MATHEMATICS HIGH SCHOOL

Simplify the following: a) ((w^-5)/(w^-9))^1/2
b) (m^6)^-2/3
c) (3x^-4y^5)/((2x^3y^-7))^-2

Answers

Answer 1
Answer: a. ((w^(-5))/(w^(-9) ))^{ (1)/(2) } \n ( (w^(9) )/(w^(5) ))^{ (1)/(2) } \n (w^(9-5))^{ (1)/(2) } \n (w^(4))^{ (1)/(2) } \n \sqrt{w^(4) } \n w^(2)
b.(m^(6))^{ (-2)/(3) } \n ((1)/(m^(6) ))^{(2)/(3) } \n \frac{ \sqrt[3]{1^(2) } }{ \sqrt[3]{m^(6) }^(2) } \n \frac{ \sqrt[3]{1} }{m^(2*2) } \n (1)/(m^(4) )
Hope this helps!
Answer 2
Answer: Problem A
((w^(-5))/(w^(-9)))^{{(1)/(2)} = ((w^(9))/(w^(5)))^{{(1)/(2)} = (w^(4))^{{(1)/(2)} = \sqrt[2]{w^(4)} = w^(2)

Problem B
(m^(6))^{-(2)/(3)} = \frac{1}{(m^(6))^{(2)/(3)}} = \frac{1}{\sqrt[3]{(m^(6))^(2)}} = \frac{1}{\sqrt[3]{m^(12)}} = (1)/(m^(4))

Problem C
((3x^(-4)y^(5))/(2x^(3)y^(-7)))^(-2) = ((3y^(12))/(2x^(7)))^(-2) = ((3y^(12))^(-2))/((2x^(7))^(-2)) = ((2x^(7))^(2))/((3y^(12))^(2-)) = (4x^(14))/(9y^(24))

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(06.03)Two car rental companies have different rental plans. Sand's Car Rental charges $50 a day and 10 cents every mile traveled. Beach Car Rental charges $60 dollars a day and no per mile charge. How many days would the trip need to be to make the costs equal, if the trip total was 300 miles? (1 point)


3 days
2 days
1 week
They will never be equal

Answers

Let x be the number of days for the trip. With this representation and dropping the dollar sign, the Sand's Car Rental will charge a total of 50x + (0.1)(300) while Beach Car Rental will charge 60x. Equating the two charges, 50x + 30 = 60x. This gives an answer of x = 3. Therefore, the trip should take 3 days for the charges to be equal. 

Answer:3 days

Step-by-step explanation: got it correct on my exam

Can someone please explain how to solve these two math equations?2x^2-3x-35=0

56z^2+2=22z

Answers

#1.

Question:  2x^2 − 3x − 35 = 0

Step 1: Factor left side of equation):    (2x + 7) (x − 5) = 0
Step 2: Set factors equal to 0.):  2x + 7 = 0 or x − 5 = 0

ANSWER: x = −7/2 or x = 5
_____________________________________________________
#2.

Question: 56z^2 + 2 = 22z

Step 1: Subtract 22z from both sides.):

56z^2 + 2 −22z = 22z − 22z
56z^2 − 22z + 2 = 0
Step 2: Factor left side of equation.):


2(7z − 1)(4z − 1) = 0

Step 3: Set factors equal to 0.):


7z − 1 = 0 or 4z − 1 = 0

ANSWER:    z = 1/7 or z = 1/4

Tito bought a baseball card for $24.00 and sold it for $37.00. what is the percent of increase rounded to the nearest tenth? a. 35.1%
b. 54.2%
c. 64.9%
d. 54.1%

Answers

Answer: Option 'b' is correct.

Step-by-step explanation:

Since we have given that

Cost price of a baseball card = $24

Selling price of a baseball card = $37

So, Profit would be

37-24=\$13

So, Profit % would be

(13)/(24)* 100\n\n=54.16\%\n\n\approx 54.2\%

Hence, Option 'b' is correct.

Answer:

The answer is B. 54.2% hopefully this helps!

Harry is building a house with a sloping roof. If the roof is 44 feet long and 10 feet high, what is the angle that the roof makes with the horizontal?

Answers

Length\ and\ high\ make\ with\ horizontal\ rectangular\ triangle\n\n Length \is \ hypotenuse\ \n\ high\ and\ horizontal\ are\ cathetuses.\n\n \angle\ \alpha\ between\ length\ and\ horizontal=?\n sin \alpha =(10)/(44)\n sin \alpha \approx0,227\n \alpha \approx\ arcsin0,227\approx\ 13^\circ

The ideal width of a certain conveyor belt for a manufacturing plant is 50 in. Conveyor belts can vary from the ideal width by at most 7/32 in.

Answers

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.

If the ideal is 50 and the max variation is 7/32in, then that's 7/32 under 50 and 7/32 over 50. 
So, 50-7/32= 49 25/32, and 50+7/32 = 50 7/32. 
So the acceptable width is 49 25/32 to 50 7/32.

Answer;

The acceptable width is 49 25/32 and 50 7/32

That is; 49 25/32 ≤ x ≥ 50 7/32

Explanation;

-If the ideal is 50 and the max variation is 7/32 inches, then that's 7/32 under 50 and 7/32 over 50.

Therefore; 50-7/32= 49 25/32, and 50+7/32 = 50 7/32.

x ≤ 50 7/32 and x ≥ 49 25/32

Thus; the acceptable width is 49 25/32 ≤ x ≥ 50 7/32.

How do I solve for y in this equation? 3xy-28=16x

Answers

The value of y is  16/3 + 28/3x

What is equation?

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S

Given:

3xy-28=16x

3xy= 16x + 28

y = 16x/ 3x + 28/3x

y= 16/3 + 28/3x

Learn more about equation here:

brainly.com/question/10413253

#SPJ2
3xy-28=16x 

3xy=16x+28    Add \ 28 \ to \ both \ sides 

xy= (16x+28)/(3)  Divide \ both \ sides \ by \ 3 

xy= (4(4x+7))/(3)   Factor \ out \ the \ common \ term \ 4 

y= (4(4x+7))/(3x)    Divide \ both \ sides \ by \ x
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