Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)
3 tan(θ) sin(θ) − 2 tan(θ) = 0

The solutions are:

[tex]x =3+2\sqrt{3}i\\\\\:x=3-2\sqrt{3}i[/tex]

Solution:

[tex]f(x) = x^2 - 6x + 21[/tex]

We have to find solutions when f(x) = 0

[tex]x^2 - 6x + 21 = 0[/tex]

Solve by quadratic formula

[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=-6,\:c=21\\\\x=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\cdot \:21}}{2\cdot \:1}[/tex]

[tex]x = \frac{6 \pm \sqrt{\left(-6\right)^2-4\cdot \:1\cdot \:21}}{2\cdot \:1}\\\\Simplify\\\\x = \frac{6 \pm \sqrt{36 - 84}}{2}\\\\x = \frac{6 \pm \sqrt{-48}}{2}\\\\x = \frac{6 \pm i \sqrt{48}}{2}\\\\simplify\\\\x = \frac{6 \pm 4\sqrt{3}i}{2}\\[/tex]

[tex]x = 3 \pm 2 \sqrt{3} i[/tex]

We have two solutions:

[tex]x = 3 + 2 \sqrt{3} i\\\\x = 3 - 2 \sqrt{3} i[/tex]

Thus the solutions are:

[tex]x =3+2\sqrt{3}i\\\\\:x=3-2\sqrt{3}i[/tex]

Answer:

I think it's $12.80 but I might be wrong.

Each person will have to contribute $6.40.

To find out how much money each person will have to contribute to get to the university and back, we can first find the total cost of the trip. The distance to the university and back is 2 times the distance to the university, which is 105 miles. So the total distance is 2 * 105 = 210 miles. Roberta's car can travel 8.2 miles per dollar of gasoline, so the total cost of the trip is 210 / 8.2 = 25.61 dollars. Since Roberta and three friends are splitting the cost evenly, each person will have to contribute 25.61 / 4 = 6.4025 dollars. Rounding to the nearest cent, each person will have to contribute $6.40.

go to negative to and move left once and that'll give you 2 and 1 6ths then go to 1 and move right once cause 7 over 6 is 1 and 1 over 6

The value of x is 13°.

Solution:

In triangle, sum of all the interior angles = 180°

m∠A + m∠B + m∠C = 180°

(3x)° + (4x – 1)° + 90° = 180°

3x° + 4x° – 1° + 90° = 180°

7x° + 89° = 180°

Subtract 89° from both sides of the equation, we get

7x° = 91°

Divide by 7 from both sides of the equation, we get

x° = 13°

The value of x is 13°.

Answer:

3 and 8/12

Step-by-step explanation:

You subtract 3 5/12 from 7 1/12 to get 3 8/12

Answer:

1 and 8/12 or 1 and 2/3

Step-by-step explanation:

    7 1/12-3 5/12

    2 1/12-   5/12

    1 8/12

Answer:

The correct answer is A.

Answer:

B

Just multiply by 4 to isolate x; because 4 isn't negative, u keep the sign the same.

Answer:

90 calories in total

Step-by-step explanation:

We can solve this equation through the following steps:

Step One: Since we are told that a banana is 20 less calories than an orange, we can create the Let Statements:

Let x= the calories in a banana

Let x-20=the calories in an orange

Step Two: Create an equation

Since we are told "7 bananas have the same calories as 9 oranges" we translate"

7x=9(x-20) Distribute

7x=9x-180 Subtract 9x from both sides of the equation

7x-9x=-180 Simplify

-2x=180 Divide both sides by -2

x=90

∴There are 90 calories in a banana.

option c {(0, -5), (2,9), (-3, -26)}  is correct  . All others doesn't satisfy the equation .

Step-by-step explanation:

We have , If y = 7x - 5, following set of ordered pairs {(0, -5), (2,9), (-3, -26)} . Let's check for this

(0, -5):

⇒ [tex]y = 7x-5[/tex]

⇒ [tex]y = 7(0)-5[/tex]

⇒ [tex]y =-5[/tex]

So , it's correct ordered pair .

(2,9):

⇒ [tex]y = 7x-5[/tex]

⇒ [tex]y = 7(2)-5[/tex]

⇒ [tex]y =9[/tex]

So , it's correct ordered pair .

