Determine the equation of the circle graphed below 100pts

Answer:

x = -3.3

Step-by-step explanation:

Answer:

x=−3.333333

Step-by-step explanation:

The linear function with the greatest rate of change is f(x) = 2x

The general linear function can be written in the following way.

y = ax + b

a is the slope or rate of change, and b is the y-intercept.

From the given options, the line with the greatest rate of change is the one that grows the fastest, and we can see that the equation for that line is:

y = 2x

So that is the correct option.

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1. One half

2. One half

3. One quarter

The dimensions of the rectangle are 63 inches and 16 inches.

Let the width of the rectangle be 'x' inches.

From the given condition, we can say,

Length of the rectangle = 31 + 2*x

Diagonal of the rectangle = 2 + Length of the rectangle = 2 + (31 + 2*x)

                                                                                             = 2*x + 33

Since the rectangle makes an angle of 90° at the sides, the diagonal, and the sides of the rectangle form a right-angle triangle, the diagonal being the hypotenuse.

Applying Pythagoras theorem for width, length, and diagonal of the rectangle, we get,

\((2x + 33)^{2} = x^{2} + (31 + 2x)^{2}\)

Since, \([(a+b)^{2} = a^{2} +b^{2} +2*a*b]\)

\(4x^{2} +33^{2} +2*2x*33 = x^{2} +4x^{2} +31^{2} +2*2x*31\)

\(33^{2} - 31^{2} + 8x = x^{2}\)  

\(x^{2} - 8x - 128 =0\)

\(x^{2} +8x-16x-128=0\)

\(x(x+8) - 16(x+8)=0\)

(x+8)(x-16) = 0

x = -8, 16

Since x is a measure of width, it cannot be negative.

Hence, x = 16

Width = 16

Length = 2x+31 = 2*16 + 31 = 63

Therefore, the dimensions of the rectangle are 63 inches and 16 inches.

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Answer:

12.25

Step-by-step explanation:

There are 36 outcomes in a throw of 2 dice throws here.

The amount we would be willing to pay is computed here as the expected product value for the 2 dice as we are risk neutral, therefore we would be using the expected value.

The expected values here are computed as:

X P(X = x) xP(X =x)

1 1 1

2 2 4

3 2 6

4 3 12

5 2 10

6 4 24

8 2 16

9 1 9

10 2 20

12 4 48

15 2 30

16 1 16

18 2 36

20 2 40

24 2 48

25 1 25

30 2 60

36 1 36

36 441

Using the above table, the expected amount here is computed as:

\(E(X) = \frac{441}{36} = 12.25 \)

Therefore 49/4 is the required expected value here.

The expected value represents the amount you are willing to pay.

The amount you are willing to pay is #12.25

Let the dice be A and B.

So, we have:

\(A = \{1,2,3,4,5,6\}\)

\(B = \{1,2,3,4,5,6\}\)

The sample space of the product of the outcomes of the dice is:

\(S = \{1,2,3,4,5,6\\2,4,6,8,10,12\\3,6,9,12,15,18\\4,8,12,16,20,24\\5,10,15,20,25,30\\6,12,18,24,30,36\}\)

The sample size is:

\(n(S) = 36\)

The amount you are willing to pay is the expected value of the sample space.

This is calculated using:

\(Expected = \frac{\sum(S)}{n(S)}\)

\(Expected = \frac{1+2+3+4+5+6+.......+36}{36}\)

\(Expected = \frac{441}{36}\)

\(Expected = 12.25\)

Hence, the amount you are willing to pay is #12.25

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The power series of the given function  is 1 + (2x) + (2x)² + (2x)³+ --------------------- + (2x)ⁿ

We know very well that sum of n terms who are in geometric progression their sum of expression is given by  a/1-r where a is first term and r is common ratio between the terms.

