prove that

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

.

​

Answer:

4.076

Step-by-step explanation:

tan27°= |AC|/8

8*tan27°= 4.076

Use the tangent to find the unknown side lengths.

This is the answer

Ac= 4.07

Ab=8.97

Answer:

A.

B.

C.

Step-by-step explanation:

all three are used in 3 dimensional objects hence the name 3 dimensions.

Answer: There are 16 Capulets and 6 Montaques.

Step-by-step explanation:Other choices were either less than or greater than 200 multiplied by each other. If we do 16x8 which is 128 for the Capulets. Also, if we do 12x6 which is 72 for the Montaques. 128+72=200 essays in total

Answer:

The answer is $1.50/bottle.

Step-by-step explanation:

To get the unit price, you need to divide the total by the amount of bottles.

[tex]9.00/6=1.50[/tex]

Answer:

C. YES

Step-by-step explanation:

If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

Answer:

[tex]\frac{75}{100}[/tex]

Step-by-step explanation:

Answer:

Mr. Pinter's class has 42 students, Mrs. Rupert's class has 21 students, and Mrs. Althouse's class has 43 students.

Step-by-step explanation:

This question is solved using a system of equations.

I am going to say that:

Mr. Pinter's class has x students.

Mrs. Rupert's class has y students.

Mrs. Althouse's class has z students.

Mr. Pinter's class has twice as many students as Mrs. Rupert's class.

This means that:

[tex]x = 2y[/tex]

Mrs. Althouse's class has 20 less than three times Mrs. Rupert's class.

This means that:

[tex]z = 3y - 20[/tex]

Together they have 106 students.

This means that:

[tex]x + y + z = 106[/tex]

We have x and z has a function of y, so:

[tex]2y + y + 3y - 20 = 106[/tex]

[tex]6y = 126[/tex]

[tex]y = \frac{126}{6}[/tex]

[tex]y = 21[/tex]

And:

[tex]x = 2y = 2(21) = 42[/tex]

[tex]z = 3y - 20 = 3(21) - 20 = 63 - 20 = 43[/tex]

Mr. Pinter's class has 42 students, Mrs. Rupert's class has 21 students, and Mrs. Althouse's class has 43 students.

Let y = √x, so that y ² = x and 2y dy = dx. Then the integral becomes

[tex]\displaystyle \int_{25}^{81} \frac{\sqrt x}{x-1}\,\mathrm dx = \int_{\sqrt{25}}^{\sqrt{81}} \frac y{y^2-1}(2y\,\mathrm dy) = 2 \int_5^9 \frac{y^2}{y^2-1}\,\mathrm dy[/tex]

Now,

y ² / (y ² - 1) = 1 + 1 / (y ² - 1) = 1 + 1/2 (1/(y - 1) - 1/(y + 1))

so integrating gives us

[tex]\displaystyle 2\int_5^9\frac{y^2}{y^2-1}\,\mathrm dy= \int_5^9\left(2+\frac1{y-1}-\frac1{y+1}\right)\,\mathrm dy \\\\= (2y+\ln|y-1|-\ln|y+1|)\bigg|_5^9 \\\\= \boxed{8+\ln\left(\dfrac65\right)}[/tex]

Answer:

the answer is false

Step-by-step explanation:

comment if you want explanation

Answer:

True

Step-by-step explanation:

When using the formulas to find the surface area, both have equal surface area

Answer:

5 Minutes

take 10 and add 12 for each minute until you pass 60

Answer:

option (B) is the answer

Answer:

8.35714285714

Step-by-step explanation:

Hope it help you

Answer:

3 hrs

Step-by-step explanation:

5 * 24 = 120 miles

64x = 120 + 24x

40x = 120

x = 3 hrs

Answer:

72 is 6% of 1200.

Step-by-step explanation:

Multiply 72 by 100.

72*100

Then divide the number by 6

(72*100)/6

You should get 1200.

