Complete the statement.

Answer/Step-by-step explanation:

Recall: SOHCAHTOA

2. Reference angle = 62°

Adjacent = 25

Opposite = x

Apply TOA:

Tan 62 = Opp/Adj

Tan 62 = x/25

25*Tan 62 = x

x ≈ 47.0 (nearest tenth)

3. Reference angle = 26°

Hypotenuse = x

Opposite = 11

Apply SOH:

Sin 26 = Opp/Hyp

Sin 26 = 11/x

x × Sin 26 = 11

x = 11/Sin 26

x ≈ 25.1 (nearest tenth)

4. Reference angle = 48°

Hypotenuse = 32

Opposite = x

Apply SOH:

Sin 48 = Opp/Hyp

Sin 48 = x/32

32 × Sin 48 = x

x ≈ 23.8 (nearest tenth)

5. Reference angle = 12°

Hypotenuse = x

Adjacent = 29

Apply CAH:

Cos 12 = Adj/Hyp

Cos 12 = x/29

29 × Cos 12 = x

x ≈ 28.4 (nearest tenth)

6. Reference angle = x

Hypotenuse = 15

Adjacent = 14

Apply CAH:

Cos x = Adj/Hyp

Cos x = 14/15

x = cos^{-1}(14/15)

x ≈ 21.0° (nearest tenth)

7. Reference angle = x

Opposite = 19

Adjacent = 23

Apply TOA:

Tan x = Opp/Adj

Tan x = 19/23

x = Tan^{-1}(19/23)

x ≈ 39.6° (nearest tenth)

8. Reference angle = x

Hypotenuse = 17

Adjacent = 9

Apply CAH:

Cos x = Adj/Hyp

Cos x = 9/17

x = Cos^{-1}(9/17)

x ≈ 58.0° (nearest tenth)

9. Reference angle = x

Hypotenuse = 45

Opposite = 43

Apply SOH:

Sin x = Opp/Hyp

Sin x = 43/45

x = Sin^{-1}(43/45)

x ≈ 72.9° (nearest tenth)

Answer:

0.2

Step-by-step explanation:

[tex]\frac{7}{15}[/tex] x [tex]\frac{6}{14}[/tex] = 0.2

Answer:

4x-6-5x-12. it can then be -24 - -60 = -84.

Step-by-step explanation:

Hope this helps!

Answer:

Wednesday

Step-by-step explanation:

Averages

Wednesday-5.5

Monday-7.5

Friday-6.5

Answer:

1. a. Q° = 95°

b. a = 20.3; b = 19.3

2. p = 36; q = 14.4

Step-by-step explanation:

Question 1:

Recall: The Exterior Angle Theorem of a Triangle states that the size of the exterior angle of a triangle equals the sum of the two sizes of the two opposite angles of the triangle.

a. Based on the theorem,

Q° = 41° + 54° = 95°

b.

✔️122° = 4a + 2a (exterior angle theorem)

122 = 6a

Divide both sides by 6

122/6 = a

a = 20.3

✔️122° + 3b = 180° (angles on a straight line)

3b = 180 - 122

3b = 58

b = 58/3

b = 19.3

Question 2:

Recall: Opposite angles of a parallelogram are equal while adjacent/consecutive angles are supplementary.

✔️2p + 3p = 180° (adjacent angles)

5p = 180

p = 180/5

p = 36

✔️2p = 5q (opposite angles)

Plug in the value of p

2(36) = 5q

72 = 5q

72/5 = q

q = 14.4

Answer:

3) 32

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Using the identities

sin(A + B) = sinAcosB + cosAsinB

cotA = [tex]\frac{cosA}{sinA}[/tex] , tanA = [tex]\frac{sinA}{cosA}[/tex]

Consider the left side

[tex]\frac{sin(A+B)}{sinAcosB}[/tex]

= [tex]\frac{sinAcosB+cosAsinB}{sinAcosB}[/tex]

= [tex]\frac{sinAcosB}{sinAcosB}[/tex] + [tex]\frac{cosAsinB}{sinAcosB}[/tex]

= 1 + [tex]\frac{cosA}{sinA}[/tex] . [tex]\frac{sinB}{cosB}[/tex]

= 1 + cotA tanB = right side , thus verified

el numerador será 512 ya que en esta suma el numero mas alto es el 512

Answer:

f(1) = 2, f(4) = 8

Step-by-step explanation:

f(1) in the interval - 3 < x ≤ 1 , then f(x) = x + 1 , so

f(1) = 1 + 1 = 2

f(4) in the interval 1 < x ≤ 4 , then f(x) = 2x , so

f(4) = 2 × 4 = 8

Answer: A) x = 1/4y^2

Step-by-step explanation:

If you graph each of the choices on a graphing calculator (I recommend Desmos!) you can see which equation could be that of the parabola shown. Sorry if this isn't the explanation you were looking for.

Answer:

$316.94

Step-by-step explanation:

Answer:

each person gets 1/4 of the pizza or .25 of the pizza if it is split equally among the people.

Step-by-step explanation:

Answer:

f(x)= 1.38x

y= 1.38x

Step-by-step explanation:

basically the cost= 1.38 per pound

you can use cost=1.38x if ur grade level isn't at f(x) yet

<3

Answer:

f(x) = 1.38x

x just stands for a number so depending on how many pounds you get you would times the pounds by 1.38. And f(x) (pronounced "f of x") means that each input has a single output. So if you bought 2 pounds of strawberries, the equation would change to this:

f(2) = 1.38(2)

The x's were just replaced with 2's, see? I wish someone had explained this to me earlier lol

Answer:

x=35°

y=145°

Step-by-step explanation:

y=180°-35°=145°

x=35

Answer:

I love algebra anyways  

the ans is in the picture with the steps  

(hope it helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer:

20 units squared

Step-by-step explanation:

Area = base times height

Area = 5 x 4 = 20

Answer:

4x=0

Step-by-step explanation:

it is true

Answer:

left hand side6+2x

6x-6

right hand side

3(2x-2)

6x-6

now

6x-6=6x-6

0=0

it has no Solution

Answer:

[tex]8[/tex] tons

Step-by-step explanation:

Divide the mass value by 2000, easy.

