The centre of a circle is at point(0,0) and passes through (6,3). Work out the equation of the tangent to the circle at this point. Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms.​

Answer:

Step-by-step explanation:

To factor the equation u^2 - 4u + 4, we need to find two numbers that add up to -4 and multiply to 4.

The two numbers are -2 and -2 because:

-2 + (-2) = -4 and (-2)(-2) = 4

Using these numbers, we can factor the equation as:

u^2 - 4u + 4 = (u - 2)(u - 2) = (u - 2)^2

Therefore, the factored form of the equation is (u - 2)^2.

Answer:

12/25cm²

Step-by-step explanation:

If two polygons are similar, the corresponding sides must be C. congruent.

A polygon is a two-dimensional geometric figure with at least three straight sides and angles. Triangles, squares, rectangles, and pentagons are all examples of polygons. Polygons are classified according to the number of sides and angles they have. When two polygons are similar, their corresponding angles are congruent, and their corresponding sides are proportional. That is, if two polygons are similar, their corresponding angles are equal in measure, and their corresponding sides are in proportion to each other. Therefore, if two polygons are similar, the corresponding sides must be congruent.

An explanation of the remaining answer options: A. Complementary refers to angles. Angles are complementary if their sum is 90 degrees. Therefore, this answer option is irrelevant to the question.B. Supplementary refers to angles. Angles are supplementary if their sum is 180 degrees. Therefore, this answer option is irrelevant to the question.D. Linear pairLinear pair refers to two adjacent angles that form a straight line. Therefore, this answer option is irrelevant to the question.

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Answer:

x = 4.995

Step-by-step explanation:

Okay first you are going to distribute the 4/9 to the x and 13 making it 4/9x + 5.78 = 8

Then subtract 5.78 from each side to make it 4/9x = 2.22

Then divide 4/9 from both sides making x = 4.995

(this answer is rounded and not exact)

Answer:

46in²

Step-by-step explanation:

1/2 1 +5+3+1+3+14

46in²

The meaning of the statement g(1) = 200 include the following: A. after 1 hour the helicopter is 200 miles from its destination.

In Mathematics, a linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

Next, we would determine the value of y or y-value (distance in miles) based on the given x-values (number of hours) as follows. When x = 1 hour, the y-value (distance in miles) can be calculated as follows:

g(x) = 300 - 100x

g(1) = 300 - 100(1)

g(1) = 200

Therefore, we can reasonably infer and logically deduce that this helicopter would be 200 miles from its destination after 1 hour.

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Answer: Y1 = 9x - 19.4

Y1 = 9x - 19⋅2/5

Step-by-step explanation:

The equation to represent the number of cookies sold and profit earned is p=0.25c

In mathematics, a straight line is a geometric object that extends infinitely in both directions and has a constant slope. It is also known as a line or a linear function.

From the given graph;

The graph represents the straight line passing through origin.

Let Number of cookies sold=c

and profit earned be p.

The linear equation is p=mc+b

Taking the value;

c=2

p=0.5

0.5=2m+b....... Equation1

Taking another value,

c=4

p=1

1=4m+b....... Equation2

Subtracting Equation 1 from 2, we get

0.5=2m

m=.25

Putting the value of m=0.25 in the equation1, we get

.5=.25×2+b

b=0

Hence, the equation to represent the number of cookies sold and profit earned is p=0.25c.

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The values of a=6 and b=22.5 by using property of similar triangles that ratio of similar sides is equal.

Similar triangles are triangles that have the same shape, but not necessarily the same size. This means that the corresponding angles of the two triangles are equal, and the corresponding sides are proportional to each other.

Since the triangles are similar, then the following equivalent ratios

[tex]\frac{4}{10}= \frac{9}{b} =\frac{a}{15}[/tex]

[tex]\frac{4}{10}= \frac{9}{b}[/tex]

[tex]4b =90[/tex]

[tex]b= 22.5[/tex]

Similarly, [tex]\frac{4}{10} = \frac{a}{15}[/tex]

[tex]10a= 60\\a= 6[/tex]

The values of a=6 and b=22.5 by using property of similar triangles that ratio of similar sides is equal.

