A recipe states that 5 servings of peanuts have 1,250 calories. How many servings is 375 calories of peanuts? *
2 answers:
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Answer:
C
Step-by-step explanation:
Okay, the catch of this question is that they do a very good job of explaining Maria's age in terms of George's age, but they leave George's age in terms of Maria's all up to you.
First start off by doing an expression of what they explicitly give you. Maria's age in terms of George's age.
Let's use variables g, representing George's age and m representing Maria's age
m = 2g + 3
Okay, this is all dandy and all, but they ask us for George's age in terms of Maria's, so we need to isolate for g.
subtract the 3 from both sides, like so:
m - 3 = 2g
then divide 2 from both sides: (remember we're dividing the whole thing)
(m-3)/2 = g
Now we have an expression for George's age in terms of Maria's.
g = (m-3)/2 or
The answer that gives us this, is C.
Answer:
(- 7, - 2 ) , (9.5, 0.75 )
Step-by-step explanation:
Given the equations
x - 6y = 5 ( add 6y to both sides )
x = 5 + 6y → (1)
xy - 2y² = 6 → (2)
Substitute x = 5 + 6y into (2)
(5 + 6y)y - 2y² = 6 ← distribute and rearrange left side
5y + 6y² - 2y² = 6
4y² + 5y = 6 ( subtract 6 from both sides )
4y² + 5y - 6 = 0 ← in standard form
(y + 2)(4y - 3) = 0 ← in factored form
Equate each factor to zero and solve for y
y + 2 = 0 ⇒ y = - 2
4y - 3 = 0 ⇒ 4y = 3 ⇒ y = = 0.75
Substitute these values into (1) for corresponding values of x
y = - 2 : x = 5 + 6(- 2) = 5 - 12 = - 7 ⇒ (- 7, - 2 )
y = 0.75 : x = 5 + 6(0.75) = 5 + 4.5 = 9.5 ⇒ (9.5, 0.75 )