Find the arc length and sector area for the following:

(Use \large \pi=3.14...do not use the \large \pi button on your calculator!)



arc length =

sector area =

The equation of a hyperbola with a=7 and c=9 is (x-0)²/a²-(y-0)²/b²=1, x²/49-y²/32=1.

A hyperbola is a kind of smooth curve that appears to lie in a plane. It is made up of two connected components or branches that are mirror reflections of one another and look like two infinite bows. A hyperbola is a collection of points whose difference in distance between two foci is a fixed amount. This discrepancy is calculated by subtracting the distance from the farther focus from the distance from the closest focus.

As we know the standard equation of the hyperbola with a horizontal transverse axis is:

(x-h)²/a²-(y-k)²/b²

Now, put the given values a=7 and c=9 in the Pythagorean theorem to get the value of b.

c²=a²+b²

(9)²=(7)²+b²

81=49+b²

81-49=b²

32=b²

Now square root both sides:√

32=√b²

√32=b

Assuming that the center of a hyperbola is (0,0):

(x-0)²/a²-(y-0)²/b²=1

x²/a²-y²/b²=1

x²/(7)²-y²/(√32)²=1

x²/49-y²/32 = 1

Therefore, the equation of a hyperbola with a=7 and c=9 (x-0)²/a²-(y-0)²/b²=1, x²/49-y²/32=1.

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The net pay of Billy after 8% taxes and 10% retirement policy is $1600.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, From Billy's salary of $2000 8% of his paycheck goes to income taxes, and 10% automatically goes into retirement.

So, To obtain a net salary of Billy we'll subtract the percentage amount of 8% and 10% from the base of $2000.

Therefore, Net pay of Billy is {2000 - (8/100)×2000 - (10/100)×2000}.

= {2000 - 160 - 200}.

= (2000 - 360).

= $1640

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Answer:

8

Step-by-step explanation:

For each different outcome of the spinner, there are 2 different outcomes of the coin flip.

4 × 2 = 8

Answer: 8

The number of cannonballs in illustration is 506.

Math Illustrations enables you to produce more useful geometry figures for your students in less time by fusing the constraint-based design of Geometry Expressions with simple-to-use sketching and graphing features.

The number of cannonballs in the first layer = 1² = 1

Number of cannonballs in the second layer = 2² = 4

Number of cannonballs in the third layer = 3² = 9

So, the generalized formula to count the balls is given as

= n(n + 1) (2n + 1)/ 6

Here, n= the total number of layers

Put n =11

11(11 + 1)(2(11) + 1) / 6

= 11(12)(23)/6

= 3036/6
= 506

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Answer:

Slope is -1

Step-by-step explanation:

-5/5= -1

I am not sure if you want an explanation or just the answer, but I am willing to explain it if needed.

Answer:

[tex]4(x^4+7)[/tex]

Step-by-step explanation:

Taking out the greatest common factor,[tex]16x^4+28=4(x^4+7)[/tex].

Answer:

p=106

Step-by-step explanation:

p and 106 are corresponding so they are =

Then translons the resulting image  units to the right is   y=0 5  units.

What is  line?

A line segment in geometry is a section of a straight line that is enclosed by two clearly defined end points and contains all of the points on the line that are inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.

Reflect [tex]$\triangle P Q R$[/tex] across the line [tex]$y=0$[/tex]. we can get [tex]$\Delta P^{\prime} Q^{\prime} R^{\prime}$[/tex]. then translate [tex]$\Delta P^{\prime} Q^{\prime} R^{\prime}$[/tex] 5 units to the right. we can get s STU. So the answer is A. y=0 5  units.

A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.

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324309

doctors were registered that year.

Explanation:

The questions says, "18.1% of all registered doctors are females"

(Consider, total number of registered doctors as

x

)

that's,

18.1

%

of

x

are female.

and

18.1

%

of

x

is

58

,

700

.

Mathematically,

18.1

100

⋅

x

=

58700

x

=

58700

⋅

100

18.1

x

=

324309

doctors were registered that year.

Answer:

Welcome to Brainly! I saw that this was your very first question. I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

We must create equations from the provided data and relationships in order to determine the length of the rectangular flower garden. The area and the relationship between the width and length are the measurements that are provided. We create the necessary equations from these. What we do is:

Area = Length x Width

where length = x ft

width = x - 3 ft

area = [tex]54 ft^2[/tex]

[tex]54 ft^2 = x ft (x -3) ft\\\54 ft^2 = x^2 - 3x ft^2[/tex]

When we solve for x, we will get two answers, one of which is x = -6 ft (NOTE: This number cannot be the solution because the length cannot have a negative value).

Which means the correct answer is:

length(x)=9ft

(Hope this helped you

Answer:

Isabella spent $1302.52 and Jesus spent $1740.99.

Step-by-step explanation:

In order to figure out how much each individual person spent, we need to write a mathematical equation to express this situation. An equation in math is a statement that relates two expressions that are equal in value, and can be used to solve for variables. A linear equation with one variable is often presented in is standard form, [tex]ax+b=0[/tex].

In this case, we can represent the amount that Isabella spent with the variable x. Since Jesus spent $438.47 more than Isabella, this amount can be represented with x + 438.47. We can set up our equation as follows:

[tex]x+(438.47+x)=3043.51[/tex]

*Note that the use of parentheses is not necessary but may be useful in making your work clearer!

To solve for x, we should combine like terms and then move the variables to one side and constants to the other. The variable can be isolated by subtracting 438.47 from 3043.51:

Now that we have the variable by itself, we can divide by 2 on both sides to solve for x.

As we defined, x equals the amount of money that Isabella spent, which is $1302.52. We can plug that number into x + 438.47 to get the amount that Jesus spent, which we calculate to be $1740.99.

Thus, Isabella spent $1302.52 and Jesus spent $1740.99.

To check our work, we can simply add up the two amounts to see if it totals to $3043.51:

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Answer:

Reflection over the line y=x

Answer:

A)  Increasing:  (-0.5, ∞)

     Decreasing:  (-∞, -2) ∪ (-2, -0.5)

B)   x = -¹/₂

C)  Concave up:  (-∞, -2) ∪ (-1, ∞)

     Concave down:  (-2, -1)

     Points of inflection:  (-2, 0) and (-1, -1)

D)  See attachments.

Step-by-step explanation:

Given function and derivatives:

[tex]f(x) = x(x+2)^3[/tex]

[tex]f'(x) = (4x+2)(x+2)^2[/tex]

[tex]f''(x) = 12(x+1)(x+2)[/tex]

[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}}\implies f'(x) > 0[/tex]

[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies f'(x) < 0[/tex]

Increasing function

[tex]\begin{aligned}f'(x) & > 0\\(4x+2)(x+2)^2 & > 0\\2(2x+1)(x+2)^2 & > 0\\(2x+1)(x+2)^2 & > 0\end{aligned}[/tex]

Therefore, the function is increasing on the Interval:

[tex]\left(-\dfrac{1}{2}, \infty \right)[/tex]

Decreasing function

[tex]\begin{aligned}f'(x) & < 0\\(4x+2)(x+2)^2 & < 0\\2(2x+1)(x+2)^2 & < 0\\(2x+1)(x+2)^2 & < 0\end{aligned}[/tex]

Therefore, the function is decreasing on the Interval:

[tex](- \infty, -2) \cup \left(-2,-\dfrac{1}{2} \right)[/tex]

Local minimum/maximum points occur when f'(x) = 0.