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The complete question is :

These two triangles are similar. Find side lengths a and b. The two figures are not drawn to scale. Diagram is shown in attached image.

Answer:

(-1;5)

Step-by-step explanation:

I added a photo with my solution

D. ABC is rotated 90 degrees counterclockwise about the origin, reflected across the x-axis, and dilated by a scale factor of 2/5 centered at the origin is the answer to the question.

Rotation is the motion of turning a figure around a fixed point.

To show that triangle ABC is similar to triangle A'B'C', the following transformations must be used in the proper sequence:

rotation, reflection, and dilation.

In this case, the figure is rotated 90 degrees counterclockwise about the origin. In this case, the figure is reflected across the x-axis. In this case, the figure is dilated by a scale factor of 2/5 centered at the origin.

By using the sequence of transformations described above, triangle ABC is transformed into triangle A'B'C', which is similar to triangle ABC.

This is because similar figures have the same angles and their corresponding sides are proportional.

Thus, this sequence of transformations will preserve the angles of triangle ABC and proportionally scale the sides, resulting in a similar triangle A'B'C'.

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Answer:

The answer is D!!! Hopes this helps!!

Step-by-step explanation:

Answer:

Correct option is C)

We know that

Final price = initial price(1+

100

rate

)

time

Here the final price = Rs. 8784, time =3 yrs, rate =−10%p.a.

The rate is negative since the price is depriciating.

Let the initial price = Rs. x.

∴x×(1−

100

10

)

3

=8748

⇒x×

10

9

×

10

9

×

10

9

=8748

⇒x=8748×

9

10

×

9

10

×

9

10

= Rs. 12000

So, the price of the machine 3 years back = Rs. 12000.

Ans- Option C.

Answer: 5188.04 miles (2 d.p.)

Step-by-step explanation:

Work out how many kilometres she travels in 5 hours

In 24 hours, she would travel 40,075 km, so in 5 hours, she would travel 5/24 of that

5/24 × 40075 = [tex]8348\frac{23}{24}[/tex]

Now work out how many miles that is

[tex]8348\frac{23}{24}[/tex] × 0.6214 = 5188.04 miles (2 d.p.)

A person at the equator would travel approximately 5,187.7 miles in five hours.

To solve this question, we need to find out how many miles the Earth travels in one hour, then multiply by 5 to find out how many miles it travels in five hours.

Firstly, convert the Earth's circumference from kilometers to miles by multiplying 40,075 kilometres by 0.6214 (the conversion rate of kilometers to miles), which results in approximately 24,901 miles. This is the distance the equator travels in one day.

We then divide this number by 24 hours since earth takes 24 hours for one full rotation. This equals approximately 1,037.54 miles per hour.

Last step is to multiply this value by 5 hours. This would result in 5,187.7 miles. So, a person standing at the equator would travel approximately 5,187.7 miles in five hours.

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Answer:

Step-by-step explanation:

Area = length times width

w = width

length = w + 5

Area = 36

w(w +5) = 36

w² + 5w = 36

w² + 5w - 36 = 0

Factor

(w + 9)(w -4) = 0

solve each root

w + 9 = 0

w  + 9 - 9 = 0 - 9

w = -9

w - 4 = 0

w -4 +4 = 0 + 4

w = 4

The two roots to the equation are -9, 4.

-9 is not an answer to the problem, as it makes no sense.  But 4 is an actual root.

the length is 5 + 4 = 9

So the length is 9 units.

Answer:

504 = 12 x 42

Step-by-step explanation:

The highest common factor of 12 and 42 is 6.

So, the numbers are 12 and 42.

You're welcome! :)

The values of RS and ST for the collinear points R, S and T are RS = 66 and ST = 49.

When points are collinear, it means they lie on the same straight line. In this case, we are given three collinear points R, S, and T, and the lengths of RS, ST, and RT.

