Answer:
a) 
b) 
c), Yes;
Step-by-step explanation:
Michael's Weight: 
Al's weight: 
a) Ratio of Michael's weight to Al's weight:
b) This ratio simplifies to: 
c) Yes, If the exponent in each expression were negative, then we have:
Ratio of Michael's weight to Al's weight: 
This ratio simplifies to: 
The two ratios are not the same.
Answer:
1) a = -⅙, b = ⅙, c = 1
2) 6 units
Step-by-step explanation:
1) f(x) = ax² + bx + c
Given the roots, we can write this as:
f(x) = a (x + 2) (x − 3)
We know that f(13) = -25, so we can plug this in to find a:
-25 = a (13 + 2) (13 − 3)
-25 = 150a
a = -⅙
Therefore, the factored form is:
f(x) = -⅙ (x + 2) (x − 3)
Distributing:
f(x) = -⅙ (x² − x − 6)
f(x) = -⅙ x² + ⅙ x + 1
Graph: desmos.com/calculator/6m6tjoodvb
2) Volume of a right prism is area of the base times the height.
V = Ah
The base is an equilateral triangle. Area of a triangle is one half the base times height.
V = ½ ab h
The height of the triangle is the same as the height of the prism.
V = ½ bh²
In an equilateral triangle, the height is equal to half the base times the square root of 3.
V = ½ b (½√3 b)²
V = ⅜ b³
Given that V = 81, solve for b.
81 = ⅜ b³
216 = b³
b = 6
Answer:
Respondió mal 64 preguntas.
Step-by-step explanation:
De acuerdo a la información proporcionada puedes plantear las siguientes ecuaciones:
x+y=120 (1)
2x-0,5y=80 (2)
x es el número de preguntas correctas
y es el numero de preguntas incorrectas
Primero debes despejar "x" en (1):
x=120-y (3)
Después, debes reemplazar (3) en (2):
2(120-y)-0,5y=80
240-2y-0,5y=80
240-80=2,5y
160=2,5y
y=160/2,5
y=64
Ahora puedes reemplazar el valor de "y" en (3) para encontrar el valor de "x":
x=120-y
x=120-64
x=56
De acuerdo a esto, la respuesta es que el postulante respondió mal 64 preguntas.
RT = RS + ST
8x - 43 = 2x - 4 + 4x - 1
8x - 43 = 6x - 5
8x - 6x = -5 + 43
2x = 38
x = 38/2
x = 19
QS = 2RS = 2(2x-4) = 2(2*19-4) = 2*34 = 68
The answer is B. x = 65, y = 10.
