Angle θ forms a reference angle that is below the positive x axis (in quadrant IV). What will be the signs on the sine and cosine of angle θ?

Applying the trigonometry ratio and rationalization, the missing lengths are:

1. x = 12/√3; y = 2√3

2. x = 5√2; y = 5√2

3. b = 24

4. 4√3

5. 5√3

The trigonometry ratios are represented as follow:

1. To find x, apply SOH:

opp = 6

hyp = x

adj = y

∅ = 60°

Equation:

sin 60 = 6/x

x = 6/sin 60

x = 6/√3/2 (sin 60 = √3/2)

x = 6 × 2/√3

x = 12/√3

Rationalize

x = 12/√3 × √3 /√3

x = 12√3/3

x = 4√3

To find y, apply TOA:

tan 60 = 6/y

y = 6/tan 60

y = 6/√3 (tan 60 = √3)

Rationalize

y = 6/√3 × √3 /√3

y = 6√3 / 3

y = 2√3

2. To find x, apply SOH:

opp = x

hyp = 10

adj = y

∅ = 45°

Equation:

sin 45 = x/10

x = (10)(sin 45)

x = 10 × 1/√2 (sin 45 = 1/√2)

x = 10/√2

Rationalize

x = 10/√2 × √2 /√2

x = 10√2/2

x = 5√2

To find y, apply CAH:

cos 45 = y/10

y = (10)(cos 45)

y = 10 × 1/√2 (cos 45 = 1/√2)

y = 10/√2

Rationalize

y = 10/√2 × √2 /√2

y = 10√2/2

y = 5√2

3. To find b, apply Pythagorean theorem:

b = √(25² - 7²)

b = 24

4. 12/√3

Rationalize

12/√3 × √3 /√3

12√3/3

4√3

5. 15/√3 × √3 /√3

15√3 /3

5√3

Learn more about trigonometry ratios on:

https://brainly.com/question/10417664

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{x(x + 6) - 2(x + 6)}\\\mathsf{\rightarrow x(x) + x(6) - 2(x) - 2 (6)}\\\mathsf{\rightarrow x(x) + 6(x) - 2(x) - 2(6)}\\\mathsf{\rightarrow x^2 + 6x - 2x - 12}\\\large\text{COMBINE the LIKE TERMS}\\\mathsf{\rightarrow x^2 + (6x - 2x) - 12}\\\mathsf{\rightarrow x^2 + 4x - 12}\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{x^2 + 4x - 12}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

Yes, The commutative property of multiplication is: a × b = b × a. In short, in commutative property, the numbers can be added or multiplied to each other in any order without changing the answer. Let us see some examples to understand commutative property. Example 1: Commutative property with addition.

No, the equation 9 x 7 = 7 x 9 does not demonstrate the commutative property of multiplication.

The commutative property of multiplication states that the order of the numbers being multiplied does not affect the result; you can switch the order, and the product will remain the same.

In the given equation, both sides evaluate to 63 (9 x 7 = 63 and 7 x 9 = 63), so it might appear to satisfy the commutative property at first glance. However, this equation represents a single instance where the numbers used happen to have the same product. The commutative property should hold true for all pairs of numbers, which is not the case here.

For example, switching the order for 3 x 5 and 5 x 3 results in different products (3 x 5 = 15 and 5 x 3 = 15). Since the equation 9 x 7 = 7 x 9 does not hold true for all pairs of numbers, it does not illustrate the commutative property of multiplication.

To know more about multiplication:

https://brainly.com/question/17192010

#SPJ6

Answer:

1. 45min

2. 1h 40min

3. 1h 45min

4. 5min

Explanation:

Complex numbers are numbers that have both imaginary and real number parts. Imaginary numbers occur when you take the square root of negative numbers. Here are some examples of imaginary numbers:

[tex]\sqrt{-1} = i[/tex] and [tex]\sqrt{-16} = 4i[/tex]

Real numbers are just normal numbers.

Complex numbers can be expressed generally in the form:

[tex]a+bi[/tex]

Answer:

omg college math is so hard omg i feel baddddddd

Step-by-step explanation:

Answer:073

Step-by-step explanation: check number is located on upper right hand corner.

Answer:

The answer is d

Step-by-step explanation:

To find out the asnwer, we need to find the value of X. First, we know that X is the same vaule in each equation so we have to find out a number can by multiplied to 9,6, and 5 and get the 3 numbers in either a,b,c, or d. 9x9=81,6x9=54, 5x9=45. These 3 answers matches the number in the choices.

Answer:

8+8, & 7+7.

Step-by-step explanation:

They help because you can add 8+8 and get 16, and just subtract 1. When you add 7+7 you get 14, and you add 1

Answer:

The answer to this question is due to the algebraic equality of the equation

Step-by-step explanation:

[tex]2(m - n) = 7 = y[/tex]

[tex]y = \frac{7}{2} [/tex]

That is, option C

Answer:

(-4,2)

Step-by-step explanation:

Knowing that/Given that:

The vertices of the triangle are rotated about the origin by 270° counter-clockwise.

In Addition, This transformation changes the co-ordinate (x,y) to (y,-x).

