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Galina-37 [17]
2 years ago
5

A line with slope 3 intersects a line with slope 5 at the point (10, 15). What is the distance between the x-intercepts of these

two lines?​
Mathematics
1 answer:
kogti [31]2 years ago
6 0

The distance between the intercepts of both lines is 2 units

The equation of a line in slope intercept form is:

y = mx + b

Where:

m \to slope

b \to y intercept

For the first line, we have:

m_1 = 3 ---- the slope

So, the equation of the first line is:

y = 3x + b_1

For the second line, we have:

m_2 = 5 --- the slope

So, the equation of the second line is:

y = 5x + b_2

Both lines intersect at (10,15) means that (10,15) is a common solution to the equation of both lines

i.e.

(x,y) = (10,15)

Substitute these values in the first equation and solve for b

y = 3x + b_1

15 = 3*10 + b_1

15 = 30 + b_1

b_1 = 15 - 30

b_1 = -15

So, the equation of the first line is

y = 3x - 15

Repeat the same process for the second line

y = 5x + b_2

15 = 5*10 + b_2

15 = 50 + b_2

b_2 = 15 - 50

b_2 =  -35

So, the equation of the second line is

y =5x - 35

The x intercept is when y =0

So, we substitute 0 for y and solve for x in the equations of both lines

For line 1

y = 3x - 15

0 = 3x - 15

3x= 15 ---- Collect like terms

x = 5 --- Divide both sides by 3

The x intercept of line 1 is 5

For line 2

y =5x - 35

0 = 5x - 35

5x = 35 --- Collect like terms

x = 7 -- Divide both sides by 5

The x intercept of line 2 is 7

The distance (d) between both is the difference in the calculated intercepts:

d = 7 - 5

d = 2

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What is the equation of a line that has a slope of 1/2 and passes through the point (2, -3)
Travka [436]

Answer:

This equation would be -3=1/2(2)+b. This is because you take the formula y=mx+b and then plug in the numerals when m=slope.

6 0
2 years ago
If a circle’s circumference is 28.26 inches, what would be the best estimate of its diameter?
bixtya [17]

Answer:

82.43

Step-by-step explanation:

The circumference formula is C = πd.

Using 3.14, the answer is 82.425.

Rounded to the nearest hundredth, it would be 82.43.

7 0
2 years ago
Number 9<br><br> (What should Brad do to correct the error that he made?)
LenaWriter [7]

The right answer is Option D.

Step-by-step explanation:

Steps done by Brad;

-3(2+w)=-45\\2+w=-15\\w=-17

Brad made the error in first step where he divided both sides by 3; but one left side, he did not put the negative sign.

In order to correct his error, Brad should divide -45 by -3 to get 15.

Therefore;

-3(w+2)=-45\\w+2=\frac{-45}{-3}\\w+2=15

Thus,

Divide -45 by -3 to get 15.

The right answer is Option D.

Keywords: linear expression, division

Learn more about division at:

  • brainly.com/question/11584312
  • brainly.com/question/116059

#LearnwithBrainly

5 0
2 years ago
Yo can someone help me out
tia_tia [17]

Answer:

Your answer is 3,947 ÷ 45 = 87 r 32

Hope this Helps

<3

4 0
2 years ago
Read 2 more answers
PLS RESPOND FAST!! What is the value of x in the diagram belo2v<br> A. 9<br> B. 8<br> C. 7<br> D. 6
Gekata [30.6K]

Answer:

C

Step-by-step explanation:

The 2 triangles are similar (AA postulate ), thus the ratios of corresponding sides are equal, that is

\frac{14}{2} = \frac{49}{x} ( cross- multiply )

14x = 98 ( divide both sides by 14 )

x = 7 → C

5 0
2 years ago
Read 2 more answers
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