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3 years ago

Rewrite the expression using positive exponents 1. 1/9x^-2y^-1 2. a^-5*a^-8

Mathematics

1 answer:

NikAS [45]3 years ago

4 0

Answer:

Property : a^-b = 1/a^b

Using this property, we can rewrite the expression using positive exponents :

$1. \frac{1}{9}*x^{-2} *y^{-1} =\frac{1}{9}\frac{1}{x^{2} } \frac{1}{y} =\frac{1}{9x^{2} y} \\2. a^{-5} a^{-8} =\frac{1}{a^{5}a^{8} } =\frac{1}{a^{13} }$

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X2 - 6x + 12 and y = 2x - 4, algebraically are

olga_2 [115]

The solution is (4, 4)

Solution:

Given system of equations are:

$y = x^2 - 6x + 12 ------ eqn\ 1\\\\y = 2x - 4 ---------- eqn\ 2$

Substitute eqn 2 in eqn 1

$x^2 - 6x + 12 = 2x - 4$

Make the right side of equation 0

$x^2 - 6x + 12 - 2x + 4 = 0\\\\x^2 -8x + 16 = 0$

Solve by quadratic equation

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=-8,\:c=16:\\\\x=\frac{-\left(-8\right)\pm \sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:16}}{2\cdot \:1}\\\\x=\frac{-\left(-8\right)\pm \sqrt{0}}{2\cdot \:1}\\\\x = \frac{8}{2}\\\\x = 4$

Substitute x = 4 in eqn 2

y = 2(4) - 4

y = 8 - 4

y = 4

Thus solution is (4, 4)

5 0

3 years ago

Marquis wrote the linear regression equation y=1.245*-3.684

Advocard [28]

I would say 35 because if you put in 35 for x you get 39.891

5 0

3 years ago

Read 2 more answers

Osama starts with a population of 1,000 amoebas that increases 30% in size every hour for a number of hours, h. The expression 1

Blizzard [7]

Answer: The correct option is A, itis the product of the initial population and the growth factor after h hours.

Explanation:

From the given information,

Initial population = 1000

Increasing rate or growth rate = 30% every hour.

No of population increase in every hour is,

$1000\times \frac{30}{100} =1000\times 0.3$

Total population after h hours is,

$1000(1+0.3)^h$

It is in the form of,

$P(t)=P_0(t)(1+r)^t$

Where $P_0(t)$ is the initial population, r is increasing rate, t is time and [tex(1+r)^t[/tex] is the growth factor after time t.

In the above equation 1000 is the initial population and $(1+0.3)^h$ is the growth factor after h hours. So the equation is product of of the initial population and the growth factor after h hours.

Therefore, the correct option is A, itis the product of the initial population and the growth factor after h hours.

3 0

3 years ago

Read 2 more answers

Aaron works as a bar attendant and receives $11 per hour. On Saturday he works for five hours at normal time and three hours ove

scoundrel [369]

Answer:

so his total pay for Saturday would be $104.50

Step-by-step explanation:

He works 5 hours at $11 per hour which gets a total of 55$

He also works 3 hours of overtime where he gets payed 1.5x pay

11 x 1.5 = 16.5 (10x1.5 = 15 1x1.5 = 1.5)

so he gets $16.5 per hour for 3 hours which = 49.5$

49.5 + 55 = $104.50

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2 years ago

Write as a decimal 23/9

Slav-nsk [51]

Answer:

2.555555555555.....

(the 5 is repeating)

Step-by-step explanation:

This is the answer because:

1) To convert the fraction to a decimal, you have to divide the numerator by the denominator.

2) Therefore, 23/9 is 2.5 (the 5 is repeating)

Hope this helps!

8 0

3 years ago