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
inessss [21]
3 years ago
14

One linear equation is defined by points (1, 6) and (3, 7), while the other is defined by points (3, 6) and (5, 8). Which point

represents the solution of this system of equations
Mathematics
2 answers:
zysi [14]3 years ago
6 0
So we need to find the two lines...y=mx+b where m is the slope and b is the y-intercept.

m=(dy/dx)=(7-6)/(3-1)=1/2 so

y=x/2+b, now I'll use (1,6) to solve for b

6=1/2+b, b=5 1/2=11/2 so

y1=(x+11)/2

now the other line...

m=(8-6)/(5-3)=2/2=1

y2=x+b, using point (3,6) we solve for b

6=3+b, b=3 so

y2=x+3

Since this is just two lines they will only intersect at a single point and when they do, y=y so we can say:

x+3=(x+11)/2

2x+6=x+11

x+6=11

x=5, now use either line to solve for the corresponding y value...

y2=x+3 becomes y=5+3=8 so the solution to this system is the point:

(5,8)
Oksi-84 [34.3K]3 years ago
5 1

Answer:

(5, 8)

Step-by-step explanation:

Since, the linear equation defined by (x_1, y_1) and (x_2, y_2) is,

y-y_1=\frac{x_2-x_1}{y_2-y_1}(x-x_1)

Thus, the linear equation defined by points (1, 6) and (3, 7) is,

y-6=\frac{7-6}{3-1}(x-1)

y-6=\frac{1}{2}(x-1)

2y-12=x-1

\implies x-2y=-11-----(1)

Similarly, the linear equation is defined by points (3, 6) and (5, 8),

y-6=\frac{8-6}{5-3}(x-3)

y-6=\frac{2}{2}(x-3)

y-6=x-3

\implies x-y=-3------(2)

Equation (1) -  equation (2),

-y = -8

⇒ y = 8

From equation (1),

x-2(8)=-11

x-16=-11

x = - 11 + 16 = 5

Hence, point (5,8) represents the solution of this system of equations.

You might be interested in
0540-0058= ???<br> In military time
Tatiana [17]

Answer:

0442 (4:42 normal time)

btw plz give brainliest

3 0
2 years ago
Define a cubic polynomial and a binomial use only one variable in each). Show how to use the Vertical Method to multiply these t
Sedbober [7]

Cubic polynomial

{x}^{3}  +  {2x}^{2}  - 5x - 10

Binomial

2x - 3

By vertical method of multiplication we get,

{2x}^{4}  +  {x}^{3}  -  {16x}^{2}  - 5x + 30

8 0
3 years ago
Which number would make this number sentence true?
nlexa [21]

Answer: 15

Step-by-step explanation: Take 12 and change the -3 to a regular 3.

(12 + 3 = 15.)

Whichever number in the question that’s bigger determines what integer it will have.

4 0
3 years ago
Read 2 more answers
g In R simulate a sample of size 20 from a normal distribution with mean µ = 50 and standard deviation σ = 6. Hint: Use rnorm(20
Illusion [34]

Answer:

> a<-rnorm(20,50,6)

> a

[1] 51.72213 53.09989 59.89221 32.44023 47.59386 33.59892 47.26718 55.61510 47.95505 48.19296 54.46905

[12] 45.78072 57.30045 57.91624 50.83297 52.61790 62.07713 53.75661 49.34651 53.01501

Then we can find the mean and the standard deviation with the following formulas:

> mean(a)

[1] 50.72451

> sqrt(var(a))

[1] 7.470221

Step-by-step explanation:

For this case first we need to create the sample of size 20 for the following distribution:

X\sim N(\mu = 50, \sigma =6)

And we can use the following code: rnorm(20,50,6) and we got this output:

> a<-rnorm(20,50,6)

> a

[1] 51.72213 53.09989 59.89221 32.44023 47.59386 33.59892 47.26718 55.61510 47.95505 48.19296 54.46905

[12] 45.78072 57.30045 57.91624 50.83297 52.61790 62.07713 53.75661 49.34651 53.01501

Then we can find the mean and the standard deviation with the following formulas:

> mean(a)

[1] 50.72451

> sqrt(var(a))

[1] 7.470221

5 0
3 years ago
4 &gt; p - 1
alexdok [17]

Answer:

p < 5

I think this is the answer?..

5 0
2 years ago
Other questions:
  • Thanks for your response!<br> Question will be show✔
    11·1 answer
  • 10 5/18-8 5/6 = anyone know
    5·1 answer
  • Pls help question b
    15·1 answer
  • Look at the figure below: What is the length, in units, of segment CD? 8 9 6.25 7.25
    11·1 answer
  • A number that is prime, between 60-100,1s place is 2 less then 10s place.
    5·1 answer
  • Melissa used 4 cups of sugar to bake 54 cookies. If she’s only used 1 cup of sugar, what would be an equivalent ratio of cups to
    7·1 answer
  • Which of the following is the equation for the line of symmetry in this figure?
    15·1 answer
  • 3 A class has 6 boys and 15 girls. What is the ratio of boys to girls?​
    13·2 answers
  • Which is greater 1.831 or 1.381?​
    15·1 answer
  • What is the distance between points (-3,2) (7,13)
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!