Now, we have function f(x)=[1 / (1-2x)]

On comparing with a/1-r with f(x),we get

=>a=1 and r=2x

Now, we know that first term of geometric progression is given by =1

second term of geometric progression is given by=a × r= 1 ×2x

third term of geometric progression is given by =a×r² =1×(2x)²

fourth term of geometric progression is given by=a×r³ =1 × (2x)³

nth term of geometric progression is given by =a×(r)ⁿ = 1 × (2x)ⁿ

Therefore, according to the given formula progression series of given function is=a+ ar +ar² + ar³ + -----------arⁿ

=>progression series = 1+ 2x + (2x)² + (2x)³ + --------- + (2x)ⁿ.

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Using the same-side interior angles theorem,

\(8x+30+6x+24=180 \\ \\ 14x+54=180 \\ \\ 14x=126 \\ \\ \boxed{x=9}\)

Using vertical angles,

\(6(9)+24=10y+2 \\ \\ 78=10y+2 \\ \\ 10y=76 \\ \\ \boxed{y=7.6}\)

Answer:

y = 0.9

Step-by-step explanation:

1.05 + 0.7y = 3.5y - 1.47

-3.5y + 0.7y = -1.47 - 1.05

-2.8y = -2.52

y = 9/10 = 0.9

Answer:

\(\textbf{HELLO!!}\)

\(0.7\left(1.5+y\right)=3.5y-1.47\)

\(1.05+0.7y=3.5y-1.47 \gets \textsl{Expand}\)

\(1.05+0.7y-1.05=3.5y-1.47-1.05 \gets Subtract\; 1.05 \from\:both\:sides\)

\(0.7y=3.5y-2.52\)

\(0.7y-3.5y=3.5y-2.52-3.5y\)

\(\mathrm{Subtract\:}3.5y\mathrm{\:from\:both\:sides} \nwarrow\)

\(-2.8y=-2.52\)

\(\frac{-2.8y}{-2.8}=\frac{-2.52}{-2.8} \hookleftarrow \mathrm{Divide\:both\:sides\:by\:}-2.8\)

\(\boxed{\boxed{\underline{\textsf{\textbf{y=0.9}}}}}\)

\(\bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet\)

\(\textbf{HOPE IT HELPS}\)

\(\textbf{HAVE A GREAT DAY!!}\)

The area of a square inscribed in a circle is 25, then the area of the circle is 25π/2 or approximately 39.27 square units.

To solve this problem, we can use the relationship between the area of a square inscribed in a circle and the area of the circle itself.

When a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. Let's assume that the side length of the square is 's' and the radius of the circle is 'r'.

We are given that the area of the square is 25, so we can find the side length of the square:

Area of square = \(s^2 = 25\)

Taking the square root of both sides, we get:

s = √25 = 5

Since the diagonal of the square is equal to the diameter of the circle, we can find the diameter of the circle:

Diagonal = Diameter = s√2 = 5√2

The radius of the circle is half the diameter, so:

Radius = 5√2 / 2 = (5√2)/2

Now, we can calculate the area of the circle using the formula:

Area of circle = \(\pi r^2\)

Substituting the value of the radius, we get:

Area of circle = π((5√2)/\(2)^2\) = π(25/2) = 25π/2

Therefore, the area of the circle is 25π/2 or approximately 39.27 square units.

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The answers are a circle, supplementary angles, collinear points, volume, circle,  lengths EF and AD, line segment, and parallel lines.

A point is said to be equally far from a group of objects if there is an equal distance between it and each member of the group. In the circle, all the points in a plane are equally spaced out from the circle's center.

The term "supplementary angles" refers to angles that sum to 180 degrees. Angles 130° and 50°, for instance, are supplementary angles since they add up to 180°.

The collinear is a word of Latin origin. Col means together and linear means belonging to a line. Therefore, collinear points are those points that are situated along a single or shared straight line.

Volume is the measure of how much three-dimensional space a closed surface encloses. For example, a cup's volume is 200 ml, for instance, if it can accommodate 200 ml of water when filled to the brim.

From the given circle diagram, we can tell that EF is the diameter of the circle and AD is the radius of the circle. Consider the radius is 5cm, then the diameter is 10 cm. The ratio of EF and AD will be 2:1.

The segment of the straight line called a line segment is enclosed by both the endpoints and the points of the line.

No matter how far in either direction they may be extended, parallel lines are ones that are equally spaced apart from one another and never intersect each other.

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Answer:

give the data in the graph form and your answer is right..

Step-by-step explanation:

8) 0.003-0.007-0.008-0.009

0.012-0.014-0.015-0.018

0.021-0.023-0.024-0.025-and so on. if it says 5 the number before will be 4 number after will be 6.

5) just adding next number from counting.

6) changes to hundredths

7) the patter for down is by every 10th number

9) 0.071-0.072-0.073-0.074-0.075-0.076-0.077- and so on...

Answer:

Step-by-step explanation:

if the garden is a square, then it each side of the garden would be 20. if there's 16 congruent square plots, it means 4 sides of a plot per side of the garden, meaning that the side length of the plot would be 5 meters

Answer:

The blue dot is -19

Step-by-step explanation:

Since every 2 ticks are worth 6 (|-10|-|-4|=6), then one tick is worth 3.

We are going backward, so we can count backward.

We have to go down 3 ticks, so -10-3=-13; -13-3=-16; -16-3=-19.

The blue dot is -19

Answer: The blue dot equals to -19.

Step-by-step explanation:

On the number line, there are the numbers -10 & -4.

-7 would fit in the middle of them. That means the number line goes by minus 3.

Count -10 , -13, -16, then you get on the the blue dot which is -19.

Therefore, -19 is the answer.

Answer:

your gayy

Step-by-step explanation:

The number of days which it would take 1000 people to sign the petition as required in the task content is; 4.35 days.

It follows from the task content that the number of days which it would take Jan to get 1000 signatures on the petition be determined.

Since it is given in the task content that 230 people sign the petition each day.

It therefore follows from proportion that the number of days needed for 1000 people to sign the petition is;

= 1000/230

= 4.3478 days.

Hence, the number of days which it would take 1000 people to sign the petition is approximately; 4.35 days.

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The gradient of the line K that is perpendicular to the line H that has a gradient of 7 is -1/7

Perpendicular lines are lines that form a right angle (90 degrees angle) at the point of their intersection, in which the slope of one of lines is the negative reciprocal of the slope of the other line.

The gradient of the line H = 7

The relationship between the lines K and line H is; Line K is perpendicular to the line H

The slope of a line a, which is perpendicular to another line b with slope m is; -1/m

Therefore, the slope of the line K is -1/7

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The mass of the radioactive sample at the beginning of the 13th day of the experiment will be around 424.7 grams.

A metric weight measurement unit. A gramme is one thousandth of a kilogramme, or about 30 times smaller than an ounce. Leave a space between the word "gramme" (or the symbol "g") and the number that comes before it when a specific number is provided. In technical and scientific writing, the unit name and the number are either written together in full (for example, ten grammes) or a numeral is used with the sign ( e.g. 10 g ).

When we find the mass of radioactive, we obtain:

m₀=initial mass=1500 grams, r = 13% and n =12 days

⇒m = m₀ x \((1 - \frac{r}{100} )^{n}\)

⇒m =1500×\((1-\frac{13}{100}) ^{12}\)

⇒m=424.7 grams.

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Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Answer:bb

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

-45 + 30 gives you -15. When subtractinf a negative number, it actually turning into addition/positive. This changes it into -15 + 60, which is 45.

Answer: 45

Step-by-step explanation:

-45+30-(-60)=
First, times the negative 60 with the negative outside the parenthesis.

-45+30+60

60+30=90

90-45=45

Answer: 45

The required value of  θ  for the trigonometric function cos(θ)=sin(θ/3-10) is 60°.

The  basic Trigonometric functions are sine, cosine, tangent, secant, cosecant and cotangent.

