the diagram shows a right angled triangle

The equations of the circles in standard form, obtained from the coordinates of the center and the points on the circle are;

5) (x + 16)² + (y + 16)² = 3²

6) (x - 15)² + (y + 7)² = 8

7) (x + 6)² + (y + 2)² = 6²

8) (x + 9)² + (y + 3)² = 89

The standard form of the equation of a circle is; (x - h)² + (y - h)² = r²

Where;

(h, k) = The coordinates of the center of the circle

5) The center of the circle is (-16, -16)

The coordinates of a point on the circle is (-13, -16)

Therefore; r² = (-13 - (-16))² = 3²

The equation of the circle in standard form is therefore;

(x - (-16))² + (y - (-16))² = 3²

(x + 16)² + (y + 16)² = 3²

6) The coordinates of the center of the circle = (15, -7)

The coordinate of a point on the circle = (17, -5)

r² = (17 - 15)² + (-5 - (-7))² = 8

The equation is; (x - 15)² + (x - (-7))² = 8

(x - 15)² + (x + 7)² = 8

7) The coordinates of the center = (-6, -2)

The coordinate of a point on the circle = (-12, -2)

The square of the radius is therefore; r² = (-6 - (-12))² = 6²

(x - (-6))² + (y - (-2))² = 6²

(x + 6)² + (y + 2)² = 6²

8) The coordinates of the center is; (-9, -3)

The point on the circle is; (-1, -8)

The square of the radius is; r² = (-1 - (-9))² + (-8 - (-3))² = 89

The equation of the circle is therefore; (x - (-9))² + (y - (-3))² = 89

(x + 9)² + (y + 3)² = 89

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We can see here that x will be = 123.4°.

A polygon is actually known to be a two-dimensional geometric shape. It is a shape that is known to be defined by a closed path. It consists of finite sequence of straight line segments.

The segments are actually known as sides or edges and which are connected at vertices or corners.

Looking at the shape, we see that the regular pentagon and heptagon are joined together on one side.

Thus, exterior angle of a regular pentagon (5 sides) = 360°/5 = 72°.

The exterior angle of a regular heptagon (7 sides) = 360°/7 = 51.4°

Thus, x° = 72° + 51.4° = 123.4°

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Answer:  D

Step-by-step explanation:

Point of tangency is where the line on the left touches the circle.  Have you ever heard the term "She's going off on a tangent"- it means they only touch the topic(tangent point and go off (tangent line) and talk way off away from where you need to be(circle)

So you can see from the graph the point of tangency (where line touches circle is (-5,0)

the equation for the line is going to be a constant.  The line only touches the x-axis never the y-axis at all points it is x=-5

so the equation of the line x= -5

The problem has no real number solutions since the discriminant is equal to -16.

Given the quadratic equation below:

-1 = 5x² -2x,

On rearranging the equation will becomes;

5x² -2x+1 = 0

The formula for calculating the discriminant is expressed as:

D = b^2 - 4ac where:

a = 5

b = -2

c = 1

Substitute to have:

D = (-2)^2 - 4(5)(1)
D = 4 - 20
D = -16

The discriminant is equal to -16, which means the equation has no real number solutions.

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Answer:

y = (x - [tex]\frac{7}{2}[/tex])² - [tex]\frac{21}{4}[/tex]

Step-by-step explanation:

y = x² −7x + 7

Complete the square for y = x² −7x + 7

(x - [tex]\frac{7}{2}[/tex])² - [tex]\frac{21}{4}[/tex]

Set y equal to the new right side.

y = (x - [tex]\frac{7}{2}[/tex])² - [tex]\frac{21}{4}[/tex]

So, the answer is y = (x - [tex]\frac{7}{2}[/tex])² - [tex]\frac{21}{4}[/tex]

The distance along the trail from X to Y, to the nearest tenth of a meter, is 600 meters.

The distance between X and Y is on a straight path from X to Y or Y to X. This means that the distance between X and Y can be found by finding the distance between the contour lines.

The distance between the contour lines is:

= Elevation of Y - Elevation of X

= 1, 900 - 1, 300

= 600 meters

In conclusion, the distance along the trail between X and Y is 600 meters.

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Given:

[tex]\sf y = 4x + 5[/tex]

Switch x and y.