(-3,-26):

⇒ [tex]y = 7x-5[/tex]

⇒ [tex]y = 7(-3)-5[/tex]

⇒ [tex]y =-26[/tex]

So , it's correct ordered pair .

Therefore, option c {(0, -5), (2,9), (-3, -26)}  is correct  . All others doesn't satisfy the equation .

The speed is the distance covered by an object at a particular time. The speed of bus B is 70 miles per hour.

The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.

[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]

Given that Bus A can travel 125 miles in 3 hours. While Bus B can travel 85 more miles than bus A within the same time. Therefore, we can write,

Distance traveled by Bus B = 125 miles + 85 miles = 210 miles

Time is taken by Bus B = 3 hours

Now, the speed of the bus B can be written as,

Speed of Bus B = Distance Covered / Time taken

                          = 210 miles / 3 hours

                          = 70 miles per hour

Hence, the speed of bus B is 70 miles per hour.

Learn more about Speed here:

https://brainly.com/question/15100898

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Answer:

it cant be kinetic unless its pushed and gains height, as its falling it is simply potential energy and gets speed in different stages of the fall.

Step-by-step explanation:

Answer:

The answer is 8 months

Step-by-step explanation:

The new computer tablet is $460. She paid $100 at the time so I subtracted $100 from $460, which equals to $360. The monthly payments are $45 a month, so I divided $360 by $45, which equals 8. It takes 8 more months to finish the payment.

MARK AS BRAINLIEST

Answer:

8 payments

Step-by-step explanation:

460-100=360

45 x 8 = 360

Answer: x=40

Step-by-step explanation:

(4x+40)=3x

Step 1: open the bracket

4x + 40 = 3x

Step 2: Combine like terms

4x - 3x = 40

x = 40

I hope this helps.

Answer:

No.

Step-by-step explanation:

3/4 cannot be simplified. Neither can 7/8. Also, 3/4 as a decimal is 0.75, and 7/8 as a decimal is 0.875.

Answer:

No

Step-by-step explanation:

Is 3/4 less than 7/8? Is 3/4 smaller than 7/8? These are the same questions with one answer.

To get the answer, we first convert each fraction into decimal numbers. We do this by dividing the numerator by the denominator for each fraction as illustrated below:

3/4 = 0.75

7/8 = 0.875

Then, we compare the two decimal numbers to get the answer.

0.75 is less than 0.875.

Therefore, 3/4 is less than 7/8 and the answer to the question "Is 3/4 less than 7/8?" is yes.

Answer:  Furniture over weeks

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

So, for the function f (w(h)) = hours /week x (furniture /hours)

Because "hours" are in both terms, and one is the numerator and the other is the denominator, they can be cancelled with each other.

f (w(h)) = furniture / week

Feel free to ask for more if needed or if you did not understand something.

Answer: D) Furniture over weeks

Step-by-step explanation:

I took the test

Answer:

18

Step-by-step explanation:

First you would have the divide 2 and 12 which is 6 then you would muplty 6 by 3 because you need to find how many fictional book which is 18

p. ls I am 99% sure this explanation is right

The number of fiction books is 18.

Ratio expresses the relationship between two values. It is the number of times that one value is contained within other value(s).

Number of books = (number of mystery books x sum of ratios) / ratio of mystery books

(12 x 5) / 2 = 30 books

number of fiction books = (ratio of fiction books / sum of ratios) x total number of books

3/5 x 30 = 18 books

To learn more about ratios, please check: https://brainly.com/question/25927869

Mariko caught 10 rockfish and 14 bluefish on her fishing trip.

Let's define the number of rockfish caught as x and the number of bluefish caught as y.

According to the given information, the average weight of each rockfish is 2.5lbs and the average weight of each bluefish is 8lbs.

We can form two equations based on the total weight of all the fish and the total number of fish caught:

We can solve this system of equations to find the values of x and y by either substitution or elimination method. Using the elimination method:

Multiplying Equation 1 by 2.5, we get 2.5x + 2.5y = 60

Subtracting this equation from Equation 2, we get 8y - 2.5y = 137 - 60

Simplifying, we have 5.5y = 77

Dividing both sides by 5.5, we get y = 14

Substituting this value back into Equation 1, we have x + 14 = 24

Simplifying, we get x = 10

Therefore, Mariko caught 10 rockfish and 14 bluefish.

