Given the vectors in component form:


r = ⟨8, 4⟩


s = ⟨–3, –4⟩


t = ⟨–5, 1⟩


Perform the operations.


5r – 3s + 8t


What is the magnitude and direction angle of the resultant vector?

A. 10.8, θ = 56.3°

B. 18.4, θ = 119.4°

C. 41.0, θ = 77.3°

D. 97.6, θ = 24.2°

Answer:

72.32

Step-by-step explanation:

i have spoken

Answer:

72.32 degrees

Step-by-step explanation:

the picture shows a supplementary angle, which equals 180 degrees.

first, solve for x.

since the entire figure equals 180 degrees, set the equation equal to 180. then add in the measurements, which are 7x, 8x, and 44.4.

180 = 7x + 8x + 44.4

combine like terms (7x and 8x).

180 = 7x + 8x + 44.4 ⇒ 180 = 15x + 44.4

subtract 44.4 from both sides. the positive 44.4 will cancel out, so all you have to do is subtract 44.4 from 180.

180 - 44.4 = 135.6

now, your equation is...

135.6 = 15x

divide both sides by 15.

(135.6)/15 = (15x)/15 ⇒ 9.04 = x, or x = 9.04

now plug 9.04 in for x in both 7x and 8x.

7x ⇒ 7(9.04) ⇒ 63.28

8x ⇒ 8(9.04) ⇒ 72.32

*the highlighted angle, 8x, is 72.32 degrees.

checking your work:

now, all your measurements are 63.28, 72.32, and 44.4

check your work by adding all the measurements together and setting that equal to 180.

63.28 + 72.32 + 44.4 = 180

180 = 180

since both sides are equal, all of the values are correct!

now that you know your work is correct, it is fully safe to say that the highlighted angle is 72.32 degrees.

Answer: x = 2,340 homes without children

There are 2,340 homes without children.

Step-by-step explanation:

'x' represent the number of homes without children

'y' represent the number of homes with children

x : y = 9 : 7

Since the total number of homes is 4160 means x + y = 4160.

From x + y = 4160 follows y = 4160 - x.

Plug y = 4160 - x into x : y = 9 : 7

x : (4160 - x) = 9 : 7

Answer:

(x+4)^2-11

hope it's helpful ❤❤❤❤

❤

THANK YOU.

Answer:

the awnser is 20

Step-by-step explanation:

10

6

÷  

1

12

=  

10

6

×  

12

1

=  

10 × 12

6 × 1

=  

120

6

=  

120 ÷ 6

6 ÷ 6

=  20

Step-by-step explanation:

10/6 / 1/12

= 20

10        12             120

     x            =  

6           1               6

120/6=20

hope it helps! :3

Answer:

Assuming the 19 stood for an exponent, q = 1.098...

Step-by-step explanation:

Plugging in [tex]q^{19} = q + 4[/tex] in the graphical calculator, we can see that the solution is approximately q=1.098. There are no ways of solving this equation algebraically.

Answer:

q = 15

Step-by-step explanation:

19 = q + 4

Subtract 4 from each side

19-4 = q + 4-4

15 = q

[tex]correct is it Because Correct[/tex]A.

Answer:

The answer of your question : 85.92 divided by 4 is equal to (21.48)

Answer:

[tex]P(First\ White\ and\ Second\ Blue) = \frac{3}{28}[/tex]

[tex]P(Same) = \frac{67}{210}[/tex]

Step-by-step explanation:

Given (Omitted from the question)

[tex]Red = 7[/tex]

[tex]White = 9[/tex]

[tex]Blue = 5[/tex]

Solving (a): [tex]P(First\ White\ and\ Second\ Blue)[/tex]

This is calculated using:

[tex]P(First\ White\ and\ Second\ Blue) = P(White) * P(Blue)[/tex]

[tex]P(First\ White\ and\ Second\ Blue) = \frac{n(White)}{Total} * \frac{n(Blue)}{Total - 1}[/tex]

We used Total - 1 because it is a probability without replacement

So, we have:

[tex]P(First\ White\ and\ Second\ Blue) = \frac{9}{21} * \frac{5}{21 - 1}[/tex]

[tex]P(First\ White\ and\ Second\ Blue) = \frac{9}{21} * \frac{5}{20}[/tex]

