2 x 6 - 21 divided by 7

Answer:

for the second question , all you have to do is substitute , the first point plotted is x and the second point is b , ploy those points in the equation and remember that to find x we make y= 0 and to find y we make x =0

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

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

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

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

I'd go back through the lesson and take notes of steps in the last pages they give the review of the lesson, help full and a time saver. other than that I would try to write down all definitions and words listed in the module, but if you want to have a complete list of every thing go to the home page and get the guided notes, you can fill them out when looking back at the lesson.

if you have a short time to gather notes just go through and right down what you can, you can always keep the glossary open when doing a DBA. hope anyone who see's this does well :)

sorry I couldn't help much i was unaware of the course you are taking

Answer:

1,254.54

Step-by-step explanation:

Answer:

1,254.54

Step-by-step explanation:

Total amount, T = $100 million.

Cost of wheat per ton, C = $300 .

Price per fighter plane, c = $15 million.

Now,

Price of 5 fighter planes, P = $( 15 × 5 ) = $75 million.

Amount left = $( 100 - 75 ) = $25 million.

So,

Number of tons of wheat government can buy is :

[tex]n=\dfrac{25\times 1000000}{300}\\\\n = 83333.33\ tons[/tex]

Therefore, number of tons of wheat the government can afford is 83333.33 tons.

Hence, this is the required solution.

Answer:

If the lines BC and DE are parallel, the value of c is c=-2

Step-by-step explanation:

We are given line segment BC with end points B(2, 2) and C(9,6) and line segment DE with endpoints  D(c, -7) and E(5, -3).

Using slope formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex] we can find point c

When 2 lines are parallel there slope is same.

So, Slope of line BC =Slope of Line DE

[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]

We have:

[tex]x_1=2, y_1=2, x_2=9, y_2=6 \ for \ line \ BC \ and \\\x_1=c, y_1=-7, x_2=5, y_2=-3 \ for \ line \ DE \[/tex]

Putting values and finding c

[tex]\frac{6-2}{9-2}=\frac{-3-(-7)}{5-c}\\ \frac{4}{7}=\frac{-3+7}{5-c} \\ \frac{4}{7}=\frac{4}{5-c} \\Cross \ multiply:\\4(5-c)=4*7\\20-4c=28\\-4c=28-20\\-4c=8\\c=\frac{8}{-4}\\c=-2[/tex]

So, If the lines BC and DE are parallel, the value of c is c=-2

Answer:

f=2 c=4

Step-by-step explanation:

8 times 2 equals 16 plus 2 times 4 equals 24 in total.

Answer:

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.

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 )

Answer:

12yd = 36ft

Why: For every 1 yard you have 3 feet

2 yards=6 3=9 and so on

Step-by-step explanation:

12 yards = 36 feet

if this answer is correct:

give a like and rate me 5

Answer:

8 spaces away

Step-by-step explanation:

hope this helped :-)

Answer:

B

Step-by-step explanation:

Answer:

729

Step-by-step explanation:

hope it helps

Answer: 27/2 = 13 1 2\

also 729

Answer:

1:8

Step-by-step explanation:

You subtract 19 and 8, and you get 11 then you put them in ration form

Step-by-step explanation:

Answer:

D. y=(×-2)^3(×-3)^3

Step-by-step explanation:

the x and y axis interception

Answer: 500

Step-by-step explanation:

The remainder of the question is:

How many units does the company need to sell to reach the target profit?

The required sales to break even will be calculated as:

= (Fixed cost + Required profit) / ( Price per unit - Variable cost)

= (120000 - 80000) / (100 - 20)

= 40000/80

= 500

The company needs to sell 500 units.

Answer:

Equivalent ratios:

3 : 10   6 : 20   9 : 30   12 : 40   15 : 50   18 : 60   21 : 70   24 : 80   27 : 90   30 : 100   33 : 110   36 : 120   39 : 130   42 : 140   45 : 150   48 : 160   51 : 170   54 : 180   57 : 190   60 : 200   63 : 210   66 : 220   69 : 230   72 : 240   75 : 250   78 : 260   81 : 270   84 : 280   87 : 290   90 : 300

( Brainlyst will help my rank <3 )

Step-by-step explanation:

7.90.

Answer:

sorry i cant answer without the picture it wont make sense.

Answer:

A, D

Step-by-step explanation:

edge 2021

Answer:

the smaller number is 13 and the larger number is 67

Answer:

92 km/h

Step-by-step explanation:

Answer:

The interest on the investment is $16,170.93811

Step-by-step explanation:

The rule of the compound interest is [tex]A=P(1+\frac{r}{n})^{nt}[/tex], where

∵ The investment is $45,000

∴ P = 45,000

∵ The interest on the investment is compounded annually at 5.25%

∴ r = 5.25% = 5.25 ÷ 100

∴ r = 0.0525

∴ n = 1 ⇒ compound annually

∵ It is for 6 years

∴ t = 6

→ Substitute them in the rule above

∵ [tex]A=45,000(1+\frac{0.0525}{1})^{1(6)}[/tex]

∴ [tex]A=45,000(1.0525)^{6}[/tex]

∴ A = 61,170.93811

∵ I = A - P, where I is the interest

∴ I = 61,170.93811 - 45,000

∴ I = 16,170.93811

∴ The interest on the investment is $16,170.93811

Answer:

-23

Step-by-step explanation:

the equation of the line is y=-2/3x-23 so the b in the equation (y=mx+b) is the y int so that is -23

Answer:

B. 16.4°

Step-by-step explanation:

reference angle = x = [tex] \theta [/tex]

Side length opposite to x = 20 ft = opp

Adjacent side length = 68 ft = adj

Apply the following trigonometric ratios formula:

[tex] tan(\theta) = \frac{opp}{adj} [/tex]

Plug in the values into the formula

[tex] tan(x) = \frac{20}{68} [/tex]

[tex] tan(x) = 0.2941 [/tex]

[tex] x = tan^{-1}(0.2941) [/tex]

[tex] x = 16.3886 [/tex]

x = 16.4° (nearest tenth)

Answer:

B. 16.4

Step-by-step explanation:

Answer:

1/2 of the 1/3 jar of paint is used for each project

Step-by-step explanation:

Answer:

6. a) 7/3

7. b) Y=20/3(x)