All categories

3 years ago

Negative exponents 3-3 x 3-2

Mathematics

1 answer:

patriot [66]3 years ago

4 0

Answer:

3^-5

Step-by-step explanation:

Whenever you multiply exponents, you add the values. Negative two plus negative three results in an answer of negative five. This will be the power. You will end up with 3^-5 as your answer.

You might be interested in

Which of these systems of linear equations has no solution? 2 x + 8 y = 15. 4 x + 16 y = 30. 2 x minus y = 18. 4 x + 2 y = 38. 4

kvasek [131]

Answer:

The correct answer is:

$4 x -3 y = 16$ and

$8 x -6 y = 34$ are the equations that have no solution.

Step-by-step explanation:

First of all, let us have a look at the rules for a pair of lines, that have solution or no solution.

Let the equations be:

$a_1x+b_1y+c_1=0$ and

$a_2x+b_2y+c_2=0$

1. There exists exactly one solution:

$\dfrac{a_1}{a_2}\neq\dfrac{b_1}{b_2}$

2. There exists infinitely many solutions i.e. lines are identical.

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$

3. There exists No solutions i.e. lines are parallel and will never intersect.

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}$

Now, let us have a look at the given pair of lines:

Option a)

$2 x + 8 y = 15\\4 x + 16 y = 30.$

The ratio:

$\dfrac{2}{4}=\dfrac{8}{16}=\dfrac{15}{30} = \dfrac{1}{2}$

Hence, the lines are identical, infinite solutions.

Option b)

$2 x - y = 18\\4 x + 2 y = 38$

The ratio:

$\dfrac{2}{4}\neq \dfrac{-1}{2}$

Hence, exactly one solution.

Option c)

$4 x + 7 y = 17\\8 x -14 y = 36$

The ratio:

$\dfrac{4}{8}\neq \dfrac{-7}{14}\\\dfrac{1}{2}\neq \dfrac{-1}{2}$

Hence, exactly one solution.

Option d)

$4 x - 3 y = 16\\8 x - 6 y = 34.$

The ratio:

$\dfrac{4}{8}= \dfrac{-3}{-6}\neq\dfrac{16}{34}\\\Rightarrow \dfrac{1}{2}= \dfrac{1}{2}\neq\dfrac{8}{17}$

Hence, There is no solution.

The correct answer is:

$4 x -3 y = 16$ and

$8 x -6 y = 34$ are the equations that have no solution.

8 0

3 years ago

Read 2 more answers

The rectangular rug in Marcia's living room measures 12 feet by 109 inches. What is the rug's area in square feet?

Marrrta [24]

Answer:

109 square feet.

Step-by-step explanation:

109 in: = 109/12 = 9.0833333.... = 9 5/60 = (540+5)/60 = 545/60

Area = L*w

L = 545/60 feet

W = 12 feet

Area = 545/60 * 12

Area = 545*12/60

Area = 545 /5 = 109 square feet.

3 0

3 years ago

Expression is equivalent question

kiruha [24]

Answer:

-40+44i

Step-by-step explanation:

4(-10+11i) = -40+44i

hope its clear

7 0

3 years ago

A rectangular box is to have a square base and a volume of 12 ft3. If the material for the base costs $0.17/ft2, the material fo

katen-ka-za [31]

Answer:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

Step-by-step explanation:

Let the dimensions of the box be x, y and z

The rectangular box has a square base.

Therefore, Volume of the box $V=x^2z$

Volume of the box $=12 ft^3\\$

$Therefore, x^2z=12\\z=\frac{12}{x^2}$

The material for the base costs $\$0.17/ft^2$ , the material for the sides costs $\$0.10/ft^2$ , and the material for the top costs $\$0.13/ft^2$ .

Area of the base $=x^2$

Cost of the Base $=\$0.17x^2$

Area of the sides $=4xz$

Cost of the sides= $=\$0.10(4xz)$

Area of the Top $=x^2$

Cost of the Base $=\$0.13x^2$

Total Cost, $C(x,z) =0.17x^2+0.13x^2+0.10(4xz)$

Substituting $z=\frac{12}{x^2}$

$C(x) =0.17x^2+0.13x^2+0.10(4x)(\frac{12}{x^2})\\C(x)=0.3x^2+\frac{4.8}{x} \\C(x)=\dfrac{0.3x^3+4.8}{x}$

To minimize C(x), we solve for the derivative and obtain its critical point

$C'(x)=\dfrac{0.6x^3-4.8}{x^2}\\Setting \:C'(x)=0\\0.6x^3-4.8=0\\0.6x^3=4.8\\x^3=4.8\div 0.6\\x^3=8\\x=\sqrt[3]{8}=2$

Recall: $z=\frac{12}{x^2}=\frac{12}{2^2}=3\\$

Therefore, the dimensions that minimizes the cost of the box are:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

7 0

3 years ago

Sam is flying a kite. The length of the kite string is 80 meters, and it makes an angle of 75° with the ground. The height of th

olya-2409 [2.1K]

Answer:

THE HEIGHT OF THE KITE FROM THE GROUND=80mtr

Step-by-step explanation:

let H be the height of kite from ground

$\sin\theta$ = $\frac{height}{hypotenuse}$

$\sin\90$ = $\frac{H}{80}$

1= $\frac{H}{80}$

H=80meters

5 0

3 years ago