What are all the solutions to the equation sin 2x = 2cos x in the interval [0, 2π)?

Step-by-step explanation:

Join C to B to form BC, thereby creating ∆ ABC

OC is the radius of the circle (O is the center of the circle).

AD is the tangent to the circle at point C

When a radius of a circle meets with a tangent of the same circle, the angle between them is 90°

<ACB = <ACO = 90°

<ABC = 180 - (<ACB + <BAC)

= 180-(90+40)

= 50

Look closely,

<ABC = x = 50°

.

.

Do same as Example 7

Join O to B to form OB, which is the radius of the circle.

<ABO= 90°

< BOA = 50°

<OAB= x+25= 180-(90+50)

x+25= 40°

x = 15°

Answer: 32 glasses

Step-by-step explanation: If 1 quart is 4 cups and 8 ounces are in 1 cup, 8x4=32 so there are 32 ounces in a quart. If he has 6 quarts 32x6+192 ounces. if each glass is 6 ounces 192/6=32.

Answer:

  400

Step-by-step explanation:

The 20 terms of the sum can be formed into 10 pairs, each with a sum of 40:

  = (1 +39) +(3 +37) +(5 +35) + ... +(19 +21)

  = 40 × 10 = 400

The indicated sum is 400.

Answer:

45.4

Step-by-step explanation:

A=πr2=π·3.82≈45.3646

Answer:

Between 9 and 10

Step-by-step explanation:

I just multiplied 2/3 by 14

Does that help?

Answer:

C

Step-by-step explanation:

first do 14/1 times 2/3

it will be 28/3, then divide that

it should be 9.3 repeating

which is in the range of 9 and 10

The product of 2.5 x 10^2 and 3.7 x 10^5 expressed in scientific notation is 9.25 x 10^7.

It is the way of writing a large number between 1 to 10 with a power of 10.

We have,

To multiply two numbers in scientific notation, we multiply their coefficients and add their exponents. So, we have:

= (2.5 x 10²) x (3.7 x 10^5)

= (2.5 x 3.7) x 10^(2+5)

= 9.25 x 10^7

Therefore,

The product of 2.5 x 10^2 and 3.7 x 10^5 expressed in scientific notation is 9.25 x 10^7.

Learn more about scientific notation here:

https://brainly.com/question/18073768

#SPJ2

Answer:

K=19

Step-by-step explanation:

MY WRITTEN RESPONCE BELOW

Answer:

[tex]\frac{7}{26}[/tex]

Step-by-step explanation:

let x be the denominator of the fraction then x - 19 is the numerator , so

[tex]\frac{x-19}{x}[/tex] ← is the original fraction

subtrating 1 from the numerator and adding 1 to the denominator , then

[tex]\frac{x-20}{x+1}[/tex] = [tex]\frac{2}{9}[/tex] ( cross- multiply )

9(x - 20) = 2(x + 1) ← distribute parenthesis on both sides

9x - 180 = 2x + 2 (subtract 2x from both sides )

7x - 180 = 2 ( add 180 to both sides )

7x = 182 ( divide both sides by 7 )

x = 26

Then the original fraction is

[tex]\frac{26-19}{26}[/tex] = [tex]\frac{7}{26}[/tex]

Answer:

-13x +8y

Step-by-step explanation:

-5x+2y-8x+6y

rearranging;

-5x-8x+2y+6y

(-5x-8x)+(2y+6y)

(-13x)+(8y)

Answer:

-13X+8Y.

Step-by-step explanation:

Combine like terms, -5x-8x = -13x.

2y+6y = 8y. goodluck.

Answer:

[tex]\huge\boxed{\sf 7.04\ grams}[/tex]

Step-by-step explanation:

A penny = 2.5 grams

A dime = 2.27 grams

2 dimes = 2.27 × 2 grams

             = 4.45 grams

Weight of a penny and 2 times:

= 2.5 + 4.54

= 7.04 grams

[tex]\rule[225]{225}{2}[/tex]

Answer:

16.3

Step-by-step explanation:

they are each 1.63 hope this helps pls mark as brainiest

Answer: $16.30

Step-by-step explanation:

$4.89÷3= $1.63

$1.63×10= $16.30

Answer:

30 cm

Step-by-step explanation:

So what we are given here is a case of similar figures.

When we are given similar figures, the ratio of the width of both figures should be similar to the ratio of the length of both figures.

I'll demonstrate it in the following problem.

We know one rectangle has a length of 18 cm and a width of 6cm.

The other rectangle has a width of 10 cm.

Let's take a ratio of the width of both rectangles.

We take the width of 6 cm for the first rectangle to the width of 10 cm for the second rectangle.

w1 = 6 cm

w2 = 10 cm

6 cm : 10 cm = 3 : 5

The ratio given is 3 : 5. Let's use these ratios to find lengths.

l1 = 18 cm

l2 = x cm

3 : 5 = 18 : x

To find x, we just solve this like an equation, where we let ratios be division signs.

3/5 = 18/x

Multiply both sides by 5x

3x = 90

Divide both sides by 3

x = 30 cm

The length of the missing side is 30 cm. We found the answer to the length by using the ratios obtained from the widths.

Answer:

  -3, 2

Step-by-step explanation:

The roots of a function are also called the "zeros" or "x-intercepts." They are the values of x where the function value is zero.