Answer:

39.79 cm

Step-by-step explanation:

a few things to make sure :

1 liter = 1 dm³ (a cube of 10cm length of edges) =

= 10×10×10 = 1000 cm³

the volume of a cylinder is

base area × height (or length, as it is called in this question).

and the base area is a circle

area = pi×r²

and r (radius) is half of the diameter.

so, we know r = diameter/2 = 4cm

and the volume is 2 liter = 2 dm³ = 2000 cm³

so, we have

2000 = pi×r² × length = pi×4² × length = pi×16 × length

length = 2000 / (pi × 16) cm = 125 / pi cm =

= 39.79 cm

40

Step-by-step explanation:

Each number is followed by a number that is half its value, so the sequence goes like

320, 160, 80, 40, 20, 10.

Step-by-step explanation:

6t-12+15t | 25+15t

21t-12 | 25+15t

21t-12 < 25+15t

hence proved..

Answer:

21t - 12 < 25 + 15t

Step-by-step explanation:

6( t - 2 ) + 15t < 5 ( 5 + 3t )

6t - 12 + 15t < 25 + 15t

21t - 12 < 25 + 15t.

Hence , Proved.

Answer:

m = 60

Step-by-step explanation:

The context is very important, the 'm' represents the minutes late the parents are and from this we can eliminate some options :

- The last one because then a parent would drop their child off earlier

- The first one and the third one because it is too long

Answer:

A

Step-by-step explanation:

Answer:

The measure of the angle is 55º.

Step-by-step explanation:

Complement of angle x:

If two angles are complementary, the sum of their measures is of 90º. Thus, the complement of an angle x is 90 - x.

In this question:

Angle is 120 less than 5 times its own complement, so:

[tex]x = 5(90 - x) - 120[/tex]

We have to solve for x

[tex]x = 450 - 5x - 120[/tex]

[tex]6x = 330[/tex]

[tex]x = \frac{330}{6}[/tex]

[tex]x = 55[/tex]

The measure of the angle is 55º.

Answer:

18

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

b = 3

y = -3

5b - y

Step 2: Evaluate

Answer:

Step-by-step explanation:

[tex]2(x-2)^2=8(7+y)\\2(x-2)^2=56+8y \Rightarrow y={1\over{8}}[2(x-2)^2-56]={1\over{4}}(x-2)^2-7\\finally\\y={1\over{4}}(x-2)^2-7\\let ~change~x~and~y\\x={1\over{4}}(y-2)^2-7\\x+7={1\over{4}}(y-2)^2\\4(x+7)=(y-2)^2\\y-2=\pm\sqrt{4(x+7)}\\\\y=2\pm\sqrt{4x+28}[/tex]

Answer:

[tex]{ \tt{f(x) = 2 {x}^{2} + 3x - 3 }} \\ { \tt{g(x) = - {x}^{2} }} \\ f(x) + 2 \times g(x) : \\ 0 {x}^{2} + 3x - 3 = 0 \\ x = 1 [/tex]

point's (1, 0)

Answer:

Problem 17)

[tex]\displaystyle y=-\frac{5}{2}x+\frac{7}{2}[/tex]

Problem 18)

[tex]\displaystyle y=\frac{3}{2}x-\frac{3}{2}+\frac{\pi}{4}[/tex]

Step-by-step explanation:

Problem 17)

We have the curve represented by the equation:

[tex]\displaystyle 4x^2+2xy+y^2=7[/tex]

And we want to find the equation of the tangent line to the point (1, 1).

First, let's find the derivative dy/dx. Take the derivative of both sides with respect to x:

[tex]\displaystyle \frac{d}{dx}\left[4x^2+2xy+y^2\right]=\frac{d}{dx}[7][/tex]

Simplify. Recall that the derivative of a constant is zero.

[tex]\displaystyle \frac{d}{dx}[4x^2]+\frac{d}{dx}[2xy]+\frac{d}{dx}[y^2]=0[/tex]

Differentiate. We can differentiate the first term normally. The second term will require the product rule. Hence:

[tex]\displaystyle 8x+\left(2y+2x\frac{dy}{dx}\right)+2y\frac{dy}{dx}=0[/tex]

Rewrite:

[tex]\displaystyle \frac{dy}{dx}\left(2x+2y\right)=-8x-2y[/tex]

Therefore:

[tex]\displaystyle \frac{dy}{dx}=\frac{-8x-2y}{2x+2y}=-\frac{4x+y}{x+y}[/tex]

So, the slope of the tangent line at the point (1, 1) is:

[tex]\displaystyle \frac{dy}{dx}\Big|_{(1, 1)}=-\frac{4(1)+(1)}{(1)+(1)}=-\frac{5}{2}[/tex]

And since we know that it passes through the point (1, 1), by the point-slope form:

[tex]\displaystyle y-1=-\frac{5}{2}(x-1)[/tex]

If desired, we can simplify this into slope-intercept form. Therefore, our equation is:

[tex]\displaystyle y=-\frac{5}{2}x+\frac{7}{2}[/tex]

Problem 18)

We have the equation:

[tex]\displaystyle y=\tan^{-1}\left(x^3\right)[/tex]

And we want to find the equation of the tangent line to the graph at the point (1, π/4).

