A square solar panel has an area of 16 square feet. Write the area as a power. Then find the side lengths of the panel.

The area of the solar panel written as a power is ___
square feet.

The side lengths of the solar panel are ___
feet.

Answer:

1) [tex]\sqrt{-48}=4\sqrt{3} \ i[/tex]

2) [tex]\sqrt{-63}=3\sqrt{7} \ i[/tex]

3) [tex]\sqrt{-72}=6\sqrt{2} \ i[/tex]

4) [tex]\sqrt{-24}=4\sqrt{6} \ i[/tex]

5) [tex]\sqrt{-84}=2\sqrt{21} \ i[/tex]

6) [tex]\sqrt{-99}=3\sqrt{11} \ i[/tex]

Step-by-step explanation:

We need to simply the following :

Note: For all questions given we know that [tex]\sqrt{-1}=i[/tex] using it in all the given questions.

1) [tex]\sqrt{-48}[/tex]

Factors of 48 are: 2x2x2x2x3

[tex]\sqrt{-48}\\=\sqrt{48}\sqrt{-1} \\=\sqrt{2\times2\times2\times2\times3}\ i\\= \sqrt{2^2\times2^2\times3}\ i\\=2\times2\sqrt{3} \ i \\=4\sqrt{3} \ i[/tex]

2) [tex]\sqrt{-63}[/tex]

Factors of 63 are: 3x3x7

[tex]\sqrt{-63}\\=\sqrt{63}\sqrt{-1} \\=\sqrt{3\times3\times7}\ i\\= \sqrt{3^2\times7}\ i\\=3\sqrt{7} \ i[/tex]

3) [tex]\sqrt{-72}[/tex]

Factors of 72 are: 2x2x2x3x3

[tex]\sqrt{-72}\\=\sqrt{72}\sqrt{-1} \\=\sqrt{2\times2\times2\times3\times3}\ i\\= \sqrt{2^2\times3^2\times2}\ i\\=2\times3\sqrt{2} \ i \\=6\sqrt{2} \ i[/tex]

4) [tex]\sqrt{-24}[/tex]

Factors of 24 are: 2x2x2x3

[tex]\sqrt{-24}\\=\sqrt{24}\sqrt{-1} \\=\sqrt{2\times2\times2\times3}\ i\\= \sqrt{2^2\times2\times3}\ i\\=2\sqrt{2\times3} \ i \\=2\sqrt{6} \ i[/tex]

5) [tex]\sqrt{-84}[/tex]

Factors of 84 are: 2x2x3x7

[tex]\sqrt{-84}\\=\sqrt{84}\sqrt{-1} \\=\sqrt{2\times2\times3\times7}\ i\\= \sqrt{2^2\times3\times7}\ i\\=2\sqrt{21} \ i[/tex]

6) [tex]\sqrt{-99}\\[/tex]

Prime factors of 99 are: 3x3x11

[tex]\sqrt{-99}\\=\sqrt{99}\sqrt{-1} \\=\sqrt{3\times3\times11}\ i\\= \sqrt{3^2\times11}\ i\\=3\sqrt{11} \ i \\=3\sqrt{11} \ i[/tex]

Answer:

3

x

6

+

x

5

−

x

4

−

6

x

3

+

x

2

+

3

x

−

1

Step-by-step explanation:

simp

Answer: =3x^6 + x^5 − x^4 − 6x^3 + x^2 + 3x − 1

Step-by-step explanation:

Answer:

C Multiply/divide both sides by the same non-zero constant

Step-by-step explanation:

Given

[tex]A:\ 3(x + 2) = 18[/tex]

[tex]B:\ x + 2 = 6[/tex]

Required

How to get B from A

It can be seen that B is a factor of A.

And to get B from A, all you need to do is divide both sides of A by 3.

i.e.

[tex]\frac{3(x+2)}{3} = \frac{18}{3}[/tex]

[tex]x+2 = 6[/tex]

Hence, from the list of given options.

Option C answers the question because 3 is a non zero constant and both sides of the equation were divided by 3

Answer: 2

Step-by-step explanation:

Answer:

2 1/4

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

Let's solve the equation:

3x+12=4x+8

12=4x-3x+8

12=x+8

12-8=x

4=x

x=4

The way i got this answer was by solving the equation using the following steps. Since you're solving for one side and have two different equations, put an equal sign in between the two equations to get the equation set up above. Then you need to have the x variable on one side, instead of both sides, so you take 3x and subtract it from both sides, leaving x on one side, because 4x-3x is equal to 1x, or just x. Then we need to have what is not attached to a variable on the other side to make it easier to solve, so you would need to subtract 8 from both sides to get rid of the 8 on the side with the variable, because if you subtract 12 from both sides, it will just make it more confusing to solve, and then 12-8 is equal to 4, so you get x is equal to 4.

