Suppose that there are two types of tickets to a show advance and same day the combined cost of one advance ticket and one same-day ticket is $70 for one performance 20 advance tickets and 35 same day tickets were sold.The total amount paid for the tickets was $1850.what was the price of each kind of ticket

Answer:

x = ±6

Step-by-step explanation:

→ Add 12 to both sides

1/3 x² = 12

→ Multiply both sides by 3

x² = 36

→ Square root both sides

x = ±6

Given x = acos³θ , y = asin³θ

Diffrentiating w.r.t. θ

dx/dθ = -3acos²θsinθ ____(1)

dy/dθ = 3asin²θcosθ ______(2)

diving (2) by (1)

dy/dθ ×dθ/dx = -( 3asin²θ cosθ /3acos²θsinθ )

dy/dx = - tanθ

dy/dx = slope of tangent = -tanθ

putting θ = π/4

∴ dy/dx =- tanπ/4 = -1

but , slope of normal = - 1/slope of tangent

∵ slope of normal = -1/-1 = 1

∴ slope of normal = 1 Answer

Answer:

Slope of normal = 1

Step-by-step explanation:

   [tex]\sf x =aCos^3 \ \theta\\\\\dfrac{dy}{d \theta} = a*3Cos^2 \ \theta (-Sin \ \theta)\\[/tex]

         [tex]\sf = -3aCos^2 \ \theta *Sin \ \theta[/tex]

[tex]\sf y =aSin^3 \ \theta\\\\\dfrac{dy}{d\theta}=a*3Sin^2 \ \theta*(Cos \ \theta)\\\dfrac{dy}{d\theta}=3aSin^2 \ \theta*Cos \ \theta[/tex]

          [tex]\sf Slope \ of \ Tangent = \dfrac{dy}{dx} =\dfrac{dy}{d\theta} \div \dfrac{dx}{d\theta}[/tex]

                    [tex]\sf = \dfrac{3aSin^2 \ \theta \ Cos \ \theta}{-3aCos^2 \ \theta \ Sin \ \theta}\\\\ = \dfrac{-Sin \ \theta}{Cos \ \theta}\\\\= -tan \ \theta[/tex]

[tex]\theta = \dfrac{\pi }{4}\\\\-tan\ \theta = -tan \ \dfrac{\pi }{4} \\\boxed{tan \ \dfrac{\pi }{4}=-1}[/tex]

Slope of tangent * slope of normal = -1

                                [tex]\boxed{\text{Slope of normal =$\dfrac{-1}{Slope \ of \ tangent}$}}[/tex]

[tex]\sf \text{Slope of normal=\dfrac{-1}{-1}}[/tex][tex]\sf Slope \ of \ normal =\dfrac{-1}{-1}[/tex]

                        = 1

Answer:

let's say you wanted to know if Gatorade increased athletic performance. Your experimental group would be given the Gatorade and your control group would be given regular water.  or  an experiment in which the researcher tests whether or not a new fertilizer has an effect on plant growth.

Step-by-step explanation:

Answer:an example of a treatment and a control group a human experimental group could receive a new medication, a different form of counseling, or some vitamin supplements. A plant treatment group could receive a new plant fertilizer, more sunlight, or distilled water. The group that does not receive the treatment is called the control group

Step-by-step explanation:

Answer:

[tex]y = 2x + 2[/tex]

Step-by-step explanation:

[tex]euation \: of \: a \: line \: has \: the \: forula \\ y - y1 = m(x - x1) \\ where \: m = slope \\ m = \frac{y2 - y1}{x2 - x1} = \frac{ - 6 - - 4}{ - 4 - - 3} \\ = \frac{ - 6 + 4}{ - 4 + 3} = \frac{ - 2}{ - 1} = 2 \\ now \: putting \: m = 2 \: into \: the \: equation \\ y - - 4 = 2(x - - 3) \\ y + 4 = 2(x + 3) \\ y + 4 = 2x + 6 \\ y = 2x + 6 - 4 \\ y = 2x + 2[/tex]

PLEASE RATE AND MARK BRIANLIEST

Answer:

5

Step-by-step explanation:

This line equation is in  y = mx + b form    m will be the slope

 m = 5     parallel line will have same slope  = 5  

Answer:

3

Step-by-step explanation:

You divide 45 and 60 then you mutliple the number by 4 then find your anser after you done sovled this is how you solve it divided by 60=0.75 mutiply by 4=3 3 or 4/3

The volume of a rectangular prism with base of 5 cm by 6 cm with a height of 12 cm is 360 cm³

An equation is an expression that shows the relationship between two or more numbers and variables.

