1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
postnew [5]
3 years ago
15

Two perpendicular lines intersect at the origin. If the slope of the first line is -1/2, what is the equation of the second line

?
Mathematics
1 answer:
Dovator [93]3 years ago
5 0

bearing in mind that perpendicular lines have <u>negative reciprocal</u> slopes.

now, they both intersect at 0,0, namely they both pass through it, we know the slope of the first one, so

\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{1}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{2}{1}}\qquad \stackrel{negative~reciprocal}{+\cfrac{2}{1}\implies 2}}

so, we're really looking for the equation of a line whose slope is 2, and runs through (0,0).

\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})~\hspace{10em} slope = m\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=2(x-0)\implies y=2x

You might be interested in
Critical points of x+5/x+2&gt;0
Scorpion4ik [409]

Answer:

{-5, -2}

Step-by-step explanation:

In a case like this please use parentheses to remove ambiguities.  If I were to take your "x+5/x+2" literally, I'd have to write x             plus 5/x           plus 2.

I suspect that you actually meant (x + 5) / (x + 2), and will start with that.

First of all, this function is not defined at x = -5 or at x = -2.  Thus, -5 and -2 are critical points.  

Secondly, there may be one or more critical points beyond this.  To find out, we have to differentiate (x+5)/(x+2):

           (x + 2)(1) - (x + 5)(1)

f '(x) = ------------------------------

                  (x + 2)

Here it's clear that x cannot = -2, which would cause division by zero.

Thus, our critical values are {-5, -2}.

8 0
3 years ago
A delivery truck traveled ¼ of its route in 2 hours How long does it take to complete one route?
stepladder [879]

Answer:

8 hours

Step-by-step explanation:

1/4 = 2h

2h times 4 = 8h

8 0
3 years ago
Read 2 more answers
1. Girl Scout Troop 321 started with 25 girls and at the end of the year party there were 31 girls. Gabby
Oksanka [162]

Answer: 24%

Step-by-step explanation:

Since we are informed that the Girl Scout Troop started with 25 girls and at the end of the year party there were 31 girls. The percentage change will be:

= (31 - 25) / 25 × 100

= 6/25 × 100

= 24%

The error that Gabby made was that she used 31 as the base. This is expressed below:

= 31 - 25) / 31 × 100

= 6/31 × 100

= 19.4%

3 0
3 years ago
Heather is making a blanket for her baby and is going to put a ribbon border around it. The blanket will be 3 feet by 5 feet. Th
mote1985 [20]

Answer:

The approximate total cost for the blanket is $10.08 ⇒ B

Step-by-step explanation:

The formula of the area of a rectangle is A = L × W

The formula of the perimeter of a rectangle is P = 2(L + W)

where:

  • L is the length of the rectangle
  • W is the width of the rectangle

∵ The baby blanket shaped a rectangle

∵ The dimensions of the blanket are 3 feet and 5 feet

- Find the area of the blanket

∵ A = 3 × 5 = 15 feet²

- Change feet to yard because the cost is by square yard

∵ 1 foot = \frac{1}{3} yard

∴ 1 foot² = (\frac{1}{3})^{2}=\frac{1}{9} yard²

∴ 15 feet² = 15 × (\frac{1}{9}) = \frac{5}{3} yards²

∴ The area of the blanket is  \frac{5}{3} yards²

∵ The fabric cost of the blanket is $1.25 per square yard

∴ The fabric cost =  \frac{5}{3} × 1.25

∴ The fabric cost = 2.08333 dollars

∵ Heather is going to put a ribbon border around it

- The length of the ribbon is equal to the perimeter of the blanket

∵ P = 2(3 + 5) = 16 feet

∴ The length of the ribbon is 16 feet

∵ The cost of the ribbon is $0.5 per foot

∴ The cost of the ribbon = 16 × 0.5

∴ The cost of the ribbon = 8 dollars

Now add the fabric cost to the ribbon cost to find the total cost of the blanket

∵ The total cost = 2.08333 + 8

∴ The total cost = 10.08333

- Round it to the nearest cent

∴ The total cost = 10.08 dollars

The approximate total cost for the blanket is $10.08

7 0
3 years ago
You are selling books for $4 each to raise money for a trip. You have to pay $10 for the table. Write a rule for the amount of b
Semmy [17]

Answer:

4b=y-10

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Thomas bought a new backpack that was 30% off the original price. The sale resulted in a $15 discount. What was the original pri
    10·1 answer
  • Use rousing or compatible numbers tu estimate the sum 87+34
    14·1 answer
  • The Lee family pays an instructor $50 for Joylin’s 40-minute drum lesson. How much does the instructor charge per minute for the
    10·2 answers
  • How do you graph this on graph paper using these coordinates? The graph is in shape of a cross. (9,4) (6,-12) (9,-12) (10,-8) (1
    15·1 answer
  • When the polynomial P(x) = 5x3 − 51x2 + kx − 9 is divided by x − 9, the remainder is 0. Which of the following is also a factor
    15·1 answer
  • Need to find perimeter
    7·1 answer
  • Passes through (-1, -5) and (2, 6)
    10·1 answer
  • You must travel 295 miles to reach the next clue. In the first two hours of the trip you drive 115 miles. If you must reach the
    10·1 answer
  • Start at the origin. Move 10 units right and 4 units up.​
    14·2 answers
  • A system of equation is shown x=10. 3x + 5y =20 what is the solution
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!