[tex]\sf x = 4y + 5[/tex]

Solve for y.

[tex]\sf 4y = x - 5[/tex]

[tex]\sf y = \dfrac{1}{4} \ x-\dfrac{5}{4}[/tex]

[tex]\Rightarrow\boxed{\sf y = \dfrac{1}{4} \ x-\dfrac{5}{4}}[/tex]

The image of △FGH after the similarity transformation is △F"G"H", with vertices F"(-2, 2), G"(-2, 6), and H"(2, 6).

To perform the similarity transformation, we first apply the translation by subtracting 3 from the x-coordinates and subtracting 1 from the y-coordinates:

F' = (2-3, 2-1) = (-1, 1)

G' = (2-3, 4-1) = (-1, 3)

H' = (4-3, 4-1) = (1, 3)

Next, we apply the dilation with a scale factor of 2 by multiplying each coordinate by 2:

F" = 2(-1, 1) = (-2, 2)

G" = 2(-1, 3) = (-2, 6)

H" = 2(1, 3) = (2, 6)

So the image of △FGH after the similarity transformation is △F"G"H", with vertices F"(-2, 2), G"(-2, 6), and H"(2, 6).

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In the given rectangle,

The value of x is 3

The value of NP is 18

From the question, we are to determine the value of x in the given diagram.

The diagram shows a rectangle with its diagonals.

Since the diagonals of a rectangle bisect each other, we can write that

2x + 3 = 12 - x

Solve the equation for x

2x + 3 = 12 - x

Add x to both sides of the equation

2x + x + 3 = 12 - x + x

3x + 3 = 12

Subtract 3 from both sides of the equation

3x + 3 - 3 = 12 - 3

3x = 9

Divide both sides of the equation of by 3

3x / 3 = 9 / 3

x = 3

Thus,

The value of x is 3

To determine the value of NP

NP = 2(12 - x)

Substitute the value of x

NP = 2(12 - 3)

NP = 2(9)

NP = 18

Hence, the value of NP is 18

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The length of the line segment AB = 16 units

Given data ,

Let the length of the line segment AB = 2x - 4

Let the length of the line segment BC = 3x + 2

Now , AC = 48 units

So , AC = AB + BC

On simplifying the equation , we get

2x - 4 + 3x + 2 = 48

5x - 2 = 48

Adding 2 on both sides , we get

5x = 50

Divide by 5 on both sides , we get

x = 10 units

So , the length of AB = 2 ( 10 ) - 4

AB = 16 units

Hence , the length is AB = 16 units

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By using the graph of y = f(x), the graph of the function g(x) = f(x + 3) include the following: D. graph D.

In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image.

In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

In order to write an equation that models the graph of g(x), we would have to apply a horizontal translation to f(x) by 3 units left:

y = f(x)

g(x) = f(x + 3)

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The measure of the obtuse angle with vertex P is 30 degrees.

We have,

If there is an acute angle with vertex Q measuring 60 degrees, then there must be a corresponding obtuse angle with vertex P that shares the same side as angle Q.

Let's call the measure of this obtuse angle x.

By the angle sum property of triangles, the sum of the measures of the three angles in any triangle is always 180 degrees.

Therefore, we can write the equation:

60 degrees + 90 degrees + x = 180 degrees

Simplifying this equation, we get:

x = 180 degrees - 60 degrees - 90 degrees = 30 degrees

Therefore,

The measure of the obtuse angle with vertex P is 30 degrees.

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0,0,0,0,0,

The number that take (a) both PE is 6 girls (b) Gymnastic but not acrobat is 7 girls (c)  At least one PE is 18 girls

How to determine the numbers?

Recall that Set theory is a branch of mathematical logic that studies sets, which can be informally described as collections of objects.

