A trail mix recipe calls for pound of peanuts, pound of raisins, and pound of
granola. Write the following ratios as fractions in simplest form.

B) 'Peanuts to Raisins:

B) Granola to Peanuts:

Answer:

1) [tex]sin \left(\dfrac{- \pi}{12} \right) = \dfrac{(\sqrt{2} - \sqrt{6} }{4}[/tex]

2) [tex]tan\left(\dfrac{ \pi}{12} \right) = 2 - \sqrt{3}[/tex]

3) [tex]tan\left(\dfrac{ 5\cdot \pi}{12} \right) = 2 + \sqrt{3}[/tex]

Step-by-step explanation:

1) [tex]sin \left(\dfrac{- \pi}{12} \right) = sin(-15^{\circ})[/tex]

sin(-15°)  = sin(30° + (- 45°)) = sin(30°)cos(-45°) + cos(30°)sin(-45°)

sin(30°)cos(-45°) + cos(30°)sin(-45°) = 1/2 × (√2)/2 + (√3)/2 × (-√2)/2

1/2 × √2/2 + √3/2 × -√2/2 = (√2)/4 - (√6)/4 = ((√2) - (√6))/4

sin(-15°)  = ((√2) - (√6))/4

[tex]sin \left(\dfrac{- \pi}{12} \right) = sin(-15^{\circ}) = \dfrac{(\sqrt{2} - \sqrt{6} }{4}[/tex]

2) [tex]tan\left(\dfrac{ \pi}{12} \right) = tan(15^{\circ})[/tex]

tan(15°)  = tan(45° + (-30°)) = (tan(-30°) + tan(45°))/(1 - tan(-30°)×tan(45°))

(tan(-30°) + tan(45°))/(1 - tan(-30°)×tan(45°)) = ((-1/√3) + 1)/(1 - (-1/√3))

((-1/√3) + 1)/(1 - (-1/√3)) = (3 - √3)/(3 + √3) = (3 - √3)·(3 -√3)/((3 - √3)·(3 + √3))

(3 - √3)·(3 -√3/((3 - √3)·(3 + √3)) = (9 - 6·√3 + 3)/(9 - 3) = (12 - 6·√3)/6

(2 - √3)

[tex]tan\left(\dfrac{ \pi}{12} \right) = tan(15^{\circ}) = 2 - \sqrt{3}[/tex]

3) [tex]tan\left(\dfrac{ 5\cdot \pi}{12} \right) = tan(75^{\circ})[/tex]

tan(75°)  = tan(30° + 45°) = (tan(30°) + tan(45°))/(1 - tan(30°)×tan(45°))

(tan(30°) + tan(45°))/(1 - tan(30°)×tan(45°)) = ((1/√3) + 1)/(1 - 1/√3)

((1/√3) + 1)/(1 - 1/√3) = (3 + √3)/(3 - √3) = (3 + √3)·(3 +√3/((3 - √3)·(3 + √3))

(3 + √3)·(3 +√3/((3 - √3)·(3 + √3)) = (9 + 6·√3 + 3)/(9 - 3) = (12 + 6·√3)/6

(12 + 6·√3)/6 = 2 + √3

[tex]tan\left(\dfrac{ 5\cdot \pi}{12} \right) = tan(75^{\circ}) = 2 + \sqrt{3}[/tex]

Answer:

992.43 cm²

Step-by-step explanation:

From the question given above, the following data were obtained:

Volume of shape X (Vₓ) = 130 cm³

Surface area of shape X (SAₓ) = 202 cm²

Volume of shape Y (Vᵧ) = 638.69 cm³

Surface area of shape Y (SAᵧ) =?

The surface area of shape Y can be obtained as follow:

Since the shape are similar, then:

Vₓ / Vᵧ = SAₓ / SAᵧ

130 / 638.69 = 202 / SAᵧ

Cross multiply

130 × SAᵧ = 638.69 × 202

130 × SAᵧ = 129015.38

Divide both side by 130

SAᵧ = 129015.38 / 130

SAᵧ = 992.43 cm²

Thus, surface area of shape Y is 992.43 cm²

Answer:

simplifying this expression (√8^4 × √6^4)^3/2 = 110592

so 2^12 ×3^3= 110592

similar 2^9 ×6^3 =110592

Answer: a=5

Step-by-step explanation: Use the pythagorean theorem and get

(a)^2+(12)^2=(13)^2

This would then be (a)^2+144=169

subtract 144 from both sides and get

(a)^2=25

Take the square root of both sides and you get a=5

Answer:

a=5

Step-by-step explanation:

Pythagorean theorem

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

substitute your values

[tex]a^{2}[/tex] + [tex]12^{2}[/tex] = [tex]13^{2}[/tex]

    - 12    - 12

[tex]a^{2}[/tex] = [tex]13^{2}[/tex] - [tex]12^{2}[/tex]

a = 169-144

a= 25

now find the square root of 25, which is 5

Answer:

no clue..................................

Answer: 2 hours=6 degrees C

              5 hours=-31 degrees C

               Half an hour=9.5 degrees C

I hope this helps. Sorry if I made a mistake. Good luck!