Answer:

6.4n - 12.8 - 31.36n

Step-by-step explanation:

multiply each term by -6.4

Answer:

x = - [tex]\frac{3}{28}[/tex]

Step-by-step explanation:

Given

- [tex]\frac{2}{3}[/tex] x + [tex]\frac{3}{7}[/tex] = [tex]\frac{1}{2}[/tex]

Multiply through by 42 ( the LCM of 3, 7 and 2 ) to clear the fractions

- 28x + 18 = 21 ( subtract 18 from both sides )

- 28x = 3 ( divide both sides by - 28 )

x = - [tex]\frac{3}{28}[/tex]

Answer:

Step-by-step explanation:

See a solution process below:

Explanation:

Step 1) Solve the second equation for

x

:

2

x

−

2

y

=

18

2

x

−

2

y

+

2

y

=

18

+

2

y

2

x

−

0

=

18

+

2

y

2

x

=

18

+

2

y

2

x

2

=

18

+

2

y

2

2

x

2

=

18

2

+

2

y

2

x

=

9

+

y

Step 2) Substitute

(

9

+

y

)

for

x

in the first equation and solve for

y

:

4

x

+

3

y

=

−

13

becomes:

4

(

9

+

y

)

+

3

y

=

−

13

(

4

×

9

)

+

(

4

×

y

)

+

3

y

=

−

13

36

+

4

y

+

3

y

=

−

13

36

+

(

4

+

3

)

y

=

−

13

36

+

7

y

=

−

13

−

36

+

36

+

7

y

=

−

36

−

13

0

+

7

y

=

−

49

7

y

=

−

49

7

y

7

=

−

49

7

7

y

7

=

−

7

y

=

−

7

Step 3) Substitute

−

7

for

y

in the solution to the second equation at the end of Step 1 and calculate

x

:

x

=

9

+

y

becomes:

x

=

9

−

7

x

=

2

The solution is:

x

=

2

and

y

=

−

7

or

(

2

,

−

7

)

The solution is:

x

=

2

and  

y

=

−

7

 or

(

2

,

−

7

)

Answer:

14 weeks. the equation would be a.

Step-by-step explanation:

120-50=70   70/5=14 it will take him 14 weeks to get 120 if he saves 5 a week on top of the additional 50 he already has.

Answer:

14 weeks

Step-by-step explanation:

Answer:

hi whats up

Step-by-step explanation:

Answer:

$4000

Step-by-step explanation:

$600 = .15x where x is the total monthly budget

x = $600/.15

x = $4000

Answer:

.725 or if its a whole with a decial 7.25 or 72.5

Step-by-step explanation:

Answer:

0.28

Step-by-step explanation:

i just took the assignment

i hope it helps :3

Given:

Principal = $3500

Rate of simple interest = 3.65% = 0.0365

Time = 4 year

To find:

The amount.

Solution:

The formula for simple interest is

[tex]I=P\times r\times t[/tex]

where, P is principle, r is rate of interest and t is time in years.

Substituting P=3500, r=0.0365 and t=4, we get

[tex]I=3500\times 0.0365\times 4[/tex]

[tex]I=511[/tex]

Now,

[tex]Amount=P+I[/tex]

[tex]Amount=3500+511[/tex]

[tex]Amount=4011[/tex]

Therefore, the amount after 4 years in pahola's account is $4011.

Answer:

Net Area = 168

Step-by-step explanation:

See attachment for complete question

I'll make reference to the attachment, when needed.

The shapes that make up the net are labelled 1 to 5.

So, to calculate the surface area of the net, we simply calculate the surface area of each label.

Label 1: Rectangle

Area = Length * Width

Area = 10 * 5

Area = 50

Label 2: Rectangle

Area = Length * Width

Area = 8 * 5

Area = 40

Label 3: Rectangle

Area = Length * Width

Area = 6 * 5

Area = 30

Label 4: Triangle

Area = ½Base * Height

Base = 6 and Height = 8

So:

Area = ½ * 6 * 8

Area = 24

Label 5: Triangle

Area = ½Base * Height

Base = 6 and Height = 8

So:

Area = ½ * 6 * 8

Area = 24

So, the net area is the summation of the calculated areas of label 1 to 5

Net Area = 50 + 40 + 30 + 24 + 24

Net Area = 168

Answer:

36 for $8.00

Step-by-step explanation:

Answer:l

Step-by-step explanation:

This question is incomplete

Complete Question

Leah is creating satin bows for a wedding. From a 15-meter-long ribbon, she first cuts a piece 3 4/9 meters long. Then she cuts a piece 6 5/9 meters long from the remaining ribbon. How much ribbon does Leah have left?

