​

f(1)=0
f(n)=f(n−1)+2
​

Answer:

[tex](x-6)^2+(y+7)^2=4[/tex]

Step-by-step explanation:

The formula for the equation of a circle is:

[tex]\boxed{(x-h)^2+(y-k)^2=r^2}[/tex]

where:

From inspection of the given graphed circle, we can see that the coordinates of its center are (6, -7), and its radius is 2 units. Therefore:

To determine the equation of the graphed circle, substitute these values into the equation of a circle formula:

[tex]\implies (x-6)^2+(y-(-7))^2=2^2[/tex]

[tex]\implies (x-6)^2+(y+7)^2=4[/tex]

Therefore, the equation of the graphed circle is:

[tex]\boxed{(x-6)^2+(y+7)^2=4}[/tex]

The value of the missing lengths are;

a. b =  17. 32, c = 20

b. x = 8. 49, y = 8.49

Note that the different trigonometric identities are;

These identities have their ratios written as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the diagram shown, we have;

tan 30 = 10/b

cross multiply the values

b = 17. 32

Also, we have;

sin 30 = 10/c

cross multiply the values

c = 20

b. Using the sine identity

sin 45 = x/12

cross multiply the values

x = 8. 49

Also,

cos 45 = y/12

cross multiply

y = 8. 49

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Answer:

The 80.6 square foot roll is less expensive per square foot since it costs $0.03/square foot compared to the other which costs $0.02/square foot

Step-by-step explanation:

Because the question asks which of the two paper towel rolls is less expensive per square foot, we must find the unit rate of both rolls (specifically, cost per 1 square foot)

We can find the unit rate using a proportion:

53.7 square foot roll

[tex]\frac{1.49}{53.7}=\frac{x}{1} \\1.49=53.7x\\0.0277=x\\0.03=x[/tex]

80.6 square foot roll

[tex]\frac{1.89}{80.6}=\frac{x}{1} \\1.89=80.6x\\0.0234=x\\0.02=x[/tex]

Thus, per square foot, the 80.6 square foot roll is less expensive than the 53.7 square foot roll

Answer:

James Abbott McNeill Whistler's Nocturne in Black and Gold: The Falling Rocket (c. 1875) is an example of "art-for-art's sake" of the Aestheticism movement.

The function is invertible and the inverse of the function is y = -3 + √[ (x + 4)/-2]

From the question, we have the following function that can be used in our computation:

y=-2(x+3)^2-4

Swap the variables x and y

So, we have

x = -2(y + 3)^2 - 4

Add 4 to both sides

-2(y + 3)^2 = x + 4

Divide both sides by -2

(y + 3)^2 = (x + 4)/-2

Take the square root and subtract 3 from both sides

y = -3 + √[ (x + 4)/-2]

This represents the inverse of the function

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The numeric value of f(x) at x = π/5 is given as follows:

f(π/5) = - 2π/5 - 2

We are given the second derivative of the function, as follows:

f''(x) = -25sin(5x).

As we have the second derivative of the function, the function itself is obtaining integrating the second derivative twice.

Using integral by substitution, the first derivative is given as follows:

f'(x) = 5cos(5x) + K1

In which K1 is the constant.

When x = 0, f'(0) = 3, hence the value of K1 is obtained as follows:

3 = 5 + K1

K1 = -2.

Hence:

f'(x) = 5cos(5x) - 2.

Integrating again, the function is given as follows:

f(x) = 5sin(5x) - 2x + K2.

When x = 0, y = -2, hence the constant K2 is obtained as follows:

K2 = -2.

Thus the function is:

f(x) = 5sin(5x) - 2x - 2.

The numeric value of the function at x = π/5 is obtained as follows:

f(π/5) = 5sin(5(π/5)) - 2(π/5) - 2.

f(π/5) = 5sin(π) - 2π/5 - 2

f(π/5) = - 2π/5 - 2 -> as sin(π) = 0.

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The measure of v is 61 degree.

We have,

Interior angle = (v - 19) or v

Exterior angle = v + 42

Using exterior Angle Property

Exterior angle= Sum of opposite interior angle

v + 42 = v - 19 + v

v + 42 = 2v - 19

v - 2v = -19 - 42

-v = -61

v= 61

Thus, the value of v is 61.

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The bearing of the airport from the plane is 245°

The bearing of a point from a location is given by the angle in degrees of rotation from the Northern direction of the location to the direction of the location of the point

The given bearing of the plane from the airport = 65°

Therefore, the direction of the plane from the Northern direction of the airport = 65°

From the Northern direction of the plane, the bearing of the airport = 245°

Hence, the bearing of the airport from the plane is 245°

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The values of x, y and z in the given simultaneous equation is:

x = 4

y = 6

z = -3

The 3 simultaneous equations are given as:

x + 7y - z = 49

2x - 5y + 2z = -28

x - 6y=-32

Rearranging the first equation  gives:

x = 49 - 7y + z

2x - 5y + 2z = -28

x - 6y = -32

Substitute 49 - 7y + z into equations 2 and 3 to get:

2(49 - 7y + z) - 5y + 2z = -28

49 - 7y + z - 6y = -32

Convert the equation in terms of u and solving simultaneously gives:

y = 6 and z = -3

Thus:

x = 49 - 7(6) + (-3)

x = 4

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B) gas mileage decreases with increase of car weight.