The given equation is,

cos(θ)=sin(θ/3-10)          (1)

To find the value of θ,

Change the whole equation into one trigonometric function,

Since, cos(θ)=sin(90-θ)

Substitute this value in equation (1)

sin(90-θ)=sin(θ/3-10)

⇒90-θ=θ/3-10

⇒4θ/3=80

⇒θ=60

The value of θ is 60°.

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The x- and y-coordinates of AJ'K'L' are related to the x- and y-coordinates of AJKL, as x-coordinate of AJ'K'L' = -y-coordinate of AJKL and y-coordinate of AJ'K'L' = x-coordinate of AJKL.

We create the x-axis and y-axis in the coordinate plane. the origin, where the x- and y-axes cross, and the coordinates ( 0,0 ). The horizontal axis represents the x-axis. The vertical axis represents the y-axis. The first and second coordinates are for the horizontal and vertical axes, respectively. On the coordinate plane, coordinates are expressed by ( x ,y ). The x-coordinate stands for the first coordinate.

When a point is rotated 90° clockwise about the origin, its x-coordinate becomes the negative of its original y-coordinate, and its y-coordinate becomes the positive of its original x-coordinate.

So, for point A(x,y), its new coordinates after a 90° clockwise rotation about the origin would be A'(-y,x). Similarly, for point J, K, and L, their new coordinates would be J'(-yj,xj), K'(-yk,xk), and L'(-yl,xl) respectively.

Therefore, the x- and y-coordinates of AJ'K'L' are related to the x- and y-coordinates of AJKL as follows:

x-coordinate of AJ'K'L' = -y-coordinate of AJKL

y-coordinate of AJ'K'L' = x-coordinate of AJKL

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Ans4863

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

b)270

Answer:

4, 118 degrees

Step-by-step explanation:

If two figures are similar, then that means that the ratio of any two corresponding sides in those figures will be equal. For example, the top side of the big parallelogram to the left side of the parallelogram will equal the top side of the small parellolgram to the left side of the small parallelogram. We know that the top side of the large parallelogram is 15 units, the left side of the large parallelogram is 10 units, and the top side of the small parallelogram is 6 units. Now, we can setup a proportion, where PS is the left side of the small parallelogram.

\(\frac{15}{10}=\frac{6}{PS}\)

Cross-multiplying, we have \(15\cdot PS=60\). Dividing by 15, we have \(PS=4\), so the answer to the first dropdown is 4. Now, in similar figures, the angles to similar triangles are congruent, because the value of the side lengths dont affect the angles as long as they are in the same ratio. That means, that the angle we are looking for, angle QRS is congruent to the same angle it corresponds to in the big parallelogram, which is angle BCD. If BCD is 118 degrees, then that means the angle QRS is also 118 degrees.

The length of PS is 4, and the angle QRS  is 118 degrees.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

If two figures are similar, then that means that the ratio of any two corresponding sides in those figures will be equal. For example, the top side of the big parallelogram to the left side of the parallelogram will equal the top side of the small parallelogram to the left side of the small parallelogram.

We know that the top side of the large parallelogram is 15 units, the left side of the large parallelogram is 10 units, and the top side of the small parallelogram is 6 units. Now, we can set up a proportion, where PS is the left side of the small parallelogram.

15 / 10 = 6 / PS

Ps = 60 / 15 = 4

Cross-multiplying, we have. Dividing by 15, we have, the answer to the first dropdown is 4. Now, in similar figures, the angles to similar triangles are congruent, because the value of the side lengths doesn't affect the angles as long as they are in the same ratio.

That means, that the angle we are looking for, angle QRS is congruent to the same angle it corresponds to in the big parallelogram, which is angle BCD. If BCD is 118 degrees, then that means the angle QRS is also 118 degrees.

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Answer:

A)     (0, -1)

Step-by-step explanation:

A relative maximum point is a point where the function changes direction from increasing to decreasing (making that point a "peak" in the graph)

(0, -1)