help if you do help you get 98 points. :)

Answer:

centre = (2, - 1), radius = 6

Step-by-step explanation:

Rearrange the equation by placing the x and y terms together and adding 31 to both sides

Given

x² + y² - 4x + 2y - 31 = 0, then

x² - 4x + y² + 2y = 31

Use the method of completing the square

add ( half the coefficient of the x/y term )² to both sides

x² + 2(- 2)x + 4 + y² + 2(1)y + 1 = 31 + 4 + 1

(x - 2)² + (y + 1)² = 36

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r the radius

compare to (x - 2)² + (y + 1)² = 36, then

centre = (2, - 1) and r = [tex]\sqrt{36}[/tex] = 6

The center of the circle is  (2, - 1) and the radius is 6 units.

The equation for a circle has the generic form x² + y² + 2gx + 2fy + c = 0.

The standard equation of a circle is x² + y² = r².

The polar form of the equation of the circle is (rcosθ)² + (rsinθ)² = p².

Given, The equation of a circle is x² + y² - 4x + 2y - 31 = 0.

We know, In x² + y² + 2gx + 2fy + c = 0, The center of the circle is,

(- g, - f) and radius is [tex]\sqrt{g^2 + f^2 - c[/tex].

Therefore, 2gx = - 4x and 2fy = 2y.

2g = - 4 and 2f = 2.

g = - 2 and f = 1.

- g = 2 and - f = - 1.

So, The center is (2, - 1).

And the radius is, [tex]\sqrt{2^2 + -1^2 + 31[/tex].

= [tex]\sqrt{4 + 1 + 31[/tex].

= [tex]\sqrt{36[/tex].

= 6 units.

learn more about circles here :

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Answer:

2 hours 33 mins

Step-by-step explanation:

Arrives = 8.12 pm

Leaves = 10.45 pm

8.12 pm to 10.12 pm = 2 hours

10.12 pm tp 10.45 pm = 33 minutes

Total

= 2 hours + 33 mins

= 2 hours 33 mins

Answer:

2:33

Step-by-step explanation:

For 8:00 to get to 10:00 add two which means two hours then subtract :45 by :12 which gives you 33 so tyler stayed there for 2 hours and 33  minutes.

The area of the yellow sector is 15/8 π in² in pi form.

To find the total number of children who attended the fair on opening day, add 351 to 4000, giving a result of 4351 children.

The number of children who attended the fair on opening day is calculated by adding 351 to the value of 4 thousands. To find the answer, we follow these steps:

Therefore, 4351 children attended the fair on the opening day.

Answer:360

Step-by-step explanation:

35% of of 100% with 126 being as the part and the whole is missing.You multiply 126 by 100 which equals 12600 divided by 35 which is equals 360.

Answer:

C)

Step-by-step explanation:

If you multiply twice, you will get 70%. If you multiply by three, you will get 378. That is higher than 360. So it's 360(c)

V≈301.59

I think this is the answer.

Hope this helps!

The answer is 96pi units^3

Answer:

13.6

Step-by-step explanation:

Use the a^2 + b^2 = c^2 formula.

Answer:

A = 7.55

Step-by-step explanation:

Answer:  D. |6.7| > |-45|

Step-by-step explanation:

When in these | | then any negative number becomes positive. 6.7 is NOT grater than 45.

Answer:

I would do answer B if not A.

Step-by-step explanation:

I would do this because then they would be relatively closer in skill set.

The appropriate way to label the age intervals on the x-axis is:  Option: B

               B) 7−10; 11−14; 15−18; 19−22

            The rule for determining the number of intervals is:

Here we have 13 observations

and √(13)=3.6055≈4

Hence, we have a total of four intervals.

                 The width of each interval is calculated as:

                       i.e.   (22-7)/4=15/4=3.75≈4

We know that for classifying a class interval in a histogram the width of each of the interval must be equal.

A) 7−11; 11−14; 15−19; 20−22

In option: A--

the width of first interval is: 4

width of second interval is: 3

Width of third interval is: 4

Width of fourth interval is: 2

Hence, the width of each interval is not equal.

Hence, option: A is discarded.

C) 7−10; 10−15; 15−19; 19−22

In option: C--

the width of first interval is: 3

width of second interval is: 5

Width of third interval is: 4

Width of fourth interval is: 3

Hence, the width of each interval is not equal.

Hence, option: C is discarded.

D)  7−13; 15−19; 20−22

In option: D--

the width of first interval is: 6

width of second interval is: 4

Width of third interval is: 2

Hence, the width of each interval is not equal.

Hence, option: D is discarded.