Take the derivative of both sides with respect to x:

[tex]\displaystyle \frac{dy}{dx}=\frac{d}{dx}\left[\tan^{-1}(x^3)][/tex]

We can use the chain rule:

[tex]\displaystyle \frac{d}{dx}[u(v(x))]=u'(v(x))\cdot v(x)[/tex]

Let u(x) = tan⁻¹(x) and let v(x) = x³. Thus:

(Recall that d/dx [arctan(x)] = 1 / (1 + x²).)

[tex]\displaystyle \frac{d}{dx}\left[\tan^{-1}(x^3)\right]=\frac{1}{1+v^2(x)}\cdot 3x^2[/tex]

Substitute and simplify. Hence:

[tex]\displaystyle \frac{d}{dx}\left[\tan^{-1}(x^3)\right]=\frac{1}{1+v^2(x)}\cdot 3x^2=\frac{3x^2}{1+x^6}[/tex]

Then the slope of the tangent line at the point (1, π/4) is:

[tex]\displaystyle \frac{dy}{dx}\Big|_{x=1}=\frac{3(1)^2}{1+(1)^6}=\frac{3}{2}[/tex]

Then by the point-slope form:

[tex]\displaystyle y-\frac{\pi}{4}=\frac{3}{2}(x-1)[/tex]

Or in slope-intercept form:

[tex]\displaystyle y=\frac{3}{2}x-\frac{3}{2}+\frac{\pi}{4}[/tex]

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)

The equation "a - 3x = 0" is correctly written because it follows the standard format of an algebraic equation.

Given that,

All the equations are,

1. a + 0.2x

2. 5b - 5x + 2

3. a - 3x = 0

Now, from equation ''a - 3x = 0'',

In this equation, the variable "a" subtracted from 3 times the variable "x" equals zero.

The equal sign (=) indicates that the expression on both sides of the equation is equivalent.

The equation is properly balanced and expresses equality between the two sides.

It accurately represents a relationship between the variables "a" and "x" where the value of "a" is dependent on the value of "x" in order to satisfy the equation.

So, The correctly written algebraic equation is:

a - 3x = 0

To learn more about the equation visit:

brainly.com/question/28871326

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Answer:

AB IS THE ANSWER !!!!!!!!!!

Answer: AB

Step-by-step explanation:

Hi! I don't know if you need help anymore ,but here you go!

Because BC=ED, I asume that AE=AB

Answer:

1849  

Step-by-step explanation:

Margin of error, E=0.03

Confidence level=0.99

z=2.58

No prior estimate of p is given, so consider p=0.5

Sample size required ,n=2.58^2*0.5*(1-0.5)/0.03^2

n=1849  

Answer: The first number is 2, the second number is 3 and the third number is -2

Step-by-step explanation:

Let the first number be 'x', the second number be 'y' and the third number be 'z'

The equations according to the question becomes:

⇒ x + y + z = 3              ....(1)

⇒ x - y + z = -3              ....(2)

⇒ x - z = 1 + y              ....(3)

Rearranging equation 3:

⇒ x - y = 1 + z                .....(4)

Putting in equation 2:

⇒ 1 + z + z = -3

⇒ 1 + 2z = -3

⇒ z = -2

Putting this value in equation 4 and equation 1, we get:

⇒ x - y = -1

⇒ x + y = 5

Cancelling 'y' by eliminiation method and equation becomes:

⇒ 2x = 4

⇒ x = 2

Putting value of 'x' and 'z' in equation 1:

⇒ 2 + y - 2 = 3

⇒ y = 3

Hence, the first number is 2, the second number is 3 and the third number is -2

Answer:

B

Step-by-step explanation:

I'm not really sure tho