From the given parameters,

(a)  The number that play both PE is given as

13 - x + x + 17 - x + 1 = 25

Solving the equation to get the value of x

13+17-x = 25

⇒ 31 -x =25

Collecting like terms we have

-x = 25 - 31

- x = -6

Dividing by a minus we have

x = 6

This means that 5 girls play both PE

(b)  Number that play gymnastic but not acrobat is given as

Gymnastic only that is

13 - x

13 - 6 = 7 girls

(c)  Number that play at least one game is calculated thus:

n(G) ∪ n(A)

That is (13 - x )  + (17 - x)

= 13-6 + 17 -6

7 + 11 = 18 girls

The surface area of the cylindrical pottery is S = 163 inches²

Given data ,

Let the surface area of the cylindrical pottery be S

Now , the radius of the pottery r = d/2

r = 4.3 / 2

r = 2.15 inches

And , the height of the cylindrical vase = 11 inches

where S = B + Ph

On simplifying , we get

S = πr² + 2πr ( h )

S = ( 3.14 ) ( 2.15 )² + 2 ( 3.14 ) ( 2.15 ) ( 11 )

S = 14.51465 + 2 ( 74.261 )

S = 163.03665 inches²

Hence , the surface area is S = 163 inches²

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Answer: y = 2x + 2

Step-by-step explanation: First, you find slope between the points with point slope form. (8-(-6))/(3-(-4) = 2.

2 is the slope.

Now we have y = 2x + b.

To find b, we pick a coordinate and insert the values.

8 = 2(3) + b

8 = 6 + b

8 - 6 = b

b = 2

Put it together, you have y = 2x + 2

Answer:

Step-by-step explanation:

Answer:

To find 40% of a number, you can multiply the number by 0.4 or divide it by 2.5.

Using this method, we get:

40% of 100 is 40 (100 x 0.4 or 100 ÷ 2.5)

40% of 110 is 44 (110 x 0.4 or 110 ÷ 2.5)

40% of 140 is 56 (140 x 0.4 or 140 ÷ 2.5)

40% of 120 is 48 (120 x 0.4 or 120 ÷ 2.5)

Therefore, 40% of 100 is 40, 40% of 110 is 44, 40% of 140 is 56, and 40% of 120 is 48.

Answer:

x = 5

y = 5√2

Step-by-step explanation:

In a 45-45-90 degree right triangle, the two legs form the right angle, and the hypotenuse is opposite the right angle.

The side lengths of a 45-45-90 right triangle are in the ratio

1 : 1 : √2

The legs are congruent, so if one leg has length 5, the other leg also has length 5.

The hypotenuse is √2 times the length of the legs.

x = 5

y = 5√2

The 90% confidence that the proportion of yellow peas is between 23.5% and 29.5%

and, 25% estimate falls within the 90% confidence limits.

We have,

Green peas= 445

Yellow peas= 161

So, Total peas:

= 445 + 161

= 606.

Now, the Proportion of yellow

= 161/606

= 0.265676

= 26.56%

Now, p= 0. 265 and q= 1-0.265= 0.735

So, np = 606 (0.265)= 160.59

nq = 606(0.735) = 445.41

As, both results are ≥ 5 and the sample can be approximated by a normal distribution.

For 90% confidence, z = 1.645.

Now, the margin error

= 1.645 √ (0.265)(0.735) / 606

= 1.645 / 0.0179

= 0.0294

Now, The confidence limits are the point estimate ± the margin of error. =

= 0.265 + 0.03

= 0.295

= 29.5%;

or, 0.265 - 0.030

= 0.235

= 23.5%

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A reflection transformation on a coordinate plane changes the figure over a line called the line of reflection. This line acts as a reflect and the picture created by the change could be a reflect picture of the first figure.

b. In case a figure is reflected over the x-axis, the x-coordinates of all the focuses within the figure will stay the same, but the y-coordinates will be increased by -1. So, in the event that a point on the initial figure has arranges (x,y), its picture after reflecting over the x-axis will have arranges (x,-y).

c. In case a figure is reflected over the y-axis, the y-coordinates of all the points within the figure will remain the same, but the x-coordinates will be copy by -1. So, in case a point on the first figure has push (x,y), its image   after reflecting over the y-axis will have arranges (-x,y).

Therefore, d. To reflect a triangle over the y-axis, we need to know the  the mirror image  of each point with regard to the y-axis. One way to do usually to increase the x-coordinate of each point by -1 and also keeping the y-coordinate the same.

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See text below

2. Reflections:

Transformations Review

a. How would you describe what this transformation looks like when performed on a coordinate plane?

b. If your figure was reflected across the x-axis, how would that affect the figure's coordinates?

c. If your figure was reflected across the y-axis, how would that affect the figure's coordinates?

d. On the coordinate plane: First, plot a triangle. Then, reflect your triangle over the y-axis and draw the result:

The simplified expression is  [tex]7 x^{3} - 14 x^{2} + 28 x - 55+\frac{124}{x + 2}[/tex]. The correct answer is an option (C).

