Explain why the square root of a number is defined to be
equal to that number to the 1/2 power

Answers

Answer 1

9514 1404 393

Answer:

  (x^(1/2))^2 = x^(2/2) = x

Step-by-step explanation:

The square root of a number, when multiplied by itself, gives the original number.

  (√x)(√x) = x

The rule for exponents is that powers of the same base, when multiplied, will be the base to the sum of those powers.

  (a^b)(a^c) = a^(b+c)

Also, the first power of a number is that number itself.

__

  [tex]x^{\frac{1}{2}}\times x^{\frac{1}{2}}=x^{\frac{1}{2}+\frac{1}{2}}=x^1=x\\\\ \text{Compare to ...}\\\\ \sqrt{x}\times\sqrt{x}=x[/tex]

Answer 2

Answer:

Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.

Step-by-step explanation:

EDGE 2020-2021


Related Questions

i will mark brainliest to whoever shows their work

Answers

Answer: -280000

Step-by-step explanation: Remove parentheses: (a)=a   =12x10 4  - 4x10 5

12x10 4 = 120000

4x10 5=400000

=120000-400000

then subtract the numbers:120000-400000= -280000

Kris bought a 6 pack of water bottles for $4.79. Find the unit rate to the nearest cent.

Answers

Step-by-step explanation:

Kris bought a 6 pack water for =4.79$

So,

1 unit of water bottle =[tex]\tt{\dfrac{4.79}{6}=0.798333....=0.80\$ }[/tex] ⠀

PLZ HELP ANSWER!!!!!

Answers

Answer:

Step-by-step explanation:

so, i might be wrong but i hope this helps.

The slope will be the same for a straight line no matter which two points you pick as you know. All you need to do is to calculate the difference in the y coordinates of the 2 points and divide that by the difference of the x coordinates of the points(rise over run). That will give you the slope.

A fence surrounds two sides of the
backyard. The total length of the fence is 86
feet, with the longest portion measuring 51.5
feet. What is the length of the second side of
the fence?

Answers

Answer:34.5

Step-by-step explanation:

86-51.5= 34.5

A koala weighs 20 pounds. In her pouch, she carries her joey that weighs 20 ounces. What is the combined weight of the adult koala and her joey in ounces? (HELP FAST)

Answers

Answer:

kjgfdhsxfcgmnhmj,kouiyf

Step-by-step explanation:ugytfguilhyuyrtdyrjcgvh

Answer:

340 oz

Step-by-step explanation:

20 lb = 320 ounces

320 oz + 20 oz = 340 oz

Giving thanks, brainliest, or rating would be appreciated!

Which of the following proportions is true?
12 pizzas
18 people
9 pizzas
24 people
24 pizzas
48 people,
8. pizzas
20 people
20 pizzas
60 people
36 pizzas
96 people
48 pizzas
24 people
48 pizzas
60 people

Answers

12 pizzas hahaisjsjskdndhdu

Which statement is true about the numbers marked on this horizontal number line?

A.
0.25 -0.25
C.
-0.25 = 0.25
D.
-0.25 > 0.25

Answers

It is C because they are both equal in distance.

Answer:

B!

Step-by-step explanation:

The answer is B. id.k how to explain tho.

Suppose that $6500 is placed in an account that pays 17% interest compounded each year. Assume that no withdrawals are made from the account.

Answers

Answer: $7,605

Step-by-step explanation:

At the end of 1 years, the amount in the account will be:

= Principal * (1 + rate)^ no. of periods

= 6,500 * (1 + 17%)

= $7,605

What is 3 3/5 x (-8 1/3)=

Answers

Answer:

Step-by-step explanation:

Convert these mixed fractions to improper fractions.

3 3/5 = 18/5

-8 1/3 = -25/3

Now, it is easier to multiply them. Multiply the numerators and the denominators.

18  x   25   =   450

5          3           15

Simplify the final answer by dividing 450 ÷ 15, which is 30.

Melissa rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total of 12.

Answers

Answer:

1/36

Step-by-step explanation:

(6,6) is the only possible outcome of getting a total of 12

The sum of three consecutive EVEN integers is is 138. Find the smallest integer.

Answers

Step-by-step explanation:

Let x be the smallest even integer.

Then (x + 2) and (x + 4) are the other even integers.

We have x + (x + 2) + (x + 4) = 138.

=> 3x + 6 = 138

=> 3x = 132

=> x = 44.

