Writing equations of lines

The complete labels to the parts of the circle such as tangent, diameter, radius and secant are found in the attchment.

The various parts of a circle are:

Center: The point inside the circle that is equidistant from all points on the circumference.

Circumference: The distance around the circle.

Radius: A line segment from the center of the circle to any point on the circumference.

Diameter: A line segment that passes through the center of the circle and has its endpoints on the circumference.

Chord: A line segment with both endpoints on the circumference.

Tangent: A line that intersects the circle at only one point, called the point of tangency.

Secant: A line that intersects the circle at two points.

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After solving for side a, we have come to know that a = 2.2. Thus, option A is correct.

The law of cosines is a trigonometrical rule that links the lengths of a triangle's sides to the cosines of one of its angles, whether the triangle is spherical or flat. When two sides and the angle between them are known, it can be used to determine the length of a side or the angle of a triangular. There are two versions of the law of cosines: one for spherical triangles and one for planar triangles.

We can use the Law of Cosines to solve for the length of BC (denoted by a) in triangle ABC, since we know two sides and the included angle.

[tex]\rm a=\sqrt{c^{2}+b^{2}-2 c b \cdot \cos A}[/tex]

[tex]\rm a=\sqrt{4^{2}+3^{2}-2(4)(3) \cdot \cos(32^{\circ})}[/tex]

[tex]\rm a=\sqrt{16+9-24\cdot \cos(32^{\circ})}[/tex]

[tex]\rm a=\sqrt{1 \cdot \cos(32^{\circ})}[/tex]

a = 2.155654

a ≈ 2.2

Thus, After solving for side a, we have come to know that a = 2.2. Thus, option A is correct.

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Margo will pay an interest of $29.75 on her loan.

According to the given data the actual cost of the repair was $393.75.

Estimated cost refers to the approximate amount of money that is expected to be spent on a particular project, task, or item. It is a prediction of the expected cost based on the available information and assumptions about the project or item being estimated. Estimated costs can be based on various factors such as labor, materials, equipment, overhead, and other expenses.

If the estimated cost was 12.5% more than the actual cost, then the actual cost was 100% - 12.5% = 87.5% of the estimated cost.

Let x be the actual cost of the repair. Then, we can set up the following equation:

87.5% of estimated cost = actual cost

0.875 * 450 = x

Solving for x, we get:

x = $393.75

Therefore, the actual cost of the repair was $393.75.

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To construct the parallelogram ABCD, follow these steps:

The diagram of the parallelogram ABCD is shown below:

      D - - - - -C

     /            |

   /              |

A - - - - - - - B

Note that AB is parallel to CD and AD is parallel to BC, and opposite sides of the parallelogram are congruent.

The empirical probability of an event is the ratio of the number of times the event occurred to the total number of observations.

So, for each game, the empirical probability of purchasing that game is given by:

So the empirical probability of purchasing game 1 is 27.3%, game 2 is 26.1%, and game 5 is 12.7%.

Answer: 45,000

Step-by-step explanation:

Let x be the total number of seats available. According to the problem, 18% of the seats are bleachers, and 42% of the seats are grandstands. That means the remaining 40% of the seats are box and club seats combined since 100% - 18% - 42% = 40%.

The problem states that there are 12,600 box seats and 5,400 club seats available, which makes a total of 12,600 + 5,400 = 18,000 box and club seats.

Now, we can set up an equation to find the total number of seats:

0.40x = 18,000

To solve for x, divide both sides of the equation by 0.40:

x = 18,000 ÷ 0.40

x = 45,000

There are a total of 45,000 seats available at the baseball game.

The average rate of change between t = 0 and t = 2 is 16 feet/second and the average rate of change between t = 1 and t = 2 is 8 feet/second.

The correct answer choice is option A and C respectively.

The average rate of change between t = 0 and t = 2

At t = 0

h(t) = -16t² + 40t + 6

= -16(0)² + 40(0) + 6

= 0 + 0 + 6

= 6 feet/second

At t = 2

h(t) = -16t² + 40t + 6

= -16(2)² + 40(2) + 6

= -16(4) + 80 + 6

= -64 + 80 + 6

= 22 feet/second

The average rate of change between t = 0 and t = 2 is

22 feet - 6 feet

= 16 feet/second

At t = 1

h(t) = -16t² + 40t + 6

= -16(1)² + 40(1) + 6

= -16 + 40 + 6

= 30 feet/second

Therefore,

The average rate of change between t = 1 and t = 2 is

30 feet - 22 feet

= 8 feet

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the principle square root of -27 is √5.196.

The balances and the running total, given the checking account record is :

The balance on the 14 th of February would be:

= Balance forward - Amount of check

= 299. 88 - 90. 48

= $ 209. 40

The balance on 2 / 15 :

= 209. 40 - 65

= $ 144. 40

The balance on 2 / 17 :

= 144. 40 + 381.33 which is a deposit

= $ 525.73

The balance and running total on 2 / 22 :

= 525. 73 - 54.47

= $ 471.26

The balance on 2 / 22 after the National Mortgage deduction is:

= 471. 26 - 375.99

= $ 95.27

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To reach their financial objective of having $130,000 accessible for their child's schooling when the youngster turns 18, the parents must set aside roughly $97,209.87 at 3% compound semiannually.

To determine how much money needs to be set aside to meet the financial goal of $130,000 for the child's education, we can use the compound interest formula:

[tex]A = P(1 + r/n)^(nt)[/tex]

where A represents the future value, P represents the principal (or initial investment), r represents the annual interest rate, n is the frequency with which interest is compounded annually, and t represents the passage of time in years.

To solve for the principal, P, in this situation, we must first identify the principal, P.

[tex]P = A / (1 + r/n)^(nt)[/tex]

Given that the child is currently 10 years old and will need the money in 8 years (at age 18), we have t = 8. The interest rate is 3%, which we need to express as a decimal (r = 0.03), and the interest is compounded semiannually, so n = 2.

Using these values and the desired future value of $130,000, we can calculate the required principal:

P = [tex]130000 / (1 + 0.03/2)^(2*8)[/tex] = $97,209.87

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The parabola's equation is as follows, with the directrix at y = 5 and the focus at (-4, 3). [tex](x + 4)^2 = 4y - 16[/tex]

A hyperbolic is a U-shaped symmetry curve that is created when a plane and a cone collide. The parabola has the characteristic that the distance between any point on the curve and a fixed point (referred to as the focus) is identical to the distance between that point and a telephone service (called the directrix). Equation y = ax2 + bx + c, at which a, b, and c are constants, gives the conventional form of a parabola. The parabola opens either upwards or downwards depending on the sign of coefficient a. The arc opens upwards if an is positive and downwards if an is negative.

given

A parabola with a vertex at (h, k) and a vertical axis of symmetry has the following standard form equation:

[tex](x - h)^2 = 4p(y - k) (y - k)[/tex]

where p is the separation between the vertex and the directrix or focus.

In this instance, the vertex's coordinates are (h, k) = since it is located halfway between the focus and directrix (-4, 4). As the directrix is a horizontal line with the coordinates y = 5, the separation between it and the vertex is p = 1.

When we enter these values into the equation in standard form, we obtain:

[tex](x + 4)^2 = 4(1)(y - 4) (y - 4)[/tex]

If we simplify, we get:

[tex](x + 4)^2 = 4y - 16[/tex]

The parabola's equation is as follows, with the directrix at y = 5 and the focus at (-4, 3). [tex](x + 4)^2 = 4y - 16[/tex] .

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Answer: To simplify the expression, we need to follow the order of operations, which is to perform the division first, then addition.

1/3 ÷ 7/6 + 1/5

To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction:

1/3 ÷ 7/6 = 1/3 × 6/7 = 2/7

Now we can substitute this value back into the original expression:

2/7 + 1/5

To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 35:

2/7 × 5/5 = 10/35

1/5 × 7/7 = 7/35

Now we can add the two fractions:

10/35 + 7/35 = 17/35

Therefore, the simplified expression is 17/35.

Step-by-step explanation:

The sequence of the transformation are - translation, then rotation, then reflection

Congruent refers to having the same size and shape. Congruent hence involves comparing two numbers, and equivalent denotes the equality of two expressions. Hence, to state two line segments are congruent implies that the two lines have equal measurements.

Angle measure is the same for congruent angles. An ordinary pentagon, for instance, has five sides and five angles, each of which is 108 degrees. The angles of a regular polygon will always be congruent, regardless of its size or scale.

here, from given figure we have triangle ABC ,where

ABC is translation,

A'B'C' is rotation of triangle ABC

A''B''C'' is reflection  ,

so,

the sequence of the transformations of triangle ABC is translation, then rotation, then reflection.

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Answer:

D

Step-by-step explanation:

Edge

Colin have £ 1392 in his bank account after 7 years.

Step-by-step explanation:

Given, Principal = P = £ 980

Rate of interest = R = 6% =  = 0.06

Time = T = 7 years

Amount = A = P + S.I

Simple Interest = S. I = PRT = 980 x 0.06 x 7 = £ 411.6

Amount after 7 years = £ 980 + £ 411.6 = £ 1391.6 ≈ £ 1392

Hence, Colin have £ 1392 in his bank account after 7 years.

Answer:

The slope of a line represents the rate of change, which in this case is the rate at which the skydiver is falling. The rate of falling is 4,800 feet in 4 seconds, which simplifies to 1,200 feet per second, therefore, the graph that has a slope of 1,200 best represents this rate.

The formula for finding the volume of a cone is [tex]\pi[/tex][tex]r^{2}[/tex] [tex]\frac{h}{3}[/tex]

Please note the following:

Radius: 5 in

Height: 13 in

(1): Substitute the radius and height into the equation.

[tex]\pi[/tex][tex](5^{2})[/tex][tex](\frac{13}{3} )[/tex]

(2): Using a calculator, solve the equation.

[tex]\pi[/tex][tex](5^{2})[/tex][tex](\frac{13}{3} )[/tex] = 340.33

(3): Round

If you were to round 340.33 to the next two decimal places, you'd get 340 as your final answer.

With that being said, the answer to your question is 340 in.

Using the Pythagorean theorem we know that the value of x in the given situation is 15 units respectively.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

So, the Pythagorean formula is as follows:

c = √a² + b²

Now, insert values as follows:

c = √a² + b²

c = √12² + 9²

c = √144 + 81

c = √225

c = 15 units

Therefore, using the Pythagorean theorem we know that the value of x in the given situation is 15 units respectively.

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The number of sandwiches Rosa and Clarice can make depends on the amount of leftover bread they have.

To determine the number of sandwiches that Rosa and Clarice can make, we need to know how much bread they have.

Let's assume that they have 10 slices of bread left over. To make a sandwich, you typically use two slices of bread, so we can make 5 sandwiches with 10 slices of bread.

However, if they have more or less bread, the number of sandwiches they can make will change accordingly.

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Therefore , the solution of the given problem of equation comes out to be  rounded to three decimal places, is 17.483 grams.

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Think about the information that y + 7 provides. When accompanied by generate y + 7, increasing results in b + 7 in this case rather than another method that could split 12 into two separate components.

Here,

We must enter t = 110 into the equation for y and solve for y in order to determine how much of the original mass is still present after 110 years:

=> y = 20(1 - 2^(-t/30))

=> y = 20(1 - 2^(-110/30))

=> y ≈ 2.517

As a result, there are roughly 2.517 grams of cesium-137 left after 110 years. We can deduct this amount from the original mass of 20 grams to determine how much of the initial mass is still present:

=> 20 - 2.517 ≈ 17.483

Thus, roughly 17.483 grams of the original 20 grams of cesium-137 are still present after 110 years.

The number, rounded to three decimal places, is 17.483 grams.

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Answer:

311.3 feet

Step-by-step explanation:

1 yard = 3 feet

Therefore, 103.76 yards = 311.28 feet (by multiplying 103.76 by 3)

Rounding to the nearest tenth gives us 311.3 feet.

Answer: it must be EXPONENTIAL as values are increasing exponentially

Step-by-step explanation:

a) The original claim in symbolic form would be: H0: μ = 69.1
b) Ha represents the claim that the mean pulse rate is not equal to 69.1.

What is null hypothesis?

A null hypothesis is a statement that there is no significant difference or relationship between two variables in a study or experiment. It is the default or initial position that is assumed to be true until evidence proves otherwise.

a) The original claim in symbolic form would be:

H0: μ = 69.1

Where μ represents the population mean pulse rate of adult males.

b) The null and alternative hypotheses can be stated as:

Null hypothesis: H0: μ = 69.1

Alternative hypothesis: Ha: μ ≠ 69.1

Where Ha represents the claim that the mean pulse rate is not equal to 69.1.

