 and this represents an enlargement.

Answer:

Step-by-step explanation:

Answer:

36 total muffins

Step-by-step explanation:

5*4=20

8*2=16

20+16=36

Hey there!

To write an expression to represent this:

We know that the four red plates each have 5 muffins, and 4 x 5 = 20.

So we can say 20 + 2y is the expression, because we add 20 to the muffins on the two yellow plates.

The number of muffins on each yellow plate is represented by the variable y.

If each yellow plate has 8 muffins, so y = 8, the expression will look like this:

20 + 2(8)

Multiply 2 x 8.

20 + 16

Add 20 + 16.

36

Belle baked 36 muffins total.

Hope this helps!

Answer:

a good estimate of the sum of 3 and 4/15 is 3 1/4.

Step-by-step explanation:

4/15 is close to 4/16, or 1/4, so a good estimate of the sum of 3 and 4/15 is

3 1/4.

The solution is 10x² + 7x - 1

Step-by-step explanation:

(8x² + 10x - 10) - (-2x² + 3x - 9) = 8x² + 10x - 10 + 2x² - 3x + 9

                                                 = 10x² + 7x - 1

Step-by-step explanation:

[tex]\huge\bold\purple{ 10x^2+7x-1 }[/tex]

Answer:

In this equation, when x = -8 , Y = 2

Answer check using either equation =

(1) 2x + y = -7y   ===> 2(-8) + 2 = -7(2)  ===>  -14 = -14

(2) Y= x + 10  ===>  2 = -8 + 10  ===> 2 = 2

Step-by-step explanation:

Assuming that you are looking for "x" and "y", Let

2x + y = -7y  ................. (1)

Y= x + 10     ................. (2)

From equation (2), Y = x + 10, therefore substitute for "Y" in equation (1) to get the value of "x"

2x + x + 10 = -7(x + 10)

3x + 10 = -7x - 70

gather like terms on each side.

3x + 7x = -70 - 10

10x = -80

divide through by 10

x = -8

Now substitute for "x" in equation (2)

Y = x + 10

Y = -8 + 10

Y = 2

Step-by-step explanation:

even number cards is 7 cards (2,4,6,8,10,12,14)

so probability is 7/15

The probability of pulling out an even number from a set of 15 numbers (1-15) is 8/15, but none of the provided multiple choice options match this answer.

The correct answer to this question could be found using the basic concepts of probability. Here, you have 15 cards in total. Among these 15, there are 8 even numbers: 2, 4, 6, 8, 10, 12, 14. The probability of choosing an even number (Event E) is thus Number of favourable outcomes (Event E) divided by Total number of outcomes.

This boils down to Probability (Event E) = Number of even numbers / Total numbers = 8 / 15. As such, none of the provided multiple choice answers are correct.

https://brainly.com/question/32117953

#SPJ5

Answer:

Step-by-step explanation:

Question

What fraction choose dogs?

Answer:

[tex]\frac {3}{8}[/tex]

Step-by-step explanation:

When 2 choose rabbits then to get the number that choose other anomals apart from dogs is given by getting the difference between total people and those who choose dogs. This then is expressed as 8-2=6 choose either cat or dogs. These six, half of them choose choose cats and the remaining choose dogs. Therefore 6/2=3

For 3 out of 8, this fraction is equal to

[tex]\frac {3}{8}[/tex]

Therefore, the fraction that choose dogs or cats is equal to

[tex]\frac {3}{8}[/tex]

Answer:

0.5972222 (2 repeats forever)

Step-by-step explanation:

Hope that helps!

Answer:

0.5972

Step-by-step explanation:

43 ÷ 72 = 0.59722222222....

This (2) is a repeating decimal.