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Andrei [34K]
3 years ago
8

The students at Riverview High School were asked to vote on their preference for new school colors. The school principal was int

erested to see how the student-athletes might vote differently from the students who are not athletes. The table shows the results of the vote. What percent of the student-athletes voted for red and gold as the new school colors? Round your answer to the nearest whole percent. 27% 42% 51% 67%
Mathematics
1 answer:
icang [17]3 years ago
5 0

Answer:

Step-by-step explanation:

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Show work please<br> \sqrt(x+12)-\sqrt(2x+1)=1
Nesterboy [21]

Answer:

x=4

Step-by-step explanation:

Given \displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1, start by squaring both sides to work towards isolating x:

\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2

Recall (a-b)^2=a^2-2ab+b^2 and \sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}:

\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1

Isolate the radical:

\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}

Square both sides:

\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2

Expand using FOIL and (a+b)^2=a^2+2ab+b^2:

\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36

Move everything to one side to get a quadratic:

\displaystyle-\frac{1}{4}x^2+7x-24=0

Solving using the quadratic formula:

A quadratic in ax^2+bx+c has real solutions \displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}. In \displaystyle-\frac{1}{4}x^2+7x-24, assign values:

\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24

Solving yields:

\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}

Only x=4 works when plugged in the original equation. Therefore, x=24 is extraneous and the only solution is \boxed{x=4}

4 0
2 years ago
Which of the following is true?
gtnhenbr [62]

Answer:

C..... I think it is a answer

6 0
3 years ago
Solve ln(6x-1) = -4 for x
Reika [66]

Answer: Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

x

=

−

1

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Decimal Form:

x

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0.5

Step-by-step explanation:

5 0
3 years ago
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If x equals 2 what is the answer to the problem 3x(x-2)plus 2
Verdich [7]

Answer:

the answer should be 2 but it could be wrong

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3 years ago
The maximum weight,w, an elevator can lift is 2,200 pounds
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Answer:

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Step-by-step explanation:

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