2. AB is tangent to •O at A (not drawn to scale). Find the length of the radius r, to the nearest tenth. (The length from the edge of the circle to B is 4.)

The length of the base of the rectangle is B = 11 yards

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be represented as A

Now , the value of A is

Let the base of the rectangle be represented as B

Area of rectangle A = 209 yards²

The length of the rectangle L = 19 yards

And , Area of Rectangle = Length x Width

Substituting the values in the equation , we get

Area of Rectangle = 19 x B

209 = 19 B

Divide by 19 on both sides of the equation , we get

B = 209 / 19

B = 11 yards

Hence , the length of the base of rectangle is 11 yards

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It is called an isosceles right angle triangle.

In a right angle triangle there is one right angle present.

In an isosceles triangle two sides are equal to each other.

But in isosceles right angle triangle both the conditions got fullfield i.e., there is one right angle with other two sides are equal to each other.

Properties of isosceles right angle triangle:

1. The two sides are equal to each other i.e. the base of the triangle is equal to the perpendicular of the triangle.

2. There is only one right angle and other two angles must be equal to each other.

3. The other two angles in isosceles right angle triangle must be 45 degree each.

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A square yard of carpet that is selling for $8.95 per square foot would cost $80.55 per square yard.

What is the conversion factor?

A conversion factor is a number used to change one set of units to another, by multiplying or dividing. When a conversion is necessary, the appropriate conversion factor to an equal value must be used. For example, to convert inches to feet, the appropriate conversion value is 12 inches equals 1 foot.

A square yard of carpet is equivalent to 9 square feet because 1 yard = 3 feet and 1 square foot = 1 foot x 1 foot.

So, to find the cost of a square yard of carpet that is selling for $8.95 per square foot, we need to multiply the price per square foot by the conversion factor of 9 square feet per square yard.

$8.95/square foot * 9 square feet/square yard = $80.55/square yard

Hence, a square yard of carpet that is selling for $8.95 per square foot would cost $80.55 per square yard.

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Answer:30:1

Step-by-step explanation:

60÷2

=30/1

=30:1

The triangle with sides 56 , 55 and 43 is acute triangle

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ABC

Now , the base of the triangle is BC

The measure of BC = 43

The height of the triangle is AB

The measure of AB = 55

The hypotenuse of the triangle is AC

The measure of AC = 56

Now , if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

On simplifying the equation , we get

BC² + AB² > AC²

Substituting the values in the equation , we get

43² + 55² > 56²

1849 + 3025 > 3136

4874 > 3136

Hence , it is an acute triangle

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Answer:

2 apples

Step-by-step explanation:

It is because she had 1 apple then she added another which made it 2.

Examples of the rules followed while applying multiplication are :

1. 0 × 9 = 0

2. 1 × 7 = 7

3. 12 × 10 = 120 , 12 × 100 = 1200.

4. 11 ×12 = 12 ×11

As given in the question,

Examples of the multiplication rules are :

1. Multiply any number by zero result is zero.

Example : 0 × 9 = 0

2. Multiply  One  to any real number result is the number itself.

Example : 1 × 7 = 7

3. Multiply any real numbers with 10 , 100 you have just add number of zero present.

Example : 12× 10 =120

12× 100 =1200

4.Order of the multiplication does not affect the result.

Example : 11 × 12 = 12 × 11

Therefore, the examples of multiplication rule  are :

1. 0 × 9 = 0

2. 1 × 7 = 7

3. 12 × 10 = 120 , 12 × 100 = 1200.

4. 11 ×12 = 12 ×11

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Answer:

Below

Step-by-step explanation:

The point-slope form of a line is:

y - y1 = m(x - x1)

Where m is the slope of the line and (x1, y1) is a point on the line.

Given that the line contains the point (-2, 1) we know that this point is on the line, so we can use it as (x1, y1) in the point-slope form.

By using the point (-2,1) we can write the point-slope form of the line as:

y - 1 = m(x + 2)

This means that the point-slope form of a line with slope that contains the point (-2, 1) is y - 1 = m(x + 2) where m is the slope of the line.

The general form for the absolute value equation to describe a graph is written as f(x) = a|x - h| + k  .

The Absolute Value Function is defined as a function in algebra where the variable is inside the absolute value bars.

The general form for absolute value function is f(x) = a |x - h| + k and  commonly used form of this function is f(x) = |x| .

Plot the graph of  function f(x) = |x| whose formula can also be expressed as f(x) = x, if x ≥ 0 and -x, if x < 0.

Consider different points for x = -1 , y is 1 ,

for x = 1 , y is 1 .

On plotting we get the graph as shown below .

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Answer:

x = -3, -1, 1, 3.

Step-by-step explanation:

x^4 - 10x^2 + 9 = 0

Step 1

Let t = x^2

So , we have the quadratic

t^2 - 10t + 9 = 0

Step 2

Factorise:

(t - 1)(t - 9) = 0

Step 3

So, t - 1 = 0 or t - 9 = 0

t = 1, 9.

But t = x^2

So, we have x^2 = 1 or x^2 = 9

So, x = ±1, ±3.

x = -3, -1, 1, 3.

The point that is equally spaced from a triangle's three vertices is known as the circumcenter.Triangle ABC's equilateral circumcenter is (-5, 2) .

The point that is equally spaced from a triangle's three vertices is known as the circumcenter.

The triangle's three vertices are all located at the center of the circle.We may insert the coordinate values for the triangle ABC's vertices A(-5,3), B(5,8), and C(-5.8) into the formulas above to determine its circumcenter.

x = (8 - 3) * (-5.8^2 + 3^2 - 5^2 - 8^2)

- (3 - 8) * (-5^2 + 3^

2 - (-5) (-5)

^2 -3^2) / 2 * (3 - (-5))

* (8 - 3) - (3 - 8) * (-5.8 - (-5))

x = (-5) (-5)

y = (3 - (-5.8))

* (-5^2 + 3^2 - (-5)^2 -3^2)

- (-5 - (-5))

* (3^2 + 3^2 - (-5.8) (-5.8)

^2 - 8^2)

/ 2 * (3 - 8) (3 - 8)

* (-5 - (-5))

- (3 - 8) * (3 - (-5.8))

y = 2

The circumcenter of triangle ABC is hence (-5, 2)

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The value of exponential growth  after 327 minutes is 1870.

Exponential growth is the process by which quantity increases over time. It occurs when a quantity's instantaneous rate of change with respect to time is proportional to the quantity itself.

An exponential function depicts the relationship between an input and an output by using repeated multiplication on an initial value to obtain the output for any given input.

We are aware that

The exponential growth equation is equal to

y = a(1 + r)ˣ

where

an is the starting point.

r denotes the growth rate.

x represents the time in hours.

y is the quantity's value.

We now have

a = 1800

r = 0.7%

 = 0.7/100

 = 0.007

By substituting,

y = 1800(1 + 0.007)ˣ

x = 5.45 hr

y = 1800(1.007)^5.45

y = 1869.748182

y = 1870

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The law of Sines is used to find the length of the third side of an obtuse triangle. The value of a i.e., third side length is equals to 6.065 units.

In geometry, obtuse triangles are defined as the triangles with an obtuse angle, which is an angle measuring greater than 90°. According to the law of sines of triangles if a triangle has sides a, b, and c, and angles A, B, and C, where side a has opposite angle A, side b has opposite angle B, and c has opposite angle C, then

sinA/a = sinB/b = sinC/c

The sum of all interior angles of a triangle is 180°. If we have two of the sides of an obtuse triangle, and two of the angles of an obtuse triangle, then we can use the law of sines to determine the third side of the obtuse triangle. Let's consider an obtuse triangle ABC present in above figure. We want to find the length of side a. We have, AB = 8 units , AC = 5 units, BC = a units.

∠A = 32° , ∠B =40° , ∠C = obtuse angle

=>∠C = 180°-∠A - ∠B = 180°- 32°- 40° = 108°

From above formula, sinA/a = sinB/b= sinC/c

=> sin 32°/5 = sin 40°/a = sin 108°/8

=> a = 5 sin 40°/ sin 32°

=> a = 5×0.6428/0.5299

=> a = 6.06529533874

=> a ≈ 6.065

Therefore, the length of third side is 6.065 units.

