A circle passes through the points (3, 2) and (7, 2) and has radius 2√2. Find the two possible equations for this circle.
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The current is defined as rate of flow of charge I = dq/dt.

The approximate range of the current is 299.5.

The current is defined as rate of flow of charge I = dq/dt

Let the equation be [tex]$q=\int i d t$[/tex]

Given: I(t) = 10 cos(120πt - 12π) + 5

We will substitute it in the above equation

q = [tex]$$\int[/tex] 10 cos(120πt - 12π) + 5 dt

now here limits of time is from t = 0.1 to t = 60 s

so here it will be given as

[tex]$\int 10 cos(120\pi t - 12\pi ) + 5 dt[/tex]

Rewrite using trig identities

[tex]$=\int_{0.1}^{60} 10 \cos (120 \pi t)+5 d t$$[/tex]

Apply the Sum Rule:

[tex]$\int f(x) \pm g(x) d x=\int f(x) d x \pm \int g(x) d x$[/tex]

substitute the values in the above equation, we get

[tex]$=\int_{0.1}^{60} 10 \cos (120 \pi t) d t+\int_{0.1}^{60} 5 d t$[/tex]

simplifying the equation,

[tex]$\int_{0.1}^{60} 10 \cos (120 \pi t) d t=0[/tex]

[tex]$\int_{0.1}^{60} 5 d t=299.5$[/tex]

= 0 + 299.5

= 299.5

Therefore, the approximate range of the current is 299.5.

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Answer:

5. -2 > x

6. 4 [tex]\leq[/tex] x

7. 0 [tex]\geq[/tex] x

8. -3 < x

Step-by-step explanation:

About 50% of Americans households have a tv except  who live in low-income, single-parent, or disadvantaged homes

Proportion: Proportion is a central principle of architectural theory and an important connection between mathematics and art. It is the visual effect of the relationships of the various objects and spaces that make up a structure to one another and to the whole

Virtually all American households have at least one tv except for adolescents who live in low-income, single-parent, or disadvantaged homes, the majority of American households have at least one tv. More than 50% of American households have at least one tv.

however, about 50% of Americans households have a tv

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Answer:

The number is 40.

Step-by-step explanation:

Step 1: Assume your variables

Consider the 'number' to be [tex]x[/tex].

Step 2: Create an equation(s)

The information in the question states that the difference between [tex]\frac{2}{5}[/tex] of [tex]x[/tex] and [tex]9[/tex], is [tex]7[/tex].

Representing this mathematically gives us:

[tex](\frac{2}{5}\times x) -9=7[/tex]

Step 3: Solve the equation

The equation we have is:

[tex](\frac{2}{5}\times x) -9=7[/tex]

So, let's solve it:

[tex](\frac{2}{5}\times x) -9=7\\\\\text{Add 9 to both sides:}\\(\frac{2}{5}\times x) -9+9=7+9\\\\\text{Simplify:}\\(\frac{2}{5}\times x)=16\\\\\text{Multiply by}~\frac{5}{2}~\text{on both sides:}\\\frac{5}{2}\times\frac{2}{5}\times x=16\times \frac{5}{2}\\\\\text{Simplify:}\\1\times x=\frac{80}{2}\\\\\text{Calculate:}\\x=40[/tex]

Answer:

ASA

Step-by-step explanation:

there are two congruent angles with an included side in between

Answer: Triangle RHS and NKW are congruent through the Congruence Theorem Angle-Side-Angle.

Step-by-step explanation:

The side HS is congruent to the side KW.

The angle H is congruent to angle K.

The angle S is congruent to angle S.

Answer:217.625

Step-by-step explanation:

The given expression is

Factor out the greatest common factor between 15x and 20y.

Then, use the product property to expand the logarithm.

At last, simplify the first logarithm because its base is equal to its argument.

Therefore, the simplest form of the logarithm is

Answer:

1st option

Step-by-step explanation:

Answer:

A=40, formula for area of a rectangle is a=L×W

Step-by-step explanation:

A=L×W = 10×4

It is to be noted that by the proof given below, the attached shape ABCD is a kite.

A kite is a quadrilateral having reflection symmetry across a diagonal in Euclidean geometry. A kite has two equivalent angles and two pairs of adjacent equal-length sides as a result of its symmetry.

The proof is as follows:

AB = AD [Given]

∠ADC = 115°   [Angles on a Straight line]

That is 180 - 65 = 115°

∠BCD = 20°    [Vertical Angles are equal]

∠ABC = (360 - (20+115+110))

= 115°              [Angles in a quadrilateral]

Hence,

ABCD = Kite    [Definition of  a Geometric Kit]

That is

QED

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ANSWER

-4.5

EXPLANATION

We want to find the opposite of the number 4.5

The opposite of a number is the number that is the same distance from 0 on the number line but on the other side.

So, if the number is on the right hand side, its opposite is on the left hand side.

In simpler terms, the opposite of a number is the negative of a number.

So, the opposite of 4.5 is -4.5.

The salesperson needs to make weekly sales of $9,500 to earn the same amount with each option.

The amount he earns by option A can be calculated as follows;

As he works 40 hours per week and the hourly wage is $19; therefore the amount he will earn can be determined by multiplication as follows;

Option A earning: 40 × 19 = $760

Thus, the salesperson earns $760 through option A.

Consider x to be the amount of weekly sales;

As the commission rate is 8% of sales therefore 8% of x should be equal to $760 for the salesman to earn the same amount with both options.

(8/100)x = 760

0.08x = 760

x = 760 / 0.08

x = 9,500

Hence the salesman needs to make weekly sales of $9,500 to earn the same amount with both options.

Although there is a mistake in your question, you might be referring to this question;

A salesperson works 40 hours per week at a job where he has two options for being paid option a is an hourly wage of $19 option B is a commission rate of 8% sales how much does he need to sell in a given week to earn the same amount with each option

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Answer:

y = ( 6 / 5 )x - 5;

Step-by-step explanation:

y = - ( 1 / m )x + c;

Convert dual intercept to standard form.

5x + 6y = 18;

Subtract 5x from both sides.

6y = - 5x + 18;

Divide both sides by 6.

y = ( - 5x + 18 ) / 6;

y = ( - 5x / 6 ) + ( 18 / 6 );

y = ( - 5 / 6 )x  + 3;

Get the perpendicular line.

y = ( 6 / 5 )x + c;

Substitute the point.

7 = ( 6 / 5 )( 10 ) + c;

7 = 12 + c;

Subtract 12 from both sides.

- 5 = c;

c = - 5;

y = ( 6 / 5 )x - 5;

Answer:

9.  [tex]256u^8 v^{16}[/tex]

10.  [tex]-32x^{10} y^{35}[/tex]

11.  [tex]-x^{12}y^{20}[/tex]

12.  1

13.  [tex]\frac{2}{3xy^3}[/tex]

14.  [tex]\frac{h^8}{3j^6k^6}[/tex]

15.  [tex]\frac{1}{4z}[/tex]

Answer:

9.  256u^8 v^16

10.  -32x^10 y^35

11.  x^12 y^21

12.  1

Step-by-step explanation:

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Answer:

                         8

3x² + 2x - 2 - ----------

                      3x + 8

Step-by-step explanation:

                 3x² + 2x - 2

               --------------------------------

3x + 8     |  9x³ + 30x² + 10x - 24

                 -9x³ - 24x²     ↓

                --------------------------------

                             6x² + 10x

                             -6x² - 16x    ↓

                        -------------------------

                                       -6x - 24

                                       +6x + 16

                                  ----------------

                                               -8

I hope this helps!

SOLUTION

The equation of the parabola is defined using

Since the vertex is at the origin the equation becomes

Since the directrix is y=5

The distance from the focus to the vertex is equal to the distance from the vertex to the directrix

It follows

Thus the equation becomes

Therefore the equation of the required parabola is

Answer: Y=-1/20x^2

Step-by-step explanation:

Answer:

Explanation:

The angular coefficient is also referred to as the slope of the line.

Given that the slope of the lining joining these pair of points are the same:

• (-2, 1) and (1, 4)

• (1, -2) and (3, p)

Then:

We solve the equation for p:

Answer:
1. Hyperbole

2. Center: (0,0)

3. Vertices: (-3, 0), (3, 0)

4. Foci: (-6, 0), (6, 0)

5. Asymptotes: y =  [tex]\frac{\sqrt{18}}{3} }[/tex]x and y = [tex]-\frac{\sqrt{18}}{3} }[/tex]x

Step-by-step explanation:

We can describe 15x-10 as an expression.

We would describe 6x-2<35 as an inequality.

In mathematics, inequalities characterize the connection between two non-equal numbers. Inequality means being unequal. If two values are not equal, we use the "not equal symbol". However, various inequalities are employed to compare the numbers, whether they are less than or higher than.

An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare two numbers on the number line based on their size. In the illustration above, there's a less than sign. This means that it's an inequality.

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The predicted distance of the ball would be 27.1.93 yards when the ball travels for a duration of 5 seconds.

Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.

The distance, y, is measured in yards and the speed, s, is measured in miles per hour.

The regression line is defined as ŷ = 3.98 + 53.59s  ... (i)

The slope and y-intercept of the regression line must be determined.

The general equation for a linear regression line is y = a + bx...(ii), where x is a variable. The variable is indicated by s in the above equation.

When I and (ii) are compared, we obtain a = 3.98 and b = 53.59.

It indicates that the slope is 53.59 and the y-intercept is 3.98.

The slope, b = 53.59, implies that for every mile per hour of speed, the distance rises by 53.59 yards.

The ball travels for a duration of 5 seconds

Substitute the value of s = 5 in equation (i) to get

ŷ = 3.98 + 53.59(5)

ŷ = 271.93

Thus, the predicted distance of the ball would be 27.1.93 yards.

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Answer:

271.93

Step-by-step explanation:

With the width and length being held constant, the height of the box decreases at rate  5 cm/s

Let:

l = length

w = wide

h = height

Then, the volume of the box is given by:

V = l . w. h

The length and the width are assumed to be constant. Hence, the derivative with respect to time is:

dV/dt = l . w dh/dt

Parameters given:

dV/dt = - 541 cm³/dt

l = 9 cm

w = 12 cm

Plug these parameters into the formula:

-541 = 12 . 9 . dh/dt

dh/dt = 5 cm/s

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Answer:

1. 1600

2. 3,000

3. 6,000

4. 7,000

5. 10,000

6. 9,000

Step-by-step explanation:

A) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.

B) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.

C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.

In this case, Rule A applies and 1565 rounded to the nearest hundred is:

1600

Answer: [tex]x=5\sqrt{3}, y=15[/tex]

Step-by-step explanation:

[tex]\sin 60^{\circ}=\frac{x}{10}\\\\x=10 \sin 60^{\circ}\\\\x=5\sqrt{3}\\\\\\\tan 30^{\circ}=\frac{5\sqrt{3}}{y}\\\\\sqrt{3}=\frac{y}{5\sqrt{3}}\\\\y=15[/tex]

In the sample space, the annotation for the event where both E and G but not F occurs is given as:( E ∩ G ) ∩ Fc (Option B).

An event is a specified set of results of a random experiment in probability theory. Because the sample space is the collection of all potential outcomes of a random experiment, another definition of an event is any subset of a sample space.

Colloquially, the sample space for a given set of events is the collection of all potential values for the events. Technically, a sigma-algebra is formed by the set of probable occurrences for a given random variate, and sample space is defined as the biggest set in the sigma algebra.

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Full Question:

Let S be any sample space, and E, F, and G be any three events. Describe the event that E and G occur, but not event F.

a) ( Ec ∪ G ) ∩ Fc

b) ( E ∩ G ) ∩ Fc

c) ( E ∪ G ) ∪ Fc

d) ( Ec ∪ Gc ) ∩ F

e) ( E ∩ G ) ∩ F

f) None of the above.

The annotation for the event in the sample space when E and G both occur but F does not is given as:( E ∩ G ) ∩ Fc which is the correct answer would be an option (B).

In probability theory, an event is a predetermined group of outcomes from a random experiment. Another definition of an event is any subset of a sample space, which is the collection of all possible results of a random experiment.

We are allowed to use here for the necessary notation, though one way to indicate this is the complement of E U F U G. This would be the area in the sample space S that lies outside E, F, and G in a Venn diagram.

Thus, the annotation for the event in the sample space when E and G both occur but F does not is given as:( E ∩ G ) ∩ Fc

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The question seems to be incomplete the correct question would be

Let S be any sample space, and E, F, and G be any three events. Describe the event that E and G occur, but not event F.

a) ( Ec ∪ G ) ∩ Fc

b) ( E ∩ G ) ∩ Fc

c) ( E ∪ G ) ∪ Fc

d) ( Ec ∪ Gc ) ∩ F

e) ( E ∩ G ) ∩ F

f) None of the above.

First, let's calculate the total amount of balls:

Since there are 2 white balls and 2 red balls, the number of white or red balls is 4.

So the probability is:

Correct option: A

If the tank contains 12 gallons and then the car consumes 10, we can know how much gasoline is left by substracting 12 with 10:

12 - 10 = 2

Then, 2 gallons of gasoline is left in the tank

Since there is still gasoline because 12 is higher than 10, then we represent this amount with a positive value.

Answer:

a: 120 = 2x + 40

80 = 2x

x = 40

b: (3x + 10) + (x-30) = 180

4x - 20 = 180

4x = 200

x = 50

c: 105 = 2x - 11

116 = 2x

58 = x

d: 8y + 36 = 14y - 24

-6y = -60

y = 10

64 = 48 + x

16 = x

y = 10, x = 16

e: 75 + (2x - 5) = 180

70 + 2x = 180

2x = 110

x = 55

2(55) - 5 =y

y = 105

f: (2x + 8) + (3x + 17) = 180

5x + 25 = 180

x = 31

3(31) + 17 = 5y + 15

110 = 5y + 15

95 = 5y

y = 19, x = 31

The expression is equal to 0.00333333333.

A = 0.00333333333

B = 0.00426666666

C = 0.03125

D = 33.3333333333

Therefore, the answer is A. Hope this helps! :)