prove that

[tex]2 \tan30 \div 1 + tan ^{2} 30 = sin60[/tex]
prove that

.

Answers

Answer 1

Step-by-step explanation:

2tan 30° / 1 + tan² 30° =

2(⅓√3) /1 + (⅓√3)² =

⅔√3 / 1+ ⅓ =

⅔√3 / 4/3 =

2/4 √3 =

½3 = sin 60° (proven)


Related Questions

Ed decided to build a storage box. At first, he was planning to build a cubical box with edges of length n
inches. To increase the amount of storage, he decided to make the box 1 inch taller and 2 inches longer,
while keeping its depth at n inches. The volume of the box Ed built has a volume how many cubic inches
greater than the box he originally planned to build?
O 3n2 + 2n
312 + 3n+3
O 6n2 + 3n
O 6n2 + 3n+3

Answers

Given:

Edge of a cubic box = n inches.

He decided to make the box 1 inch taller and 2 inches longer, while keeping its depth at n inches.

To find:

How many cubic inches greater than the box he originally planned to build?

Solution:

Edge of a cubic box is n inches, so the volume of the original cube is:

[tex]V_1=(edge)^3[/tex]

[tex]V_1=n^3[/tex]

According to the given information,

New width of the box = n+1

New length of the box = n+2

New height of the box = n

So, the volume of the new box is:

[tex]V_2=Length\times width\times h[/tex]

[tex]V_2=(n+2)(n+1)n[/tex]

[tex]V_2=(n^2+2n+n+2)n[/tex]

[tex]V_2=(n^2+3n+2)n[/tex]

[tex]V_2=n^3+3n^2+2n[/tex]

Now, the difference between new volume and original volume is:

[tex]V_2-V_1=n^3+3n^2+2n-n^3[/tex]

[tex]V_2-V_1=3n^2+2n[/tex]

So, the volume of new box is 3n^2+2n cubic inches more than the original box.

Therefore, the correct option is A.

Which terms in the following expression are like terms?

x3 + 5x - 3x + 3y + 4 - 1

3x and 3y
x 3, 3x, and 3y
5x and 3x, and 4 and 1
x 3 and 3x, and 4 and 1

Answers

9514 1404 393

Answer:

  (c)  5x and 3x, and 4 and 1

Step-by-step explanation:

Like terms have the same variable(s) to the same power(s).

The terms of this expression are ...

x^3: variable x, power 35x: variable x, power 1-3x: variable x, power 13y: variable y, power 14: no variable-1: no variable

The like terms are {5x, -3x}, which have the x-variable to the first power, and {4, -1}, which have no variable.

HELPP
-1-3(5m+8) ≥-85
i need help :D

Answers

Answer:

- 1 - 3(5m + 8) ≥ -85

-1 - 15m - 24 ≥ -85

-15m ≥ -85 + 1 + 24

-15m ≥ 25 - 85

-15m ≥ -60

(-1)(-15)m ≤ -60(-1)

15m ≤ 60

m ≤ 4

Given n(A) = 1300, n(A U B) = 2290, and n(A n B) = 360, find n(B).

Answers

Answer:

n(B) = 1350

Step-by-step explanation:

Using Venn sets, we have that:

[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)[/tex]

Three values are given in the exercise.

The other is n(B), which we have to find. So

[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)[/tex]

[tex]2290 = 1300 + n(B) - 360[/tex]

[tex]940 + n(B) = 2290[/tex]

[tex]n(B) = 2290 - 940 = 1350[/tex]

So

n(B) = 1350

6. What are the coordinates of W? (0,t) W 0 (,0) Rhombus (0, -1) o (-r, o) (0,r). (t,0)​

Answers

Answer:

B. (-r, 0)

Step-by-step explanation:

W is on the x axis, so the y coordinate is 0.

It is also r away from the origin, so the x coordinate is -r

Hope this helps!