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Answer:

No

Step-by-step explanation:

Notice when x increases by 1, y increases by $6?

When x goes from 1.5 to 2.5 gigabytes ( increase by 1 ), y increases from $65 to $71. That's a $6 increase for x increasing by 1 gigabyte.

In addition, when x goes from 2.5 to 3.5 gigabytes ( increase by 1), y increases from $71 to $77. This is also a $6 increase for x increasing by 1 gigabyte.

Yet...

65 / 1.5 doesn't equal 71 / 2.5

65 / 1.5 = 43 1/3

71 / 2.5 = 28.4

43 1/3 [tex]\neq[/tex] 28.4, so there is no proportion

Answer: No.

Step-by-step explanation:

      In a proportion relationship, y = kx. In other words, x times the constant of proportionality will equal y. Without a given constant of proportionality, we can use k =[tex]\frac{y}{x}[/tex]. In all instances, y divided by x should equal the same value (k). We will see if this stands true for all the given values.

      65 / 1.5 = 43.33333

      71 / 2.5 = 28.4

      74 / 3 = 24.66667

      77 / 3.5 = 22

      No. The x and y values do not have a proportional relationship.

The sum of the roots of the equation is

97/9

Generally, The roots of equation 3x^2 + 4x + 12 = 0 can be found by factoring or by using the quadratic formula.

By factoring: 3x^2 + 4x + 12 = 0 \Rightarrow (3x + 4)(x + 3) = 0$

Thus, the roots are

r = [tex]-\frac{4}{3}[/tex][tex]-\frac{4}{3}[/tex]

s = -3.

By using the quadratic formula:

[tex]r,s = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\ = \frac{-4 \pm \sqrt{4^2 - 4(3)(12)}}{2(3)} \\\\= \frac{-4 \pm \sqrt{-48}}{6}\\\\ = -\frac{2}{3} \pm \frac{\sqrt{-3}}{3}i[/tex]

The sum of squares of roots is

r^2+s^2 =[tex](-\frac{4}{3})^2 + (-3)^2[/tex]

[tex]= \frac{16}{9} + 9\\\\ = \frac{16+81}{9}[/tex]

= [tex]\boxed{\frac{97}{9}}[/tex]

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Y form is the slope-intercept form of a straight line.

Here, x and y are the coordinates of the points, m is the gradient, and b is the intercept of the y-axis.

y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept.

The value of b is equal to y when x = 0, and m shows how steep the line is. The slope of the line is also called the gradient.

To find the equation of the straight line, we use the slope-intercept form, y = mx + b, where m is the slope of the line, b is the y-intercept of the line.

We can find the equation of a line in the form of y = mx + b, if the coordinates of points forming the line are known to us.

Thus, Y form is the slope-intercept form of a straight line.

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Answer:

26 skittles are not red

Explenation:

35%of 40 is 14 because 40*0.35=14 red skittles

total number of skittles (40)-red skittles (14)=26

Answer:

26 skittles are not red

Step-by-step explanation:

Simplify the percentage.

35% = 35/100 = 0.35

Multiply 40 by 0.35.

40 x 0.35 = 14 (This is how many skittles are red.)

Now subtract the red skittles from the packet.

40 - 14 = 26

Hence, there are 26 skittles that are not red, and 14 skittles that are red.

Yes, the square root of 64 is a rational number.

and Square root of 64 is 8

Now, According to the question:

Square numbers are those numbers that are produced by multiplying an integer to itself. If n is an integer, then n2 is the square of n.

What are the examples of square numbers?

The examples for square numbers are:

[tex]6^2[/tex] = 36

[tex]10^2[/tex] = 10 x 10 = 100

[tex]15^2[/tex] = 15 x 15 = 225

[tex]12^2[/tex] = 12 x 12 = 144

Hence, Yes, the square root of 64 is a rational number. As we know that √64 = 8, a rational number.

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The set of values that satisfy a given set of equations or inequalities is known as a solution set in mathematics.

