Mathematics, 03.08.2019 04:30 jbuchjr13

Solve the linear equation step-by-step

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Answer from: TaraDean

Solving for x: three denominators: 4, 6, and 12.we can find the lcm of those denominatorswe can write each denominator as a product of prime factors $\begin{aligned} 4 & = 2 \cdot 2 = 2^2\\ 6 & = 2 \cdot 3 \\ 12 & = 2 \cdot 2 \cdot 3 =2^2 \cdot 3 \end{aligned}$ get the primes appearing the greatest number of times in any of the factors.we have unique factors of 2 and 3 highest power of 2 is 2² highest power of 3 is 3the lcd you get from multiplying those highest powers of prime lcd is 2² · 3 = 12the point here is that we want all the fractions to have the same denominator. then we can multiply both sides of the equation by that denominator to cancel it out. $\dfrac{x+7}{12} = \boxed{\dfrac{5}{6}} + \dfrac{x-4}{4}$ to make $\frac{5}{6}$ have denominator of 12, we need to multiply the numerator and denominator by 2 (because 6 · 2 = 12): $\begin{aligned} \dfrac{x+7}{12} & = \dfrac{5 \cdot 2}{6 \cdot 2} + \dfrac{x-4}{4} \\ \dfrac{x+7}{12} & = \dfrac{10}{12} + \dfrac{x-4}{4} \\ \dfrac{x+7}{12} & = \dfrac{10}{12} + \boxed{\dfrac{x-4}{4}} \end{aligned}$ to make $\frac{x-4}{4}$ have a denominator of 12, we need to multiply the numerator and denominator by 3 (because 4 · 3 = 12): $\begin{aligned} \dfrac{x+7}{12} & = \dfrac{10}{12} + \dfrac{3\cdot(x-4)}{3 \cdot 4} \\ \dfrac{x+7}{12} & = \dfrac{10}{12} + \dfrac{3x-12}{12} \end{aligned}$ multiply both sides of the entire equation by 12 so that it will cancel out all the denominators (distributes on the right-hand side) $\begin{aligned} 12\left(\dfrac{x+7}{12}\right) & = 12\left(\dfrac{10}{12} + \dfrac{3x-12}{12} \right) \\ \frac{x+7}{1} & = \dfrac{12 (10)}{12} + \dfrac{12(3x-12)}{12} \\ x + 7 & = 10 + 3x - 12 \end{aligned}$ 10 and -12 sum up to get -2 $x + 7 = 3x - 2$ get rid of x on left side by subtracting both sides by x. $\begin{aligned} 7 & = 3x - 2 - x\\ 7 & = 2x - 2 \end{aligned}$ add 2 to both sides $\begin{aligned} 7 + 2& = 2x \\ 9 & = 2x \end{aligned}$ divide both sides by 2 $x = \frac{9}{2}$ answer is x = 9/2======checking our answer: plug in x = 9/2 into the original equation and see if we get a true statement. $\begin{aligned} \frac{x+7}{12} & = \frac{5}{6} + \frac{x-4}{4} \\ \frac{\frac{9}{2}+7}{12} & = \frac{5}{6} + \frac{\frac{9}{2}-4}{4} \end{aligned}$ multiplying the entire numerator and denominator of the fraction $\frac{\frac{9}{2}+7}{12}$ to get rid of the little denominators of "2" $\begin{aligned} \frac{2\left(\frac{9}{2}+7\right)}{2(12)} & = \frac{5}{6} + \frac{2\left(\frac{9}{2}-4\right)}{2(4)} \\ \frac{9 + 14}{24} & = \frac{5}{6} + \frac{9 - 8}{8} \\ \frac{23}{24} & = \frac{5}{6} + \frac{1}{8} \end{aligned}$ the left-hand side has 24 in denominator; let us aim for thatget $\frac{5}{6}$ to have a denominator of 24 by multiplying num and denom by 4 (because 6 (denominator) · 4 = 24).get $\frac{1}{8}$ to have a denominator of 24 by multiplying num and denom by 3 (because 8 · 3 = 24). $\begin{aligned} \frac{23}{24} & = \frac{5 \cdot 4}{6 \cdot 4} + \frac{1 \cdot 3}{8 \cdot 3} \\ & = \frac{20}{24} + \frac{3}{24} \\ & = \frac{20 + 3}{24}\\ & = \frac{23}{24} \end{aligned}$ we get a true statement as 23/24 = 23/24.
Solve the linear equation step-by-step

Answer from: Quest

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation: