Consider the diagram shown and answer the following questions; the radius of this circle is 6 inches.

a. Define how lines a, b, c, and d relate to circle P. (What special names do these lines have in relation to the circle?)
b. If the measure of angle OPS is 139°, what extra information would we need to calculate the measure of angle ORS using intersecting chords? Explain how we can use this information to calculate the angle.
c. Segment NS is 14 the length of segment TO. Explain how theorem 65 would allow us to calculate the length of segments RO, RS, RV, and RT.

All the expressions after completing the square each equation are,

⇒ (x - 1/2)² = 5/4

⇒ (x - 5/2)² + 3/4 = 0

⇒ (2x + 3/2)² = 57/4

Given that;

Expressions are,

⇒ 2x² - 2x + 7 = 5

⇒ -2x² + 10x = 14

⇒ 4x² + 6x = 12

Now, We can completing the square each equation as;

⇒ 2x² - 2x + 7 = 5

⇒ x² - x + 7/2 = 5/2

⇒ x² - x + 1/4 - 1/4 + 7/2 = 5/2

⇒ (x - 1/2)² = 1 + 1/4

⇒ (x - 1/2)² = 5/4

⇒ -2x² + 10x = 14

⇒ - x² + 5x = 7

⇒ x² - 5x = - 7

⇒ x² - 5x + 25/4 - 25/4 = - 7

⇒ (x - 5/2)² = - 7 + 25/4

⇒ (x - 5/2)² = - 3/4

⇒ (x - 5/2)² + 3/4 = 0

⇒ 4x² + 6x = 12

⇒ (2x)² + 2×2x×3/2 + 9/4 -9/4 = 12

⇒ (2x + 3/2)² = 12 + 9/4

⇒ (2x + 3/2)² = 57/4

Thus, All the expressions after completing the square each equation are,

⇒ (x - 1/2)² = 5/4

⇒ (x - 5/2)² + 3/4 = 0

⇒ (2x + 3/2)² = 57/4

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572 square inches nylon will Lyndon need.

To determine how much nylon Lyndon will need to make a case for his snare drum, we need to calculate the surface area of the drum.

The surface area of a cylinder can be calculated using the formula:

Surface Area = 2π[tex]r^2[/tex] + 2πrh

where r is the radius of the base of the cylinder and h is the height of the cylinder.

Since the diameter of the drum is 14 inches, the radius is 7 inches.

The height of the drum is 6 inches.

So, the surface area of the drum is:

Surface Area = 2π[tex](7)^2[/tex] + 2π(7)(6)

Surface Area = 2π(49) + 2π(42)

Surface Area = 98π + 84π

Surface Area = 182π

Surface Area = 182 pi

Surface Area = 182 x 22/7

Surface Area = 572 squae inches

Therefore, Lyndon will need 182π square inches of nylon to make a case for his snare drum.

This is approximately 572 square inches when rounded to the nearest hundredth.

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Answer:

Step-by-step explanation:

The equation of the plane pi is: -6x-7y-9z=0.

To find the equation of the plane that contains the given line L and the origin as well, we first need to find two vectors that lie on the plane. One vector can be the direction vector of the line L, which is (2i - j + 3k). Now to find the second vector, we can take the vector from the origin to any point on the line L, and this vector will lie on the plane.

Let us now take t=0, and find the point on the line L:

r = 3i + 3j - k + 0(2i - j + 3k)

= 3i + 3j - k

So, the vector from the origin to this point is simply (3i + 3j - k). We can just take (3i + 3j - k) as our second vector.

Now, we can find the normal vector of the plane by taking the cross-product of two vectors that we just found, we get:

n = (2i - j + 3k) * (3i + 3j - k)

= -6i - 7j - 9k

Therefore, the equation of the plane pi is: -6x-7y-9z=0.

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Answer:

(a) 5 ft^2

Step-by-step explanation:

The formula for area of a triangle is given by the formula,

A = 1/2bh, where

Thus, we can plug in 5 for b and 2 for h in the formula to find the area of the triangle in square feet:

A = 1/2(5)(2)

A = (5/2)(2)

A = 10/2

A = 5

Thus, the area of a triangle whose base is 5 ft and whose height is 2 ft is 5 ft^2

Answer:

43.47 feet (2 d.p.)

Step-by-step explanation:

Points A, B and C form a triangle.

We have been given sides a and b, and their included angle C.

The distance between points A and B is side c of triangle ABC.

Therefore, we can solve this problem using the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.

[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines (for finding sides)} \\\\$c^2=a^2+b^2-2ab \cos (C)$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]

Given values:

Substitute the given values into the Law of Cosines formula and solve for side c:

[tex]\implies c^2=72^2+54^2-2(72)(54)\cos(37^{\circ})[/tex]

[tex]\implies c^2=8100-7776\cos(37^{\circ})[/tex]

[tex]\implies c=\sqrt{8100-7776\cos(37^{\circ})}[/tex]

[tex]\implies c=43.4719481...[/tex]

[tex]\implies c=43.47\; \sf ft\;(2\; d.p.)[/tex]

Therefore, the width of the pond from point A to point B is 43.47 feet, to two decimal places.

Answer:

The function is given by p(x) = x^2 - 5x^2 + x + 15. The potential rational zeros of the function are given by the factors of the constant term (15) divided by the factors of the leading coefficient (1).

So the potential rational zeros are ±1, ±3, ±5, ±15.

The list of potential rational zeros of the function includes all of the options listed except option (b) -2. Therefore, the answer is (b) -2.

Step-by-step explanation:

The coordinates of vertex D in the parallelogram are (-7, -10).

We have,

To find the coordinates of vertex D of the parallelogram, we need to use the properties of a parallelogram.

One of these properties states that opposite sides of a parallelogram are parallel and have equal lengths.

Given that A = (8, 2), B = (6, -4), and C = (-5, -4), we can find the coordinates of D as follows:

Find the vector representing one of the sides of the parallelogram.

We can use the vector AB.

Vector AB = (x-coordinate of B - x-coordinate of A, y-coordinate of B - y-coordinate of A)

= (6 - 8, -4 - 2)

= (-2, -6)

Add this vector to point C to find the coordinates of D.

Coordinates of D = (x-coordinate of C + x-coordinate of AB, y-coordinate of C + y-coordinate of AB)

= (-5 - 2, -4 - 6)

= (-7, -10)

Therefore,

The coordinates of vertex D are (-7, -10).

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The total volume of the air space of spherical ball is A = 12.265625 inches³

Given data ,

Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.

The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.

The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.

The formula for the volume of a cylinder is:

V = πr²h

V = ( 3.14 ) ( 1.25 )² ( 7.5 )

V = 36.796875 inches³

where V is the volume, r is the radius, and h is the height.

So, the volume of the one ball is:

V₁ = ( 4/3 )π(1.25)³

V₁ = 8.177083 inches³

The total volume of three balls is = volume of 3 spherical balls

V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches

Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³

A = 12.265625 inches³

Hence , the volume of air space is A = 12.265625 inches³

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The 91-day T-bill that Nadeen bought at an interest rate of 4.30% p.a. and face value of $5,000 indicates;

a) Nadeen paid about $4,946.24 for the T-bill

b) Barbara's selling price for the T-bill is about $4,962.74

A Treasury bill (T-bill), is a short-term obligation that is issued by the U.S. Department of Treasury and which is backed by the United States government, and has a maturity of less than a year. T-bills are low risk investment as they are backed by the credit and full faith of the U.S. government.

The formula for the price of the T-bill can be calculated with the formula;

Price = Face Value/(1 + (Interest Rate × Days to Maturity/360))

Plugging in the value from the question, we get;

Price = 5000/(1 + (0.043 × 91/360)) ≈ 4946.24

b) The formula for the selling price can be presented as follows;

Selling Price = Face Value/(1 + (Interest Rate × Remaining Days to Maturity/360))

Plugging in the known values, we get;

Selling Price = 5,000/(1 + (0.053 × (91 - 40)/360)) ≈ $4,962.74

Therefore, Barbara sold the T-bill to her friend for $4,962.74

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Answer:

y = 5x + 11

Step-by-step explanation:

Step 1:  When two lines are parallel, they have the same slope, as indicated by the following equation as m2 = m1, where

Thus, since the slope of line 1 is 5, the slope of line 2 is also 5.

Step 2:  Now we can plug in (-2, 1) for x and y and 5 for m to solve for b, the y-intercept of the other line:

1 = 5(-2) + b

1 = -10 + b

11 = b

Thus, the equation of the line parallel to y = 5x + 2 and passing through (-2, 1) is y = 5x + 11

Answer:

12

Step-by-step explanation:

206

5x10 12x13=206 it may be incorrect but i not sure if it is incorrect

Solving a system of equations we can see that Gavin worked 7 hours tutoring.

Let's define the variables:

x = number of hours tutoring.

y = number of hours land scaping.

We know that he worked for 10 hours and earned $137, then we can write a system of equations:

x + y = 10

14x + 13y = 137

Isolating y on the first equation we get:

y = 10 - x

Replace that in the second one to get:

14x + 13*(10 - x) = 137

14x + 130 - 13x = 137

x = 137 - 130 = 7

He worked 7 hours tutoring.

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The measure,

⇒∠s = 124 degree

In the given figure of kite,

PQRS,

Measure of angle p = 22 degree

And angle R is a right angle

Therefore,

∠R = 90 degree

Now we know that for a kite PQRS

Angle Q and Angle S are equal

Now consider,

Angle s is equal to x degree

Therefore,

∠S = ∠ Q = x degree

We know that,

For a kite the sum of interior angle is equal to 360 degree.

Therefore,

⇒ ∠P + ∠Q + ∠R + ∠S = 360

⇒ 22 + x + 90 + x = 360

⇒ 22 + x + 90 + x = 360

⇒                     2x  = 248

⇒                        x  = 124 degree.

Thus,

Measure of angle s = 124 degree.

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The value of tan (A-B) is equal to 715/2052.

To find the value of tan(A - B), we can use the trigonometric identity:

tan(A - B) = (tan(A) - tan(B))/(1 + tan(A)tan(B))

Given that tan(A) = 40/9 and sin(B) = 45/53, we can determine the values of cos(B) and tan(B) using the Pythagorean identity:

sin^2(B) + cos^2(B) = 1

cos(B) = sqrt(1 - sin^2(B))

cos(B) = sqrt(1 - (45/53)^2)

cos(B) = sqrt(1 - 2025/2809)

cos(B) = sqrt(784/2809)

cos(B) = 28/53

tan(B) = sin(B)/cos(B)

tan(B) = (45/53)/(28/53)

tan(B) = 45/28

Now we can substitute the values into the formula for tan(A - B):

tan(A - B) = (tan(A) - tan(B))/(1 + tan(A)tan(B))

tan(A - B) = (40/9 - 45/28)/(1 + (40/9)(45/28))

tan(A - B) = [(1120/252 - 405/252)] / (1 + (1800/252))

tan(A - B) = (715/252) / (2052/252)

tan(A - B) = 715/2052

Therefore, tan(A - B) is equal to 715/2052.

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Answer:

  (x +4)²/25 +(y -3)²/16 = 1

Step-by-step explanation:

You want the equation of the ellipse with center (-4, 3) and semi-axes 5 and 4 in the x- and y-directions, respectively.

The standard form equation for an ellipse with center (h, k) and sem-axes 'a' and 'b' in the x- and y-directions, respectively, is ...

  (x -h)²/a² +(y -k)²/b² = 1

Using the given values, we find the equation to be ...

  (x +4)²/25 +(y -3)²/16 = 1

__

Additional comment

The longer of the two axes is the "major" axis, and its end points are the "vertices". For the purpose of an ellipse with center, vertices, and co-vertices specified, the equation is not affected by which axis is longer.

Effectively, this is the equation of a circle with different scale factors in the x- and y-directions.

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A single log statement from the many log statements to 1 is: [tex]log(7wy^{(-8)}/x^3)[/tex]

The exponent that indicates the power to which a base number is raised to produce a given number are called logarithm.

Use the logarithmic identity:

log[tex](a^n)[/tex] = n*log(a)

to convert the coefficients 2, 3, and 8:

log w + log 7 - 3log x - 8log y

= log w + log 7 - log [tex]x^3[/tex] - log [tex]y^8[/tex]

Combine the terms on the right-hand side using the logarithmic identity:

log(a) + log(b) = log(ab)

log w + log 7 - log[tex]x^3[/tex] - log [tex]y^8[/tex]

= log([tex]7wy^{-8}/x^3[/tex])

Therefore, the single log statement is from the many log statements to 1 is: log[tex](7wy^{-8}/x^3)[/tex]

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Answer:

a) r(t) = (10, 5, -5) + (5, 5, 0)*t

b) (0, -5, -5)

Step-by-step explanation:

a) 2x + 4 -2y -5 = -3z -6

2x - 2y +3z +5 =0

(10, 5, -5)

(15, 10, -5)

(5, 5, 0)

r = (10, 5, -5) + (5, 5, 0)*t

b) The yz plane is given by the equation x = 0.

x = 0  in the vector equation of a straight line if and only if  t = -2, than r ( - 2) = (0, -5, -5) is the desired intersection point.

Answer:

3



Step-by-step explanation:

Area = 7pi/5

56/360 × pi r² = 7pi/5

Pi is canceled on both sides.

r² = 7/5 ÷ 56/360 = 9

r = root 9 = 3

The solution of the system of linear equations, is (1.167, 3.667).

Given that the system of linear equations, y = -2x+6 and y = 4x - 1, we need to find the solution for the same,

y = -2x+6............(i)

y = 4x - 1.......(ii)

Equating the equations since the LHS is same,

-2x+6 = 4x-1

6x = 7

x = 1.167

Put x = 1.16 to find the value of y,

y = 4(1.16)-1

y = 4.66-1

y = 3.667

Therefore, the solution of the system of linear equations, is (1.167, 3.667).