Answer:

IT'S

7.143 Tons

Step by Step:

For an approximate result,

divide the mass value by 2205

Answer:

216

Step-by-step explanation:

300 x .28 = 84

300 - 84 = 216

Answer:

216

Step-by-step explanation:

300 -> 100% (Total candies)

___ -> 72% (NOT Blue candies)

___ -> 28% (Blue candies)

Next:

28% = 0.28

300 x 0.28 = 84

84 = Number of candies that are Blue

300 -> 100% (Total candies)

___ -> 72% (NOT Blue candies)

84   -> 28% (Blue candies)

Now:

300 - 84 = 216

300 -> 100% (Total candies)

216 -> 72% (NOT Blue candies)

84 -> 28% (blue candies)

216 equals the number of candies that are NOT Blue

Answer:

[tex]\displaystyle J'(3) = -1[/tex]

General Formulas and Concepts:

Algebra I

Calculus

Derivatives

Derivative Notation

Derivative Rule [Chain Rule]:                                                                                       [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Derivative:                                                                                                                     [tex]\displaystyle \frac{d}{dx} [e^u]=e^u \cdot u'[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle J(x) = e^{f(x)}[/tex]

Step 2: Differentiate

Step 3: Evaluate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

The answer is G

Step-by-step explanation:

So what I did was I went on a website that it wont let me name and typed in each equation and then the ordered pair and checked to see if (8,-1) was a solution and it was for G.

Answer:

Angle Z = 180-32 -90 = 58 degrees

sine (32) = y / 16

y = 16 * sine (32)  

y = 16 * 0.52992

y = 8.47872

x^2 = 16^2 -y^2

x^2 = 256 -71.888

x^2 = 184.112

x = 13.568

Step-by-step explanation:

Answer:

x = 13·568, y = 8·47 and z = 58

Step-by-step explanation:

I don't think the question required you to use the Pythagoras theorem but here are some pointers anyway.

The reason I said that this question might not solely require you to use the Pythagoras theorem is because you need to have two variables for the equation to work, maybe this is what got you confused.

For this question, you're required to use Tangents, Sines and Cosines, or you can combine this method and Pythagoras method.

Method one: Using Tangents, Sines and Cosines AND the Pythagoras theorem

Step 1: Looking for x(Using Sin, Cos and Tan)

To find the length of side x, we need to use the Cosine of 32°

Cos 32° = Adjacent side ÷ Hypotenuse

0·8480 = x/16

Make x the subject and multiply both sides by 16

0·8480 × 16 = x/16 × 16

13·568 = x

∴ side x is 13·568

Step 2: Looking for y( using the Pythagoras theorem)

a² + b² = c²

a = y, b = x = 13·568, c = 16

y² + 13·568² = 16²

y² + 184·0906 = 256

y² = 256 - 184·0906

y² = 71·9094

y = √71·9094

y = 8·4799

Method 2: Using Tan, Cos and Sin only

Step 1 remains the same as shown above; x = 13·568

Step 2: Looking for y

Y can be gotten by using the Sine of 32°

Sin 32° = Opposite ÷ Hypotenuse

Sin 32° = y ÷ 16

0·5299 = y/16

Make y the subject and divide both sides by 16

0·5299 × 16 = y/16 × 16

8·4784 = y

∴ y is equal to 8·4784

(I know there's a difference in points of the two values of y, but if you round them off to 2 decimal places we see it remains 8·47

   2. Looking for z:

Using addition and subtraction

The simpler method would be to just add all the internal angles.

32 + 90 + z = 180

122 + z = 180

z = 180 - 122

z = 58

∴ z is equal to 58°

Using Tan, Sin and Cos

The cosine of Z is equal to y divided by 16, where y = 8·47

Cos z = 0·5294

Make z the subject and divide both sides by Cos.

z = 0·5294/Cos

z = 58·04° (I just used the anti-cos to get this number. Press shift, and cos on your calculator then type 0.5294 in front of it)

Here there is also a slight difference in points between the two steps but if you round off step 2 to a whole number you get 58, so it's all good :)

HOPE THIS HELPS!!! :)

Answer:

7/16=7/16

8/16=1/2

9/16=9/16

10/16=5/8

11/16= 11/16

12/16=3/4

13/16=13/16

14/16=7/8

Step-by-step explanation:

The ones that didn't change are the ones that cannot be simplified :)

Answer:

5x+2=0

Step-by-step explanation:

When factoring you add or subtract your factors that are similar.

For example 9x-4x+ 5x

and this is how you get 5x+2=0

Any Questions?

Answer:5x+2=0

Step-by-step explanation:

Answer:

9 miles per hour

Step-by-step explanation:

Answer: 360 apples were taken

Step-by-step explanation:

Here, we are asked to find the number of apples taken, which means it is the difference between original and after. So the expression we are going to use is: Original-After=number of apples taken

------------------------------------------------------------------------------------

Given

Original=409 apples

After=49 apples

Solve

Original - After=409 - 49=360 apples

Hope this helps!! :)

Please let me know if you have any questions

Step-by-step explanation:

x =7-y

subs x in eqn 2

3(7-y)+y=15

21-3y+y=15

21-2y=15

21-15=2y

6=2y

y=6/2

y=3