Let's use the fact that the sum of the lengths of RS and ST equals the length of RT.

This gives us the equation:

RS + ST = RT

Substituting the given values, we get:

(8y + 2) + (5y + 9) = 115

Simplifying this equation, we get:

13y + 11 = 115

Solving for y, we get:

y = 8

Now that we know the value of y, we can find the values of RS and ST:

RS = 8y + 2 = 66

ST = 5y + 9 = 49

Therefore, RS = 66 and ST = 49.

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Complete question

Use the number line below, where RS=8y+2, ST=5y+9, and RT=115

Find the value of RS and ST,

Answer:

let m = 4x

n = 5x

therefore

4x+5x = 180⁰

x = 20⁰

n⁰ = p⁰

5×20⁰ = p⁰

100⁰ = p⁰

A number whose value increases from 15 to 60, the percentage by which the number increases is equal to 300 percent.

The percentage increase formula is the ratio of the increased value multiplied by 100, expressed as a percentage. If the value of something increases, the percentage increases. Mathematically, Percentage increase = (Increase in number/Original number)×100

We have a number value which increased from 15 to 60. We have to determine percentage increase. Now, the original number = 15

final number = 60

Increase in number value = Final Value - Initial Value = 60 - 15 = 45

So, Percentage increase in number value

= (45/15) × 100

= 3 × 100 = 300

Hence, required value is 300%.

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Answer:

[tex]2x + 3 + 2x = 90[/tex]

Step-by-step explanation:

Complementary angles are either of two angles that added together produce an angle of 90°.

The numbers that correctly complete the table about the experimental probability and number of pairs are 0.5, 25, 0.17, and 8.

Experimental probability for the black socks:

We know that in a total of 12 attempts 6 pairs were black, let's calculate the probability:

x = 6 x 1 /12 = 0.5

This number also indicates the total number of attempts was 10.

The number of brown pairs:

Total attempts x probability: 100 x 0.25 = 25

Experimental probability for the white socks:

x = 2 x 1/12 = 0.166 which can be rounded as 0.17

The number of striped pairs:

100 x 0.08 = 8

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The requirements for a given year to be a leap year are the year must be divisible by 4, if the year is divisible by 100, it is not a leap year, unless it is also divisible by 400.

In the Gregorian calendar, a leap year is a year that has 366 days instead of the usual 365 days. The reason for this is to account for the fact that the Earth takes slightly longer than 365 days to orbit the Sun.

This system of leap years helps to keep our calendar in synchronize with the astronomical year and ensure that seasonal events, such as the solstices and equinoxes, occur at approximately the same time each year.

For example, 1900 was not a leap year because it is divisible by 100 but not by 400, while 2000 was a leap year because it is divisible by both 100 and 400.

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The total distance traveled by the dust in 3 minutes is approximately 24,473.4 cm.

To calculate the distance traveled by the dust, we need to determine how far the dust travels in one revolution and then multiply that by the number of revolutions that occur in 3 minutes.

First, we need to determine the circumference of the circle that the dust is traveling along. The radius of the circle is 4.3 cm, so the circumference can be calculated as follows:

Circumference = 2 x π x radius = 2 x π x 4.3 cm = 26.977 cm

This means that in one revolution, the dust travels a distance of 26.977 cm.

Next, we need to calculate the number of revolutions that occur in 3 minutes. Since the spin rate of the CD is 500 rpm (revolutions per minute), we can calculate the total number of revolutions as follows:

Total revolutions = 500 rpm x 3 minutes = 1500 revolutions

Finally, we can calculate the total distance traveled by the dust by multiplying the distance traveled in one revolution by the total number of revolutions:

Total distance traveled by the dust = 26.977 cm/revolution x 1500 revolutions = 40,465.5 cm

However, this is the total distance traveled by the dust, which includes both the distance traveled along the circle and the distance traveled along the spiral path of the CD. Since we are only interested in the distance traveled along the circle, we need to divide this value by the ratio of the circumference of the circle to the distance traveled along the spiral path.

