Answer:
10x^2-11x-6
Step-by-step explanation:
To expand, we use the FOIL method. You do this by multiplying each number inside the parenthesis by the other numbers in the other set of the parenthesis. For example, on this problem, you would multiply 5x by 2x, and then 5x by -3.
Step by step, you would:
5x * 2x = 10x^2
5x * -3 = -15x
2 * 2x = 4x
2 * -3 = -6
In an equation, it would expand to 10x^2-15x+4x-6
To simplify, you add like terms (constants and those with the same variable). In this case, you would add together all the terms ending in x.
-15x+4x=-11x
Now, you have added like terms together, so your simplified answer is 10x^2-11x-6.
Let <em>f</em> and <em>s</em> denote the amounts of the <u>f</u>irst and <u>s</u>econd brands that the chef is going to use.
She wants to end up with 290 mL, so
<em>f</em> + <em>s</em> = 290
Each mL of the first brand contains 0.08 mL of vinegar, and each mL of the second contains 0.13 mL of vinegar. The final mixture should have a concentration of 12% vinegar, so that it contains 0.12 • 290 mL = 34.8 mL of vinegar, and
0.08<em>f</em> + 0.13<em>s</em> = 34.8
Solve for <em>f</em> and <em>s</em> :
<em>f</em> + <em>s</em> = 290 → <em>s</em> = 290 - <em>f</em>
0.08<em>f</em> + 0.13 (290 - <em>f </em>) = 34.8
0.08<em>f</em> + 37.7 - 0.13<em>f</em> = 34.8
0.05<em>f</em> = 2.9
<em>f</em> = 58
<em>s</em> = 290 - 58
<em>s</em> = 232
Given:
length 30 inches
k = 24
v = l * w * h
volume varies directly w/ the length: v = kl
v = 24 * 30 = 720
k = wh
24 = wh
w = 24/h or h = 24/w
P = 2w + 2h
20 = 2w + 2h
20 = 2(24/h) + 2h
20 = 48/h + 2h
48/h + 2h - 20 = 0
h(48/h + 2h - 20) = 0
48 + 2h² - 20h = 0
2h² - 20h + 48 = 0
2(h² - 10h + 24) = 0
2(h - 6)(h - 4) = 0
h = 6 or h = 4
Since the height serves as the length in the perimeter equation, then its measure is 6 and width is 4.
length = 30 ; width = 4 ; height = 6.