[tex]P(First\ White\ and\ Second\ Blue) = \frac{9*5}{21*20}[/tex]

[tex]P(First\ White\ and\ Second\ Blue) = \frac{45}{420}[/tex]

[tex]P(First\ White\ and\ Second\ Blue) = \frac{3}{28}[/tex]

Solving (b) [tex]P(Same)[/tex]

This is calculated as:

[tex]P(Same) = P(First\ Blue\ and Second\ Blue)\[/tex][tex]or\ P(First\ Red\ and Second\ Red)\ or\ P(First\ White\ and Second\ White)[/tex]

[tex]P(Same) = (\frac{n(Blue)}{Total} * \frac{n(Blue)-1}{Total-1})+(\frac{n(Red)}{Total} * \frac{n(Red)-1}{Total-1})+(\frac{n(White)}{Total} * \frac{n(White)-1}{Total-1})[/tex]

[tex]P(Same) = (\frac{5}{21} * \frac{4}{20})+(\frac{7}{21} * \frac{6}{20})+(\frac{9}{21} * \frac{8}{20})[/tex]

[tex]P(Same) = \frac{20}{420}+\frac{42}{420} +\frac{72}{420}[/tex]

[tex]P(Same) = \frac{20+42+72}{420}[/tex]

[tex]P(Same) = \frac{134}{420}[/tex]

[tex]P(Same) = \frac{67}{210}[/tex]

Answer:

[tex]Ratio = 9 :80[/tex]

Step-by-step explanation:

Given

[tex]A_1 = 18ft^2[/tex] --- Area of smaller rectangle

[tex]A_2 = 160ft^2[/tex] --- Area of bigger rectangle

Required

Determine the area of the areas.

The ratio is calculated by the dividing the areas of rectangles.

[tex]Ratio = \frac{A_1}{A_2}[/tex]

Substitute values for A2 and A1

[tex]Ratio = \frac{18ft^2}{160ft^2}[/tex]

[tex]Ratio = \frac{18}{160}[/tex]

Simplify the fraction

[tex]Ratio = \frac{9}{80}[/tex]

Represent as ratio

[tex]Ratio = 9 :80[/tex]

Hence, the ratio of the rectangles is 1 to 9

Answer:

[tex]Cost = \$28[/tex]

Step-by-step explanation:

Given

Represent Goldfish with g and hermit crabs with h.

The first statement, we have:

[tex]7g + 3h = 26[/tex]

The second statement, we have:

[tex]4g + 5h = 28[/tex]

Required

Determine the selling price of 6 goldfish and 4 hermit crabs

The equations are:

[tex]7g + 3h = 26[/tex] --- (1)

[tex]4g + 5h = 28[/tex] --- (2)

Make g the subject in (2)

[tex]4g + 5h = 28[/tex]

[tex]4g = 28 - 5h[/tex]

Divide both sides by 4

[tex]g = \frac{1}{4}(28 - 5h)[/tex]

Substitute [tex]\frac{1}{4}(28 - 5h)[/tex] for g in (1)

[tex]7g + 3h = 26[/tex]

[tex]7(\frac{1}{4}(28 - 5h)) + 3h = 26[/tex]

[tex]\frac{7}{4}(28 - 5h) + 3h = 26[/tex]

Multiply through by 4

[tex]4 * \frac{7}{4}(28 - 5h) + 4*3h = 26*4[/tex]

[tex]7(28 - 5h) + 4*3h = 26*4[/tex]

Open bracket

[tex]196 - 35h + 12h = 104[/tex]

[tex]196 -23h = 104[/tex]

Collect Like Terms

[tex]-23h = 104-196[/tex]

[tex]-23h = -92[/tex]

Make h the subject

[tex]h = \frac{-92}{-23}[/tex]

[tex]h = \frac{92}{23}[/tex]

[tex]h = 4[/tex]

Substitute 4 for h in [tex]g = \frac{1}{4}(28 - 5h)[/tex]

[tex]g = \frac{1}{4}(28 - 5*4)[/tex]

[tex]g = \frac{1}{4}(28 - 20)[/tex]

[tex]g = \frac{1}{4}(8)[/tex]

[tex]g = 2[/tex]

This implies that:

1 goldfish = $2

1 hermit crab = $4

The cost of 6 goldfish and 4 hermit crabs is:

[tex]Cost = 6g + 4h[/tex]

[tex]Cost = 6*\$2 + 4*\$4[/tex]

[tex]Cost = \$12 + \$16[/tex]

[tex]Cost = \$28[/tex]

Answer:

$257,681.60

Step-by-step explanation:

What's happening here is called "compounding," and the appropriate formula is  A = P(1 + r)^t, where r is the rate of increase as a decimal fraction.

