What is the value of B in terms of π?

____π in.2

Answer:

See Below.

Step-by-step explanation:

Since ΔABC is an equilateral triangle, this means that ∠A, ∠B, and ∠C all measure 60°.

Furthermore, all sides of the triangle measure 2a.

We know that AD⊥BC. Since this is an equilateral triangle, any altitude will be a perpendicular bisector. Therefore, BD = DC, ∠CAD = 30° and ∠C = 60°.

Additionally, the measures of the segments are: BD = DC = (2a) / 2 = a.

Let’s use the right triangle on the right. Here, we have that DC = a and AC = 2a.

Recall that sine is the ratio of the opposite side to the hypotenuse. Therefore, sin(C) or sin(60°) will be AD / AC. We can find AD using the Pythagorean Theorem:

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

a is DC, b is AD, and c is AC.

Substitute in appropriate values:

[tex]a^2+(AD)^2=(2a)^2[/tex]

Solve for AD:

[tex]\displaystyle \begin{aligned} a^2+(AD)^2&=4a^2\\(AD)^2&=3a^2\\AD&=\sqrt{3a^2}=a\sqrt{3}\end{aligned}[/tex]

Sine is the ratio of the opposite to the hypotenuse:

[tex]\displaystyle \sin(C)=\sin(60\textdegree)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]

Substitute:

[tex]\displaystyle \sin(60\textdegree)=\frac{AD}{AC} = \frac{a\sqrt{3}}{2a}[/tex]

Simplify. Hence, regardless of the value of a:

[tex]\displaystyle \sin(60^\circ)=\frac{\sqrt3}{2}[/tex]

Answer:

74g:148g

Step-by-step explanation:

If the yogurt portion is 3, then your answer is 148g.

You have a total of 5 portions (2+3=5). Since all portions must be equal, you can divide the total (185g) by 5. That means each portion is 37g each. To find the total weight of the yogurt, we multiply by the number of portions, either 2 or 3. That would be your result.

Answer:

a=-55

Step-by-step explanation:

-3=2+a/11

-3=1/11 a+2 simplify

flip

1/11 a+2=−3

1/11 a+2−2=−3−2  subtract 2

1/11 a=−5

11*(1/11 a)=(11)*(−5) multpily both sides by 11

a=-55

Answer:

30

Step-by-step explanation:

Hi I am so not helpful do not use this answer

Answer:

x = 24

Step-by-step explanation:

First, substitute x = -6y into the top equation:

-6y + 3y = 12

-3y = 12

Divide both sides by -3, and you get:

y = -4

Now, you plug in the y value to the second equation:

x = -6(-4)

x =24

Given :

[tex]{ \longrightarrow\qquad \sf x + 3y = 12 \: –––– \sf \: (i)}[/tex]

⠀

[tex]{ \longrightarrow\qquad \sf x = - 6y \: –––– \sf \: (ii)}[/tex]

⠀

(i) – (ii) we get :

⠀

[tex]{ \longrightarrow \qquad \sf \: {x + 3y -x = 12 - ( - 6y)}}[/tex]

⠀

[tex]{ \longrightarrow \qquad \sf \: { \cancel{x} + 3y \: \cancel{ - \: x }= 12 + 6y}}[/tex]

⠀

[tex]{ \longrightarrow \qquad \sf \: { 3y - 6y = 12 }}[/tex]

⠀

[tex]{ \longrightarrow \qquad \sf \: { - \: 3y = 12 }}[/tex]

⠀

[tex]{ \longrightarrow \qquad \sf {- \: y = \dfrac{12}{3} }}[/tex]

⠀

[tex]{ \longrightarrow \qquad \bf \: { y = - \: 4 }}[/tex]

⠀

Now, Substituing the value of y in equation (i) :

⠀

[tex] \longrightarrow \qquad \sf{x + 3( - 4)= 12}[/tex]

⠀

[tex] \longrightarrow \qquad \sf{x - 12= 12}[/tex]

⠀

[tex] \longrightarrow \qquad \sf{x = 12 + 12}[/tex]

⠀

[tex]\longrightarrow \qquad \bf{x = 24}[/tex]

⠀

Therefore,

Answer:

Step-by-step explanation:

The order of operations is the key to solving this problem.

The PEMDAS acronym stands for:

Parenthesis

Exponents

Multiply

Divide

Add

Subtract

10+(28-8)÷4

First, solve parenthesis.

[tex]\sf{10+(28-8)\div4}[/tex]

[tex]\sf{28-8=20}[/tex]

Rewrite the problem down.

[tex]\sf{10+20\div4}[/tex]

Then, divide.

20/4=5

Rewrite the problem down.

10+5

Add.

[tex]\sf{10+5=\boxed{\sf{15}}[/tex]

So, the correct answer is 15.

I hope this helps you! Please let me know if my answer is incorrect.

Answer:

[tex]\displaystyle 15[/tex]

Step-by-step explanation:

[tex]\displaystyle Grouping\:Symbols \hookrightarrow G \\ Exponents, Indices, or\:Radicals \hookrightarrow E \\ Multiplication\:and/or\:Division \hookrightarrow M \\ Subtraction\:and/or\:Addition \hookrightarrow S \\ \\ 10 + (28 - 8) \div 4 \hookrightarrow 10 + 20 \div 4 \\ \\ \boxed{15} = 10 + 5[/tex]

By using GEMS, the result is fifteen.