The solution set, for instance, is the subset of a set of polynomials over a ring on which all of the polynomials formal disappear (evaluate to 0).

Plug in each value from the replacement set and evaluate both sides of the equation to determine the solution set from the replacement set. The value is a solution to the equation if the two sides are equal. One example: From the replacement set, choose the set with the solution 11 - 5w = 1.

The set of values that satisfy a given inequality is called a solution set. This indicates that the inequality will be satisfied by every value in the solution set and by no other value. Example: 2x + 3  7, where x is a natural number, is the solution.

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Sum in math the sum of the series is computed using the summation formulas.

The sum of the series is computed using the summation formulas. There are many different kinds of sequences, including arithmetic and geometric sequences, and consequently, there are many different kinds of summing formulas for those different kinds of sequences.

There are also summation formulas that determine the sum of natural numbers, sum of natural number squares, sum of natural number cubes, sum of natural number evens, sum of natural number odds, etc. The list of summation formulas is provided here. Each of these formulas will be covered in detail in the section that follows.

a₁ + a₂ + a₃ +.......aₙ = Σ a

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30-60-90 and 45-45-90 triangles are called special right triangles because they have specific ratios of their side lengths.

A 30-60-90 triangle is a special right triangle in which the angles measure 30 degrees, 60 degrees and 90 degrees, and the side length ratio is 1: √3: 2.

where the hypotenuse is twice the length . 45-45-90 triangle is a special right triangle in which the angles measure 45 degrees, 45 degrees and 90 degrees, and the side length ratio is 1:1: √2, where the hypotenuse is the square root of 2 times the length of each leg.

These ratios are unique and special among right triangles, which makes these triangles special. They are also easy to remember and use in various mathematical calculations. Because of this property, they are widely used in trigonometry and geometry and are very useful in solving problems related to the right triangles in general.

Additionally, these triangles have certain symmetry and specific relationships between the legs and hypotenuse, which makes it easy to calculate unknown sides or angles in a triangle. This makes them very useful in real-world applications such as construction, engineering, and design.

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Yes, I would like to purchase a ticket for the movie. The discounted sale price would be $8.37 after factoring in the 20percentage student discount and the 5.75% tax rate.

Original Price: $10.90

Student Discount: 20% of 10.90 = 2.18

Subtotal: 10.90 - 2.18 = 8.72

Tax Rate: 5.75% of 8.72 = 0.50

Final Sale Price: 8.72 + 0.50 = 8.37

Yes, I would like to purchase a ticket for the movie. The original price of the ticket is $10.90. As a student, I am eligible for a 20% discount, which when applied to the original price brings it down to $8.72. To calculate the final sale price, I then need to factor in the 5.75% tax rate. This is done by multiplying the subtotal of $8.72 by 0.0575, which gives me a tax amount of $0.50. When this amount is added to the subtotal, the final sale price becomes $8.37.

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Answer:

11,000 or to be more specific $11,000

Step-by-step explanation:

Well there is no equation provided so one has to go by the graph

The y-intercept is where the line intersects the y-axis

Looking at the graph we see this is at y ≅ 11,000

Of course it all depends on your best fit line that you have drawn though it looks OK

Basically the y-intercept for this graph is $11,000 which is the cost of the Prius in 2004

In mathematics, particularly in algebra, there are mainly two types of solutions for an equation: real and complex solutions.

Real solutions: These are type of solutions that are real numbers, which can be found by solving the equation algebraically. For example, if the equation is x² + 2x - 3 = 0, the real solutions are x = -1 and x = 3.

Complex solutions: These are solutions that are complex numbers, which can be found by solving the equation algebraically. Complex numbers are numbers that have both real and imaginary parts, represented by a + bi, where a and b are real numbers and i is the imaginary unit (i² = -1). For example, if the equation is x² + 1 = 0, the complex solutions are x = i and x = -i.

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To solve complex numbers using steps:

A complicated equation is one that requires the use of complex numbers to solve. A number with both a real element and an imaginary part is referred to as a complex number. It is written as follows: A and B in the previous equation both denote numerical values. A complex number is, as an illustration, <4+3i>.

