prove by factorization √16×81=√16×√81

Answers

Answer 1

Answer:

√16×81 = 4×9 or √1296 = 36

√16×√81 = 4×9 = 36

Step-by-step explanation:

√81×16

We simplify 81 and 16 by prime factorisation (expressing a number as a product of its prime factors).

√81 = √3×3×3×3 = √9×9 = √9² = 9

√16 = √2×2×2×2 = √4×4 = √4² = 4


Related Questions

76%
Here are ten numbers:
3 7 2 4 7 5 7 1 8 8
a) Write down the mode.
b)
Work out the median.
c)
Calculate the mean.
d)
What is the range?​

Answers

Answer:

Mode = 7

Median = 6

Mean = 5.2

Range = 7

Step-by-step explanation:

Mode:

The most repeated number is 7 (thrice).

Median:

First, arrange them in order.

1, 2, 3, 4, 5, 7, 7, 7, 8, 8

The two middle numbers are 5 and 7. Find their average.

(5 + 7)/2 = 6

Mean:

(3+7+2+4+7+5+7+1+8+8)/10 = 5.2

Range:

Largest number - smallest number

8 - 1 = 7

Hope this helps!

Write and graph an inequality to represent each situation.
The stock is worth at least $3.5

Answers

Answer:

Step-by-step explanation:

Let stock worth be x.

The inequality will be x ≥ 3.5

The graph will be a number line with numbers 1, 2, 3 , 4 , 5 , 6 . . .

Then darken a small circle at 3.5 and darken the line

moving towards 4, 5 , 6 . . .  and finally end with an arrow mark. showing it goes to ∞  

Identify complementary angles in the given figure.

Answers

Answer:

<6 and <4

Step-by-step explanation:

Complemetary angles are angles that their measure add up to 90 degrees

the angles meet this requirment in this image are angle <6 and angle <4

What is the equation of a circle with radius 4 and center (0,8)?

Answers

The equation of circle with the center at (h,k) is:

[tex] \large \boxed{ {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} }[/tex]

r stands for radius. Therefore r^2 = diameter or 2×radius.

The question has already given the information we need, which are:

radius = 4the center at (0,8)

Since the center is (h,k) - therefore the center is at h = 0 and k = 8 making it (h,k) = (0,8).

Substitute the values in the equation:

[tex] \large{ {(x - 0)}^{2} + {(y - 8)}^{2} = {4}^{2} }[/tex]

Simplify to the simplest form

[tex] \large \boxed{ {x}^{2} + {(y - 8)}^{2} = 16} \: \: \: \: \huge{ \green{\checkmark}}[/tex]

Answer

The equation of a circle is x^2+(y-8)^2 = 16

Choose all of the symbols that make the following sentence true.


4 ^0 ___ 5 ^-1


=

<







>

Answers

Answer:

≠ and >

Step-by-step explanation:

_________________

Keiko brought $51.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1/6 as much as the sketchbook, and the sketchbook cost 3/4 the cost of the paint set. Keiko had $3.00 left over after buying these items.
What was the cost of each item?

Answers

Step-by-step explanation:

[(1/6 × 3/4) + (3/4) + 1] n = 51.75 -3

(⅛ + ¾ +1)n = 48.75

15/8 n = 48.75

1.875 n = 48.75

n = 48.75/1.875

n = 26

so, the cost of :

the brush = ⅛×26 = $ 3.25

the sketchbook = ¾×26 = $ 19.5

the pain set = $ 26

What is the solution to this system of equations?

Answers

Answer:

the equation has no solution

i need help with this one plz! (marking BRAINLIST) :) ​

Answers

Answer: (a) = 110 degrees, (b) = 8

If I understand the picture correctly, (a) wants you to find the angle K. It first shows us that both J to K, and L to K are equal in length of 11, thus there is no deviation in angle 35 degrees with L (so they both equal each other). Therefore, the angle K will equal 180 degrees subtracted by the sum of J and L, which is 110 degrees.

For (b), it appears that all the angles have the same singular mark at the edges, so all sides will equal 8.

I hope this helped!

