Michael and his friends bought three packs of gum for $1.50 each and three bottles of fruit juice for $2 each. Use the distributive property to find the total cost.

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:

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:

pretty sure its c if not than d

Step-by-step explanation:

Answer: 8.32462851 × 10-5 m4

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

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:

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:

58%

Step-by-step explanation:

58 cuz 40+18=58

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:

PIK is the angle of elevation from car to Carlos.

Answer:

C.

Step-by-step explanation:

Answer:

x=32 makes this equation true

Step-by-step explanation:

Well first we have to solve this to see-

25=-7+x     Add 7 to both sides to get x by itself

+7   +7           Adding 7 to -7 makes it 0 so it goes away

32=x    This is our final answer

100+2y = 180

2y=180-100

2y=80

y=40

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]

Answer:

B

Step-by-step explanation:

Answer:

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

Answer:

(b) 310 mi, 12.76km/liter

Step-by-step explanation:

We are told that Toronto is 500 km north on Highways. Since 1 km = 0.62 mi, then Toronto is: 500 × 0.62 = 310 miles

Aanya’s car averages 30 mi/gallon.

We are told that 1 mi = 1.61 km

Thus, her average is now;

30 × 1.61 km/gallon = 48.3 km/gallon

We are told that 1 qt = 0.946 liters

But also, 0.25 gallon = 1 qt

Thus;

0.25 gallon = 0.946 litres

Thus, 1 gallon = 0.946/0.25 litres = 3.784 litres

Thus, 48.3 km/gallon to km/litres = 48.3/3.784 = 12.76 km/litres

Answer is 310 miles and 12.76 km/litres

What is the whole question?

Answer: aₙ = -12 + (n - 1) 4

Step-by-step explanation:

aₙ = a + (n - 1) d

a = -12

d = 4

aₙ = -12 + (n - 1) 4

Answer:

a(n)=4n-16

Step-by-step explanation:

for those of you who are on acellus

Answer:

Step-by-step explanation:

Let the ratios be 2x and 7x respectively.  

Now,

2x + 7x = 18

= 9x = 18

= x = 18/9

= x = 2

Hence, 2x = 2*2 = 4

And, 7x = 7*2 = 14

Answer:

there is no info

Step-by-step explanation:

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:

b. 75,71 +57

Step-by-step explanation:

edge

Answer:

B on edg2021

Step-by-step explanation:

just took the test

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

Answer:

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

so 2^12 ×3^3= 110592

similar 2^9 ×6^3 =110592

Answer:

Step-by-step explanation:

1,2,3,3,3,3,5,6,7,10,10,10,11,11,12,12,13,13,

14,15

Answer:

No.2163075981

Step-by-step explanation:

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:

Ok?

Step-by-step explanation: