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
Schach [20]
1 year ago
11

A line passes through the points (-8, 1) and (-1, 6). A second line passes through the points (-3,0) and (-8,-5). What is the po

int of intersection of the two lines?
Mathematics
1 answer:
finlep [7]1 year ago
6 0
\begin{gathered} y=mx+b \\ m=\frac{6-1}{-1+8}=\frac{5}{7} \\ 6=\frac{5}{7}(-1)+b \\ 6+\frac{5}{7}=b \\ b=\frac{42+5}{7}=\frac{47}{7} \\ y=\frac{5}{7}x+\frac{47}{7} \end{gathered}

For the second line

\begin{gathered} y=mx+b \\ m=\frac{-5-0}{-8+3}=\frac{-5}{-5}=1 \\ 0=1(-3)+b \\ b=3 \\ y=x+3 \end{gathered}

The intersection will be

\begin{gathered} y=\frac{5}{7}x+\frac{47}{7} \\ x+3=\frac{5}{7}x+\frac{47}{7} \\ x-\frac{5}{7}x=\frac{47}{7}-3 \\ \frac{7x-5x}{7}=\frac{47-21}{7} \\ \frac{2x}{7}=\frac{26}{7} \\ 14x=182 \\ x=\frac{182}{14} \\ x=13 \\  \\ y=13+3=16 \end{gathered}

Therefore, the point of intersection is (13, 16)

You might be interested in
What numbers add to 10 and multiply to negative 144?
Ilya [14]
The answers would be -8 and 18

-8×18 = -144
-8+18 = 18-8 = 10
4 0
3 years ago
The table shows the relationship between the cost of renting a car from the Wrecko Car Rental Company and the number of days for
Fudgin [204]

Answer:

The cost of renting the car for 20 days is $481

Step-by-step explanation:

The table of values can be formed as follows;

Day,   Cost

1,         $44

2,        $67

3,        $90

4,        $113

7,        $182

10,      $251

From the given values and the scatter plot, there is a straight line relationship between the cost and the number of days of rental of a car.

The line of best fit is therefore a straight line and from the constant increase in cost ($23) for each extra day of rental, it is possible to find the slope, m, of the data as follows;

Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}

(x₁, y,) and (x₂, y₂) can be taken as (1, $44) and (3, $90) respectively to give;

Slope, \, m =\dfrac{90-44}{3-1} = \dfrac{46}{2} = 23 \ as \ stated \ above

The equation in slope and intercept form is therefore, y  - 44 = 23×(x - 1), which gives;

y - 44 = 23·x - 23

y = 23·x - 23 + 44 = 23·x + 21

The cost of renting the car for 20 days is then;

10×23 + 21 = $481

The cost of renting the car for 20 days = $481.

5 0
3 years ago
Solve the inequality. –8 ≤ 2x – 4 < 4
Nostrana [21]
First;
-8≤2x-4
-4≤2x
-2≤x

Then;
2x-4<4
2x<8
x<4

-2≤x<4
C is the correct answer.
4 0
3 years ago
4/5 miles in 1/5 hour unit rate
eduard

Answer:

4 miles an hour

Step-by-step explanation:

5 0
2 years ago
Write the number in standard form. 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000)
Nookie1986 [14]

Answer:

374.392

Step-by-step explanation:

3*100=300

4*10=40

7*1=7

3*(1/10)=0.3

9*(1/100)=0.09

2*(1/1000)=0.002

Put them together and you get 347.392

3 0
3 years ago
Other questions:
  • vbnthe length of a rectangle is 4 1/2 centimeters the width of the rectangle is 2 2/5 centimeters what is the area of the rectan
    11·1 answer
  • The map shows the location of the airport and a warehouse in a city. Though not displayed on the map, there is also a factory 64
    7·1 answer
  • Write the solution as an inequality -10x&gt;250
    12·2 answers
  • What is the lcm for 21,28,and 35
    6·2 answers
  • Question 4 of 10
    12·2 answers
  • Dasher spent half as much as prancer did on holiday presents this year and cupid spent 3 times more than dasher. If the total sp
    10·1 answer
  • The sum of Jada and Sophie's ages is, at most, 18. Sophie is 3 years older than twice Jada's age. Write an inequality model Jada
    13·1 answer
  • Landen has his daily video gaming time each day for 7 days. But one day he plays and extra 50 minutes. His total video playing t
    6·1 answer
  • Find the slope of the line that passes through the pair of points (6,-2) and (5,-4).
    8·2 answers
  • Bank statement practice
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!