12. Determine whether the given number belongs
to each set.
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Whole
Numbers
Integers
Rational
Numbers
es
- 34

Answer:

[tex]\bold{x =cos\theta}\\\bold{y=sin\theta}[/tex]

Step-by-step explanation:

The given system of linear equations is:

[tex](cos\theta)x+(sin\theta)y=1\\(-sin\theta)x+(cos\theta)y=0[/tex]

We have to solve the equations for the values of [tex]x, y[/tex].

Let us use elimination method in which we eliminate one of the variables from the two variables.

For this, let us multiply the first equation by [tex]sin\theta[/tex] and second equation by [tex]cos\theta[/tex]

Now, the equations become:

[tex](cos\theta.sin\theta)x+(sin\theta.sin\theta)y=sin\theta\\\Rightarrow (cos\theta.sin\theta)x+(sin^2\theta)y=sin\theta ....... (1)\\\\(-sin\theta.cos\theta)x+(cos\theta.cos\theta)y=0\\\Rightarrow (-sin\theta.cos\theta)x+(cos^2\theta)y=0 ..... (2)[/tex]

Now, let us add (1) and (2):

[tex](sin^2\theta)y+(cos^2\theta)y=sin\theta\\\Rightarrow (sin^2\theta+cos^2\theta)y=sin\theta\\\Rightarrow (1)y=sin\theta\\\Rightarrow y = sin\theta[/tex]

Using the equation:

[tex](-sin\theta)x+(cos\theta)y=0[/tex]

Putting value of [tex]y[/tex]:

[tex]\Rightarrow (-sin\theta)x+(cos\theta)sin\theta=0\\\Rightarrow (sin\theta)x=(cos\theta)sin\theta\\\Rightarrow x = cos\theta[/tex]

So, the answer to the system of linear equations is:

[tex]\bold{x =cos\theta}\\\bold{y=sin\theta}[/tex]

Answer:

$1.5

Step-by-step explanation:

[tex]160\:hot\:dogs = \$240\\1 \: hot \:dog = \$x\\\\160x = 240\\\\\frac{160x}{160} = \frac{240}{160} \\\\x = \$1.5[/tex]

Answer:

I think u messed ur numbers up

Answer:

5

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

The bus fare in a city is $1.50. People who use the bus have the option of purchasing a monthly coupon book for $21.00. With the coupon book, the fare is reduced to $0.50. Determine the number of times in a month the bus must be used so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book.

Solution

Let

y = number of bus fares.

Cost of bus fares without coupon book = 1.50y

Cost of bus fares with coupon book = .50y + 21

Equate cost of bus fares without coupon book and cost of bus fares with coupon book

1.50y = .50y + 21

Subtract .50y from both sides of the equation

1.50y - .50y = .50y + 21 - .50y

1.00y = 21

Divide both sides by 1.00

y = 21 / 1.00

y = 21 times

Answer:

23

Step-by-step explanation:

3x = 69°

This is because they are vertically opposite angles.

You would have to divide 69 by 3.

69 ÷ 3 = 23

23 · 3 = 69

Answer:

The solution of the Given matrix

  ( x₁ ,    x ₂ ) = ( - 5 , 4 )

Step-by-step explanation:

Step(i):-

Given equations are  x₁+4 x₂ = 11 ...(i)

                                 2 x₁ + 7 x₂= 18 ...(ii)

The matrix form

                                A X = B

            [tex]\left[\begin{array}{ccc}1&4\\2&7\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}11\\8\\\end{array}\right][/tex]

Step(ii):-

      [tex]\left[\begin{array}{ccc}1&4\\2&7\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}11\\8\\\end{array}\right][/tex]

The Augmented Matrix form is

[tex][AB] = \left[\begin{array}{ccc}1&4&11\\2&7&18\\\end{array}\right][/tex]

