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
elixir [45]
1 year ago
12

34. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.

Mathematics
1 answer:
skad [1K]1 year ago
5 0

Answer:

The linear equation for the line which passes through the points given as (-1,4) and (5,2), is written in the point-slope form as $y=\frac{1}{3} x-\frac{13}{3}$.

Step-by-step explanation:

A condition is given that a line passes through the points whose coordinates are (-1,4) and (5,2).

It is asked to find the linear equation which satisfies the given condition.

Step 1 of 3

Determine the slope of the line.

The points through which the line passes are given as (-1,4) and (5,2). Next, the formula for the slope is given as,

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substitute 2&4 for $y_{2}$ and $y_{1}$ respectively, and $5 \&-1$ for $x_{2}$ and $x_{1}$ respectively in the above formula. Then simplify to get the slope as follows,

m=\frac{2-4}{5-(-1)}$\\ $m=\frac{-2}{6}$\\ $m=-\frac{1}{3}$

Step 2 of 3

Write the linear equation in point-slope form.

A linear equation in point slope form is given as,

$y-y_{1}=m\left(x-x_{1}\right)$

Substitute $-\frac{1}{3}$ for m,-1 for $x_{1}$, and 4 for $y_{1}$ in the above equation and simplify using the distributive property as follows,

y-4=-\frac{1}{3}(x-(-1))$\\ $y-4=-\frac{1}{3}(x+1)$\\ $y-4=-\frac{1}{3} x-\frac{1}{3}$

Step 3 of 3

Simplify the equation further.

Add 4 on each side of the equation $y-4=\frac{1}{3} x-\frac{1}{3}$, and simplify as follows,

y-4+4=\frac{1}{3} x-\frac{1}{3}+4$\\ $y=\frac{1}{3} x-\frac{1+12}{3}$\\ $y=\frac{1}{3} x-\frac{13}{3}$

This is the required linear equation.

You might be interested in
Jamie's dog eats 3/4 pound of dog food each day. How many pounds of dog
Lena [83]

Answer:

The dog will eat 3 lbs

Step-by-step explanation:

Take the amount eaten per day and multiply by the number of days

3/4 * 4 = 3

The dog will eat 3 lbs

5 0
2 years ago
Read 2 more answers
Please it URGENT i am being timed on a test
elena-14-01-66 [18.8K]

Answer:

angle 1 = angle 7 = angle 9 = angle 15 and angle 3 = angle  5 = angle 11 = angle 13

Also,

angle 2 = angle 8 = angle 10 = angle 16 and angle 4 = angle 6 = angle 12 = angle 14

Step-by-step explanation:

Let suppose a and b are two parallel lines, and c and d be the transverse lines.  

The pairs of corresponding angles for a non-vertical line c are:

2-10, 7-15, 1-9, 8-16.

The pairs of corresponding angles for a non-vertical line d are:

4-12, 5-13, 3-11, 6-14.

Angles are formed at the intersection between the transverse lines and parallel lines. As the vertical angle is the opposite of the intersection. So, vertical angles are equal.

The pairs of vertical angles for a non-vertical line c are 1-7, 2-8, 9-15, 10-16

The pairs of vertical angles for a non-vertical line v are 3-5, 4-6, 11-13, 12-14

For transverse line c:

As the vertical angles are equal so the angles 1 = 7 = 9 = 15

As the corresponding angles are equal, so the angle ∠ 10 = ∠ 2 and the opposite of ∠2 is ∠8 which is vertical to ∠8 and vertical angles are also equal.

So, the angles 10 = 16 = 2 = 8 are also equal.

For transverse line d:

As the vertical angles are equal so the angles 3 = 5 = 11 = 13

As the corresponding angles are equal, so the angle ∠12 = ∠4 and the opposite of ∠4 is ∠6 which is vertical to ∠6 and vertical angles are also equal.

So, the angles 12 = 14 = 4 = 6 are also equal.