The volume of the rectangular prism = length * width * height = 5 cm * 6 cm * 12 cm = 360 cm³

The volume of a rectangular prism with base of 5 cm by 6 cm with a height of 12 cm is 360 cm³

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Answer:

see explanation

Step-by-step explanation:

12(3)+12(5)=use a calculator.

Type it in a calculator.

the answer is ±5i :)

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the concept of Surface areas and volumes.

Here we will find surface areas by adding individual parts.

Surface area ==> Small rectangle + big rectangle + base rectangle + 2* right angled triangles.

so we get as,

area of shape = 721.1 yards.

option D.) is correct.

Answer:

A. 560

Step-by-step explanation:

multiply 600 by 0.93 in order to find out what 93% of 600 is.

600 x 0.93 = 558

since 558 isn't one of the options you find which one is closest to it, then divide by 600 in order to see if it's still 93%

a) 560/ 600 = 0.93333 = 93.3%

there's your answer.

but to compare it with the rest of the answer choices:

b) 540 / 600 = 0.9 = 90%

c) 470 / 600 = 0.78333 = 78.3%

d) 490 / 600 = 0.81667 = 81.6%

none of these are in the range of 93, so they're incorrect

Answer:

[tex]y = kx \\ formula \: connecting \: y \: and \: x[/tex]

The number of days that had either rain or high winds for the considered case is 77

For two subsets A and B of the universal set U, we have:

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

Assume that:

A and B be the subsets of what happens on each day.

Then in the days of last several weeks , we take:

then, as per the data given, we get:

Thus, we get:

[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)\\n(A \cup B) = 67 + 23 - 13 = 77[/tex]

Thus, n(A ∪B) = number of days seeing either rain or high winds = 77

Thus, the number of days that had either rain or high winds for the considered case is 77

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Step-by-step explanation:

[tex] - \sqrt{2 } \div 2[/tex]

Use the unit circle to help you!

Answer:

10 miles

Step-by-step explanation:

3600 ÷ 90 is 40 then 40÷4 is 10

Answer: 1/6mile

Step-by-step explanation:

¼mile in 1½hr

In 1½hr He biked ¼mile

in 1hr He biked ¼ ÷ 1½

¼ ÷ 1½

¼ ÷ 3/2

¼ × ⅔ = 2/12 = ⅙mile

Answer:

hj means has a job

nj means no job

Step-by-step explanation:

Answer:

B) 868

Step-by-step explanation:

1. You add 700+300 which is 1000

2. You subtract the amount wasted or withdrawn which will get you 880

3. You subtract the fees which will then get you 868 as your answer

Answer:

69.71%

Hope this helps!

Answer: 69.7142857%

Step-by-step explanation:

Answer:

[tex]\tan (A+B) =-\frac{680}{111}[/tex]

Step-by-step explanation:

[tex]\tan A=\frac{12}{5}[/tex]

[tex]\cos B=\frac{45}{53}\implies \sec B=\frac{53}{45}[/tex]

Now, by trigonometric identity:

[tex]\tan^2 B =\sec^2B-1[/tex]

[tex]\implies \tan^2 B =\bigg(\frac{53}{45}\bigg)^2-1[/tex]

[tex]\implies \tan^2 B =\frac{(53)^2-(45)^2}{(45)^2}[/tex]

[tex]\implies \tan^2 B =\frac{(28)^2}{(45)^2}[/tex]

[tex]\implies \tan B =\pm\sqrt{\frac{(28)^2}{(45)^2}}[/tex]

[tex]\implies \tan B =\pm\frac{28}{45}[/tex]

It is given that: Angles A and B are in quadrant I.