The circle with a chord are those that have a line joining two points on the circumferences

Recall that a chord a chord of a circle is a line segment that joins any two points on the circumference of the circle

From question number 1,  the chords are circles 1, 2 and 5.  This is because each of the circles has a line joining two points

2)  From question 2 all the chords intercepted each other.  This is because an intercept is a point where two straight lines meet. or you can say that An intercept in mathematics is a point on the y-axis through which the slope of a line passes

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The steps to graph the absolute value functions are given below.

We have,

Absolute value functions of form f(x) = |ax + b| have a characteristic shape, which depends on the values of a and b.

Here are some general guidelines for graphing these functions:

Find the y-intercept:

To find the y-intercept of the graph, set x=0 and solve for y.

This gives f(0) = |b|, so the y-intercept is at the point (0,|b|).

Find the x-intercept(s):

To find the x-intercepts of the graph, set y = 0 and solve for x.

If b > 0, there are two x-intercepts: x = -b/a and x = b/a.

If b = 0, there is one x-intercept at x=0.

If b < 0, there are no x-intercepts.

Determine the direction of the graph:

If a > 0, the graph opens upwards, like a "V".

If a < 0, the graph opens downwards, like an upside-down "V".

Determine the vertex:

The vertex is the point where the graph changes direction.

If a > 0, the vertex is at (-b/a, 0).

If a < 0, the vertex is at (b/a, 0).

Sketch the graph:

Use the information above to sketch the graph of the absolute value function.

Plot the y-intercept, the x-intercept(s), and the vertex, and then draw a smooth curve connecting these points.

Thus,

The graph of the absolute value functions is given above.

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Answer:5.6

Step-by-step explanation:

28 divided by 5 is 5.6

Answer: $33.6

Step-by-step explanation: 28(.20) will give us our $5.6 discount. now add that on top of 28.

Answer:

  132175.2 cm³

Step-by-step explanation:

You want the volume of a sphere with radius 31.6 cm.

The volume of a sphere is given by the formula ...

  V = 4/3πr³

For a radius of 31.6 cm, we find the volume to be ...

  V = 4/3π(31.6 cm)³ ≈ 132,175.2 cm³

The volume of the sphere is about 132,175.2 cm³.

Answer:

rectangular pyramid has 8 edges

The corresponding height of similar rectangular prism m is 9 centimeter.

Given that, the volume of rectangular prism m is 17 cm³ and the volume of rectangular prism n is 136 cm³.

If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.

The height of n is 18 cm.

Here, m³/n³ = 17/136

m³/18³ = 17/136

m³/18³ = 17/136

(m/18)³ = 1/8

(m/18)³ = (1/2)³

m/18 = 1/2

m=9 cm

Therefore, the corresponding height of similar rectangular prism m is 9 centimeter.

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Answer:

Step-by-step explanation:

You want to know the number of hours Liz worked at each job, when the total pay for a total of 28 hours work was $175.80. Job A paid $6 per hour, and job B paid $6.60 per hour.

We can let 'b' represent the number of hours worked at job B. Then (28-b) is the number of hours worked at job A. Liz's total pay was ...

  6(28 -b) +6.60(b) = 175.80

Simplifying the equation gives ...

  0.60b +168.00 = 175.80

  0.60b = 7.80 . . . . . . . . . . . subtract 168

  b = 13 . . . . . . . . . . . . . . divide by 0.6

  28-b = 28-13 = 15 . . . hours at Job A

Liz worked 15 hours at Job A, and 13 hours at Job B.

__

Additional comment

Here, we used one equation. If you use two equations, you can get this same equation by substituting for the variable representing hours at Job A. Letting the variable represent hours at the higher-paying job generally results in arithmetic using positive numbers. If you write the equation for the hours at Job A, negative numbers will usually be involved. Though it shouldn't, sometimes that causes confusion.

A graphing calculator may offer two or three ways (or more) you use to can solve the equations. One of them is illustrated in the attachment. It solves the equations ...

The expression for h(x) is,

⇒  h (x) = √(x - 2) + 4

Now, Given that;

Initially the graph f (x) is shifted horizontally to the right.

When the graph shifts to right the function then becomes

f (x) → f (x-b)

Where b is the units by which it is shifted towards right .

So, in the figure we can see that it is shifted 2 units to the right .

So, f(x) → f(x-2)

Since f(x) is,

⇒ f (x) = √x

So, f (x-2) = √x - 2

Now, the new obtained graph is again shifted vertically upward

When the graphs shifts upward;

⇒ f(x) → f(x) + b

where b is the units by which it is shifted upward

So, our obtained f(x-2) when shifted upward by 4 units so using the above given transformation of upward shift

i.e. f(x) → f(x) + b

So, Our new graph h(x) = f(x-2) + 4

⇒  h (x) = √(x - 2) + 4

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The measure of the arc length AB is [tex]\frac{16\pi }{15}[/tex] centimeters.