<u>LETS TAKE AN EXAMPLE</u>:

Let suppose the angle 1 is 110°

Since, vertical angle are equal. So, angle 7 will be also 110°.

Hence, angle 1 = 110° = angle 7

We also know that corresponding angles are equivalent. So,

angle 9 would also be equal to 110°, and as the opposite of angle 9 would also be equal to angle 9. So, the angle 9 and angle 15 have same angles.

So, angle 9 = 110° = angle 15

Hence, angle 1 = angle 7 = angle 9 = angle 15 will all be equal to 110°.

As, the angle 2 is the supplementary to this angle 1.

As the angle 1 is 110, so the angle 2 will be 70°  as they are supplementary to each other.

And if angle 2 is 70°, then its opposite angle will be equal to 8. As angle 2 and 8 are equal.

So, angle 2 = 70° = angle 8

As the corresponding angles are equal, so the corresponding of 2 will be the angle 10 which will be also equal to 70°, and the opposite of angle 10 is angle 16, which is again equal to angle 10.

So, angle 10 = 70° = angle 16

Hence:  angle 2 = angle 8 = angle 10 = angle 16 will be equal to 70°.

Since the transverse line d is parallel to c. So,

angle 1 = angle 7 = angle 9 = angle 15 which are equal to 110° will have same angles as of angle 3 = angle  5 = angle 11 = angle 13

So, angle 3 = angle  5 = angle 11 = angle 13 will also be equal to 110°

And,

angle 2 = angle 8 = angle 10 = angle 16 will which are equal to 70° will have same angles as of angle 4 = angle 6 = angle 12 = angle 14

So, angle 4 = angle 6 = angle 12 = angle 14 will be equal to 70°

Keywords: line, parallel lines, transverse line, angles

Learn More about simplifying radical expression from brainly.com/question/13209798

#learnwithBrainly

3 0
3 years ago
||<br> Area of a regular polygon
ELEN [110]

Answer:

The area of any regular polygon is given by the formula: Area = (a x p)/2, where a is the length of the apothem and p is the perimeter of the polygon. Plug the values of a and p in the formula and get the area. As an example, let's use a hexagon (6 sides) with a side (s) length of 10.

Step-by-step explanation:

idk if you added a picture but

5 0
3 years ago
WILL GIVE BRAINLIEST
Andre45 [30]

Probability formula P(wanted)=wanted/total

using this we can see P(red)=62/100

then reduce the fraction we get

31/50

Please give brainlliest thanks!

6 0
3 years ago
Read 2 more answers
Please show all work thank you math experts you’re the best !
Ne4ueva [31]

Answer:

1. -141

2. 0.98

3. 62.13

Step-by-step explanation:

1. 35 - 176 -> 176 - 35 = 141, then just make it negative

2. 0.55 x 1.79 = 0.9845 -> 0.98

3. 11.38 x 5.46 = 62.1348 -> 62.13

6 0
2 years ago
Other questions:
  • BRAINIEST ANSWER! Please Help :)
    15·1 answer
  • Solve the equation.<br><br> 5x + 8 − 3x = −10
    11·1 answer
  • If 0° &lt; θ&lt; 90°, θ is a/an what angle?​
    14·1 answer
  • A paper company needs to ship paper to a large printing business. The volume of each small box is 7 cubic feet and the volume of
    11·1 answer
  • Assume that the population of the world in 2010 was 6.9 billions and is growing at the rate of 1.1 percent a year. (a) set up a
    15·2 answers
  • Find the slope of the line that contains the points named.
    15·1 answer
  • Solve for x. enter you answer below as a fraction ​
    9·2 answers
  • PLEASE HELP (IM GIVING 100 POINTS)
    14·1 answer
  • The length of a rectangle is 4 cm less than twice its width. The perimeter of the
    8·1 answer
  • A stick of gum is 2 inches long. Are 10 sticks of gum longer than 3 feet? <br>​
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!