Answer: <u>4 pounds</u> of brand X sugar
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Reason:
n = number of pounds of brand X sugar
5n = cost of buying those n pounds, at $5 per pound
Brand Y costs $2 per pound, and you buy 8 lbs of it, so that's another 2*8 = 16 dollars.
5n+16 = total cost of brand X and brand Y combined
n+8 = total amount of sugar bought, in pounds
3(n+8) = total cost because we buy n+8 pounds at $3 per pound
The 5n+16 and 3(n+8) represent the same total cost.
Set them equal to each other. Solve for n.
5n+16 = 3(n+8)
5n+16 = 3n+24
5n-3n = 24-16
2n = 8
n = 8/2
n = 4 pounds of brand X sugar are needed
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Check:
n = 4
5n = 5*4 = 20 dollars spent on brand X alone
16 dollars spent on brand Y mentioned earlier
20+16 = 36 dollars spent total
n+8 = 4+8 = 12 pounds of both types of sugar brands combined
3*12 = 36 dollars spent on both types of sugar brands
The answer is confirmed.
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Another way to verify:
5n+16 = 3(n+8)
5*4+16 = 3(4+8)
20+16 = 3(12)
36 = 36
Let's solve this by using the quadratic formula:
Note that we only use the coefficients so a=12, b=-14, and c=-6.
Plug values in the quadratic equation:
And so by evaluating those values we obtain:
Now we have two answers which are our factors one where we add another where we subtract and so:
First factor:
Second Factor:
And so your factors are
meaning that those are your roots/x-intercepts.
Answer:
x = - 1 and x = 5
Step-by-step explanation:
Given
(x - 3)² + 2(x - 3) - 8 = 0
Let u = x - 3, then
u² + 2u - 8 = 0 ← solve for u
(u + 4)(u - 2) = 0 ← in factored form
Equate each factor to zero and solve for u
u + 4 = 0 ⇒ u = - 4
u - 2 = 0 ⇒ u = 2
Convert back to x, that is
x - 3 = - 4 ( add 3 to both sides ) ⇒ x = - 1
x - 3 = 2 ( add 3 to both sides ) ⇒ x = 5
Answer:
d) 1⃣
Step-by-step explanation:
Multiply -5 by -2 to get , then deduct 7 to get 3. So, you now know that 3 = 3a; 1 = a.
Answer:
x=3
Step-by-step explanation:
Since they are similar triangles, we can use ratios to solve
x 3.5
----- = -------
6 7
Using cross products
7x = 21
Divide each side by 7
7x/7 = 21/7
x = 3