Apply Row operations,  R₂ → R₂-2 R₁

[tex][AB] = \left[\begin{array}{ccc}1&4&11\\0&-1&-4\\\end{array}\right][/tex]  

The matrix form

                   [tex]\left[\begin{array}{ccc}1&4\\0&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}11\\-4\\\end{array}\right][/tex]

The equations are

                     x₁ + 4 x₂ = 11 ...(a)

                         - x ₂ = - 4

                            x ₂ = 4

Substitute   x ₂ = 4 in equation (a)

                      x₁ + 4 x₂ = 11

                      x₁ = 11 - 16

                        x₁ = -5

Final answer:-

The solution of the Given matrix

  ( x₁ ,    x ₂ ) = ( - 5 , 4 )

Answer:

a. ∠ABE  b. ∠DC   c. obtuse  angle  d.∠ FBC: OBTUSE ANGLE    

                                                              ∠EBF: REFELX ANGLE

                                                              ∠ABC: ACUTE ANGLE

e. ∠ DBC                f. 108+117 ÷36= 6.25

Step-by-step explanation:

Answer:

[-4, 2]

Step-by-step explanation:

the domain is between -4 and 2, but it also includes those numbers, so you get:

[-4, 2]

Answer :

6. x=28

7.x =6

8. x =9

9. x =9

Step-by-step explanation:

[tex] \frac{x + 2}{10} = 3[/tex]

[tex]x + 2 = 3 \times 10 \\ x + 2 = 30 \\ x = 30 - 2 \\ x = 28[/tex]

6.

(x+2)/10 = 3

Cross multiply

x+2 = 10 ×3

x+2 =30

Collect like terms and simplify

x =30-2

x = 28

7.

[tex]8x + 9 - 5x = 27 \\ 8x - 5x = 27 - 9 \\ 3x = 18[/tex]

[tex] \frac{3x}{3} = \frac{18}{3} \\x = 6[/tex]

8x +9 -5x= 27

Collect like terms and simplify

8x-5x =27-9

3x =18

Divide both sides of the equation by 3

3x/3 = 18/3

x = 6

8.

10x+8=8x+26

Collect like terms

10x-8x=26-8

2x = 18

Divide both sides of the equation by 2

2x/2 = 18/2

x = 9

9.

2(x-5)+4x=x+35

Use 2 to open the bracket

2 × x =2x

2×(-5) =-10

2x-10+4x =x+35

Collect like terms and simplify

2x+4x-x = 35+10

5x = 45

Divide both sides of the equation by 5

5x/5 = 45/5

x =9

Answer:

f(5)=13 g(8)=12 f(-8)= -26 g(-10)=-15

Step-by-step explanation:

1) 5*3=15

15-2=13

2) 8*.5*3=12

3) -8*3=-24

-24-2= -26

4) -10*.5*3= -15

Answer:

15-13=2

13+2=15

x=2

now double check the answer and

2+13=15

x = 2 is your answer

Answer: y=3x-3

Step-by-step explanation:

To find a line that is parallel to the function, we know that the slope must stay the same. Parallel lines NEVER cross. This means the slope MUST be the same. All we have to change is the y-intercept. We can use the given point to find the correct y-intercept.

y=3x+b                                     [plug in (4,9)]

9=3(4)+b                                 [multiply]

9=12+b                                     [subtract both sides by 12]

b=-3    

Now, we know that the y-intercept is -3, we can put together our equation. y=3x-3

Answer:

[tex]\boxed{3}[/tex]

Step-by-step explanation:

[tex]6\frac{1}{2} /1\frac{3}{4} =\frac{13}{2} /\frac{7}{4}=\frac{13}{2} *\frac{4}{7}=\frac{52}{14} =\frac{26}{7} =3.714[/tex]

Answer:

6 1/2 pies =   26/4 pies and 7/4 are sold per day

It will last

26/4 divided by 7/4 days =

104 / 28 = 26 / 7 = 3.7142857143  days

Step-by-step explanation:

[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

[tex]M=(\frac{8-6}{2},\frac{-2-5}{2})[/tex]

[tex]M=(1,-\frac{7}{2})[/tex]

Hope this helps.