[tex]\begin{aligned}f'(x) &= 0\\(4x+2)(x+2)^2 & = 0\\2(2x+1)(x+2)^2 & = 0\\(2x+1)(x+2)^2 &= 0\\\\2x+1&=0 \implies x=-\dfrac{1}{2}\\(x+2)^2&=0 \implies x=-2\end{aligned}[/tex]

[tex]f''\left(-\dfrac{1}{2}\right) = 12\left(-\dfrac{1}{2}+1 \right)\left(-\dfrac{1}{2}+2 \right)=9 > 0\implies \textsf{minimum}[/tex]

[tex]f''\left(-2\right) = 12\left(-2+1 \right)\left(-2+2 \right)=0\implies \textsf{point of inflection}[/tex]

Therefore, the value of x where f(x) has a local minimum is x = -¹/₂.

At a point of inflection, f''(x) = 0.

[tex]\begin{aligned}f''(x) &=0\\12(x+1)(x+2)&=0\\(x+1)(x+2)&=0\\\\x+1&=0 \implies x=-1\\x+2&=0 \implies x=-2\end{aligned}[/tex]

Substitute the found values of x into the original function to the find the y-coordinates of the points of inflection:

[tex]\implies f(-1) = -1(-1+2)^3=-1[/tex]

[tex]\implies f(-2) = -2(-2+2)^3=0[/tex]

Therefore, the inflection points are:

A curve y = f(x) is concave up if f''(x) > 0 for all values of x.

A curve y = f(x) is concave down if f''(x) < 0 for all values of x.

Concave up

[tex]\implies f''(x) > 0[/tex]

[tex]\implies 12(x+1)(x+2) > 0[/tex]

[tex]\implies (x+1)(x+2) > 0[/tex]

Therefore, the function is concave up at:

[tex]\left(-\infty,-2\right) \cup \left(-1,\infty \right)[/tex]

Concave down

[tex]\implies f''(x) < 0[/tex]

[tex]\implies 12(x+1)(x+2) < 0[/tex]

[tex]\implies (x+1)(x+2) < 0[/tex]

Therefore, the function is concave down at:

[tex](-2,-1)[/tex]

See attachment 1 for how to sketch the graph using the information from parts A-C.

See attachment 2 for the final sketch of the graph.

Answer: it is a

Step-by-step explanation:

Step-by-step explanation:

It is not possible to determine the congruent angles in the given statement, as it is incomplete and does not provide enough information. In order to determine congruent angles, we need to know the shape and the specific angles being compared. For example, if the statement was "In a triangle ABC, angles A and C are congruent," then we would know that angles A and C are congruent.

A. −5x+3y=−5=a vertical plane

B.  x=3=a =a vertical plane

C. y=−9=a=a vertical plane

D. z=−10=b=a horizontal plane

A plane that crosses a vertical line: a perspective plane that is parallel to both the ground plane and the image and passes through the point of sight.

The body is divided into superior and inferior halves by an anatomical plane called the transverse plane, also referred to as the horizontal plane, axial plane, and transaxial plane. Its angle with the coronal and sagittal planes is perpendicular.

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Answer:

write the given equation in a standard form of y = mx + c

7x + 2y = 0

2y = -7x

y = -7/2x

parallel lines have equal gradient

m = -7/2

y - y1 = m(x - x1)

y - 2 = -7/2(x - (-7) )

y - 2 = -7/2( x + 7 )

y - 2 = -7/2x - 49/2

y = -7/2x - 49/2 + 2

y = -7/2 - 45/2

Answer:

Hope the picture will help you........

The graph equation has been plotted on the graph which crosses the points  (0, 10) and (20, 0) on the y and x axis.

Write the equation in the form y = MX + b to determine the slope m and the y-intercept.

This will allow you to graph the equation using the slope and y-intercept (0, b).

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

So, we have the equation:

8x+16y=160

Where:

x represents the short sleeves.

y represents the long sleeves.

Now, we need to plot the equation as follows:

(Refer to the graph attached below)

So, the equation crosses the points (0, 10) and (20, 0) on the y and x axis.