Hence the smallest integer is 44.

please help will give u brainliest pls help me​

Answers

Answer:

19

Step-by-step explanation:

1/2*(5+x)*4=48

The formula for finding the area of a trapezium is:
Area= 1/2 x (a+b) x h
So the formula will work oppositely
4 cm is the height while 5 and the other 5 is sides.. sorry i can’t find the formula now

It’s a picture^^^^^^^^

Answers

Answer: F

Step-by-step explanation: 5+6+7x8=67

TWO wires support a young tree. The wires reach the tree 2 teet above the ground
and are each 3.5 feet from the base of the tree.

Answers

Answer: 5.74 Feet Hope this helps <3

Step-by-step explanation:

17/15 - 4/5 please answer

Answers

Answer:

1/3

Step-by-step explanation:

17/15-4/5

17/15-4*3/5*3

17/15-12/15

17-12/15

5/15

1/3

The equivalent value of the fraction is A = 1/3

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first fraction be p

Let the second fraction be q

Now , A = p - q

when the value of p = 17/15

And , when the value of q = 4/5

On simplifying the equation , we get

A = 17/15 - 4/5

So , the left hand side of the equation is equated to the right hand side by the value of ( 17/15 - 4/5 )

A = ( 17/15 - 4/5 )

Taking the LCM of the denominators of the fraction , we get

A = ( 17 - 12 ) / 15

On simplifying , we get

A = 5/15

A = 1/3

Therefore , the value of A = 1/3

Hence , the fraction is A = 1/3

To learn more about fractions click :

https://brainly.com/question/29766013

#SPJ6

is the equation a true statement when x equals -3 in other words is -3 a solution to the equation 6 x + 5 = 5x +8 + 2x explained? explain

Answers

Answer: Yes

Step-by-step explanation: bc 6(-3)+5=5(-3)+8+2(-3)

Becomes -18+5=-15+8+-6 which equals -13 on both sides meaning -3 is a solution

6x+5=5x+8+2x

6x+5=(5x+2x)+(8)(Combine Like Terms)

6x+5=7x+8

6x+5=7x+8

Step 2: Subtract 7x from both sides.

6x+5−7x=7x+8−7x

−x+5=8

Step 3: Subtract 5 from both sides.

−x+5−5=8−5

−x=3

Step 4: Divide both sides by -1.

−x

−1

=

3

−1

x=−3

Answer:

x=−3

Please help with this

Answers

Answer: 86

Step-by-step explanation:

Answer:

86

Step-by-step explanation:

I did this before I think it was 86 not sure

Helppppp!
Regular pentagon RSTUV has sides that are half the length of regular pentagon JKLMN,
What is the ratio of the perimeter of pentagon RSTUV to the perimeter of pentagon JKLMN?
A 1:2
B, 1:4
C, 1:5
D. 1:10
E, 1:25

Answers

Answer:

A, 1:2 ratio

Explanation:

Since 1 is half of 2, and the problem states that RSTUV is half of JKLMN, A is the correct ratio.

Answer:

c

Step-by-step explanation:

68/7 in fraction form

Answers

Answer:

9.71 in decimal form

Step-by-step explanation:

19. Malik is 10 years less than half his mother's age. If
Malik is 12 yrs. old, how old is his mother?

Answers

Answer:

34

Step-by-step explanation:

12+12=24

24+10=34

Answer:

If he is 12 his mom would be 22.

Step-by-step explanation:

12+10=22

       </3 PureBeauty

Tashi Beverages Ltd. company manufacture a coca
cola juice. In a manufacturing process, 3% of tools
produced turn out to be defective. Find the
probability that in a sample of 30 tools, at most 2
will be defective?

Answers

Answer:

you spam answered my question

Step-by-step explanation:

consider this revenge

find the equation of the straight line passing through the point (0,1) which is perpendicular to the line y=-2x+2

Answers

Answer:

y = 1/2x + 1

Step-by-step explanation:

In order to evaluate a slope that is perpendicular to the given equation, you need to find the opposite reciprocal of the original slope. This means you take the original slope, flip the numerator and the denominator, and change the sign in front.

-2 ⇒ 1/2

Next, we need to substitute the information given into the point-slope formula.

The point-slope formula is:

y - y₁ = m(x - x₁)

y - 1 = 1/2(x - 0)

y - 1 = 1/2x

y = 1/2x + 1

Therefore, the line perpendicular to y = -2x + 2 is y = 1/2x + 1.

What is the volume of the rectangular pyramid shown belown?

Answers

9514 1404 393

Answer:

  168 cubic inches

Step-by-step explanation:

The formula for the volume of a pyramid is ...

  V = (1/3)Bh

where B is the area of the base, and h is the height.

The base is a rectangle, whose are is given by the formula ...

  A = LW

  A = (8 in)(7 in) = 56 in²

Then the pyramid volume is ...

  V = (1/3)(56 in²)(9 in) = 168 in³

The volume of the pyramid is 168 cubic inches.

