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WORTH 100 POINTS WORTH 100 POINTS WORTH 100 POINTS WORTH 100 POINTS HELPPPPPWrite an equation parallel to x-4y=20 that passes through the point 2,-5

Answers

Answer 1
Answer:

Answer:

  • x - 4y = 22

Step-by-step explanation:

Given line:

  • x - 4y = 20

Convert the equation into slope-intercept form:

  • x - 4y = 20
  • 4y = x - 20
  • y = 1/4x - 5

It has a slope of 1/4.

Parallel lines have equal slopes.

Find the parallel line lines that passes through the point (2, - 5):

  • y = 1/4x + b

Substitute x and y values to work out the value of b:

  • - 5 = 1/4*2 + b
  • - 5 = 1/2 + b
  • b = - 5 - 1/2
  • b = - 11/2

The line is:

  • y = 1/4x - 11/2

Covert this into standard form:

  • y = 1/4x - 11/2
  • 4y = x - 22
  • x - 4y = 22
Answer 2
Answer:
  • x-4y=20

Isolate y

\n \sf\longmapsto x-20=4y

\n \sf\longmapsto y=(1)/(4)x-5

  • m=1/4
  • Parallel lines have equal slope

Equation of line in point slope form

\n \sf\longmapsto y-y_1=m(x-x_1)

\n \sf\longmapsto y+5=1/4(x-2)

\n \sf\longmapsto 4y+20=x-2

\n \sf\longmapsto x-4y+22=0

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The number line below represents which combined inequality?number line with a closed circle on negative 4 and 3 with shading in between

x greater than or equal to −4 and x less than or equal to 3
x greater than or equal to −4 or x less than or equal to 3
x less than or equal to −4 and x greater than or equal to 3
x less than or equal to −4 or x greater than or equal to 3

Answers

x greater than or equal to −4 and x less than or equal to 3

This is because of the fact that it is in between.

Answer:

Step-by-step explanation:

X greater or equal to -4 and X less than or equal to 3

Answer number one

Sixteen college freshmen were asked to record the number of alcoholic drinks they typically consume in a week. Here are their data: 2, 4, 6, 0, 1, 10, 9, 0, 6, 3, 6, 8, 5, 4, 6, 2. What is the variance of the number of alcoholic drinks consumed per week?a.3.26
b.2.96
c.12.25
d.8.75

Answers

Solution: The correct option is d. 8.75

Explanation:

The formula for variance is:

Variance =\frac{\sum(x-\bar{x})^(2)}{n}

First we need to find the mean \bar{x} of the given data:

\bar{x}=(2+4+6+0+1+10+9+0+6+3+6+8+5+4+6+2)/(16)=(72)/(16) =4.5

Now let's find \sum(x-\bar{x})^(2), please have a look at the attached picture:

\therefore Variance = (140)/(16)=8.75

N f(x) =10-2( x ), Solve when given f(12) function notation

Answers

Answer:

-14

Step-by-step explanation:

10 - 2(12) = - 14

Find the following for the function f(x) = 3x2 + 4x - 4.(a) f(0)
(e) - f(x)
(b) f(3)
(f) f(x+3)
(c) f(-3)
(g) f(3x)
(d) f(-x)
(h) f(x+h)
(a) f(0) = (Simplify your answer.)
(b) f(3) = (Simplify your answer.)
(c) f(-3)=(Simplify your answer.)

Answers

Answer:

f(0)=2

f(3)=14

f(3)=14

Two vectors are said to be parallel if they point in the same direction or if they point in opposite directions. Part A Are these two vectors parallel? Show your work and explain. Part B Are these two vectors parallel? Show your work and explain.

Answers

Answer:

Knowing that those vectors start at the point (0,0) we can "think" them as lines.

As you may know, two lines are parallel if the slope is the same, then we can find the "slope" of the vectors and see if it is the same.

A) the vectors are: (√3, 1) and (-√3, -1)

You may remember that the way to find the slope of a line that passes through the points (x1, y1) and (x2, y2) is s = (y2 - y1)/(x2 - x1)

Because we know that our vectors also pass through the point (0,0)

then the slopes are:

 (√3, 1) -----> s = (1/√3)

 (-√3, -1)----> s = (-1/-√3) =  (1/√3)

The slope is the same, so the vectors are parallel.

Part B:

The vectors are: (2, 3) and (-3, -2)

the slopes are:

(2, 3) -----> s = 3/2

(-3, -2)----> s = -2/-3 = 2/3

the slopes are different, so the vectors are not parallel.

∥v∥=√((6)^2+(-8)^2)=√(36+64)=√100=10. Dividing v by its magnitude, we get the unit vector u=(v/∥v∥)=(6i−8j)/10=(3/5)i−(4/5)j. Therefore, two unit vectors parallel to v are (3/5)i−(4/5)j and −(3/5)i+(4/5)j.

a. Two unit vectors parallel to v=6i−8j can be found by dividing the vector v by its magnitude. The magnitude of v can be calculated using the formula ∥v∥=√(v1^2+v2^2), where v1 and v2 are the components of v in the x and y directions, respectively. In this case, v1=6 and v2=−8. Thus,

b. To find the value of b when v=⟨1/3,b⟩ is a unit vector, we need to calculate the magnitude of v and set it equal to 1. The magnitude of v is given by ∥v∥=√((1/3)^2+b^2). Setting this equal to 1, we have √((1/3)^2+b^2)=1. Squaring both sides of the equation, we get (1/3)^2+b^2=1. Simplifying, we have 1/9+b^2=1. Rearranging the equation, we find b^2=8/9. Taking the square root of both sides, we get b=±(2√2)/3. Therefore, the value of b when v is a unit vector is b=(2√2)/3 or b=−(2√2)/3.

c. To find all values of a such that w=ai−a/3j is a unit vector, we need to calculate the magnitude of w and set it equal to 1. The magnitude of w is given by ∥w∥=√(a^2+(-a/3)^2). Setting this equal to 1, we have √(a^2+(-a/3)^2)=1. Simplifying, we get a^2+(a^2/9)=1. Combining like terms, we have (10/9)a^2=1. Dividing both sides by 10/9, we get a^2=(9/10). Taking the square root of both sides, we have a=±√(9/10). Therefore, the values of a such that w is a unit vector are a=√(9/10) or a=−√(9/10).

Learn more about vectors parallel here:
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For what value of c is the relation a function?

Answers

Answer:the answer is 1, b option i just take the tes

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

the answer is one
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