Write an equation of the line passing through point P(4,0) that is parallel to the line -x + 2y = 12.

Answers

Answer 1
arallel lines have the same slope
-x+2y=12
2y=x+12
y=(1/2)x+6
the slope is 1/2
using the point-slope form of a line...
y-y1=m(x-x1) where m is the slope and (x1,y1) is (4,0)
y-0=(1/2)(x-4)
y=(1/2)x-2 is the equation of the line
check: 0=(1/2)(4)-2
0=2-2
0=0
Answer 2
Answer: y= 1/2x-2
___________________
Explanation:

-x+2y=12
2y=12+x
divide both sides by 2
y= 6+ x/2
as they are parallel, therefore, their slopes are equal
hence,
put P(4;0) in the equation to find y intercept( y=kx+b, there b is y intercept)
0= 1/2 * 4+ b
b=-2
hence,
our equation is
y=1/2x-2
Hope it helps :)


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Answer:-3/7
Use two points and then do y-y/x-x

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6. a) 7/3

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(4,-3) and (-1,-9) The Distance Between the two points in simplest radical form

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Answer:

(5,6)

Step-by-step explanation:

so first yall

u find the difference between 4 and -1 which is 5 so u go 5 spaces right so it would be 5

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Which of the following results in the expression 0.22 x 86?

Answers

Answer:

18.92

Step-by-step explanation:

Im preatty sure this is right

Answer:

18.92

I multiplied 0.22 and 86


Which of them is true?

A. [ -18]< 6
B.[ -6] < [ -8]
C.[8]<[-6]
D.[-6] < -8 ​

Answers

the answer is A
positive > negative

Answer:

B. |-6| < |-8|

Step-by-step explanation:

The absolute value will always make the number positive. B is the only option in which (once absolute value is used) will make a true statement.

|-6| < |-8| = 6 < 8

( 6 is less than 8 )

The resultant of the vectors a = 3i - 2j and b = pi - 2pj is parallel to the vector c = 2i - 3j.
a) Find the value of p
b) Find the resultant of vectors a and b.

Please help me with this question, thank you ​

Answers

Part (a)

The resultant vector is the vector formed by adding the two vectors a and b. So we effectively add the corresponding components.

You can use the parallelogram law as a visual alternative.

Adding a and b leads to

a+b = (3i-2j) + (pi-2pj)

a+b = (3i+pi) + (-2j-2pj)

a+b = (3+p)i - (2+2p)j

Define vector d to be d = a+b so we can use it later below.

Recall that parallel vectors point in the same direction. This means the ratio of their components or coordinates are equal.

We can say the following

(x coord of d)/(x coord of c) = (y coord of d)/(y coord of c)

(3+p)/(2) = (-(2+2p))/(-3)

Let's solve for p

(3+p)/(2) = (-(2+2p))/(-3)

(3+p)/(2) = (2+2p)/3

3(3+p) = 2(2+2p) .... cross multiply

9+3p = 4+4p

4p+4 = 3p+9

4p-3p = 9-4

p = 5

Answer:  p = 5

========================================================

Part (b)

Since p = 5, from part (a), we can determine vector b

b = pi - 2pj

b = 5i - 2*5j

b = 5i - 10j

Then add vectors a and b to get

a+b = (3i-2j) + (5i - 10j)

a+b = (3i+5i) + (-2j - 10j)

a+b = (3+5)i - (2+10)j

a+b = 8i - 12j

Or we can say

a+b = (3+p)i - (2+2p)j  .... from part (a)

a+b = (3+5)i - (2+2*5)j ... plugging in p = 5

a+b = 8i - 12j

Note the ratio of the components of vector d and vector c are such

(x coord of d)/(x coord of c) = (y coord of d)/(y coord of c)

8/2 = -12/(-3)

4 = 4

This helps confirm the answer

You could also graph the vectors c = 2i - 3j and d = 8i - 12j to note the two lines produce the same slope -3/2. We can see that -12/8 = -3/2. Lines of the same slope are parallel lines

Answer:  8i - 12j

a.

The value of p is 5

Since vector a = 3i - 2j and vector b = pi - 2pj, the resultant of vectors a and b is R = a + b

= 3i - 2j + pi - 2pj

= (3 + p)i - 2(1 + p)j

Since R is aparallel to vector c = 2i - 3j, it implies that the cross product of R and c is zero.

The cross product of two vectors a and b is a × b = absinФ where a and b are the magnitudes of a and b and Ф is the angle between them.

So, R × c = [(3 + p)i - 2(1 + p)j] × [2i - 3j]

= (3 + p)i × 2i + (3 + p)i × (-3j) + (-2(1 + p)]j × 2i + (-2(1 + p)]j×(-3j)

= 0 - 3(3 + p)k - 4(1 + p)(-k) + 0

= -3(3 + p)k + 4(1 + p)k

= [-3(3 + p) + 4(1 + p)]k

= [-9 - 3p + 4 + 4p)]k

= [-9 + 4 - 3p + 4p)]k

=  [-5 + p]k

[-5 + p]k = RcsinФ.

Since R and c are parallel, Ф = 0°

So, Rcsin0° = Rc × 0 = 0

So,   [-5 + p]k = 0

-5 + p = 0

p = 5

The value of p is 5

b.

The resultant of vectors a and b is R = 8i - 12j

Since p = 5 and the resultant of vectors a and b is R = (3 + p)i - 2(1 + p)j

Substituting the value of p = 5 into r, we have

R = (3 + p)i - 2(1 + p)j

R = (3 + 5)i - 2(1 + 5)j

R = 8i - 2(6)j

R = 8i - 12j

So, the resultant of vectors a and b is R = 8i - 12j

Learn more about resultant of vectors here:

https://brainly.com/question/14358602

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Lin needs 3 cups of flour and 6 cups of sugar. Noah needs 6 cups of sugar and 4 cups of flour.

Step-by-step explanation:

I want you to figure out how to do.

Read and understand the situation below, and make a complete plan to solve Mang Jose’s problem.

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Answers

Explanation:

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3. Luxury: Green = $20 per gallon.

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2. if he chooses the Golden sun brand/color white then he will need approximately 11 gallons of paint  (2700/250 square fit) = 10.8, which would cost = $165 (11*$15).

3. if he chooses the Luxury brand/color green then he will need approximately 11 gallons of paint  (2700/250 square fit) = 10.8, which would cost = $220 (11*$20).

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Answer:

c

Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

If a cotton candy vendor has 16 blue cones which is 50% of the total number of cones, then how many TOTAL cones does he have i need answers FAST like before the end of the week

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Step-by-step explanation:

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She will get back 48.60

Answer:

$46.10

Step-by-step explanation:

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Step-by-step explanation:

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Answer:

33

Step-by-step explanation:

Answer:

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How much refund is due? Tax withheld $3578 and Tax due $2365.
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Answers

B. Subtract both numbers to find the refund amount

Answer:

The answer is B) $1,213

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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