A person who weights 100 pounds on earth weights 16.6 lb. on the moon. a. which variable is the dependent variable and why?
b. what is an equation that relates weight on earth to the weight on the moon?
c. how much would a 185-pound astronaut weight on the moon? use an equation to explain how you know.
d. how much would a man who weighs 50 pounds on the moon weigh on earth?

Answers

Answer 1

Answer: A. Weight on the moon
B. 16.6/100=0.166
C. 30.71
D. 50=0.166(e), 50/0.166= 301.20 lbs

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If s(x) = x – 7 and t(x) = 4x2 – x + 3, which expression is equivalent to (t*s)(x)

Answers

Answer:

$4(x-7)^2-(x-7)+3$

Step-by-step explanation:

Given the functions:

$s(x)=x-7$ and $t(x)=4x^2-x+3$

We have to find the $(t \circ s)(x)$

$(t \circ s)(x) = t(s(x))$

Substitute the function s(x) we have;

⇒ $t(s(x)) = t(x-7)$

Replace x with x-7 in t(x) we have;

⇒ $t(x-7) = 4(x-7)^2-(x-7)+3$

⇒ $(t \circ s)(x) = 4(x-7)^2-(x-7)+3$

Therefore, the expression which is equivalent to $(t \circ s)(x)$ is:

$4(x-7)^2-(x-7)+3$

(t o s)(x) = t(s(x))
s(x) = x - 7
t(x - 7) = 4(x-7)^2 - (x - 7) + 3

Which equations are true for x = –2 and x = 2? Check all that apply.A.x2 – 4 = 0
B.x2 = –4
C.3x2 + 12 = 0
D.4x2 = 16
E.2(x – 2)2 = 0

Answers

А. х²-4=0; х²=4; х=±2, true. B. x²=-4; there is no solution. C. 3x²+12=0; 3x²=-12; x²=-4; there is no solution. D. 4x²=16; x²=4; x=±2, true. E. 2(x-2)²=0; 2(x²-4x+4)=0; 2x²-8x+8=0; x²-4x+4=0; x1=2; x2=2. False. The answer: A, D.

Find the volume of a cube whose diagonal measures 36√3 cm.

Answers

Answer:

$46656 cm^3$

Step-by-step explanation:

If a cubes diagonal measures you can solve for its sidelength by creating a triangle. Visualize the diagonal as the hypotenuse of our triangle inside the cube. Then, one of the legs would be the side of the cube itself, and the other leg would be the diagonal of the bottom side of the cube. Knowing this is a cube, we can call each side s. If each side is s, then the diagonal of the bottom face is $s√(2)$ ( this is a special triangle property, $45-45-90$ triangle.) Then we know our triangle is a right triangle, so we can use the Pythagorean theorem to solve for s.

$s^(2) + (s√(2) )^(2) = (36√(3))^2$

Solve this equation for s.

$s^(2) + 2s^(2) = 3888$

$3s^(2) = 3888$

$s^(2) = 1296$

$s = 36$

Since we now found the side length of the cube, we can find its volume by cubing the side length:

$s^3 = (36)^3 = 46656$ $cm^3$

6. A group of friends wants to go to theamusement park. They have $311 ta
spend on parking and admission.
Parking is $15, and tickets cost $32
per person, Write and solve an
equation which can be used to
determine p, the number of people
who can go to the amusement park.
2