Tutor profile: Mackenzie K.
Five less than the sum of 4 times a number and three times a number is 30. What is the number?
Answer: n=5 This can be represented by $$4n+3n-5=30$$ where n is the desired number. We can solve for n to find our solution. In order to do this, we need to combine like terms. When we combine like terms, we get $$7n-5=30$$. Our next step is to add 5 to both sides of the equation. We now have $$7n=35$$. The last step would be to divide both sides of the equation by 7. We get that n=5. We can check our solution by plugging 5 in for n. If we do this, we get that 4(5)+3(5)-5=20+15-5=30.
Subject: Basic Math
Answer: $$43/30$$ In order to add two fractions, we need common denominators. The lowest common denominator between two numbers is also the least common multiple of the two numbers. The least common multiple of 6 and 5 is 30. We need to find an equivalent fraction to 5/6 that has a denominator of 30 and an equivalent fraction to 3/5 that has a denominator of 30. In order to do this, we multiple 5/6 by 5/5 (or 1) and we multiply 3/5 by 6/6 (or 1). This gives us $$25/30 + 18/30 = 43/30$$. The answer can be written as an improper fraction (43/30) or a mixed number (1 13/30)
The equation of a line is $$y=1/4x+6$$. Find the equation of a line that is perpendicular to the given line and passes through the point (2,6)
Answer: $$y=-4x+14$$ The original equation is given in the form of $$y=mx+b$$. The slope of a line perpendicular to the given line is the opposite reciprocal. Since m=1/4 in the original equation, m=-4 in our solution. To find the y- intercept of the new equation, we plug in (2,6) for x and y to solve for b. We find that b= 14. The equation of a line perpendicular to $$y=1/4x+6$$ that passes through (2,6) is $$y=-4x+14$$.
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