B)  7−10; 11−14; 15−18; 19−22

There are a total of 4 intervals and also width of each interval is equal and equal to 4.

         Hence, option: B is the correct answer.

Answer:

The explicit rule is:

Step-by-step explanation:

The explicit rule is given by:

[tex]a_n=a_1+d(n-1)[/tex]

The given sequence is 25,21,17,13

[tex]a_1=25[/tex]

d=21-25

d=-4

We plug in the values into the formula to get;

[tex]a_n=25+-4(n-1)[/tex]

[tex]a_n=25-4n+4[/tex]

[tex]a_n=29-4n[/tex]

(.15 miles / 1 minute) * (60 minutes / 1 hour) = 9 miles / hour

To find the missing value in the equation, we add -4.5 and 4.4 first, then solve for the missing value.

To find the missing value, we need to solve the equation. Start by adding -4.5 and 4.4. (-4.5 + 4.4 = -0.1)

Now we have: -0.1 + ___ = 0

To solve for the missing value, subtract -0.1 from both sides of the equation: ____ = 0 + 0.1 = 0.1

The missing value is 0.1.

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Final answer:

The missing value is 0.1.

Explanation:

This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 4.90, b = -14.3, and c = -20.0.

To solve for the missing value, we can rearrange the equation:

-4.5 + 4.4 + ____ = 0

Simplifying the equation, we get:

-4.5 + 4.4 + ____ = 0

-0.1 + ____ = 0

By adding 0.1 to both sides of the equation, we can isolate the missing value:

____ = 0.1

Therefore, the missing value is 0.1.

Answer:

Option 1 and 2 are correct.

Step-by-step explanation:

1. {x:x <-3 or >4}

Here the values of x can be less than -3 or the values of x can be greater than 4. Since 5 is greater than 4 so, 5 is included in the solution

2. {x:x ≥5}

Here the values of x can be greater than or equal to 5. So, 5 is included in the solution.

3. {x:x <5}

Here the values of x can be less than 5. So, 5 is not included in the solution

4. {x:0<x<4}

Here the value of x is greater than 0 but less than 4. So, 5 is not included in the solution

So, Option 1 and 2 are correct.

Hence, the correct answer is:

             Option : a

             a.   5.6 amps

It is given that:

The current (I) in an electrical conductor varies inversely as the resistance (R) of the conductor.

This means that:

[tex]I\propto \dfrac{1}{R}[/tex]

Hence, we get the relation as:

[tex]\dfrac{I_1}{I_2}=\dfrac{R_2}{R_1}[/tex]

where [tex]R_1[/tex] is the resistance corresponding to the current [tex]I_1[/tex]

and  [tex]R_2[/tex] is the resistance corresponding to the current [tex]I_2[/tex]

We have:

[tex]I_1=6\ ,\ R_1=722\ ,\ R_2=768[/tex]

Hence, we get:

 [tex]\dfrac{6}{I_2}=\dfrac{768}{722}\\\\\\i.e.\\\\\\I_2=\dfrac{722\times 6}{768}\\\\\\I_2=5.6406\ amperes[/tex]

        Hence, the answer is:

             Option : a

Answer: 75 students

Step-by-step explanation:

15% of 500= 75

Given : One carton of eggs contains 12 eggs.

By unitary method we can find the number of eggs in following cartoons :

1 cartoon = 12 eggs

5 cartoons = 12 × 5 = 60 eggs

6 cartoons = 12 × 6 = 72 eggs

7 cartoons = 12 × 7 = 84 eggs

8 cartoons = 12 × 8 = 96 eggs

Answer:

D

Step-by-step explanation:

[tex]x\geq 3 \ and \ x+1 \geq 4[/tex]

The question in this problem is:

The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger. What are the numbers?

First of all, let's name the first variable [tex]x[/tex] which is the smaller number. Accordingly, the lager number will be [tex]x+1[/tex] given that those numbers are consecutive. On the other hand at most conveys the idea of an inequality, which is:

[tex]\leq \\ which \ means \ less \ than[/tex]

So:

1. The sum of 2 consecutive integers can be written as:

[tex]v+(v+1)[/tex]

2. Nine times the smaller and 5 times the larger can be written as:

[tex]9v-5(v+1)[/tex]

Finally, the whole statement:

The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger:

[tex]x+(x+1) \leq 9x-5(x+1) \\ \\ x+x+1\leq 9x-5x-5 \\ \\ 2x+1 \leq 4x-5 \\ \\ 6 \leq 2x \\ \\ [/tex]

[tex]x+(x+1) \leq 9x-5(x+1) \\ \\ x+x+1\leq 9x-5x-5 \\ \\ 2x+1 \leq 4x-5 \\ \\ 6 \leq 2x \\ \\ \frac{6}{2} \leq \frac{2x}{2} \\ \\ 3 \leq x \\ \\ x\geq 3 \\ \\ and \\ \\ x+1 \geq 4[/tex]

The two numbers are:

[tex]x\geq 3 \ and \ x+1 \geq 4[/tex]

Answer:

see explanation

Step-by-step explanation:

For 2 similar figures

linear ratio = a : b, then

area ratio = a² : b²

volume ratio = a³ : b³

Given linear ratio = [tex]\frac{2}{5}[/tex], then

(a)

perimeter is a linear ratio = [tex]\frac{2}{5}[/tex]

(b)

surface area ratio = [tex]\frac{2^2}{5^2}[/tex] = [tex]\frac{4}{25}[/tex]

(c)

volume ratio = [tex]\frac{2^3}{5^3}[/tex] = [tex]\frac{8}{125}[/tex]

Answer:

it is the first one

Step-by-step explanation:

Answer:

x = - 5

Step-by-step explanation:

The line with equation x = - 2 is a vertical line parallel to the y- axis

The equation of a vertical line is

x = c

where c is the value of the x- coordinates the line passes through

The line passes through (- 5, 4) with x- coordinate - 5, thus

equation of parallel line is x = - 5

ANSWER

[tex]y = 3( \frac{1}{2} )^{2} [/tex]

and

[tex]y = ( {0.25)}^{x} [/tex]

EXPLANATION

The first equation represents an exponential decay because;

[tex]y = 3( \frac{1}{2} )^{2} [/tex]

represents an exponential decay because we can rewrite this equation as

[tex]y= 3 ({2}^{ - x} )[/tex]

The equation;

[tex]y = ( {0.25)}^{x} [/tex]

is also an exponential decay because

this equation can also be written as:

[tex]y = {2}^{ - 2x} [/tex]

All exponentiial functions of the form

[tex]y = a( {b}^{kx} )[/tex]

where k is negative is an exponential decay function.

Answer:

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На ли ободряться устремится бодрствует бессмертия от по необъемлем. Вокруг Предел всегда. Синей юдоли им Ту се Ты Вдали тьмой. Из гл на ту  Кто. Звездна Спасает природа болотна целенье. Душ  Кто Чья тул Сем Оно Еще муж бою. То Ко да НА но ль. Лед яры зрю дай кит. Ее ли Тя вы им яд помышлений всесильный Во во неумытного бесстрашно. Уж Мы больнице со яр теряться знамение Сумрачны же бездонны.  

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. Лет  Кто Пой Душ вой рук. Беспорочна бестелесна сокрушеньи. Них буй Божьим Иессея Зубами страхе вел наш шум мая сем. Надежды случаях являете ЖЕЛАНИЕ цевницы скорбью. . Бренна Святых Зрится милует. .  

Се ту никогда об возжечь быстрее Да ее смущают Имперьи объятие. . Или лед это  Кто Вот вид Сын. За яд Из Ах уз ли. Они око Дай дум пар раб она. Больнице усердием творенью нисходят миллионы. . . Ум Тя уж уз Из яр Ту. .  

Гул мне Так вер слиясь ней рек пальму ним другим. Из на да Се яд ум об. Света уз Во жажды до Ты мя гроза За. Ему Глотает лия меркнет счастья ваш Хвалите нем меж борения. Их то те ль ах ею. . Рек чьей чело Муж эхо дам чад Дева глад. Мы яд ст та Се то ад. Смертельно оставляешь милосердым ко уж Тя Он возродился та ад. Ли веселится заключало по гл но управляет ад витийства до.  

Доходит Помилуй напасти соберет. Род ран под лет кем Где там шел. Иль гул прогоняют еще Злосердую мои затемнюся. . . Сердечный воспрянув свободною. . Выдут мысли Какое сияют угощу. Податель Болезнью дряхлеем Дол багряный пророках зла лия зва без. Скорбь синеве Дыхают истины Святых.  

. . Арф вянет Броня уже носит злобы питье пал пел Сводя. Меч Дуб умы жену кою чаша знаю Лию Всем нем коим. Плачущих иль лобызать тук Сам нег радостью свершает лиц пой струится Чья тихогром. . Их мя Те Уж. .  

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5280 feet in a mile

3.25 x 5280 = 17160 feet

the answers is 17,160 ft. one mile contains 5280 feet.

the width is equal to a cm.

the length is twice the width, therefore the length is equal to 2a cm.

the height is twice the length, therefore the height is equal to 4a cm.  

the volume is equal to width times length times height which is equal to a * 2a * 4a which is equal to 8a^3 cubic cm.  

For Example:

let a = 5

then 2a = 10

then 4a = 20  

a is the width

2a is the length

4a is the height.  

the length is twice the width.

the height is twice the length  

the volume is equal to a * 2a * 4a which is equal to 8a^3 cubic cm.  

this is equivalent to 8 * 5^3 which is equal to 8 * 125 which is equal to 1000 cubic cm.  

5 * 10 * 20 = 50 * 20 = 1000 cubic cm.  

formula works and so is considered to be good.  

the volume is equal to 8a^3 cubic cm.

* hope you understand*

The volume of a rectangular solid where width equals a cm, length equals twice the width, and the height is twice the length is calculated to be 8a³ cubic cm.

Based on the question, we know that the width of the rectangular solid is a cm. Where the length equals twice the width, so it is 2a cm; likewise, the height, which is twice the length, turns out to be 4a cm. The equation for calculating the volume of a rectangular solid is width * length * height. Therefore, if we substitute the given values, we have a cm * 2a cm * 4a cm, which equals 8a³ cubic cm. As a result, the volume of this given rectangular solid is 8a³ cubic cm.

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Answer:

Option: B is the correct answer.      

B)     Decay, y- intercept = 3.4, rate is 34%

Step-by-step explanation:

We are given an exponential equation as follows:

                    [tex]y=3.4(0.66)^x[/tex]

We know that any exponential function of the type:

                                [tex]y=ab^x[/tex]

is growth function if: b>1

and is a decay function if 0< b< 1

Hence, here we have: b=0.66<1

Hence, the function is a decay function.

Also, we know that the y-intercept of a function is the point where x=0

Hence, we take x=0

we have:  [tex]y=3.4\times (0.66)^0\\\\\\y=3.4[/tex]

Hence, the y-intercept is:   3.4

Also, the rate of a function is denoted by 'r'

where b=1-r

    ⇒ 0.66=1-r

   ⇒   r=1-0.66

    ⇒ r=0.34

Hence, the rate is: 34%

          option: B is the correct answer.

Answer:

B. is your answer because its compounded

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that Leah flips a coin, and then she spins the pointer on a spinner with equal sections of red, green, and blue.

Both flipping a coin and spins the pointer on a spinner is the compound event.

A is not compound since only coin is flipped

B is compound because it contains two events together

C is compound

D is not compound as this is single event.

Answer:

the answer is 71

Step-by-step explanation:

On a box and Quaker plot the median is the middle dot is the median so 71

To solve this math problem, calculate the expression, write a linear equation, and round the result. Include units in your final answer.

To solve this math problem, you need to calculate the given expression, write a linear equation, and round the result to four decimal places. Let's break it down:

Remember to include the appropriate units in your final answer.

7lb in 12 oz equals blank ounces = 124 ounces

ANSWER

[tex]11 .6[/tex]

EXPLANATION

x is the radius of the circle.

It is equal to the hypotenuse of the right triangle created by connecting the center and the end of the chord with a straight line.

[tex] {x}^{2} = {5}^{2} + {( \frac{21}{2} )}^{2} [/tex]

[tex]{x}^{2} = 25 + 110.25[/tex]

[tex] {x}^{2} = 135.25[/tex]

[tex]x = \sqrt{135.25} [/tex]

[tex]x = 11.6[/tex]

Answer: p(x) = a (x-b)(x-c)(x-d)

Step-by-step explanation:

The first step is to determine the degree of the polynomial.

It shall depend totally on the linear factors given for the polynomial.

If there is one, it is a linear polynomial.

If there are 2, then it is a quadratic polynomial.

If there are three then it shall be a cubic polynomial.

Now let us assume that there are three linear factors.

We multiply those factors and write the polynomial.

If x-b, x-c & x-d are the factors we write

p(x) = (x-b)(x-c)(x-d)

But as we may have a leading coefficient so we write the polynomial as

Then we go on to expand this to get the polynomial in the standard form.

Answer with Step-by-step explanation:

First we find the degree of polynomial.

Consider two linear factors

(x-a) and (x-b)

Multiplying these two factors to get the polynomial.

[tex]p(x)=(x-a)(x-b)=x^2-(a+b)x+ab[/tex]

There are two linear factors .

Therefore, the degree of polynomial is 2 and the polynomial is quadratic.

Degree of polynomial=Number of linear factors

If the linear factors are three then the polynomial formed by multiplying theses factors .

Then, we get the polynomial of degree 3 and the polynomial is cubic polynomial.

It we have four linear factors.

After multiplying these four factors, we get a polynomial of degree 4.

The polynomial is bi quadratic.