In order to accomplish vaguely defined goals that cannot be attained through normal behaviors, complex issue solving is a set of self-regulated psychological processes and activities. A wide range of tactics and inventive knowledge combinations are required.

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Answer:

Step-by-step explanation:

Liam went into a movie theater and bought 9 bags of popcorn and 8 drinks costing a total of $97.50. This will be:

9p + 8d = 97.50

Jacob went into the same movie theater and bought 5 bags of popcorn and 4 drinks, costing a total of $51.50. This will be:

5p + 4d = 51.50

where P = popcorn

d = drink

The equations will be:

9p + 8d = 97.50

5p + 4d = 51.50

Multiply equation i by 5

Multiply equation ii by 9

45p + 40d = 487.50

45p + 36d = 463.50

Subtract

4d = 24

Divide.

d = 24/4

d = 6

Since 9p + 8d = 97.50

9p + 8(6) = 97.50

9p + 48 = 97.50

9p = 97.50 - 48

p = $5.50

where P = popcorn and d = drink

The distance between the pair of points (- 5, 7) and (- 1, 3) is 5.7 units.

We know that the distance formula.

The distance between points (x₁, y₁) and (x₂, y₂) is given by,

[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}[/tex]

Here we have been given a pair of points (- 5, 7) and (- 1, 3)

Let us assume that  (x₁, y₁) = (-5, 7)

and (x₂, y₂) = (-1, 3)

Using above distance formula,

[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]} \\\\ d = \sqrt{[(-1 - (-5))^2 + (3 - 7)^2]}\\\\d = \sqrt{[(-1+5)^2 + (-4)^2]}\\\\d = \sqrt{[(4)^2 + (-4)^2]}\\\\d = \sqrt{(16+16)}\\\\d = \sqrt{32}\\\\d = 5.7~ units[/tex]

So, the distance is 5.7 units.

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The complete question is:

What is the distance between the pair of points (- 5, 7) and (- 1, 3)?.

The equation for a line that passes through the points (-5, 3) and (3, -3) is y=-3/4(x+1)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Slope of line that passes through the points (-5, 3) and (3, -3)

m=-3-3/3+5

m=-6/8=-3/4

Now let us find y intercept.

3=-3/4(-5)+b

3=15/4+b

b=3-15/4

b=-3/4

So the slope intercept form is y=-3/4x-3/4

Hence, the equation for a line that passes through the points (-5, 3) and (3, -3) is y=-3/4(x+1)

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The other equation of the system of linear equation that has no solution is y = 2x - 2.

If a system of linear equations has no solution, it means that the equations are inconsistent, which means that the two lines represented by the equations will not intersect. Therefore, the lines are parallel with each other.

One way to find the equation of the other line that would make the system inconsistent is to find the equation of a line that is parallel to the given equation but has a different y-intercept.

The given equation is in slope-intercept form, y = mx + b, where m is the slope (in this case, m = 2) and b is the y-intercept (in this case, b = -1).

A line that is parallel to the given line will have the same slope (m = 2), but a different y-intercept. For example, a line with y-intercept of -2: y = 2x - 2.

So, one equation that could be the other equation of the system and make it inconsistent is y = 2x - 2.

The problem seems incomplete, it must have been...

"A system of linear equation has no solution. One of the equations of the system is shown. y = 2x − 1 Which equation could be the other equation of the system?"

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5([tex]x^{2}[/tex] + 10/2[tex]x[/tex]) + 2

The number in the brackets is b/2a.

So:

5(x + 10/2(5))^2

5(x + 10/10)^2

5(x + 1)^2

Expand the double brackets for (x + 1)^2:

[tex]x^{2}[/tex] + [tex]x[/tex] + [tex]x[/tex] + 1

This simplifies to:

[tex]x^2[/tex] + 2[tex]x[/tex] + 1

5([tex]x^2[/tex] + 2[tex]x[/tex] + 1)

5x^2 + 10x + 5

2 - 5 = -3

5(x + 1)^2 - 3

Answer:

5(x + 1)^2 - 3