Please answer test!

Are these shapes similar?

Answers

yes they are! hope this helps :)

A certain city's power company charges their residents for electricity usage on a daily basis. There is a basic charge of 11.6 cents. For each day the first 10 kWh cost 4.59 cents per kWh and any additional kWhs are 9.71 per kWh. (A kWh, or kilowatt-hour, is a unit of energy.)

Complete the following table using the information provided above.

KWh 0 5 10 15 20
cost(dolllar)

KWh 25 30 35 40
cost(dolllar)

Answers

Answer:

Table of charges:

KWh                                                        0       5           10          15           20    

Basic charge (cents)                          11.60    11.60     11.60      11.60       11.60

Charge for first 10 kWh (4.59cents)    0     22.95   45.90    45.90     45.90

Additional usage above 10 kWh          0       0           0         48.55      97.10

(9.71 cents)

Total (cents)                                     11.60   34.55   57.50   106.05    154.60

cost (dollar)                                       0.12     0.35      0.58   1.06         1.55

KWh                                                           25           30          35           40

Basic charge (cents)                               11.60        11.60        11.60        11.60

Charge for first 10 kWh (4.59cents)    45.90      45.90       45.90      45.90

Additional usage above 10 kWh         145.65    194.20    242.75     291.30

(9.71 cents)

Total (cents)                                        203.15    251.70     300.25    348.80                                  

cost (dollar)                                         2.03        2.52          3.00       3.49

Step-by-step explanation:

a) Data:

Basic charge = 11.6 cents (0.116)

Charge for the first 10 kWh = 4.59 cents (0.0459)

Charge for additional usage above 10 kWh = 9.71 cents (0.0971)

b) Each kWh consumed or not attracts the basic charge of 11.6 cents.  The first 10 kWh consumed is billed at 4.59 cents, while the additional kWh consumed is charged at 9.71 cents.  The charge per consumption is first totaled in cents before being converted to dollars by dividing by 100.

4. Show that FD=1/2CB, FE - 1/2AB, and DE = 1/2AC.

Answers

can you take a picture of the problem?

If 1 inch on a map represents 20 miles, what is the mileage represented by 2.5 inches?
A 40 miles
B 10 miles
C 45 miles
D 50 miles

Answers

Answer:

50 miles(D)

Step-by-step explanation:

20 x 2.5

A closed-top cylindrical container is to have a volume of 250 in2. 250 , in squared , . What dimensions (radius and height) will minimize the surface area?

Answers

Answer:

radius r = 3.414 in

height h = 6.8275 in

Step-by-step explanation:

From the information given:

The volume V of a closed cylindrical container with its surface area can be expressed as follows:

[tex]V = \pi r^2 h[/tex]

[tex]S = 2 \pi rh + 2 \pi r^2[/tex]

Given that Volume V = 250 in²

Then;

[tex]\pi r^2h = 250 \\ \\ h = \dfrac{250}{\pi r^2}[/tex]

We also know that the cylinder contains top and bottom circle and the area is equal to πr²,

Hence, if we incorporate these areas in the total area of the cylinder.

Then;

[tex]S = 2\pi r h + 2 \pi r ^2[/tex]

[tex]S = 2\pi r (\dfrac{250}{\pi r^2}) + 2 \pi r ^2[/tex]

[tex]S = \dfrac{500}{r} + 2 \pi r ^2[/tex]

To find the minimum by determining the radius at which the surface by using the first-order derivative.

[tex]S' = 0[/tex]

[tex]- \dfrac{500}{r^2} + 4 \pi r = 0[/tex]

[tex]r^3 = \dfrac{500 }{4 \pi}[/tex]

[tex]r^3 = 39.789[/tex]

[tex]r =\sqrt[3]{39.789}[/tex]

r = 3.414 in

Using the second-order derivative of S to determine the area is maximum or minimum at the radius, we have:

[tex]S'' = - \dfrac{500(-2)}{r^3}+ 4 \pi[/tex]

[tex]S'' = \dfrac{1000}{r^3}+ 4 \pi[/tex]

Thus, the minimum surface area will be used because the second-derivative shows that the area function is higher than zero.

Thus, from [tex]h = \dfrac{250}{\pi r^2}[/tex]

[tex]h = \dfrac{250}{\pi (3.414) ^2}[/tex]

h = 6.8275 in

which graph shows a system of equations with infinitley many solutions

Answers

Answer:

where are the equation I don't see them

Which expression has the same value as the sum of 45 and 25?
14+10
5(9+5)
9(5+5)
5(8) +5(5)

Answers

5(9+5)
when you open the parentheses you get 45+25
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