Therefore, the graph equation has been plotted on the graph which crosses the points  (0, 10) and (20, 0) on the y and x axis.

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After solving the equation for x, the resultant answer is (3, -2).

The definition of an equation in algebra is a mathematical statement that shows the equivalence of two mathematical expressions.

For example, the equation 3x + 5 = 14 comprises the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So, we have the equation:

y = -2x +4

Now, get value of x for y = -2 as follows:

Fill in the equation with the value of y and find x:

-2 = -2x +4 . . . . use -2 for y

-6 = -2x . . . . . . . subtract 4

3 = x . . . . . . . . . .divide by -2

Therefore, after solving the equation for x, the resultant answer is (3, -2).

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Complete question:
y=−2x+4y, equals, minus, 2, x, plus, 4

Complete the missing value in the solution to the equation.

use y = mx + b

this is slope and y intercept

m is slope       b is y intercept

y = 1/4x -2

The ordered pair (1, 12) lies on the graph of the exponential function f(x) = 3(2)2x. which is the correct answer would be option (A).

The graph of an exponential function of the form f(x) = abˣ is a curve that passes through the point (0, a), where a is the initial value of the function.

In the given equation, the initial value is 3, so the graph of f(x) passes through the point (0, 3).

To find other points on the graph of f(x), we can plug different values of x into the equation and solve for the corresponding value of y.

For example, if we plug x = 3 into the equation, we get:

f(3) = 3(2)² × 3

= 3(16)

= 48

Therefore, point (3, 48) does not lie on the graph of f(x).

Similarly, if we plug x = 1 into the equation, we get:

f(1) = 3(2)² × 1

= 3(4)

= 12

Thus, point (1, 12) lies on the graph of f(x).

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Answer:

54% are females

Step-by-step explanation:

In total there would be 225 participants -

104 + 121 = 225

Next, Divide 121 and 225. After, multiply by 100.

225/121(100)=53.78

53.78 rounded to the nearest percent is 54.

I hope this helped your question!

The four tables available in choices, table option D is not a function. This is because there is the same x value, x = 2 i.e : ( 2, 3 ) , ( 2, 5 ) , ( 2, 7 ).

What is Function?

Function is a relation which each member of the domain is mapped onto exactly one member of the codomain.

There are many types of functions in mathematics such as :

Linear Function → f(x) = ax + b

Quadratic Function → f(x) = ax² + bx + c

Trigonometric Function → f(x) = sin x or f(x) = cos x or f(x) = tan x

Logarithmic function → f(x) = ln x

Polynomial function → f(x) = axⁿ + bxⁿ⁻¹ + ...

If function f : x → y , then inverse function f⁻¹ : y → x

Let us now tackle the problem!

According to the definition above, it can be concluded that a function cannot have the same x value.

Of the four tables available in choices, table option D is not a function. This is because there is the same x value, x = 2 i.e :

( 2, 3 ) , ( 2, 5 ) , ( 2, 7 ).

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The composition function for the given situation is (c·r·b)(x) or (r·c·b)(x). Therefore, options B and F are the correct answers.

The given functions are c(x)=2x, b(x)=x+5 and r(x)=0.75x.

When the result of one function is used as the input for another, this is known as a composite function.

The most common kind of critical hit simply deals additional damage, most commonly dealing double the normal damage that would have been dealt, but many other formulas exist as well (such as ignoring defense of the target or always awarding the maximum possible damage).

A critical hit has the base damage x multiplied, next the damage reduction is applied to the critical hit. Bonus damage is not subject to damage reduction or critical hits, so this is applied last.

Here, Critical hit × Bonus × Damage reduction

That is, (c·r·b)(x) or (r·c·b)(x)

The composition function for the given situation is (c·r·b)(x) or (r·c·b)(x). Therefore, options B and F are the correct answers.

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Answer:

11

Step-by-step explanation:

Answer:

Step-by-step explanation: