Two parallel lines are cut by a transversal as shown below. Suppose m4=83°. Find m5 and m7​
​

At that particular critical point, the second derivative needs to be negative in order to obtain the dimensions of the cylinder with the maximum volume. The values of the function that contain both variables are then substituted to obtain the dimensions.

A right circular cone with a height of 2.5 and a base radius of 7.5 inscribes the given cylinder.

Assume that h is the height and r is the radius of the cylinder. Using triangles that are similar, express h in terms of r as follows:

2.5/7.5 = 2.5-h/r

2.5r = 18.75 x 7.5 x 2.5 h = 2.5 x 1/3r

V= πr²h is the formula for the cylinder's volume.

As a result, only write the volume in terms of r.

V= r2h V= r2(2.5-1/3r)

V= 2.5πr² - 1/3πr³

As a result, the cylinder must have dimensions of r=5 and h=0.83.

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The rate, in inches per hour, at which the rain fell during that time on Friday is 3/8 inches per hour.

Time for which the rain fell = 2 hours

The total amount of rain that fell = 3/4 inch

So, in 2 hours, the amount of rain that fell = 3/4

In 1 hour, the amount of rain that fell = 3/8 inches

Hence, The rate, in inches per hour, at which the rain fell during that time on Friday = 3/8 inches per hour.

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Answer: The constant of variation, k , is 54

Step-by-step explanation: Step 1: Check whether the graph is a straight line. If the graph is not a straight line, it does not represent a proportional relationship. Step 2: Check whether the line goes through the origin. If the graph does not go through the origin, it does not represent a proportional relationship.

The ratios of the right triangle to solve for x is as follows;

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The sides of a right angle triangle can be named base on the position of the angles.  

The sides of a right angle triangles are hypotenuse sides, opposite and adjacent side. The hypotenuse side is the longest side of the right triangle.

Therefore, let's find the ratio that can be used to find the angle x.

Triangle PNM

sin x = opposite / hypotenuse

sin x = 6 / 10

Triangle ABC

cos x = adjacent / hypotenuse

cos x = 5 / 10

Triangle DEF

tan x = opposite / adjacent

tan x = 4 / 6

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Answer:

False

Step-by-step explanation:

The correct answer is y = -25x + 450

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &100\\ r=rate\to 5.8\%\to \frac{5.8}{100}\dotfill &0.058\\ t=\textit{hours}\dotfill &2\\ \end{cases} \\\\\\ ~\hfill A=100(1 - 0.058)^{2} ~\hfill[/tex]

The equation represents the grams of the compound will remain after 2 hours will be;

⇒ C = 100 (1 - 0.058)²

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A radioactive compound with mass 100 grams decays at a rate of 5.8% per hour.

And, Time = 4 hours

Now,

Since, We know that;

Amount for Exponential Decay is,

⇒ [tex]C = P (1 - r)^t[/tex]

Where, C is current amount, P is initial amount, r is rate and t is timeeee

Substitute all the values, we get;

The equation represents the grams of the compound will remain after 2 hours will be;

⇒ C = 100 (1 - 0.058)²

Thus, The equation represents the grams of the compound will remain after 2 hours will be;

⇒ C = 100 (1 - 0.058)²

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Answer: 2/3

Step-by-step explanation:

12 out of 18 prefer summer sports so as a fraction it would be 12/18 = 6/9 = 2/3

Answer:

33.3333%

Step-by-step explanation:

EXPLANATION

Based on the given conditions, formulate: (18-12) ÷ 18

Calculate the sum or difference:[tex]\frac{6}{18}[/tex]

Cross out the common factor:[tex]\frac{1}{3}[/tex]

Rewrite a fraction as a decimal: 0.333333

Multiply a number to both the numerator and the denominator: 0.333333x[tex]\frac{100}{100}[/tex]

Write as a single fraction:[tex]\frac{33.33333x100}{100}[/tex]

Calculate the product or quotient:[tex]\frac{33.333}{100}[/tex]

Rewrite a fraction with denominator equals 100 to a percentage: 33.3333%

Answer: 33.3333%

Answer: It will take 24 years to have 7 million.

Step-by-step explanation:

1.65% of 5.04 million is 83,160.

2018 is 6 years from 2012.

83,160 x 6 = 498,960.

498,960k + 5,040,000mil =5,538,960mil. still not quite 7 million.

498,960k x 4 = 1,995,840mil.

1,995,840mil + 5,040,000mil = 7,035,840mil.

It will take the city 24 years to have 7 million.