Find the simple interest earned, to the nearest cent, for the principal, interest rate, and time.
$650, 5%, 1 year
Help

Answers

Answer:

32.5

Step-by-step explanation:

I=Prt

I= 650*0.05*1

I=32.5

find the value of variable x

Answers

Answer:

[tex]x=33[/tex]

Step-by-step explanation:

Since all three angles marked form one side of a line, they must add up to 180 degrees. Therefore, we have the following equation:

[tex]90+(x+1)+(3x-43)=180,\\x+1+3x-43=90,\\4x-42=90,\\4x=132,\\x=\boxed{33}[/tex]

Answer:

x=33

Step-by-step explanation:

The three angles form a straight line, which is 180 degrees

90+ x+1 + 3x-43 = 180

Combine like terms

4x+48 = 180

Subtract 48 from each side

4x+48-48 = 180-48

4x = 132

Divide by 4

4x/4 = 132/4

x=33

si se vendieron 8 refrescos y cada uno tiene un costo de $9.50 ¿cuánto dinero colectó
con esa venta?​

Answers

Colecto $76 en total

A car that is normally $4200 is on sale for 80% of its original cost.
what is the sale price of the car? ​

Answers

Answer:

$3360

Step-by-step explanation:

4200(.80) = 3360

anything less than 1.00 will be a decreasing amount, so i just took the 80% and put it as a decimal and multiplied to find the current cost of the car

i need help with this one plz! (marking BRAINLIST) :)​

Answers

Answer:

Sinx = c/b

cosx = a/b

tanx = c/a

Step-by-step explanation:

B is hypotenuse, a is adjacent, c is opposite of angle x.

Sin = opposite/hypotenuse

cos = adjacent/hypotenuse

tan = opposite/adjacent

Evan invested $800 in an account that pays 3.25% interest compounded annually.
Assuming no deposits or withdrawals are made, find how much money Evan would
have in the account 12 years after his initial investment. Round to the nearest tenth
(if necessary).

Answers

Answer:

Evans would have $852.8

Step-by-step explanation:

Given

[tex]PV = \$800[/tex]

[tex]r = 3.25\%[/tex]

[tex]t = 2[/tex]

[tex]n = 1[/tex] --- annually'

Required

The future value

This is calculated using:

[tex]FV = PV*(1 + \frac{r}{n})^{nt[/tex]

So, we have:

[tex]FV = 800 * (1 + 3.25\%/1)^{2*1}[/tex]

[tex]FV = 800 * (1 + 3.25\%)^{2}[/tex]

[tex]FV = 800 * (1 + 0.0325)^{2}[/tex]

[tex]FV = 800 * (1 .0325)^2[/tex]

[tex]FV = 852.845[/tex]

[tex]FV = 852.8[/tex]

FV =

A table cost $ 495.00 There is a 9% tax. What is the final price?

Answers

Answer:

i also need help with these one please help

Step-by-step explanation:

Answer:

$539.55

Step-by-step explanation:

help fast The graphs below have the same shape. What is the equation of the red
graph?

no links plz​

Answers

B because the graph just shifted down 3

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]B)\text{ } G(x)=x^3-5[/tex]

»»————- ★ ————-««  

Here’s why:  

According to the question provided, functions 'f' and 'g' are the same shape. The parent function 'f' is shifted 5 units down to create function 'g'.

⸻⸻⸻⸻

[tex]\boxed{g(x)=x^3-5}[/tex]

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

Identify horizontal or vertical compression stretch of the function g(x) = 6x

Answers

Answer:

dhjfydhftb7cuvdihcdjxuihy

You want to deposit $1000 in a savings account for 3 years. One bank
adds a $100 bonus to your principal and offers a 2% simple annual
interest rate. Another bank does not add a bonus, but offers 6% simple
interest per year. Which bank should you choose? Explain.

Answers

Answer:

2nd bank

Step-by-step explanation:

bank one:10*2=(20*3=60)

                $1000+$100+$60=$1160

                total after 3 years = $1160

bank two:$10*6=(60*3=180)

                 $1000+$180=$1180

                total after 3 years = $1180

If JK is formed by J(-7,-8) & K(1,4), determine if L(-9,5), lies on the perpendicular bisector.


Part A: What elements do you you need to know to confirm that Point L is on the perpendicular bisector of JK?

Part B: Find the elements you described in Part A , explain your work.

Part C: Verify if Point L is on the perpendicular bisector of JK. Justify your conclusion.

Answers

Answer:

Following are the responses to the given question:

Step-by-step explanation:

For point a:

Bisector Theorem: When a point has been on the perpendicular bisector of a segment, the perpendicular bisector is equivalent towards the segment endpoints. They understand that conversation also valid in addition to the Theorem including its perpendicular bisector. So the distance b/w L and J, L, and k must be found. Examine it then.

For point b:

Calculating the distance among two point:

[tex]d_0 = \sqrt{(x_1-x_2)^2 +(y_1-y_2)^2}[/tex]

Calculating the distance among J and L

[tex]d_1 = \sqrt{((-9)-(-7))^2 + (5)-(-8))^2}[/tex]

    [tex]=\sqrt{(-2)^2+(13)^2}\\\\ = \sqrt{173}[/tex]

Calculating the distance among  K and L  

[tex]d_2 = \sqrt{((-9)-(1))^2 + (5)-(4))^2}[/tex]

    [tex]=\sqrt{(10)^2+(1)^2}\\ = \sqrt{101}[/tex]

For point c:

As these two distances are not equal, L doesn't really lie on the JK bisector.

You have decided after graduating from an institution beyond high school, you want to live on your own. You have entered a career with a net income of $4785 per month. You search the local area finding an amazing deal at Succex Apartment Homes in Grapevine, Texas. Floor plan C fits within your budget.

The apartment is empty when you move in, so you will have to decorate making some adjustments on your financial budget to afford a place to stay. A floor plan will be provided to you.


What is the area of the Masters Bedroom? *


16.51 square meters

19.11 square meters

14.04 square meters

29.4 square meters

Answers

Answer:

16.51 square meters.

Step-by-step explanation:

The area of the bedroom can be determine by the formula:

Area = Length * Width

Length of the room is 4.3 meters while width of the master bedroom is 2.4 meters. The length of the closet is 0.6 meters and width is 1.5 meters. The area can be determined by:

2.4 - 1.5 = 0.9 meters

4.3 - 0.6 = 3.7 meters

Area = 3.7 * 0.9

= 3.3 meters.

Conversion from meters to square meters = 3.3^2

Area = 16.51 square meters.

Hector has 10 cups of flour which equation shows how to determine the number of 2/5 of a cup servings there are in the 10 cups of flour?

Answers

Answer:

10 divided by two-fifths = 25.

Heeeeeeeeeeelppppppppppppppppppp

Answers

I wrote all the solution and work you need and the answer turned out to be

A)

So please brainliest my answer I would really appreciate it and best of wishes!!

When do creative people get their best ideas? USA Today did a survey of 966 inventors (who hold U.S. patents) and obtained the following information.

Time of Day When Best Ideas Occur
Time Number of Inventors
6 A.M.-12 noon 271
12 noon-6 P.M. 123
6 P.M.-12 midnight 327
12 midnight-6 A.M. 245

Required:
a. Assuming that the time interval includes the left limit and all the times up to but not including the right limit, estimate the probability that an inventor has a best idea during each time interval: from 6 A.M. to 12 noon, from 12 noon to 6 P.M., from 6 P.M. to 12 midnight, from 12 midnight to 6 A.M.
b. Do the probabilities add up to 1? Why should they?

Answers

Answer:

a.

0.2805 = 28.05% probability that an inventor has a best idea from 6 A.M. to 12 noon.

0.1273 = 12.73% probability that an inventor has a best idea from 12 noon to 6 P.M.

0.3385 = 33.85% probability that an inventor has a best idea from 6 P.M. to 12 midnight.

0.2536 = 25.36% probability that an inventor has a best idea from 12 midnight to 6 A.M.

b. They do, as the the sum of the probabilities of all possible outcomes should be 1, as is in this question.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the total outcomes.

We have:

A total of 966 inventors.

Question a:

6 A.M. to 12 noon

271 out of 966, so:

[tex]p = \frac{271}{966} = 0.2805[/tex]

0.2805 = 28.05% probability that an inventor has a best idea from 6 A.M. to 12 noon.

12 noon to 6 P.M.

123 out of 966, so:

[tex]p = \frac{123}{966} = 0.1273[/tex]

0.1273 = 12.73% probability that an inventor has a best idea from 12 noon to 6 P.M.

6 P.M. to 12 midnight

327 out of 966, so:

[tex]p = \frac{327}{966} = 0.3385[/tex]

0.3385 = 33.85% probability that an inventor has a best idea from 6 P.M. to 12 midnight.

12 midnight to 6 A.M.

245 out of 966. So

[tex]p = \frac{245}{966} = 0.2536[/tex]

0.2536 = 25.36% probability that an inventor has a best idea from 12 midnight to 6 A.M.

b. Do the probabilities add up to 1? Why should they?