The expression is given as follows:

[tex]\dfrac{7 x^{4} + x + 14}{x + 2}[/tex]

We can use polynomial long division to simplify the expression:

         7x² - 14x² + 28x - 55

        ______________________

x + 2 ) 7x⁴ + 0x³ + 0x² + x + 14

          7x⁴ + 14x³

       ___________

               -14x³ + 0x²

               -14x³ - 28x²

               ____________

                        28x² + x

                        28x² + 56x

                        __________

                               -55x + 14

                               -55x - 110

                               ________

                                       124

[tex]\dfrac{7 x^{4} + x + 14}{x + 2}=7 x^{3} - 14 x^{2} + 28 x - 55+\dfrac{124}{x + 2}[/tex]

Hence, the simplified expression is as follows:

[tex]7 x^{3} - 14 x^{2} + 28 x - 55+\dfrac{124}{x + 2}[/tex]

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The population of Kentucky is nearly 5.9 times that of North Dakota.

To determine how many times larger Kentucky's population is than North Dakota's population, divide Kentucky's population by North Dakota's population:

4.47 x 10^6 / 7.62 x 10^5

We can simplify the fraction by dividing both the numerator and denominator by 7.62 x 10: 4.47 x 106 / 7.62 x 105 = 5.87

5.9, rounded to the closest tenth.

As a result, the population of Kentucky is nearly 5.9 times that of North Dakota.

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The area of the rhombus is 33 square unit.

We have,

x = 6 units, y = 3 units, and h = 5 units.

Now, area of Triangle

= 2 x 1/2 x b x h

= 2 x 1/2 x 6 x 3

= 18 square unit

and, area of Rectangle

= l w

= 5 x 3

= 15 square unit

Thus, the Area of Rhombus

= 18 + 15

= 33 square unit

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Check the picture below.

The length of each rope if all the ropes had the same length is 3 ft

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

The dot plot

From the dot plot, we can see that the data are normally distributed

This means that the length of each rope is the mean, the median and the mode

Given that the data on the dot plot is normally distributed, we have the following values

So, we can conclude that the length is 3 ft

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The total number of meals received by the company this month = 40 meals

Given data ,

Let the number of meals received by the company this month be A

Now , the proportion is given as

The number of boxes of meals in the past month = 3 boxes

The number of meals in 3 boxes = 15 meals

The number of boxes in the present month = 8 boxes

So , the proportion is

15 / 3  = A / 8

Multiply by 8 on both sides , we get

A = 5 x 8

A = 40 meals

Hence , the number of meals is A = 40 meals

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Answer:

  $2080

Step-by-step explanation:

You want to know the annual cost of coffee purchased 5 mornings and 3 afternoons per week when each purchase amounts to $5.

Five morning visits and three afternoon visits to the coffee shop will be a total of 8 visits per week. At $5 each, the cost per week is ...

  8 × $5 = $40

The cost for a year will be the cost for 52 weeks:

  52 × $40 = $2080

Carla spends $2080 per year on coffee.

Whether this is a "little indulgence" or not will depend on Carla's budget.

A function which has the greater maximum value is: function f(x).

In Mathematically, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:

Axis of symmetry (vertex), Xmax = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = -x² - 3x + 1, we have:

Axis of symmetry, Xmax = -(-3)/2(-1)

Axis of symmetry, Xmax = 3/-2 = -1.5.

For the value of k in vertex, we have:

f(x) = -x² - 3x + 1

f(-1.5) = -(1.5)² - 3(-1.5) + 1

f(-1.5) = 3.25

For g(x), the maximum value or vertex is 2 and as such, quadratic function f(x) has the greater maximum value.

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The amounts of people in attendance are given as follows:

The amounts are obtained by a system of equations, for which the variables are given as follows:

There were 400 people total, hence:

x + y + z = 400.

There were twice as many parents as grandparents, hence:

y = 2z.

50 more children than parents, hence:

x = y + 50

x = 2z + 50.

Replacing on the first equation, the value of z is obtained as follows:

2z + 50 + 2z + z = 400

5z = 350

z = 70.

Then the values of x and y are given as follows:

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