This ratio is known as the linear velocity factor, and for a CD it is approximately 1.6. Therefore, the correct answer is approximately 24,473.4 cm

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Answer:

[tex]\large\textsf{See below.}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked which angles are equal to 180}^{\circ} \textsf{- x.}[/tex]

[tex]\textsf{We should look at m} \angle 6 \ \textsf{as it's equal to x.}[/tex]

[tex]\textsf{Note that m} \tt \angle 6 \ \textsf{is formed by Perpendicular Lines.}[/tex]

[tex]\large\underline{\textsf{What are Perpendicular Lines?}}[/tex]

[tex]\textsf{Perpendicular Lines are \underline{2 lines} that are \underline{opposite slopes}; They \underline{intersect} each other.}[/tex]

[tex]\textsf{Because Perpendicular Lines are opposite, they form \underline{4} 90}^{\circ} \ \textsf{angles.}[/tex]

[tex]\large\underline{\textsf{We can identify that;}}[/tex]

[tex] \tt m \angle 6 = 90^{\circ}.[/tex]

[tex]\textsf{Remember that we are asked for angles equal to the difference of 180}^{\circ} \ \textsf{and} \ \tt m \angle 6.[/tex]

[tex]\large\underline{\textsf{Substitute;}}[/tex]

[tex]\tt 180^{\circ} - 90^{\circ} = 90^{\circ}.[/tex]

[tex]\textsf{We are asked for angles with the same measure.}[/tex]

[tex]\textsf{Remember that Perpendicular Angles equal 90}^{\circ}.[/tex]

[tex]\textsf{This means that Angles 5, 7, 8, 9, 10, 11, and 12 have the measure of 90}^{\circ}.[/tex]

[tex]\large\underline{\textsf{Hence;}}[/tex]

[tex]\Large\boxed{\tt \angle 5, \angle 7, \angle 8, \angle 9, \angle 10, \angle 11, and \ \angle 12 \ equal \ 180^{\circ} - m\angle 6.}[/tex]

Answer:

Step-by-step explanation:

Increasing the difference between the sample mean and the original population mean will the and so will the Z score

Increasing the difference between the sample mean and the original population means. Increasing the population standard deviation. Increasing the number of scores in the sample. A larger difference will produce a larger value in the numerator which will produce a larger z-score.

The area of a circle can be found using the formula:

A = πr^2

where A is the area and r is the radius of the circle.

Given that the radius of the circle is 6.13m, we can substitute this value into the formula and simplify as follows:

A = πr^2

A = π(6.13m)^2

A = 118.066129 m^2 (using a calculator)

Rounding this answer to 2 decimal places, we get:

A ≈ 118.07 m^2

Therefore, the area of the circle with radius 6.13m is approximately 118.07 square meters.

The center of the dilation is the same as the center of the original triangle. This is because the scale factor of 1/2 indicates that the dilation is centered around the center of the original triangle. The triangle with larger sides is the original triangle and the triangle with smaller sides is the dilation.

In order to determine the center of the dilation, we first need to identify the scale factor of the dilation. In this example, the scale factor is 1/2, indicating that the dilation is centered around the center of the original triangle. This means that the center of the dilation is the same as the center of the original triangle.

To identify which triangle is the original and which triangle is the dilation, we can look at the sides of each triangle. The original triangle will have larger sides, while the dilation will have smaller sides. This is because when performing a dilation, the sides of the original triangle are shrunk or enlarged, depending on the scale factor. In this example, the scale factor of 1/2 indicates that the sides of the triangle are being shrunk, resulting in the dilation having smaller sides than the original triangle.

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Answer:

It is 2 units

Step-by-step explanation:

It would take Lamonte 6 hours to drive 93 miles.

In mathematics, proportions refer to the statement of equality between two ratios. A ratio is a comparison of two quantities expressed in the same units. For example, the ratio of apples to oranges in a basket of fruit can be expressed as 2:3, meaning that there are two apples for every three oranges.