0.2805 + 0.1273 + 0.3385 + 0.2536 = 1

They do, as the the sum of the probabilities of all possible outcomes should be 1, as is in this question.

A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow.
Age Group
Hours of Sleep 39 or younger 40 or older
Fewer than 6 38 36
6 to 6.9 61 58
7 to 7.9 76 74
8 or more 65 92
(a) Conduct a test of independence to determine whether hours of sleep are independent of age.
(b) What is your estimate of the percentages of individuals who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more per night?

Answers

Answer:

Sleep hours per night is independent.

Step-by-step explanation:

Given the data:

Hours of Sleep 39 or younger 40 or older

> 6 _____38 36

6 to 6.9 _ 61 58

7 to 7.9 __76 74

8 or more 65 92

The Chisquare statistic is to be used to perform the analysis :

The hypothesis :

H0: Sleep hours per night is independent

H1: Sleep hours per night is not independent

χ² = (observed - Expected)² / Expected

To save computation time. We could use a Chisquare calculator to perform the analysis :

The test statistic = 4.0061

The degree of freedom = (row - 1) * (column - 1)

Degree of freedom = (4-1)*(2-1) = 3*1 = 3

The Pvalue = 0.261

Since, Pvalue > α ; We fail to reject the H0 ;and conclude that sleep hours per night is independent.

______________total ___%

> 6 _____38 36__ 74 __ 14.8

6 to 6.9 _ 61 58 __ 119 __23.8

7 to 7.9 __76 74___150__30

8 or more 65 92___157__31.4

_______240 _260__500_100

01 1 point If a customer spends more than $20, he receives a 10% discount on his total bill: What does a customer whose bill is $80 /pay?​

Answers

Answer:

try 40%

Step-by-step explanation:

This year, a small business had a total revenue of
$
62
,
100.
If this is
35
%
more than their total revenue from the previous year, what was the total revenue the previous year?

Answers

Answer:

21,735

Step-by-step explanation:

Find the area of the sector in
terms of pi.
90°
24
Area = [?]
Enter

Answers

Step-by-step explanation:

area of a circle is r x r x pi

so one quarter of it us r x r x pi /4

What is the nearest quarter hour to 12.09

Answers

Answer:

I think 12:00

Step-by-step explanation:

please thank my answer

Answer:

I think 12:15

there only 6 minutes to 12:15. But at 12:00 there are 9 minutes

PLZ HELP ASAP


The white triangle drawn on the road sign in the picture has a height of 8 and a base of 5 which formula would be correct to find the area of this triangle


1) A= 1/2 (8) (5)
2) A=2(8)+2(5)
3) A=1/2(8+8)(5+5)
4) A=2(8)(8)+2(5)(5)

Answers

Answer:

[tex]\text{1) }\frac{1}{2}(8)(5)[/tex]

Step-by-step explanation:

The area of a triangle with base [tex]b[/tex] and height [tex]h[/tex] is equal to [tex]A=\frac{1}{2}bh[/tex]. Since we're given a base of 5 and a height of 8, the area is given by [tex]\boxed{\text{1) }\frac{1}{2}(8)(5)}[/tex].


Can someone please help me with this

Answers

Answer:

y = 4x

y = -1/3 × x + 6

y = x + 1

y = 1

y = 5x

Step-by-step explanation:

the slope of a line is the factor of x in the equation representing the ratio of y/x. it stands for the number of units y changes, when x changes by another number of units.

like the factor 4 tells us that when x changes by 1, then y changes by 4.

a line parallel to another line means their slopes are identical (otherwise they could not be parallel).

the slope of a perpendicular line (cutting the other line in a 90 degree angle) is simply reversing y and x in the slope ratio. so, a slope of 4 (4/1) would simply turn into 1/4.

now the 5 tasks are easy, right ?

A y=4x-1, B y=4x + c

and because B passes through the origin = (0,0),

c is 0 (0=4×0 + c = c)

