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Sholpan [36]
4 years ago
7

David says he has 2/3 of a pipe length​ left, while Don says he has 11/16 of a length left. Which person has the longest section

​ left?
Mathematics
1 answer:
Kruka [31]4 years ago
5 0

Answer:

Don

Step-by-step explanation:

1. We make the fractions have common denominators so it is easier to compare them. We can do this buy multiplying 2/3 by a factor of 16, so it becomes 32/48. For 11/16, we multiply by a factor of 3 so it becomes 33/48. It is now apparent that Don has the longer pipe.

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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
What is the rule for the reflection?
Dvinal [7]

Answer:

Incident ray, the reflection ray and the normal to thereflection surface at the point of the incidence lie in the same plane

5 0
3 years ago
What is 5a*2 -6a+7a*2+3a-2+8a+7= <br> Distribute and combine like terms
andrey2020 [161]
5a^2-6a+7a^2+3a-2+8a+7\\\\=5a^2+7a^2-6a+3a+8a-2+7\\\\=12a^2+5a+5
6 0
3 years ago
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Nora needs at least $115 for a new cell phone. She has already saved $45. She earns $7 an hour at her job. Write and solve an in
Volgvan

Answer:

she only needs to work ten hours

Explanation: if you subtract 45 from 115 you well end up with 70 a and if you work for ten hours 7 ×10=70 so you would have enough.

8 0
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RideAnS [48]

Answer:

P(X<1200) is 0.8212

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Test statistic (z) = (X - mean)/sd

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z = (1200 - 1497)/322 = -297/322 = -0.92

The cumulative area of the test statistic is the probability that X<1200. The cumulative area is 0.8212.

Therefore, P(X<1200) = 0.8212

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3 years ago
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