An arc length is simply the distance between two points along a section of a curve.

The arc length is expressed as:

s = 2πr × (θ/360°)

Where s is the arc length, r is the radius, θ is the angle and π is constant pi.

Given that:

Plug the values into the above formula

s = 2πr × (θ/360°)

s = 2 × π × 3cm × ( 64°/360°)

[tex]s = \frac{16\pi }{15} cm[/tex]

Therefore, the arc length is [tex]\frac{16\pi }{15}[/tex] cm.

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The fraction of the cookies that are peanut butter cookies is 1/5

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

Total = 10

Peanut butter = 2

using the above as a guide, we have the following:

Fraction = Peanut butter /Total

So, we have

Fraction = 2/10

Evaluate

Fraction = 1/5

Hence, the fraction is 1/5

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Edouard Manet's Luncheon on the Grass was shown in the Salon des Refuses after it was rejected for the annual salon.

Option D is the correct answer.

We have,

Edouard Manet's painting "Luncheon on the Grass" was first rejected by the Paris Salon in 1863, as it was considered scandalous due to the nudity of the female figure in the painting.

In response to this rejection,

Emperor Napoleon III ordered an exhibition to be held for all the rejected paintings, which was known as the Salon des Refusés (Salon of the Refused).

Thus,

Edouard Manet's Luncheon on the Grass was shown in the Salon des Refuses after it was rejected for the annual salon.

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Answer:

Kenneth's average stacking time is less than 8.2 seconds.

Brainly wouldn't allow me to give an explanation because apparently, it contains inappropriate words..? How odd.

Answer:

The data does not provide sufficient evidence to conclude that Kenneth's mean stacking time is is less than 8.2 seconds

Do not reject the null hypothesis because the p-value 0.0401 is greater than the significance level.

Step-by-step explanation:

Null hypothesis (H0): mu = 8.2 seconds

Alternate hypothesis (Ha): mu < 8.2 seconds

Significance level = 0.04

p-value = 0.0401

Using the p-value approach for testing hypothesis, do not reject H0 because the p-value 0.0401 is greater than the significance level 0.04.

There is not sufficient evidence to conclude that Kenneth's mean stacking time is less than 8.2 seconds.

The equivalent area of the parallelogram is 44.4m^2

The formula for finding the area of a parallelogram is expressed as:

Area = base * height

Given the following parameters

Base = 12m

Height = 3.7m

Substitute the given parameters into the formula to have:

Area = 12m * 3.7m

Area of the parallelogram = 44.4m^2

Hence the area of the parallelogram given is 44.4m^2

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Answer:non linear

Step-by-step explanation: since the exponent is greater than 1

9 divided by 11.91 rounded to the nearest hundredth is: 0.76

To show that two numbers are divided, we can add a division sign '÷' between them. So, for example, if we have to show 36 divided by 6, we can write it as 36 ÷ 6. We can also show it in a fraction form as 36/6.

We want to find 9 divided by 11.91 . Thus, this can be expressed as:

9/11.91

where:

9 is the dividend

11.91 is the divisor

Using calculator, we have:

9/11.91 = 0.76

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1. The Height of the stone after 5s is 490feet

2. The time it will reach the ground 8.98s

3. The velocity of the stone when it hits the ground is 287.33 feet/s

Motion under gravity refers to the movement of an object whose vertical motion is affected by the presence of gravity.

The equation of motion under gravity is given as;

H = ut ± 1/2gt²

v² = u²±2gh

v = u ± gt

1. The height = 18 × 5 -1/2 ( -32) 5²

h = 90+ 400

h = 490 feet

2. The time to reach the ground is calculated as;

h = ut + 1/2gt²

at max height u = 0

total height = 490+800

= 1290m

1290 = 1/2 × 32t²

2580 = 32t²

t² = 80.6

t = √80.6

t = 8.98s

3. The velocity when it reach the ground is

v² = u²+ 2gh

v² = 2× 32 × 1290

v ² = 82560

v = √82560

v = 287.33feet/s

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The volume of a cylinder whose diameter measures 2.5 cm and has a height of 15.5 cm is equal to 76.10 cubic centimeters.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Note: Radius = diameter/2 = 2.5/2 = 1.25 cm.

By substituting the parameters, we have:

Volume of cylinder, V = 3.142 × 1.25² × 15.5

Volume of cylinder, V = 76.10 cubic centimeters.

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Complete Question:

Calculate the volume of a cylinder whose diameter measures 2.5 cm and has a height of 15.5 cm.

The volume of 8 rectangular prism stacked base to base is 2560 in³.

Volume is a measure of three-dimensional space.

To calculate the volume of 8 rectangular prism stacked base to base, we use the formula below

Formula:

Where:

From the question,

Given:

We find the value of h using the formula for the surface area of a prism

Given:

Substitute these values into equation 2

Finally, we subtitute into equation 1

Hence the volume is 2560 in³.

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