You can also find the solution using the graphical method,

Plot the equations in the graph, the point of the intersection of both the lines will be the solution of the system of linear equations, [attached]

Hence, the solution of the system of linear equations, is (1.167, 3.667).

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The equation of the line that passes through point (-3,-7) and point (-3,10) is x = -3.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the points through which the line passes: (-3,-7) and (-3,10).

The two given points (-3, -7) and (-3, 10) have the same x-coordinate -3

Hence, the two lines  lie on a vertical line.

since the slope of the vertical line is undefined.

The equation of the line passing through these two points is simply the equation of the vertical line:

x = -3

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The amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

Recall the compounding formula:

A = P * [tex]e^{rt}[/tex]

Where:

A = Final amount in the account

P = Initial principal (deposit)

e = Euler's number (approximately 2.71828)

r = Annual interest rate (as a decimal)

t = Time in years

Given:

Initial principal (P) = $16,000

Annual interest rate (r) = 2%  = 0.02

time (t) = 4 years.

Substitute these values into the formula, we get:

A = $16,000 * [tex]e^{0.02 * 4}[/tex]

Using a calculator, we can calculate:

A = $16,000 * [tex]e^{0.08}[/tex]

A = $16,000 * 1.0833

A = $17,332.8

Therefore, the amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

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The calculated value of the mode(s) of the data is (a) 1

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

1, 0, 2, 2, 3, 0, 1, 1, 4, and 5

By definition, the mode of a data is the data that has the highest frequency

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

The data element 1 has the highest frequency of 3

Other data elements have lesser frequencies

Hence, the mode(s) of the data is (a) 1

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The area of the given figure with rectangle and triangle is 27.5 square centimeters.

The given figure has a rectangle and two triangles.

The area of the rectangle is length times width

Length = 5 cm

Width = 4 cm

Area of rectangle = 5×4

=20 square centimeters

Area of triangle =1/2 base ×height

=1/2×2.5×3

=3.75  square centimeters

As there are two triangles, 2(3.75)=7.5   square centimeters

Total area = 20+7.5

=27.5 square centimeters

Hence, the area of the given figure with rectangle and triangle is 27.5 square centimeters.

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37 million can be written as 3.7 × 10⁶ in the power of ten exponent notation.

In scientific notation, a number is written as the product of a coefficient and a power of ten.

To convert 37 million to scientific notation, we need to move the decimal point to the left until we have a number between 1 and 10.

Starting with 37 million, we can move the decimal point six places to the left to obtain the number 3.7:

= 37,000,000 -> 3.7

Now, we express this number as a product of the coefficient (3.7) and 10 raised to the power of the number of places we moved the decimal point.

In this case, since we moved the decimal point six places to the left, the exponent of ten is 6:

37 million = 3.7 × 10⁶

Therefore, 37 million can be written as 3.7 × 10⁶ in the power of ten exponent notation.

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Answer: 0 , 5

Step-by-step explanation:

Imagine a plane taking off, first it drives to gain speed then flies, thats what you can use for coordinates.

X is the driving and Y is the flight.

The X is at 0, and the Y is at 5.

The designer can choose from 84 possible combinations of tiles, and they can create 6 different sample designs using the 3 chosen tiles when placing them side by side.

To determine the number of possible combinations of tiles that the designer can choose, we can use the concept of combinations.

Since the designer has 9 different kinds of tiles and wants to choose 3 of them, we can calculate the number of combinations using the formula for combinations, which is [tex]nCr = n! / (r! \times (n - r)!).[/tex]

Number of combinations of tiles = 9C3 [tex]= 9! / (3! \times (9 - 3)!)[/tex]

Simplifying further:

[tex]9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1[/tex]

[tex]3! = 3 \times 2 \times 1[/tex]

[tex](9 - 3)! = 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1[/tex]

Plugging these values into the formula:

Number of combinations of tiles[tex]= 9 \times 8 \times 7 / (3 \times 2 \times 1 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1)[/tex]

Simplifying the expression:

Number of combinations of tiles = 84

The designer can choose from 84 possible combinations of tiles, and they can create 6 different sample designs using the 3 chosen tiles when placing them side by side.

Therefore, the designer can choose from 84 possible combinations of tiles.

Now, let's calculate the number of different sample designs the designer can make using the 3 chosen tiles.

Since the tiles are placed side by side, the order of the tiles matters.

To calculate the number of different arrangements, we can use the concept of permutations.

Number of sample designs = 3!

Calculating:

[tex]3! = 3 \times 2 \times 1 = 6[/tex]

Therefore, the designer can create 6 different sample designs using the 3 chosen tiles when placing them side by side.

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