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2 years ago

Consider the following equation

Mathematics

1 answer:

ser-zykov [4K]2 years ago

6 0

Answer:

The perpendicular line is:

y = 1/3 x + 2/3

Step-by-step explanation:

The given equation can be reduced to its slope-intercept form as shown below:

3x + 9y = 8y - 2

subtract 8 y from both sides

3 x + y = -2

subtract 3 x from both sides

y = - 3 x -2

therefore we know that the slope of this line is -3, and then, a perpendicular line to it must have slope given by the "opposite of the reciprocal" of this slope. That is, the slope of any perpendicular line to this one must be: 1/3

We use this slope to find the equation of the line passing through the point (13. 5)

y = 1/3 x + b

passing through (13, 5) means:

5 = 1/3 (13) + b

therefore, we can find b from the above equation

b = 5 - 13/3 = 15/3 - 13/3 = 2/3

Then the equation of this perpendicular line is:

y = 1/3 x + 2/3

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Perpendicular to y=2x+9 and has the point (4,-1)

Wewaii [24]

Answer: y = $-\frac{1}{2}$ x + 1

Step-by-step explanation:

First, we will find the slope. The slope of perpendicular lines are negative reciprocals.

In this case, the first slope is 2. The negative of 2 is -2, and the reciprocal of -2 is $-\frac{1}{2}$ .

Now, we will plug in this new slope, the point given, and solve for the b, or the y-intercept.

y = mx + b

(-1) = ( $-\frac{1}{2}$ )(4) + b

-1 = -2 + b

1 = b

Lastly, we will write our equation.

y = mx + b

y = $-\frac{1}{2}$ x + 1

The line is y = $-\frac{1}{2}$ x + 1, or y = 1 - $\frac{x}{2}$ .

4 0

1 year ago

Read 2 more answers

Jack types 162 words in 3 minutes. Jack types at a constant rate. How many words does Jack type per minute?

Arte-miy333 [17]

Answer:

Step-by-step explanation:

162/3 = 54

3 0

2 years ago

Samantha is making goodie bags for a birthday party. She puts 2 slices of pie in each goodie bag. Her sister then puts an equal

Diano4ka-milaya [45]

5 goodie bags
25 pies
25/2= 12.5
12.5=2.5
The answer varies if you choices are whole numbers or fraction, right now it would be 2 and a half pies but it could change if they are asking for a whole number

7 0

2 years ago

What is the value of the discriminant of the quadratic equation −1 = 5x2 −2x, and what does its value mean about the number of r

Zepler [3.9K]

For the equation:
-1=5 x^2 - 2 x
5 x^2 - 2 x + 1 = 0, then we substitute: a=5, b=-2, c =1
to discriminant formula: D= b^2 - 4 a c = (-2)^2 - 4 * 5 * 1 = 4 - 20 = - 16
Answer:
The discriminant is equal to -16 which means the equation has no real number solutions.

7 0

2 years ago

Read 2 more answers

Answer with the explanation step by step

andrey2020 [161]

Answer:

The answer is A. $\frac{3(x-21)}{(x+7)(x-7)}$ .

Step-by-step explanation:

To find the difference of this problem, start by simplifying the denominator, which will look like $\frac{3}{x+7}-\frac{42}{(x+7)(x-7)}$ . Next, multiply $\frac{3}{x+7}$ by $\frac{x-7}{x-7}$ to create a fraction with a common denominator in order to subtract from $\frac{42}{(x+7)(x-7)}$ . The problem will now look like $\frac{3}{x+7}*\frac{x-7}{x-7}-\frac{42}{(x+7)(x-7)}$ .

Then, simplify the terms in the problem by first multiplying $\frac{3}{x+7}$ and $\frac{x-7}{x-7}$ , which will look like $\frac{3(x-7)}{(x+7)(x-7)}-\frac{42}{(x+7)(x-7)}$ . The next step is to combine the numerators over the common denominator, which will look like $\frac{3(x-7)-42}{(x+7)(x-7)}$ .

Next, simplify the numerator, and to simplify the numerator start by factoring 3 out of $3(x-7)-42$ , which will look like $\frac{3(x-7-14)}{(x+7)(x-7)}$ . Then, subtract 14 from -7, which will look like $\frac{3(x-21)}{(x+7)(x-7)}$ . The final answer will be $\frac{3(x-21)}{(x+7)(x-7)}$ .

4 0

3 years ago