A.) -12 meters

B.) -5 meters

C.) 5 meters

D.) 12 meters

Answer:

C.) 5 meters

Step-by-step explanation:

From a 15-meter-long ribbon, she first cuts a piece 3 4/9 meters long. Then she cuts a piece 6 5/9 meters long from the remaining ribbon.

Step 1

3 4/9 meters + 6 5/9 meters

Least Common Denominator = 9

(3+ 6) + [ 4/9 + 5/9)

9 + [4 + 5/9]

9 + [9/9]

9 + 1

= 10 meters

This means, the total number of ribbons cut is 10 meters

The amount of ribbon Leah has left =

Initial length of ribbon - Amount of ribbon cut

= 15 meters - 10 meters

= 5 meters

Hence, Leah has 5 meters long of ribbon left

Answer:

the answer is 5 meters left

Step-by-step explanation:

Answer:

I think its 33.333333333333%

Step-by-step explanation:

Answer: 1.37 miles

Step-by-step explanation:

13.7=100%

13.7/10=1.37=10%=1/10

Answer:

The philosophy of life would include things like how you decide what is “good” and “bad”, what “success” means, what your “purpose” in life is (including if you don't think there is a purpose), whether there is a God, how we should treat each other, etc

Step-by-step explanation:

Answer:

No, he is not financially responsible

Step-by-step explanation:

Given that:

Amount saved for tractor purchase = $1325

Original cost of tractor = $1600

Amount spent on bungee jumping = $360

Discounted price of tractor :

$1600 - (1600 * 0.2) = $1280

Saved amount left after bungee jumping :

$1325 - $360 = $965

The saved amount had exceeded the discounted price, hence, the discount served as an opportunity to make the purchase, However, spending $360 from the saved amount meant that the amount left could not afford the tractor despite the discount. Hence, Missing out on such opportunity due to jumping shows lack of financial responsibility.

Answer:

y - 12 = -3 (x - 6)

y = -3x +6

6 minutes

The delivery times decreased by 3 minutes each day

Step-by-step explanation:

Point Slope:

Let's pick a point first (6,12)

The Slope of the line is -3

y - y1 = m (x - x1)

y - 12 = -3 (x - 6)

Slope-intercept:

The y-intercept is not shown on the graph but we can turn the point slope form of the equation to slope-intercept

y - 12 = -3x + 18

y = -3x +6

y-intercept:

y = mx + b

y = -3x + 6

m = 6

6 minutes

Slope:

we already know the slope is 3

The delivery times decreased by 3 minutes each day

Answer:

see explanation

Step-by-step explanation:

The angle at the circumference b , is half the angle subtended at the centre by the arc XZ, that is

b = 0.5 × 72 = 36

OZ and OX are congruent ( both radii of the circle )

Thus Δ OXZ is isosceles with base angles congruent, thus

a = [tex]\frac{180-72}{2}[/tex] = [tex]\frac{108}{2}[/tex] = 54

∠ XZY = 90° ( angle in a semicircle is right )

Answer:

28

Step-by-step explanation:

Answer: 28

Step-by-step explanation:Use the values of a b and c for the discrimiant

Answer:

Step-by-step explanation:

1. Solution for 3(6a)a=3 equation:

Simplifying

3(6a) * a = 3

Remove parenthesis around (6a)

3 * 6a * a = 3

Multiply 3 * 6

18a * a = 3

Multiply a * a

18a2 = 3

Solving

18a2 = 3

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Divide each side by '18'.

a2 = 0.1666666667

Simplifying

a2 = 0.1666666667

Take the square root of each side:

a = {-0.408248291, 0.408248291}

2.Solution for 5d(4)d=-2 equation:

Simplifying

5d(4) * d = -2

Reorder the terms for easier multiplication:

5 * 4d * d = -2

Multiply 5 * 4

20d * d = -2

Multiply d * d

20d2 = -2

Solving

20d2 = -2

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Divide each side by '20'.

d2 = -0.1

Simplifying

d2 = -0.1

Reorder the terms:

0.1 + d2 = -0.1 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0

0.1 + d2 = 0.0