B y = 4x

A y=-3x+1, B y=-1/3 × x + c

and B passes through (12,2), 2 = -1/3 × 12 + c = -4 + c,

c = 2 + 4 = 6

B y = -1/3 × x + 6

A y = ax + c for (5,6) and (7,8), B is identical

6 = a×5 + c => c = 6 - a×5

8 = a×7 + c => 8 = a×7 + 6 - a×5 = a×2 + 6

=> a×2 = 8-6 = 2

=> a = 1, c = 6 - 1×5 = 1

=> A and B y = x + 1

A is vertical. B is perpendicular to it. perpendicular to vertical is horizontal. so, B is a flat line. which means y is a constant value (the same value for whatever value of x you want to use). so it goes flat in parallel to the x-axis through what value of y ? the point (4,1) tells us that y=1

and that is the equation for B

A 15x -3y = -6 => 3y = 15x + 6 => y = 5x + 2

B is parallel, so y = 5x + c

and B passes through (4,20), 20 = 5 × 4 + c = 20 + c,

c = 20 - 20 = 0

B y = 5x

Other Questions
A mother brings her 15-month-old daughter to your office for evaluation of a rash and fever. She says the rash started one day and the fever developed the next day. Her daughter has had all of her vaccinations up to 10 months. The mother sheepishly admits that she hasn't had time to bring her daughter in since her 10-month check-up. On examination you see a mildly sick- appearing toddler with a 102-degree temperature. Looking at her skin you see at least 100 of a variety of papules, vesicles, and ulcers in different stages of development.What illness prevented by proper vaccination does this toddler have?A) Varicella (chickenpox)B) MeaslesC) Smallpox Which substance would require the most heat to produce a temperature change liquid water or gaseous water vapor? Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 247 feet and a standard deviation of 41 feet. Use your graphing calculator to answer the following questions. Write your answers in percent form. Round your answers to the nearest tenth of a percent. a) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 216 feet please help me immediately What is the height of a rectangular prism with a volume of 60 cubic feet, a length of 3 ft and width 4 ft? Fifteen identical particles have various speeds: one has a speed of 2.00 m/s, two have speeds of 3.00 m/s, three have speeds of 5.00 m/s, four have speeds of 8.00 m/s, three have speeds of 9.00 m/s, and two have speeds of 15.0 m/s. Find: a. the average speedb. the rms speedc. the most probable speed of these particles. PLEASE HELP!!!!!!!!!!!!!!!!!! the ratio of the ages of Charlie and Kelvin is 2:3 if Charlie is 8 year old ,how old is Kelvin If capital rents for $25 per unit per hour, labor can be hired for $9 per unit per hour, the level of total factor productivity is normalized to 1, and the firm is minimizing costs.(a) Determine whether the production function exhibits diminishing marginal returns to each input. A baseball diamond is a square that measures 90 feet on each side. How far does the third baseman have to throw the ball to reach first base? Please help!! I dont need the answer i just need explaining on how to do this!!!! A researcher wants to assess the difficulty of test questions in an algebra class at a high school. To test it, he takes one question from each test, each week in the first semester. In statistical language, each test question is part of the: the cost price of a refrigerator is $1850.00. A buyer who is given a discount of 5% for cash purchase will pay? 3 upper M n upper O subscript 2 (s) plus 4 upper A l (s) right arrow 2 upper A l subscript 2 upper O subscript 3 (g) plus 3 upper M n (s). What is the enthalpy of the reaction? Sarah and Kell have stickers in a ratio of 2:4.Together they have a total of 48 stickers. Usethe tape diagram to represent how manystickers each girl has.DirectiequestiFor afoSarahKelly IN A FEW PARAGRAPHS SUMMARIZE THE WAR IN THE PACIFIC VS. JAPAN.DAHACHASE. CAN SOMEONE PLEASE HELP Question 2 (Essay Worth 10 points)(02.03, 02.05 MC)The linear function f(x) = 0.5x + 80 represents the average test score in your math class, where x is the number of the test taken. The linear function g(x) represents the averagetest score in your science class, where x is the number of the test taken.x g(x)1 812 833 85Part A: Determine the test average for your math class after completing test 2. (2 points)Part B: Determine the test average for your science class after the completing test 2. (2 points)Part C: Which class had a higher average after completing test 4? Show work to support your answer. (6 points) Choose the best selection for thequadrilateral with vertices at thefollowing points:(-5,0), (0,4), (5,0), (0,-4)Hint: Start by graphing the points.Distance Formula: d= (x2 x1)2 + (72 - y)2A. RectangleB. SquareC. RhombusD. Trapezoid The Camden street Debate team is planning a trip to Florida. The trip cost $17,250for 15 students to attend. How much is the cost per student? Write a equation tohelp you solve the model. Garcia Company issues 11.5%, 15-year bonds with a par value of $450,000 and semiannual interest payments. On the issue date, the annual market rate for these bonds is 9.5%, which implies a selling price of 113 3/4.Required:Prepare the journal entry for the issuance of these bonds for cash on January 1.