頑張って!

Answer:

y= x-2 /4

Step-by-step explanation:

x=4y+2

4y=x-2

answer:

y= x-2 / 4

Answer:

well the 6 in 683.5 is in the hundreds, and the 6 in 30.67 is in the tenths so the one in 30.67 is actually smaller than the 6 in 683.5

Step-by-step explanation:

a. The number of chips Data should order to achieve a 95 percent service probability before his trip is 40.

b. The maximum order quantity of chips Data will ever have to order to ensure a 95 percent service probability.

Given:

Lieutenant Commander Data needs a 95 percent service probability for his monthly trip to Gamma Hydra City to pick up iso-linear chips.

The trip takes Data about four days.

Data uses iso-linear chips at an average rate of seven per day (seven days per week).

The standard deviation of demand for iso-linear chips is three per day.

Data currently has 40 chips in inventory.

To find:

a. The number of chips Data should order to achieve a 95 percent service probability before his trip.

b. The maximum order quantity of chips Data will ever have to order to ensure .

Therefore, to determine the order quantity, Data needs to calculate the safety stock using the formula:

Safety Stock = Z x Standard Deviation of Demand

where:

For the maximum order quantity, Data should consider the worst-case scenario.

The maximum order quantity will be the safety stock plus the maximum daily demand during the trip (four days) and the current inventory (40 chips).

By calculating these values, Lieutenant Commander Data can ensure a sufficient inventory level and meet the 95 percent service probability during his trip to Gamma Hydra City.

Learn more about service probability here:

https://brainly.com/question/33811154

#SPJ4

Answer:

$24.50

Step-by-step explanation:

$35 - 30% = $24.50.

Thus, that is the answer.

Hope this helps!

Answer- $24.50

$35 - 30% is $24.50.

Gorgi saved $10.50 as well.

Hope this helps!

Step-by-step explanation:

5y - 1 = 4y + 5

5y -4y = 5 + 1

Y (1y) = 6

Answer:

Hello!

You can compare graphs by looking at their rate of change, and y intercept.

Another way you can compare graphs is that you can see if both graphs' lines intersect. I hope this helps you! :)

Have a nice day! :D

Answer:

D. 6 seconds.

Step-by-step explanation:

When the ball hits the ground f(t) = 0 , so:

-1/2t^2 + 2t + 6 = 0

Take out the -1/2:

-1/2(t^2 - 4t - 12) = 0

-1/2(t - 6)(t + 2) = 0

t = -2 , 6.  We ignore the negative zero.

So the answer is 6 seconds.

Answer:

6 seconds is right!

I got it right in class

Hello. This question is incomplete. The full question is:

There is a harvest festival each year on the planet Bozone. During that time, most of the Bozone residents sit down to rejoice and eat roast snig. Past history shows that a reasonable price-demand equation is:

p=300−4x where x is the number of kilograms of snig sold, and p is the price per kilogram of snig in the local currency, the Bozat.  

To sell an additional kilogram of snig, how much does the price need to decrease?   Price needs to decrease by  Bozats.

Answer:

It is necessary to decrease 4 bozats in the price so that an additional 1 kq of snig can be sold.

Step-by-step explanation:

You can achieve this result through a very simple and straightforward calculation.

First it is necessary that you assume the equation (x + 1) for X. This way you will have the mathematical expression:

300-4 (X + 1) = 300-4x-4.

Answer:

X=4

Step-by-step explanation:

collect like term than move the rate and divide by 12

Answer:

B. $8.50 and $8.99

Step-by-step explanation:

Answer:

B. $8.50 and $8.99

Step-by-step explanation:

Answer:

Subtract 4y from both sides of the equation.

Hey there! The answer is C. I can help you with more if you need it.