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3 years ago

Solve the problem 1/4(2x -14)=4

Mathematics

2 answers:

I am Lyosha [343]3 years ago

5 0

Multiplying by 4, we get 2x-14=16. Adding 14, we get 2x=30, and dividing by 2, we see that x=15.

zalisa [80]3 years ago

3 0

1/4(2x - 14) = 4

Divide by 1/4. (dividing by a fraction = multiplying by its reciprocal, so ÷1/4 = ×4)

2x - 14 = 16

Add 14 to each side.

2x = 30

Divide by 2.

x = 15

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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

Write an expression that evaluates to true if the int associated with number_of_prizes is divisible (with no remainder) by the i

hodyreva [135]

We need to find the expression for " number_of_prizes is divisible number_of_participants". Also there should not remain any remainder left. On in order words, we can say the reaminder we get after division is 0.

Let us assume number of Prizes are = p and

Number of participants = n.

If we divide number of Prizes by number of participants and there will be not remainder then there would be some quotient remaining and that quotent would be a whole number.

Let us assume that quotent is taken by q.

So, we can setup an expression now.

Let us rephrase the statement .

" Number of Prizes ÷ Number of participants = quotient".

p ÷ n = q.

In fraction form we can write

p/n =q ; n ≠ 0.

4 0

3 years ago

How to solve 2x2+50=100

Ugo [173]

Answer:

It would be 54.

Step-by-step explanation:

It would be 2 times 2, which is four, and then you would add by 50.

2 x 2 = 4

4 + 50 = 54

So, it will not be 100, it will be 54.

4 0

3 years ago

Read 2 more answers

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Lady_Fox [76]

X equals 125 and y equals 55

3 0

3 years ago

Denise is checking to determine if the expressions x+x+6 and 4+3x-2 are equivalent. When x=4, she correctly found that both expr

gayaneshka [121]

The answer would be 8 when the value of x = 2

3 0

4 years ago

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