---------------------> Angles A and B would be positive.

[tex]\implies \tan B =\frac{28}{45}[/tex]

Next,

[tex]\tan (A+B) =\frac{\tan A +\tan B}{1-\tan A \tan B}[/tex]

[tex]\implies \tan (A+B) =\frac{\frac{12}{5} +\frac{28}{45}}{1-\bigg(\frac{12}{5}\bigg) \bigg(\frac{28}{45}\bigg)}[/tex]

[tex]\implies \tan (A+B) =\frac{\frac{108}{45} +\frac{28}{45}}{1-\bigg(\frac{336}{225}\bigg)}[/tex]

[tex]\implies \tan (A+B) =\frac{\frac{136}{45}}{\bigg(\frac{225-336}{225}\bigg)}[/tex]

[tex]\implies \tan (A+B) =\frac{\frac{136}{45}}{\frac{-111}{225}}[/tex]

[tex]\implies \tan (A+B) =-\frac{680}{111}[/tex]

Answer:

32

Step-by-step explanation:

4×4×4=64 then you divide 2 will be 32

Answer:

32

Step-by-step explanation:

4x4=16

16x4=64

64/2=32

[tex]Hence,TheAnswerTo...\\\frac{4^{3} }{2} =32[/tex]

Answer:

4.

Step-by-step explanation:

Area = 1/2 * base + height

= 1/2 * 2 * 4

= 4 unit^2.

Answer:

4 For Small

8 For big

Step-by-step explanation:

80 Square Inches in terms of pie, since one of the radius points are 2 times the other we can setup a equation

(Leaving out pi for simplicity)

R^2 + 2R^2= 80

Now since R is doubled in spot we can plug in points until we get the answer

1:2 (Too small)

2:4 (Too Small)

3:6 (Too small)

4:8 (Fits)

If we plug 4 for R it satisfies the equation for our criteria.

Answer:

273.00

Step-by-step explanation:

The center of a circle whose equation is x^2 +y^2 – 12x – 2y  +12 = 0 is (6,1)

The standard equation of a circle is expressed as:

x^2 + y^2 + 2gx + 2fy + c = 0

where:

(-g, -f) is the centre of the circle

Given the equations

x^2 +y^2 – 12x – 2y  +12 = 0

Compare

2gx = -12x

g = -6

Similarly

-2y = 2fy

f = -1

Centre = (6, 1)

Hence the  center of a circle whose equation is x^2 +y^2 – 12x – 2y  +12 = 0 is (6,1)

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Answer:

[tex] a = ( \frac{ - 6}{2} )[/tex]

Step-by-step explanation:

-2g=?

[tex] - 2( \frac{3 }{ - 1} ) \\ \\ ( \frac{ - 6}{2} )[/tex]

===========================================================

Explanation:

The function can be broken down into the form

f(x) = g(x) - 3*h(x)

where,

g(x) = sin(x)

h(x) = cos(x)

Both g and h are sinusoidal with the same period of 2pi. Therefore, the linear combination of these functions is also sinusoidal with the same period of 2pi. If the periods didn't match up, then it's likely the function isn't sinusoidal and instead some other complicated crazy curve.

Extra notes:

The equation of c is an illustration of subject of formula

The equation of c in terms of r and t is c = r - 15/t

The equation is given as:

t = 15/(r - c)

Cross multiply

t(r - c) = 15

Divide both sides by t

r - c = 15/t

Subtract r from both sides

-c = -r + 15/t

Multiply both sides by -1

c = r - 15/t

Take LCM

[tex]c = \frac{rt - 15}{t}[/tex]

Hence, the equation of c in terms of r and t is [tex]c = \frac{rt - 15}{t}[/tex]

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Answer:

N=17

?=15

Explanation;

Check out my attached work

Hope it helps, let me know if you have any questions