__

Here, the graph crosses the x-axis at x=-3 and x=2. The roots of the function are -3 and 2.

The average change in distance for each increase of 1 in the iron number is -10, and the y-intercept of the graphs are not the same

From the graph, we have the following points:

(x,y) = (4, 145) and (3,155)

The average change in distance is calculated using:

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

So, we have:

[tex]m = \frac{155 - 145}{3 - 4}[/tex]

Evaluate

m = -10

Hence, the average change in distance for each increase of 1 in the iron number is -10

The rate, -10 in (a) means that:

The distance decreases by 10 yards for each number of iron

The y-intercept is the point where the graph crosses the y-axis

From the attached graphs, we have:

Hence, the y-intercept of the graphs are not the same

Read more about linear regression at:

https://brainly.com/question/17844286

#SPJ1

Answer:

140°

Step-by-step explanation:

edge just did the assignment

Step-by-step explanation:

Step 1:  Answer question 1

[tex]6(4) = x(3)[/tex]

[tex]\frac{24}{3} = \frac{3x}{3}[/tex]

[tex]8 = x[/tex]

Answer: [tex]x=8[/tex]

Step 2:  Answer question 2

The radius of a circle is equal to the halfway point of a circle and in this example it is 29.5 cm.  To find the diameter of a circle we multiply the radius of the circle by 2.

[tex]29.5\ cm * 2[/tex]

[tex]59\ cm[/tex]

Answer:  [tex]59\ cm[/tex]

Step 3:  Answer question 3

The diameter of a circle is a line across a circle and in this example it is 22 cm.  To find the radius of a circle we divide the diameter of the circle by 2.

[tex]\frac{22\ cm}{2}[/tex]

[tex]11\ cm[/tex]

Answer: [tex]11\ cm[/tex]

Answer:

1. x=8

2. a

3. d

Step-by-step explanation:

Answer:

Please find the answer attached :)

Answer:

8

Step-by-step explanation:

When you calculate it -4/3 times is 4 so add 4 to that and you get 4. Hope this helps

Answer:

$160

Step-by-step explanation:

75/15=5 which means he makes $5 per hour

5*32=160

Answer:

I don't see the equation for the line, but I describe the process.

Step-by-step explanation:

Let's look for a line that has the form y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).

The slope of a perpendicular line is the negative inverse of the slope of the reference line.  In this case the equation for the reference line is missing.  If it is in the form y=mx+b, take the m value, invert it, and then give it a "-" sign.  For example, if the line is y = 2x +1, the negative inverse of the slope of 2 would be -(1/2).

The new line will have this new slope [-(1/m)] to make it y = -(1/m)x + b.

To find b, use the given point of (3,-2) in the equation and solve for b:

y = -(1/m)x + b

-2 = -(1/m)*(3) + b

Then solve for b and you'll have the equation for the solution to the problem.

Answer:

Divide by 4

In this case one side would be 27.5

Step-by-step explanation:

A square has four sides so 110/4=27.5

The sector of the circle is bounded by 2 radii, and the measure of the central angle that forms the sector is 120 degrees

The given parameters are:

The area is calculated using

Area = α/360 * πr^2

So, we have:

α/360 * π * 15^2 = 75π

Evaluate the exponent

α/360 * π * 225 = 75π

Divide both sides by 75π

α/360 * 3 = 1

Multiply

α/120  = 1

Multiply both sides by 120

α = 120

Hence, the measure of the central angle that forms the sector is 120 degrees

Read more about sectors at:

https://brainly.com/question/10090807

Answer:

Step-by-step explanation:

To solve for t, you have to isolate it on one side of the equation.

First, you have to switch sides.

→ -9+4t=-17

Add by 9 from both sides.

[tex]\Longrightarrow: \sf{-9+4t+9=-17+9}[/tex]

Then, you solve it.

-17+9=-8

4t=-8

Divide by 4 from both sides.

[tex]\sf{\dfrac{4t}{4}=\dfrac{-8}{4}}[/tex]

Solve.

Divide the numbers from left to right.

-8/4=-2

[tex]\Longrightarrow: \boxed{\sf{t=-2}}[/tex]

I hope this helps. Let me know if you have any questions.

Answer:

[tex]t = -2[/tex]

Step-by-step explanation:

Step 1:  Add 9 to both sides

[tex]-17 = -9 + 4t[/tex]

[tex]-17 + 9 = 4t - 9 + 9[/tex]

[tex]-8 = 4t[/tex]

Step 2:  Divide both sides by 4

[tex]\frac{-8}{4} = \frac{4t}{4}[/tex]

[tex]-2 = t[/tex]

Answer:  [tex]t = -2[/tex]

Answer:

1

Step-by-step explanation:

The formula for slope is y2 - y1 over x2 - x1.

-8--2 = -6

6-12= -6

-6/-6 = 1

Answer:Median=7.42

Mean=7.61

Step-by-step explanation:

Answer: x = 10 and the angles are both corresponding angles

Step-by-step explanation: it is what it is

Corresponding angles are equal

Answer:

0.856 seconds

Step-by-step explanation:

just subtract mona's time from ashley's

Answer:

b = 2

Step-by-step explanation:

[tex]\frac{a}{b-2}[/tex]

the denominator cannot be zero as this would make the expression undefined. Equating the denominator to zero and solving gives the value that b cannot be

b - 2 = 0 ( add 2 to both sides )

b = 2 ← excluded value