I am joyous to assist you at any time.

Answer:

The answer would be x = 20. First, you must set up a proportion, since you know that the two polygons are similar: 12/48 • 5/x. Then, you have to do cross multiplication which would result in 12x = 240. Afterwards, you must divide both sides by 12, giving you x = 20.

Answer:

Step-by-step explanation:

Answer:

19.6

Step-by-step explanation:

35% of 56

=35/100×56      

19.6

hope this helps

pls brainliest!!!!!

Answer:

19.6 is the answer

Step-by-step explanation:

35%of 56

35/100×56

19.6 answer

Answer:

The midpoint is 7/2 -9/2

Step-by-step explanation:

The formula for finding the midpoint of a line is

This means the formula for the x-coordinate of the midpoint is , and the formula for the y-coordinate of the midpoint is .

First, let's find the x-coordinate of the midpoint:

Add the two x values of the coordinates given, then divide that by two.

Next, let's find the y-coordinate of the midpoint:

Add the two y values of the coordinates given, then divide that by two.

Therefore, the midpoint of the line segment is . Hope this helps!

Answer:42 x27

Step-by-step explanation:Calculate how much paint and primer you need by entering the dimensions of your room below. Estimate how many gallons are needed based on average paint/primer coverage. Optionally, include ceiling paint in your estimate.

The number of gallons that are needed will be 6 gallons.

The number of gallons of paint that will be needed in order to paint a wall that is 42 feet wide and 27 feet high if one gallon will cover 200 square feet will be:

= (27 × 42) / 200

= 1134 / 200

= 5.67

= 6 gallons.

Learn more about division on:

https://brainly.com/question/19127052

Answer:

lemon pie is 7.5 and blueberry is 4.5

Step-by-step explanation:

Answer:

0.48911

Step-by-step explanation:

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score, = 27.21 Ib

μ is the population mean = 26.86 lb

σ is the population standard deviation. = 12.82 lb

z = 0.027301

Probability value from Z-Table:

P(x<27.21) = 0.51089

P(x>27.21) = 1 - P(x<27.21) = 0.48911

The proportion of weeks in which the waste disposal facility is overloaded is

0.48911

Answer:

If the maximum measurement error is at most 0.08 oz. , write and solve an absolute value inequality for the range of the possible number of ounces, Z, that can be in a jug of orange juice.

Simplify your answer and write it in interval notation.

Step-by-step explanation:

I will only give you that. I am so sorry that my response is this late love. If there was some way to receive your question, I would most definitely help you! I hope you did well on this problem!

=)

Answer:

950

Step-by-step explanation:

Not gonna lie I kinda stole yo answer other person deserves all the credit

The triangle above can be solved using cosine rule, the value of a using cosine rule is approximately 18.5

The side can be found using cosine formula for triangles.

a² = b² + c² - 2bc cos A

where

a = ?

b = 8 units

c = 14 units

Therefore,

a² = 64 + 196 - 2 × 8 × 14 cos 112

a² = 260 - 224 cos 112

a² = 260 + 83.9118769252

a = √343.9118769

a = 18.5448611993

a = 18.5

Therefore, the value of a is approximately 18.5

learn more on triangle here: https://brainly.com/question/7140765

Answer:

Well we know this is a parallelogram

-A theorem states that if both opposite side of a quadrilateral (4 sided shape) are congruent then it’s a parrlelogram.
-We also know this is a rhombus becuase all sides are congruent and has no right angle present. A theorem to support this is, If two consecutive sides of a parallelogram are congruent, then the parallelogram is a a rhombus.

So we’re trying to find x.

A theorem states that “The diagonals of a rhombus bisects two angles of the rhombus.”

Bisect means cut in a way that both angles are equal.

That means the two angles given have to be equal to each other.

We can make an equation.

110-x = x

Now solve
2x= 110

X= 55

X would equal 55

x=55

Answer:

[tex]2x-3y[/tex]

Step-by-step explanation:

Apply the distributive property by multiplying the outside to both terms on the inside:

[tex]-\frac{1}{4}[/tex] of -8x is equal to 2x

[tex]-\frac{1}{4}[/tex] of 12y is equal to 3y.

circumference = 2 x pi x r

r = 65 cm

so C ≈ 2 x 3,14 x 65 ≈ 408,20

Answer: C=408.41 centimeters

Step-by-step explanation:

2 times pi times 65

130 pi

Approximately 408.41

Answer:

Step-by-step explanation:

We can use the equation of a straight line to model the cost of servicing the car.

let the cost be y and the number of hours be x

and the charge per hour is m

y=mx+c

y=50x+25

given that the time is 3.45 hours it is assumed that the charge is for 4 hours since for a fraction of 0.45 hours we are charged $50

y=50(4)+25

y=200+25

y=$225

Answer:10 books per shelf

Step-by-step explanation:

30 books

3 shelves

30x3=10

10 books per shelf

Answer:

[tex]y = 0.5x + ( - 3)[/tex]

or

[tex]y = 0.5x - 3[/tex]

Answer:

84

Step-by-step explanation:

70% of 120= 84

Answer:

the correct answer is B. 18 in

Answer:

29 weeks or 4 months (not exactly)

Step-by-step explanation:

300/10.5 is 28.57

which 29 weeks, you earn 4 dollars and 50 cents left over

Answer:

He has four outfits if he switches shirts once.