Answer:

b>19

Step-by-step explanation:

15<b−4

Rewrite so b is on the left side of the inequality.

b−4>15

Move all terms not containing b to the right side of the inequality.

Add 4 to both sides of the inequality.

b>15+4

Add 15 and 4.

b>19

b>19

The result can be shown in multiple forms.

Inequality Form:

b>19

Interval Notation:

(19,∞)

The true statement about the function of area of by rectangle and width of rectangle are:

The correct answer option is options A and D

A rectangle is a quadrilateral having opposing sides parallel and four right angles.

At point (x, y) = (10, 100) the area is maximum.

This means that the area of the rectangle is maximum when width is 10m.

If the width of the rectangle is more than 10m, the area reduces or decreases.

Therefore, the statement Greater width relates to greater area as long as the width is more than 10 m is false.

The statement "To get the greatest area, the width should be 20" is false.

Complete question:

Simon has a certain length of fencing to enclose a rectangular area. The function A, models give the rectangles area (in square meters) as a function of its width (in meters).

Wlhich of these statements are true?

A. Greater width relates to greater area as long as the width is less than 10.

B. Greater width relates to greater area as long as the width is more than 10.

C. To get the greatest area, the width should be 10

D. To get the greatest area, the width should be 20

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Zeros of the given polynomial are -2, 2, -3/2, 3/2

Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole.

Given a polynomial 1/4(4[tex]x^{4}[/tex] - 25[tex]x^{2}[/tex] + 36)

1/4(4[tex]x^{4}[/tex] - 25[tex]x^{2}[/tex] + 36) = 0

(4[tex]x^{4}[/tex] - 25[tex]x^{2}[/tex] + 36) = 0

4[tex]x^{4}[/tex] - 16[tex]x^{2}[/tex] - 9[tex]x^{2}[/tex] + 36= 0

4[tex]x^{4}[/tex]([tex]x^{2}[/tex] - 4) - 9([tex]x^{2}[/tex] - 4) = 0

(4[tex]x^{4}[/tex]-9)([tex]x^{2}[/tex] - 4) = 0

(x+2)(x-2)(2x+3)(2x-3) = 0

x = -2, 2, -3/2, 3/2

Hence, Zeros of the given polynomial are -2, 2, -3/2, 3/2

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She will have run a total of 2.25 racers in 27 racers

From the question, we have the following parameters that can be used in our solution:

Total number of racers = 27 racers

Number of racers in a run = 12 racers

From the above parameter, we can calculate the total number of racers using the following equation

The total number of racers is calculated as

Total number of racers in the run = Total number of racers/Number of racers in a run

Substitute the known values in the above equation

So, we have the following equation

Total number of racers in the run = 27/12

Evaluate the quotient

Total number of racers in the run = 2.25

Hence, the total number of racers in the run is 2.25 racers

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Answer:

Step-by-step explanation:

The equation where y is the price of the ticket with the coupon, and x is the original price of the ticket.

y= 0.55 x.

Given:

A movie theater sends out a coupon for 45% off the price of a ticket. Write an equation for the​ situation, where y is the price of the ticket with the​ coupon, and x is the original price of the ticket.

If x is the price of the ticket without the coupon, and the theater offers a discount if you have a coupon, then having a coupon means that the price a person ultimately  pays (y) is  the original price (x) minus a 45% of this price:

y= x -0.45 x

By association: y= (1-0.45) x

and then y= 0.55 x.

The line should be in the first quadrant because the first quadrant allows you to represent a situation in which the dependent variable (y) and the independent variable (x) are both positive. This is the case in this exercise, because both prices, the one without discount (x) and the one with discount (y) are necessary positive (you can not pay a negative price!).

Hence we get the required equation.

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The measure of angle 4 is 125° for the given triangle.

According to the question,

We have the following information:

A figure is given of triangle and its exterior angles.

m∠1 = 70°

Now, the two sides (with line on them) of the triangle are equal. So, it means that it is an isosceles triangle.

We know that sum of three angles of a triangle is 180°.

Let's take the two equal angles to be x°.

x+x+70 = 180

2x+70 = 180

2x = 180-70

2x = 110

x = 110/2

x = 55°

We know that angles made on a straight line is 180°.

∠4 and angle x will make a straight line.

∠4 = 180-55

∠4 = 125°

Hence, the correct option is A.