Angles A and B are complementary. If sin A = 4x + 10 and cos B = 2x + 16, what is the value of x? (

Answers

Answer:

x is 10.66

Step-by-step explanation:

What are complementary angles?

They are angles that up to 90

So we have Sin A and Cos B

4x + 10+ 2x + 16= 90

collect like terms

6x+ 26= 90

6x= 90-26

6x= 64

x= 64/6

x= 10.66

Hence the value of x is 10.66

Answer:

not 10.66

Step-by-step explanation:

Write 0.851 as a fraction in simplest form.

Answers

Answer:

[tex]\frac{851}{1000}[/tex]

Step-by-step explanation:

First, we can simply multiply that number by 1000, and divide again by 1000 to get a base fraction:

[tex].851\\\\= \frac{1000}{1000} \times .851\\\\= \frac{1000 \times .851}{1000}\\\\= \frac{851}{1000}[/tex]

851 is a secondary prime, having only two factors, both of which are prime.  Those factors are 23 and 37, neither of which is a factor of 1000, so this is already in simplest form.

A student has test scores of 75 and 82respectively. What is the student’s average score for a third test

Answers

Answer:

78.5 (I think 90% sure)

Step-by-step explanation:

sum of both scores

75+82 = 157

average for a third test

157÷2=78.5

If four pounds of potatoes cost $6.00, how much would 10 pounds of potatoes cost.
SHOW ALL YOUR WORK!!!!!

Answers

Answer:

10 pounds of potatoes would cost $15.

Step-by-step explanation:

Set up proportion.

4/6=10/x

simplify 4/6 into 2/3,

2/3=10/x

cross product,

2*x=3*10

2x=30

x=30/2

x=15

lemme just add some to the great reply above,

[tex]\begin{array}{ccll} lbs&\$\\ \cline{1-2} 4&6\\ 10&x \end{array}\implies \cfrac{4}{10}=\cfrac{6}{x}\implies 4x = 60\implies x = \cfrac{60}{4}\implies x = 15[/tex]

im stuck on this question!!!!

Answers

Answer:

reflected across the y axis: (5,2)

reflected across the x axis: (-2,5)

Answer:

Answer: (5,2) when reflected off the y-axis. (-5,-2) when reflected off the x-axis

-8(9r - 1) - 9(-8r+2)
Simplest form

Answers

Answer:

-10

Step-by-step explanation:

Step-by-step explanation:

-8(9r-1)-9(-8r+2)-72r+8-72r-18-72r-72r+8-18-144r-10-(144r+10)

hope it helps

stay safe healthy and happy...

In a particular year, the mean score on the ACT test was 22.5 and the standard deviation was 5.3. The mean score on the SAT mathematics test was 526 and the standard deviation was 101. The distributions of both scores were approximately bell-shaped. Round the answers to at least two decimal places.

Answers

Question is incomplete ; The questions solved were picked from similar questions but different parameters. However, the solution pattern are exactly the same.

Answer:

- 0.0943

- 0.386

30.185

Step-by-step explanation:

Given :

ACT:

Mean score, m = 22.5

Standard deviation, σ = 5.3

SAT :

Mean score, m = 526

Standard deviation, σ = 101

1.)

Zscore for ACT score of 22:

Since the distribution is normal ; we use the relation ;

Zscore = (score - mean) / standard deviation

Score = 22

Zscore = (22 - 22.5) / 5.3 = - 0.0943

B.)

Zscore for SAT of 487

Zscore = (score - mean) / standard deviation

Score = 487

Zscore = (487 - 526) / 101 = - 0.386

C.)

ACT score, for ACT Zscore of 1.45

Zscore = (score - mean) / standard deviation

ZScore = 1.45

1.45 = (score - 22.5) / 5.3

1.45 * 5.3 = (score - 22.5)

7.685 = score - 22.5

Score = 7.685 + 22.5

Score = 30.185

Please help I’m really stuck this is my last attempt

What is the mode for the set of data?