Step-by-step explanation:

9 x 2 hours = 18 C        14-8= 6 degrees C

9 x 5 hours = 45 C       14-45= -31 degrees C

9 x 0.5 = 4.5 C              14-4.5= 9.5 degrees C

Answer:

The surface area is 200.96 square feet

Step-by-step explanation:

Given

[tex]r = 2[/tex]

[tex]h =14[/tex]

Required: Determine the surface area

This is calculated using:

[tex]SA = 2\pi r^2 + 2\pi rh[/tex]

So:

[tex]SA = 2 * 3.14 * 2^2 + 2 * 3.14 * 2 * 14[/tex]

[tex]SA = 25.12 + 175.84[/tex]

[tex]SA =200.96[/tex]

Answer:

there is no info

Step-by-step explanation:

Answer: 8.32462851 × 10-5 m4

Step-by-step explanation: I multiplied them and got this. Hope this helps :)

in order to find d,we need to remove that 6 on 6d.so in order to remover 6,we divide both 6# and 108 by 6.so 6 divided by 6 we will be left with d = 108 devided by 6

so the answer is d=18

Answer:

58%

Step-by-step explanation:

58 cuz 40+18=58

Answer:

[tex]c. \: \frac{3}{4} [/tex]

Step-by-step explanation:

[tex] \frac{1}{2} = 0.5 \\ \frac{2}{3} = 0.667 \\ \frac{3}{4} = 0.75 \\ \frac{5}{12} = 0.417[/tex]

Step-by-step explanation:

1. 16

2. 16

3. 24

4.39

5. 68

6. 51

Answer:

1 is letter d

2 is letter d

3 is letter e

4 is letter b

5 is letter a

6 is letter f

your very welcome

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

6b+4b first because you have to combine like terms so 10b and the others aren't like terms so you just plug them in so 10b+3ab+3

Answers are

1.

∠ABC and ∠EBD are vertical angles.

∠ABE and ∠CBD are vertical angles.

∠ABE and ∠DBE are adjacent angles.

∠ABC and CBD are adjacent angles.

2.

∠LMN and <RMQ are vertical angles.

∠SML and ∠QMP are vertical angles.

∠LMN and ∠PMN are adjacent angles.

∠NMP and ∠PMQ are adjacent angles.

Adjacent and vertical angles:

Adjacent angles: Two angles with a common arm and vertex are called adjacent angles.

They share  a common arm and common vertex.

Adjacent angles are not always equal in measure

Vertical angles: When two lines intersect each other, then the pair of opposite angles formed at the vertex are called vertical angles.

They share a common vertex, but no common arm.

Vertically opposite angles are equal in measure.

(Here)

For question - 1,

∠ABC and ∠EBD are vertical angles.

∠ABE and ∠CBD are vertical angles.

∠ABE and ∠DBE are adjacent angles.

∠ABC and CBD are adjacent angles.

For question - 2,

∠LMN and <RMQ are vertical angles.

∠SML and ∠QMP are vertical angles.

∠LMN and ∠PMN are adjacent angles.

∠NMP and ∠PMQ are adjacent angles.

Learn more about Adjacent angles and vertical angles here:

https://brainly.com/question/12838185?referrer=searchResults

#SPJ2

Answer:

C. [tex]7^{5}[/tex]

Answer:

square

Step-by-step explanation:

Hope this helps.

Answer:

D

Step-by-step explanation:

Answer:

PIK is the angle of elevation from car to Carlos.

Answer:

C.

Step-by-step explanation:

Answer:

line b and c are perpendicular because the product of their slope is -1

Step-by-step explanation:

For two lines to be parallel they must have the same slope

For two line to be perpendicular, the product of their slope must be -1

Line a: 2x-7y=14      

Rewrite in the form y = mx+c

-7y = -2x + 14

y = -2/-7 x + 14/-2

y = 2/7x  - 7

The slope of line a is 2/7

Line b: y=7/2x-8

This is already in standard format

mx = 7/2 x

m = 7/2

The slope of line b is 7/2

Line c: 2x+7y=21

Rewrite in standard form

7y = -2x + 21

y = -2/7 x + 21/7

y = -2/7 x + 3

The slope of line c is -2/7

Take the product of line b and c

mb * mc  = 7/2 * -2/7

mb * mc = -1

Hence line b and c are perpendicular because the product of their slope is -1

100+2y = 180

2y=180-100

2y=80

y=40

Answer:

b. 75,71 +57

Step-by-step explanation:

edge

Answer:

B on edg2021

Step-by-step explanation:

just took the test

Answer:

9 units

Step-by-step explanation:

the distance from 5 and -4 is 9

5(to)0= 5    -4(to)0=4    5+4=9

not a very good explanation but hope it helps

Answer:

7 or -7

Step-by-step explanation:

the question is asking for x to to the second power which is x squared or x^2

so setting x^2=49

square root both sides of the equation so that x is by itself and the other side is just ±√(49). which ±√49 is just 7 or -7

Hope that helps :)

Please gve brainliest

Answer:

they are parallel to each other, use desmos graphing calculator, that thing is GOAT

Step-by-step explanation:

Answer:

26?

Step-by-step explanation

because they are vertical? (i think the word) they are equal so set them equal to each other then solve for x

Answer:

It pretty much just mirrors the image or points but on the other side of the line of reflection :D

Step-by-step explanation:

Answer:

Ok?

Step-by-step explanation:

Answer:

Yes correct

Step-by-step explanation:

Answer:

Thank You!

Step-by-step explanation:

You the people that are good