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Answer:

x= -2

Step-by-step explanation:

-2 = 3x + 8/2

-2+2=3x+4+2          (add 2 to both sides)

0=3x+6                          

-6=3x+6-6

3x=-6

x=-6/3

x= -2

Answer:

x = 154

Step-by-step explanation:

[tex]\frac{x}{11}[/tex] + 16 = 30 ( subtract 16 from both sides )

[tex]\frac{x}{11}[/tex] = 14 ( multiply both sides by 11 to clear the fraction )

x = 11 × 14 = 154

Answer:

x = 154

Step-by-step explanation:

Given equation,

→ (x/11) + 16 = 30

Now the value of x will be,

→ (x/11) + 16 = 30

→ x/11 = 30 - 16

→ x = 14 × 11

→ [ x = 154 ]

Hence, value of x is 154.

Answer:

y=2x-2

Step-by-step explanation:

2.5y=5x-5

 /2.5. /2.5

y=2x-2

Hopes this helps please mark brainliest

Answer:

y=2x−2

Step-by-step explanation:

The slope-intercept form is

y=mx+b, where m

is the slope and b

is the y-intercept.y =mx+b

Divide each term in 2.5y=5−5 by 2.5

and simplify. y=2x−2

Answer:327

Step-by-step explanation:

Because you already have the equation, all you need to do is plug in the value for X. If X is equal to 4, our equation would look like this:

y = 78 * 4 + 15

Because of order or operations (PEMDAS), we do multiplication first.

y = 312 + 15

y = 327

Hope this helped!

Answer:  After 5 Years Alex will receive 90 Dollar.

Step-by-step explanation 5 x 6% of 300 = 30% is 90 Dollar.

The original amount is $92.202.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is primarily used to compare and determine ratios and is represented by the symbol %.

Given:

Total amount = 83.82

rate of increase = 10%

So, the original amount

= 83.82 + 83.82 x 0.1

= 83.82 + 8.382

= $92.202

Hence, the original amount is $92.202.

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Answer: 18

Step-by-step explanation:

There are no parenthesis or exponents, so you use multiplication first.

6 x 2 = 12

That makes your equation 14 + 12 - 16 + 8

Now you only have adding and subtracting left, which you’ll do from left to right.

14 + 12 = 26

26 - 16 + 8

26 - 16 = 10

10 + 8 = 18

Hope this helps!

Answer:

Part B: (0, -6)

Part C: x = -1

Part D: (-1, -8)

Explanation:

see the attached pdf

The rate written in miles per hour is 2.67 mph.

What is constant rate?

A rate of change is constant when, at any given point along the function, the ratio of the output to the input remains constant. The slope is another name for the rate of change that is constant. A linear function will change at a constant rate.

Let, John walks at a constant rate of 8 miles every 3 hours.

Therefore, the rate per hour is,

[tex]\frac{8}{3} = 2.6666\\ = 2.67 miles per hour.[/tex]

Therefore, the rate written in miles per hour is 2.67 miles per hour.

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Answer:

it is 3 0 o 90 not up okbg 56

Answer:

a) 6.2%
b) £13,687

Step-by-step explanation:

a)

To find the rate of interest, we first find the interest itself.
£7965.00 - £7500.00 = £465.00
Using this, we find the rate of interest in percentage as a fraction of the original loan.

(£7500.00 ÷ £465.0) × 100 = 6.2%

Thus, the rate of interest is 6.2%.

b)
Compound interest is found using the formula
[tex]A = P(1 + \frac{r}{100})^{t}[/tex]
Where

A = final amount

P = initial principal balance

r = interest rate

t = number of time periods elapsed

Thus, with an initial balance of £7500, an interest rate of 6.2% and a time period of 10 years, calculated per annum, we can plug the numbers into the formula, giving us

[tex]A = 7500(1 + \frac{6.2}{100})^{10}[/tex]
   [tex]=[/tex] £13,686.94
   ≈ £13,687 (to nearest £1)

Some things to note: number of time periods elapsed mean the amount of times it is compounded; if the question says compounded quarterly for 3 years, t = 12 as it is compounded 4 times a year for 3 years, giving is 12 time periods. This also applies to monthly, bi-weekly etc.

Answer:

  -425

Step-by-step explanation:

You want the sum of the first 8 terms of the geometric series with first term 5 and common ratio -2.

The sum is given by the formula ...

  Sn = a1·(r^n -1)/(r -1) . . . . . . a1 = first term, r = common ratio

The sum of 8 terms of the given series is ...

  S8 = 5·((-2)^8 -1)/(-2 -1) = 5(255/-3) = -1275/3 = -425

The sum of 8 terms is -425.

Answer:

you can do the favour of marking the answer brainlest pls