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Answer:The total number of cubes required is the product of the dimensions in cube-lengths: 3×4×2 = 24 cubes.

Step-by-step explanation:

Another way to figure this is to compute the prism volume in the given dimensions (cm³) and the cube volume in the same dimensions, then find the number of cube volumes in the prism volume.

The value of the y -intercept is -4 and the slope of the equation is 1/2.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

The slope of the line is given by the formula:

m = y2 - y1 / x2 - x1

From the table the coordinates are: (-6, -7) and (2, -3).

m = -3 + 7 / 2 + 6

m = 4 / 8

m = 1/2

Now, using the slope intercept form we have:

y - y1 = m(x - x1)

y + 7 = 1/2 (x + 6)

2 (y + 7) = x + 6

2y + 14 = x + 6

2y = x - 8

The y- intercept is found when x = 0

Thus, 2y = -8

y = -4

Hence, the value of the y -intercept is -4 and the slope of the equation is 1/2.

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The total volume of Cubic Yards of Concrete needed to fill in the footer is approximately 225.19 cubic yards.

To calculate the total volume of Cubic Yards of Concrete needed to fill in the footer, we need to use the formula for the volume of a rectangular prism, which is length x width x height. In this case, the length and height are both 20 feet since that is the size of the enclosed frame in the left of the diagram.

The width of the footer needs to be 2 feet, which means we need to subtract 4 feet (2 feet on each side) from the total width of the frame to get the inside width of the trench, which is 16 feet.

The depth of the footer needs to be 1 foot, which means we need to subtract 1 foot from the height of the frame to get the height of the trench, which is 19 feet.

Using these measurements, we can calculate the volume of the trench by multiplying length (20 feet) x width (16 feet) x height (19 feet) which gives us a total volume of 6,080 cubic feet.

To convert cubic feet to cubic yards, we need to divide the total volume by 27 (since there are 27 cubic feet in a cubic yard). Therefore, the total volume of Cubic Yards of Concrete needed to fill in the footer is approximately 225.19 cubic yards.

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Note the full question is

1) Calculate the total volume of Cubic Yards of Concrete needed to fill in the footer. (That is the enclosed frame in the left of the diagram above) (the footer needs to be 2 ft wide and 1 ft deep. (remember there is a 2 ft difference between the outside and the inside of trench)

2) What is the square footage of the footer trench ?

3) If the footer trench is 2 ft deep, would 10 Cubic-yards of concrete overfill this trench? By how much. ?

The correct sequence of transformations that proves AMNO and APQR are congruent is: OAMNO was dilated by a factor of 3 about the origin, then reflected across the y-axis to form APQR.

The correct sequence of transformations that proves AMNO and APQR are congruent is:

OAMNO was dilated by a factor of 3 about the origin, then reflected across the y-axis to form APQR.

To see why, let's examine the properties of the two triangles:

Triangle MNO has vertices at (-2,-1), (-2,4), and (3,1).

Triangle PQR has vertices at (-6,-3), (-6,12), and (9,3).

If we dilate triangle MNO by a factor of 3 about the origin, we get a new triangle with vertices at (-6,-3), (-6,12), and (9,3). This is because each coordinate of MNO is multiplied by 3:

(-2,-1) -> (-6,-3)

(-2,4) -> (-6,12)

(3,1) -> (9,3)

If we reflect this new triangle across the y-axis, we get a new triangle with vertices at (6,-3), (6,12), and (-9,3). This is because the x-coordinates of each point are negated:

(-6,-3) -> (6,-3)

(-6,12) -> (6,12)

(9,3) -> (-9,3)

This final triangle, with vertices at (6,-3), (6,12), and (-9,3), is congruent to triangle PQR. Therefore, we have shown that AMNO and APQR are congruent.

This theorem relates to theorems previously studied in the sense that it involves transformations of geometric shapes, which is a fundamental concept in geometry. In real-world applications, these transformations can be used in computer graphics, architecture, and engineering, among other fields, to manipulate and analyze shapes and structures.

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