Step-by-step explanation:

6 ( 3 - √-16) + √-64 ( 3- √-16)

18 - 6(-4)^2*1/2 + 3 × (-8)^2*1/2 - √1024

18 - 6 (-4) + 3× (-8) - 32

18 + 24 - 24 - 32

18 - 32

-14

Answer:

192 inches

Step-by-step explanation:

I dont know I tried

It will take approximately 1.5 hours for the snowfall in both towns to be equal.

The question asks to determine when the snowfall in two different towns will be equal. The first town starts with 2 inches of snow and accumulates 6 inches every hour. The second town starts with 8 inches of snow and accumulates 2 inches every hour. To find when the depths will be equal, we need to set up an equation where the snow depths of both towns are set equal to each other and then solve for time (t).

Let t be the number of hours required for the snow depths to be equal.

For the first town: Initial depth + (Rate of snowfall * Time) = 2 inches + (6 inches/hour * t)

For the second town: Initial depth + (Rate of snowfall *Time) = 8 inches + (2 inches/hour *t)

Setting both expressions equal, we get: 2 + 6t = 8 + 2t. By solving for t, we subtract 2t from both sides and also subtract 2 from both sides to obtain: 4t = 6. Then we divide both sides by 4 to find t = 1.5 hours.

So, it will take 1.5 hours for the snow depths in both towns to be equal.

Answer:

[tex]10/10 = 1[/tex]

[tex]x=\frac{19}{6} \\[/tex]

[tex]5/6 =0.83[/tex]

[tex]6/19 = 0.31578947[/tex]

[tex]19/6 = 3.16[/tex]

Reduce the expression by cancelling the common factors.

= 32/37

In decimal;

0.864

Answer:

I'm assuming the equation is:

2x^2 -10x +7 = 0

x = (-b +- sqr root (b^2 - 4ac)) / 2a

x = (--10 +-sqr root (100 -4*2*7)) / 4

x = (10 +- sqr root (44)) / 4

x1 = (10 + 6.6332495807 ) /4

x1 = 16.6332495807 / 4

x1 = 4.1583123952

x2 =(10 - 6.6332495807 ) /4

x2 = 3.3667504193  / 4

x2 = 0.8416876048

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

5^2 = 25

5 * 5 = 25

Answer:

25

Step-by-step explanation:

Step 1:  Convert words into an expression

5 to the power of two

5^2

Step 2:  Solve

5^2

25

Answer:  25

32 + 5% = 1.6

The tax is $1.60

The final bill is $33.60

Answer: the answer is $33.60

Answer:

y = -3/4x + 5

Step-by-step explanation:

Slope intercept form is y=mx + b

First, find the slope of the line. the points are (0,5) and (4,2), as marked. To find the slope, you do (y2-y1)/(x2-x1). Fill in the numbers and you get

(2-5)/(4-0). Simplify and you get -3/4 is the slope. Then, to find b, you have to fill in one coordinate pair and the slope into y=mx+b. So, I used (0,5).

5=(-3/4)(0) + b

Then you get 5=b by solving, and you fill in the slope and the y intercept in the slope intercept form equation. y = -3/4x +5. This is how you find the answer.

Answer:

See below

Step-by-step explanation:

The inequality is d<-80 since the problem states you go deeper than -80 feet.

As for graphing the inequality, you use a open circle with the arrow pointing left.

<= means closed

>= means closed

< means open

> means open

Answer:

Question:  You need to figure out the inequality. Here is the full question: On their first dive, scientists explore a part of the ocean floor that is 80 feet below sea level. This depth can be represented by the integer -80. On their second dive, they explore a deeper depth. Write an inequality that represents the possible depth, d, of the scientist's second dive. After you figure that out you can answer the question above.

d < -80

Open ended at -80 pointing toward -200

Answer:

3(7) -15+8

21-15+8

6+8= 14

Answer:

0

Step-by-step explanation:

i/8=0

i=0*8

i=0