Ages
Stem Leaves
5 0, 4, 6
6 0, 2, 3, 4, 8, 8, 9
7 0, 2, 3, 4, 4, 4, 8, 9
8 4, 5, 6, 8
5|0 = 50 years old


33
68
4
74

Answers

Answer:

I THINK IT IS 74 NOT 4

I HOPE THIS HELPS!!!!!

Read the following scenario, and then answer the question.

Juan assumes that the temperature of the hot tea cooling on his desk can be modeled with an exponential function like this one: T(t)=179(0.92)t. He bases his assumption on the following: The tea cools about 8% every minute. The tea's current temperature is around 179 degrees Fahrenheit.

Which explanation correctly addresses Juan's assumption?

He is incorrect. The tea will cool linearly since it cools at the same number of degrees every minute.
He is correct. The tea will cool exponentially since it cools at a percentage rate every minute.
He is incorrect. The tea will cool along the curve of a parabola since it cools at an increasing percentage rate every minute.

Answers

9514 1404 393

Answer:

  (b)  He is correct. The tea will cool exponentially since it cools at a percentage rate every minute.

Step-by-step explanation:

Newton's Law of Cooling says the change in temperature is proportional to the temperature. This relation gives rise to an exponential function describing the temperature.

In this description, the temperature referred to is the difference between the temperature of the object and the temperature of the environment to/from which heat is being transferred.

Juan is only partially correct. The function is exponential, but the temperature that should be used in his equation is not the temperature of the tea, but the temperature difference between the tea and his desk.

__

The curve is not linear and not parabolic, excluding the other answer choices.

Step by step please help answer.
The diameter of a circular reservoir is 840 feet. To walk around the reservoir, you would walk approximately how far? (Use tt = 22/7.)

(1) 267 ft
(2) 2,640 ft
(3) 2,800 ft
(4) 18,480 ft
(5) Not enough information is given.​

Answers

Answer:

(2) 2,640 ft

Step-by-step explanation:

I'm going to assume that in this question, you are walking 1 full circle around the reservoir. That would mean you need to calculate the circumference of the circular reservoir.

The circumference formula is:

C = ⫪d

C stands for Circumference

d stands for diameter

I will use 22/7 instead of pi, so the formula looks more like this:

C = (22/7)(d)

The diameter is 840 feet, so we will substitute the variable d with 840:

C = (22/7)(840)

You can plug this part into the calculator, but by hand, it'll look something like this:

(22/7)*840 = (22*840)/7

18,480/7 = 2.640

Hope it helps (●'◡'●)

What sum is represented by the following number line?

Answers

Answer:

[tex]2\frac{3}{4} +(-4\frac{1}{4} )=-1\frac{2}{4}[/tex]

Step-by-step explanation:

That's the only equation that makes sense to the number line

What is the median of Restaurant A's food quality ratings?

4
5
1
3
2

Answers

Can’t read it good I would repost this
it's 3, if you put the rating in order from least to greatest you get

1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5

in the middle of all these numbers is the median, 3

Find the missing term in the pattern.

Answers

Answer:

1/108

Step-by-step explanation:

each denominator triples, so just triple 36.

Answer:

1/108

Step-by-step explanation:

This is a geometric sequence, where each number is 3 times the previous. Normally you would use the actual formula, however you're just asked to pick up on a pattern so just multiplying the second number by 3 works.

The sum of two numbers is 85. If four times the smaller number is subtracted from the larger number, the result is 5. Find the two numbers.
The larger number is
The smaller number is

Answers

Answer:

the larger number is 69

the smaller number is 16

Step-by-step explanation:

x is the smaller number

y is the larger number

x + y = 85

y - 4x = 5

y = 5 + 4x

x + 5 + 4x = 85

5x = 80

x = 16

y = 69

Find the slope of the line graphed below.

Answers

Answer:

Step-by-step explanation:

two points are (-5,-2) and (-1,3)

slope=(3-(-2))/(-1-(-5))=(3+2)/(-1+5)=5/4

1. S = 10 mm
V= S×S×S
=___×___×___
=____ mm3

Answers

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]V=1000\text{mm}^3[/tex]

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

I am assuming by the infomation given that the figure is a cube.

