HELP PLEASE!!! Find an equation of a line through (√3,12) parallel to the line:

The system of equations is coincident. What are the missing values?

FrozenT [24]

$\rm x+3y=5|*4 \\ \\ 4*x+4*3y=4*5 \\ \\ \boxed{\rm 4x+12y=20}$

7 0

3 years ago

Can anyone help me solve 23, 24?

zimovet [89]

Answer:

Problem 23) $y=3x+6$

Problem 24) $y=-\frac{1}{3}x-5$

Step-by-step explanation:

step 1

Find the slope of the given line

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$A(0,2)\ B(3,1)$

Substitute the values

$m=\frac{1-2}{3-0}$

$m=-\frac{1}{3}$

step 2

Problem 23

we know that

If two lines are perpendicular then the product of its slopes is equal to minus 1

so

$m1*m2=-1$

Find the slope of the line

we have

$m1=-\frac{1}{3}$

substitute in the equation and solve for m2

$(-\frac{1}{3})*m2=-1$

$m2=3$

with the slope m2 and the point $(0,6)$ find the equation of the line

Remember that

The equation of the line in slope intercept form is equal to

$y=mx+b$

we have

$m=3$

$b=6$ -----> the given point is the y-intercept

substitute

$y=3x+6$

step 3

Problem 24

we know that

If two lines are parallel, then its slopes are the same

so

with the slope m1 and the point $(0,-5)$ find the equation of the line

The equation of the line in slope intercept form is equal to

$y=mx+b$

we have

$m=-\frac{1}{3}$

$b=-5$ -----> the given point is the y-intercept

substitute

$y=-\frac{1}{3}x-5$

8 0

3 years ago

Please help: A box contains 5 yellow balls, 3 blue, and 1 red ball. Two balls are drawn at random. Find the probability that:

Y_Kistochka [10]

Answer:

a) 0.2778

b) 0.3611

c) 0.1389

d) 0.0833

Step-by-step explanation:

We have a total of 5 + 3 + 1 = 9 balls

a) First ball being yellow: we have 5 yellow balls, so P1 = 5/9

Second ball being yellow after one yellow was drawn: we have 4 yellows and 8 balls, so P2 = 4/8 = 1/2

Both yellows: P = P1 * P2 = 5/18 = 0.2778

b) Both blues:

P1 = 3/9 = 1/3

P2 = 2/8 = 1/4

P = P1 * P2 = 1/12 = 0.0833

Both yellows or both blues: 5/18 + 1/12 = 0.2778 + 0.0833 = 0.3611

c) First yellow: P1 = 5/9

Second red: P2 = 1/8

Pa = P1 * P2 = 5/72

or

First red: P3 = 1/9

Second yellow: P4 = 5/8

Pb = P3 * P4 = 5/72

P = Pa + Pb = 10/72 = 5/36 = 0.1389

d) First blue: P1 = 3/9 = 1/3

Second red: P2 = 1/8

Pa = P1 * P2 = 1/24

or

First red: P3 = 1/9

Second blue: P4 = 3/8

Pb = P3 * P4 = 1/24

P = Pa + Pb = 2/24 = 1/12 = 0.0833

8 0

3 years ago

The measure of one of the acute angles in a right triangle is 42 1/3 . What is the measure of the other acute angle in the trian

Alex17521 [72]

Explanation: The sum of the measure of the internal angles of any triangle is 180o . In a right angled triangle, one angle will be 90o . Since we know the measure of one of the other acute (less than 90o ) angles, we subtract the sum of the two known angles from 180 to calculate the measure of the other acute angle.

8 0

3 years ago

Use the graph below to determine the number of solutions the system has. x=4 y=-x-1

GrogVix [38]

Answer:

The system x = 4 and y = -x - 1 has one solution

Step-by-step explanation:

x = 4 and y = -x - 1 intersects only once on the graph

5 0

3 years ago

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