Before (x,y)                                        After ( y, - x)

Vertices                         New vertices after 270° rotation

R= (1,1)                                              R' = (1,-1)

S= (-2,-4)                                          S' = (-4,2)

T= (-3,-3)                                          T' = (-3,3)

Hence, the answer is (-4,2)

~Lenvy~

SPINACH SPINACH SPINACH SPINACH SPINACH SPINACH SPINACH SPINACH SPINACH SPINACH

the remainder when f(x) = x⁴ - 5x³ + 3x² - 2x +7 is divided by x - 1 is 4

Step-by-step explanation:

Round 93,411 to nearest tens

93,411

93,410

sorry if wrong

Answer:

-5/2

Step-by-step explanation:

c is -14

then, b is 5

then quadratic equation,

x=2 or -7

the turning point = (-7+2)/2 = -5/2

if still can't get it pls comment below ask me

Answer:

[tex]\frac{5}{8}[/tex]  

I hope this helps!

Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

to multiply fractions, multiply the numerators together then the denominators.

5 * 3 = 15

6 * 4 = 24

15/24

now simplify that fraction.

15/24

divide both sides by 3

5/8

Answer:

x= -6

Step-by-step explanation:

Recall the double angle identity,

sin(2x) = 2 sin(x) cos(x)

Then we can write

sin(9x) cos(9x) = 1/2 sin(2 • 9x) = 1/2 sin(18x)

Then

∫ sin(9x) cos(9x) dx

= 1/2 ∫ sin(18x) dx

= -1/2 • 1/18 cos(18x) + C

= -1/36 cos(18x) + C

though you could continue with another double angle identity,

cos(2x) = cos²(x) - sin²(x)

to rewrite the antiderivative as

= -1/36 (cos²(9x) - sin²(9x)) + C

= 1/36 (sin²(9x) - cos²(9x)) + C

Answer:

is called a controlled operation

Step-by-step explanation:

that's what its called i just know

Answer:

the data show a quadratic relationship

Answer:

Edge202 is B and E

Step-by-step explanation:

Edge2020

Its really easy D and E i took the test

Answer:

d e

Step-by-step explanation:

Answer:

we need more info.

Step-by-step explanation:

Answer:

Step-by-step explanation:

18 muffins for Millie,

18 muffins for August,

18 muffins for herself,

80 muffins for a church,

18+18+18+80 = 134 muffins in total

Answer:

7.16 x 3 = 21.48

She weighs 21.48 pounds at her 1 year checkup.

Hope this helps!

Answer:

21.48 pounds

Step-by-step explanation:

7.16 x 3 = 21.48

Answer:

3. (-10)^2

Answer: 100

Answer is B.

4.  12,400,000

Answer: 1.24 * 10^7

Answer is A.

I hope this can help you advance to the other questions!

Answer:

3) b. 100

4) a. 1.24 x 10 ^7

Step-by-step explanation:

-10 x -10 = 100

1.24 x 10 ^7 = 12,400,000

[tex]\\ \sf\Rrightarrow 4^x-4^{x-1}=24[/tex]

[tex]\\ \sf\Rrightarrow 4^x-4^x4^{-1}=24[/tex]

[tex]\\ \sf\Rrightarrow 4^x(1-0.25)=24[/tex]

[tex]\\ \sf\Rrightarrow 4^x(0.75)=24[/tex]

[tex]\\ \sf\Rrightarrow 4^x=32[/tex]

[tex]\\ \sf\Rrightarrow 2^{2x}=2^5[/tex]

[tex]\\ \sf\Rrightarrow 2x=5[/tex]

[tex]\\ \sf\Rrightarrow (2x)^x=(5)^x[/tex]

Answer:

Step-by-step explanation:

Let [tex]4^{x}=y[/tex], then we obtain that:

[tex]4^{x}-4^{x-1}=24\rightarrow y-(y/4)=24 \rightarrow \frac{3y}{4}=24[/tex]

So, we can get: [tex]3y=96 \rightarrow y = 96/3 = 32[/tex]

Now, because [tex]y=4^{x}=32[/tex], we can obtain the value of x as follows:

[tex]4^{x}=(2^{2})^{x}=(2^{5}) \rightarrow 2x = 5 \rightarrow x=5/2[/tex]

Then [tex](2x)^{x}=(2(5/2))^{5/2}=5^{5/2}=\sqrt{5^{5}}=25\sqrt 5[/tex]

There is no answer in your question.

Answer:

Angle(b)= 79°

Step-by-step explanation:

Because M and N are parallel so the answer is 79°

Also see the angle is less than 90°

A logarithm function is a function that uses the log keyword, and it is the opposite of an exponential function

Assume the logarithm function is:

[tex]y = a\log_b(x - h) + k[/tex]

Where b represents the base of the function.

The first step is to determine the vertical asymptote of the function

The vertical asymptote of [tex]y = a\log_b(x - h) + k[/tex] is:

[tex]x = h[/tex]

The second step is to determine the x-intercepts

To do this, we set the function to 0

i.e. [tex]a\log_b(x - h) + k = 0[/tex]

The next step is to determine the y-intercepts

To do this, we set the x to 0

i.e. [tex]y = a\log_b(0- h) + k[/tex]

The next step is to plot the vertical asymptote, the intercepts and few points on the graph

Lastly the points that were plotted on the graph must be connected

Read more about logarithm function at:

https://brainly.com/question/13473114

If a function is non-linear, there must be an exponent in the equation. For example, [tex]x^{2}[/tex]  or [tex]x^{3}[/tex].

Since this function has no exponent attached to the x-variable, we can assume this function is linear.