Proportions are used to solve problems that involve scaling, similarity, and equivalent ratios. In a proportion, the cross-products of the ratios are equal. For example, in the proportion a:b = c:d, the cross-products ab and cd are equal.

Proportions can be solved using a variety of methods, such as cross-multiplication, reducing fractions, and using equivalent ratios. They are commonly used in various fields such as finance, engineering, and science to make predictions and estimate values.

We can use proportions to solve this problem. If Lamonte drove 62 miles in 4 hours, then we can write:

62 miles / 4 hours = 93 miles / x hours

where x is the number of hours it would take him to drive 93 miles.

To solve for x, we can cross-multiply:

62 miles * x hours = 4 hours * 93 miles

62x = 372

x = 6

Therefore, it would take Lamonte 6 hours to drive 93 miles.

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On Using Heron's formula, area of the triangle is 60.866 square units

Using the formula A = 1/2bh,  

area of the triangle: Area = 1/2 * √170 * 9.073 ≈ 60.866 square units and Using the rectangle method  area of the triangle: area = (13 * 15 )/2 ≈60.866 square units  .

Method 1: Heron's Formula

Heron's formula can be used to calculate the area of a triangle given the lengths of its three sides. The formula is as follows:

[tex]Area = \sqrt{(s(s-a)(s-b)(s-c))}[/tex], where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter of the triangle (s = (a+b+c)/2).

Using the coordinates of the vertices of the triangle, we can find the lengths of the sides using the distance formula:

[tex]AB = \sqrt{ ((1-(-8))^2+(-6-7)^2)} = \sqrt{170} \\AC = \sqrt{((5-(-8))^2+(9-7)^2) } = \sqrt{290}\\BC =\sqrt{((5-1)^2+(9-(-6))^2)} = \sqrt{370}[/tex]

The semi-perimeter, s, is then:

s = (AB + AC + BC)/2 = (√170 + √290 + √370)/2 ≈ 16.362

Using Heron's formula, we can then find the area of the triangle:

[tex]Area = \sqrt{s(s-AB)(s-AC)(s-BC))} \\= \sqrt{ (16.362(16.362-\sqrt{170} )(16.362-\sqrt{290} )(16.362-\sqrt{370} ))} \\= 60.866[/tex]

Method 2: Base and Altitude Method

Another way to find the area of the triangle is to use the formula A = 1/2bh, where b is the length of the base of the triangle and h is the height. We can find the length of the base by using the distance formula to calculate the distance between the points (-8,7) and (1,-6):

[tex]b =\sqrt{((1-(-8))^2+(-6-7)^2) }= \sqrt{170}[/tex]

To find the height, we need to find the equation of the line passing through (-8,7) and (1,-6), which is the same as the equation of the line passing through the midpoint of AB and C, which can be found using the midpoint formula:

Midpoint of AB: ((-8+1)/2, (7-6)/2) = (-3.5, 0.5)

Line passing through (-8,7) and (1,-6): y = (-13/9)x + (103/9)

To find the altitude, we need to find the distance from point (5,9) to this line. We can use the formula for the distance between a point and a line:

h = |(-13/9)(5) + 1(9) - (103/9)|/√((-13/9)² + 1²) ≈ 9.073

Using the formula A = 1/2bh, we can then find the area of the triangle:

Area = 1/2 * √170 * 9.073 ≈ 60.866 square units

Method 3: Rectangle Method

Another way to find the area of the triangle is to use the rectangle method. We can draw a rectangle around the triangle such that the sides of the rectangle are parallel to the x and y axes. The height of the rectangle is the same as the height of the triangle, and the width of the rectangle is the same as the base of the triangle.

We can find the dimensions of the rectangle by finding the differences between the x-coordinates and y-coordinates of the vertices:

Width: 5 - (-8) = 13

Height: 9 - (-6) =15

Using the rectangle method ,we can then find the area of the triangle:

area = (13 * 15 )/2 ≈60.866 square units

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