MATHEMATICS HIGH SCHOOL

Check all that apply. The center of gravity of a triangular solid with uniform thickness and density is... A. The point at which one can balance the triangle.
B. The point shared by a triangle's altitudes.
C. The centroid.
D. The orthocenter.

Answers

Answer 1
Answer: The answers are options A and C. The center of gravity of a triangular solid with uniform thickness and density is the centroid which is the point at which one can balance the triangle. It is the center of mass of an object with uniform density.

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An electronics company has been producing 1705 CD players a day working two shifts. The second shift has produced 95 Cd players fewer than four-fifths of the number of Cd players produced by the first shift. Determine the number of CD players produced by the second shift.

Answers

4/5 multiplied by 95 which is 76

Is 9/12. Bigger than 3/4?

Answers

No it is the same and u will tell is u simplify 9/12 down 
No,9/12 is equal to 3/4 because when you find the LCM of the number it is three then you multiply the number to 3/4 and you get 9/12.



or 9/12 is = to 3/4

Luis was served 145 grams of meat and 217 grams of vegetable at a meal. what was the total mass of the meat and the vegetable?

Answers

145 grams + 217 grams = 362 grams

If point A is between B and C then BA + AC = BC.

Answers

If point A is between B and C then BA + AC = BC. This is always true.
Yes, that is correct

Problem 3. if f(x) = /2x-5 and g(x) = 5x? -- 3, find (gºf)(x).(Step by step please<3)

Answers

(1)f(x) = x² - 4x + 2, g(x) = 3x - 7

(f o g) (x) = f(g(x)) = f (3x - 7)

= (3x - 7)² - 4(3x - 7) + 2

= (9x² - 42x + 49) + (-12x + 28) + 2

= 9x² - 57x + 79

(2)g(x) = -6x + 5, h(x) = -9x - 11

(g o h) (x) = g(h(x)) = g (-9x - 11)

= -6(-9x - 11) + 5

= 54x + 66 + 5

= 54x + 71

(3)f(x) = √(2x - 5), g(x) = 5x² - 3

(g o f) (x) = g(f(x)) = g(√(2x - 5))

= 5 (√(2x - 5))² - 3

= 5 (2x - 5) - 3

= 10x - 25 - 3

= 10x - 28

Ray is purchasing a laptop that is on sale for 25% off. He knows the function that represents the sale price of his laptop is c(p) = 0.75p, where p is the original price of the laptop. He also knows he has to pay 8% sale's tax on the laptop. The price of the laptop with tax is f(c) = 1.08c, where c is the sale price of the laptop.Determine the composite function that can be used to calculate the final price of Ray's laptop by solving for f[c(p)].

f[c(p)] = 1.83p
f[c(p)] = 1.83cp
f[c(p)] = 0.81p
f[c(p)] = 0.81cp

Answers

Answer: f[c(p)]=0.81p

Step-by-step explanation:

Given: Ray is purchasing a laptop that is on sale for 25% off.

The function that represents the sale price of his laptop :

c(p) = 0.75p, where p is the original price of the laptop.

The price function of the laptop with tax :

f(c) = 1.08c, where c is the sale price of the laptop.

Now, consider the composite function that can be used to calculate the final price of Ray's laptop .

\text{ i.e.  }f[c(p)]=f[0.75p]\n\n\Rightarrow f[c(p)]=1.08(0.75p)\n\n\Rightarrow f[c(p)]=0.81p
c(p) = 0.75p   where p is the original price of the laptop
f(c) = 1.08c    where c is the sales price of the laptop

the composite function is:

f(c(p)) = 1.08(0.75p)
f(c(p)) = 0.81p
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