⸻⸻⸻⸻

[tex]\boxed{\text{Finding the volume of the cube...}}\\\\S = 10mm; V= s^3\\--------------\\\rightarrow V = 10^3\\\\\rightarrow V = 10 * 10 * 10\\\\\rightarrow \boxed{V=1000\text{mm}^3}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

Solve the equation x^2+6x+1=0

Answers

Hello!

x² + 6x + 1 = 0 <=>

<=> x = -6±√6²-4×1×1/2×1 <=>

<=> x = -6±√36-4/2 <=>

<=> x = -6±√32/2 <=>

<=> x = -6±2²√2/2 <=>

<=> x = -6±4√2/2 <=>

<=> x = -6+4√2/2 <=>

and

<=> x = -6-4√2/2 <=>

<=> x = -3+2√2 <=>

and

<=> x = -3-2√2 <=>

x1 = -3-22 and x2 = -3+22

Good luck! :)

X^2+6X+1=0
X^2+6X+3^2-3^2+1=0
(X+3)^2-9+1=0
(X+3)^2=8
X+3= ± 2√2
X= ±2√2-3

A case of 6 cost 7.5 what it the price per item

Answers

1.25 hope this helps

What does y equal in the solution of the system of equations below? 5y-3x-4z=22 2z-2x=-6 2z+3x=-6

Answers

9514 1404 393

Answer:

  y = 2

Step-by-step explanation:

Subtracting the second equation from the third gives ...

  (2z +3x) -(2z -2x) = (-6) -(-6)

  5x = 0

  x = 0

Using this in the third equation, we have ...

  2z +0 = -6

  z = -3

And substituting these values into the first equation, we have ...

  5y -3(0) -4(-3) = 22

  5y = 10 . . . . . subtract 12

  y = 2

__

The solution to the system is (x, y, z) = (0, 2, -3).

Quadrilateral A'B'C'D'A

B

C

D

A, prime, B, prime, C, prime, D, prime is the result of dilating quadrilateral ABCDABCDA, B, C, D about point AAA by a scale factor of \dfrac{1}{2}
2
1

start fraction, 1, divided by, 2, end fraction.

Answers

Answer:

[tex]A' = (2,0)[/tex]

Step-by-step explanation:

Given

See attachment for ABCD

[tex]k = \frac{1}{2}[/tex] --- the scale factor

Required

The coordinates of A'

From the attachment, we have:

[tex]A = (4,0)[/tex]

So:

[tex]A' = k * A[/tex]

[tex]A' = \frac{1}{2} * (4,0)[/tex]

[tex]A' = (2,0)[/tex]

Answer:

on khan, both are false

Step-by-step explanation:

3x7 I need help with this i do not know the answer pls help.

Answers

Answer:

21

Step-by-step explanation:

7+7+7=21

1000^1000

i would like to simplify it into 10^x, how?

Answers

Answer:

10^3000

Step-by-step explanation:

1000¹⁰⁰⁰

= (10³)¹⁰⁰⁰

= 10^(3×1000)

= 10³⁰⁰⁰ or 10^3000

Answered by GAUTHMATH

Which number is a solution of the inequality x less-than negative 4? Use the number line to help answer the question.

A number line going from negative 9 to positive 1.

–3
0
2

Answers

Answer:

-5 it is

Step-by-step explanation:

Write the rule that describes the first transformation?
RED —> BLUE

Answers

Looking at Point A to A', the rectangle moves 5 places to the left which is the x value + 5 and it shifts 1 place down which would be the y value - 1

This gets written as:

(x+5, y-1)

if my child had 115 of 149 questions right what percentage is the grade

Answers

Answer:

77.18%

Step-by-step explanation:

115:149*100 =

(115*100):149 =

11500:149 = 77.18

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