Select the equation of the line that passes through the point (5, 7) and is perpendicular to the line x = 4.

2 answers:

8 0

Yes, I think the answer is y = 7. The line x = 4 runs vertical (because all of the points in that line have an x-value of 4) so any line that is perpendicular to it has to be horizontal. Any line that is horizontal is in the form y = (some number). In order for the new line to run through the point (5,7) it would have to have the same y-value as that point, which is 7. So the new line is y = 7. Hope this helps :) (P.S. try graphing them both if you need a visual.)

Amanda [17]3 years ago

7 0

Yes , it would be y = 7 As, the required line is perpendicular to x = 4 it will definitely pass through y axis and it will be a straight line passing through the y coordinate of the point (5,7)

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Gary received a 3.5% raise in salary. If he is now paid $140 374.85, what was his previous salary?

Ostrovityanka [42]

Answer:

$135461.73

Step-by-step explanation:

140374.85 decrease 3.5% =

140374.85 × (1 - 3.5%) = 140374.85 × (1 - 0.035) = 135461.73025

3 0

2 years ago

Solve for x: 1 1/5 x -2 1/3 < 1/7 x+ 1 1/2

Firlakuza [10]

Solving inequalities is similar to solving a regular equation. The only thing you need to worry about with inequalities is that when you are dividing or multiplying by a negative number, you must flip the inequality sign. You won't have to worry about that here if the coefficient in front of x is positive when you divide!

Also remember:
- To add/subtract fractions, you have to turn all mixed numbers into improper fractions (if needed), find a common denominator on both fractions (if needed), add/subtract the numerators, put the sum/difference over the common denominator, and simplify if needed.

- To multiply fractions, multiply the numerators and multiply the denominators. Put the product of the numerators over the product of the denominators.

- To divide fractions, remember that dividing by a fraction is the same as multiplying by the inverse of that fraction (aka fraction flipped).

- To turn mixed numbers into improper fractions, multiply the whole number by the denominator of the fraction. Add the numerator of the fraction to the product you get, and put that final sum over the original denominator.

Back to the problem:
You are told that $1 \frac{1}{5} x - 2 \frac{1}{3} \ \textless \ \frac{1}{7} x + 1 \frac{1}{2}$ and you have to solve for x.

1) Using the info for converting mixed numbers to improper fractions from above, you know that $1 \frac{1}{2} = \frac{3}{2}$ and $2 \frac{1}{3} = \frac{7}{3}$ and $1 \frac{1}{5} x = \frac{6}{5} x$ . Now add/subtract using the info above, isolating the variable x by adding $2 \frac{1}{3}$ to both sides and subtracting $\frac{1}{7} x$ from both sides.
$1 \frac{1}{5} x - 2 \frac{1}{3} \ \textless \ \frac{1}{7} x + 1 \frac{1}{2}\\
\frac{6}{5} x - \frac{7}{3} \ \textless \ \frac{1}{7} x + \frac{3}{2}\\
(\frac{6}{5} x - \frac{1}{7} x) \ \textless \ (\frac{3}{2} + \frac{7}{3})\\
(\frac{42}{35} x - \frac{5}{35} x) \ \textless \ (\frac{9}{6} + \frac{14}{6})\\
 \frac{37}{35} x \ \textless \ \frac{23}{6}$

2) Divide both sides by $\frac{37}{35}$ to get the inequality for x. Remember the info for dividing from above:
$\frac{37}{35} x \ \textless \ \frac{23}{6}\\
x \ \textless \ \frac{23}{6} \div \frac{37}{35} \\
x \ \textless \ \frac{23}{6} \times \frac{35}{37} \\
x \ \textless \ \frac{805}{222}$

Your final answer is x < $\frac{805}{222}$ or x < $3 \frac{139}{222}$ .