With the given data, we have:

A = $160,000(1 + 0.10)^(5), or:

    = $160,000(1.10)^5, or:

     = $160,000(1.6105) = $257,681.60 :  condo value after 5 years

Answer:

30 mg

Step-by-step explanation:

Flow rate of dopamine per hour:

Flow rate of dopamine per hour =  (95g)*(30ml/hr) / 95ml

Flow rate of dopamine per hour = 30mg

Answer:

Y=1/2x

Step-by-step explanation:

the y intercept is 0 so we dont show it, and slope is rise over run, it goes up one unit every two times to the right

i hope this help!

Answer:

11 h and 32 m is the answer

Answer:

114

Step-by-step explanation:

A= length x width

A= 6x9

A=114

B!!!!!!!!!!!!!!!!!!!!!!

hope this helps

Answer:

None so im assuming its the final one?

Step-by-step explanation:

Answer:

c i think

Step-by-step explanation:

Charlie travelled greater amount of time.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

D(t) = 60 |t- 3|

for, t=0

D(0) = 60*3 = 180

For t=1,

D(1) = 120

For t= 2

D(2) = 60

According to the data of Charlie and Annabeth it can bee seen that charlie had been travelling greater amount of time.

Learn more about function here:

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Answer:

Charlie!

Step-by-step explanation:

Answer:

you would divide

Step-by-step explanation:

325 ÷ 13= $25 a week

I hope this helped

Answer:

325 divided by 13 = 25

Step-by-step explanation:

Answer:

The cup will be filled 6 times.

Step-by-step explanation:

If her measuring cup only holds 1/4 cups then we need to find how many 1/4 cups are in 3/4 cups:

(1/4) + (1/4) + (1/4) = 3/4

3/4 = 3/4

The measuring cup will have to be filled 3 times for 1 loaf.

If she has 2 loaves that means that she has to fill her 1/4 measuring cup 6 times (because 2 * 3 = 6)

Hope this helps!!

- Kay :)

Answer:

1%=0.07

Step-by-step explanation:

Im going to assume the question says what is 1% of 7.

so 100%=7

divide my 10 to get to 10%

10%=0.7

do the same thing.

1%=0.07

you just go backwards when dividing by 10.

9514 1404 393

Answer:

  700

Step-by-step explanation:

You want to find x such that ...

  1% of x = 7

  0.01x = 7 . . . . . . . . . . use math symbols

  x = 7/0.01 = 700 . . . . divide by the coefficient of x

1% of 700 is 7.

Answer:

21

Step-by-step explanation:

126/6= 21 sit ups per minute

Answer:

-5

Step-by-step explanation:

f(x) is a function.

f(0) means when x=0 what is the y value

We can look at the graph and when x=0 y is at -5

so the answer is -5

Answer:

50(1.25p) and 50(0.25p + 1.00)

Step-by-step explanation:

They both equal the same answer.

50(1.25p) = 62.5

50(0.25p + 1.00) = 62.5

when in parentheses, you multiply

50 * 1.25 = 62.5

50 * 0.25 + 1.00 = 62.5

The expression for the given scenario is 50(0.25p+1.00). Therefore, option A and C are the correct answers.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Given that, Mr. Hamilton sponsors the creative writing club.

He went to a local printing shop that charges $0.25 per page in the book and $1.00 to bind the pages together.

The booklet Mr. Hamilton is making has p pages, and he plans to make 50 booklets.

So, the expression is 50(0.25p+1.00)

= 12.50p+50.0

Therefore, option A and C are the correct answers.

To learn more about an expression visit;

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Answer:

angle 2 is 63 reason is interior angle

angle 3 is 117 corresponding angle

Answer:

measure 1 = 117 degrees

measure 2 = 180 - 117 = 63 degrees

i dont know he reason because i cant see the options

Step-by-step explanation:

its the ch eating off the principal test for me