Which of the following is an infinite set?
A)The Set of numbers between 4 and 5
B){1,2,3,…………..1000}
C)The Set of positive integers less than 100
D)None of these

On solving the provided question we cans ay that -  equation of ellipse is given by (x2/a2) + (y2/b2) = 1.

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

distance of the focus from the centre of the ellipse is given by the equation c = √(a2 – b2).

equation of ellipse is given by (x2/a2) + (y2/b2) = 1.

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Answer:

D.

Hope this helps!

Step-by-step explanation:

A and C are both squares and B is a rectangle but is different because the values are in different spots than the on the solid figure shown.

Answer:

0.24=0.2 x 1.2

0.24= 0.4 x 0.6

0.24=0.3 x 0.8

The perimeter of rectangle M'N'O'P' is given as follows:

54 cm.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The ratio between the areas is given as follows:

126/14 = 9.

The area is measure in square units, while the perimeter is measured in units, hence the ratio of the perimeters is the square root of the ratio of the areas, that is:

3.

Hence the perimeter of rectangle M'N'O'P' is given as follows:

3 x 18 = 54 cm.

The complete problem is:

Rectangle MNOP has a perimeter of 18 cm and an area of 14 cm2. After rectangle MNOP is dilated, rectangle M'N'O'P' has an area of 126 cm2. What is the perimeter of rectangle M'N'O'P'?

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Answer:

Substitute 6 for the variable, n, using parentheses. Then simplify by multiplying 8 and 6. 8(6) = 48. So you have 56 = 48, which is not a true statement. 6 is not a solution to the equation.

Step-by-step explanation:

Answer:

False.

Step-by-step explanation:

Question: 56 = 8n for n = 6

8 *6 = 56

48 = 56

Answer:

$63.53

Step-by-step explanation:

you start by multiplying 35 and 8.25 to figure out the total amount in the pay check

then you turn the 22 percent into a decimal (.22) and multiply the total by it giving you 63.525 which rounds to 63.53

Answer:

$63.53

Step-by-step explanation:

First, by looking at the problem, we will have to find the amount of Thomas's paycheck that he used for his friend's Birthday Gift.

35 × 8.25 = 288.75 $

Now we know that Thomas got 288.75 for his paycheck.

The problem says he spent 22% on that, we need to find 22% of 288.75

How we can do this is by first converting the percent into a decimal: 0.22, then multiplying it by the whole.

0.22 × 288.75 = 63.525

So now we know that Thomas spent 63.525 on his Freind.

If we round that number, it will be 63.53...

Therefore, $63.53 is the answer.

-kiniwih426

Answer:

\(x =\sqrt{5} ,-\sqrt{5} ,-i,i\)

Step-by-step solution:

\(0=x^4-4x^2-5\)   \(u = x^2\)
\(0 = u^2-4u-5\)
\(0 = (u -5)(u+1)\)
\(u = 5\)  \(u=-1\)
\(x^2 =5\)    \(x^2 = -1\)
\(x= +-\sqrt{5}\)   \(x = +-i\)

9514 1404 393

Answer:

  all real numbers except x = 0

Step-by-step explanation:

The given equation has undefined terms when x=0, so the domain must exclude that value.

The domain of the terms of the equation is "all real numbers except 0."

__

The solution can be found by adding 1/(2x) to both sides and comparing the terms.

  9/4 = 8/(2x) +1/(2x)

  9/4 = 9/(2x)

  4 = 2x . . . . match denominators of the same numerator

  2 = x . . . . . the solution to the equation

Answer:

-7.225 according to a calculator.

The factoring of the quadratic function as a product of two binomials is given as follows:

x² + 10x + 24 = (x + 6)(x + 4).

The quadratic function for this problem is given as follows:

x² + 10x + 24.

To factor the quadratic function as a product of the two binomials, we must obtain it's roots, that is, solve:

x² + 10x + 24 = 0.

The coefficients of the quadratic function are given as follows:

a = 1, b = 10, c = 24.

Hence the discriminant is of:

D = 10² - 4 x 1 x 24 = 4.

The first root of the quadratic function is given as follows:

x = (-10 - square root of (4))/2 = -6.

The second root of the quadratic function is given as follows:

x = (-10 + square root of (4))/2 = -4.

Hence, using the Factor Theorem, the binomial product is given as follows:

x² + 10x + 24 = (x + 6)(x + 4).

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Answer:

At the time the ball was thrown, it was 8 feet above the ground.

h'(x) = -32x + 64 = 0, so x = 2

The ball reaches its maximum height after 2 seconds.

The percentage change in GDP is 2.04%

Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.

The formula of percentage change is given as

Percentage change =[ (New increase - old value) / old value] * 100

Percentage change = [(14.72 - 14.42) / 14.72] * 100

Percentage change = 2.04%

In this case, there is a percentage decrease of 2.04%

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The equation of a line: y = 2x + 5 has a slope of 2 and intercepts the y-axis at the point (0, 5).

The slope indicates that given some point on the line, there is another point located 1 unit to the right and 2 units up. For example, considering the point (0, 5), another point will be (0+1, 5+2) = (1, 7).

Now we have two points of the line, then we have to connect them with a line as follows:

Answer:

A = 22.62°

B = 67.38°

c = 26

Step-by-step explanation:

\(a^2+b^2=c^2\\10^2+24^2=c^2\\100+576=c^2\\676=c^2\\26=c\)

\(\sin A=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{10}{26}\\\\A=\sin^{-1}(\frac{10}{26})\\\\A\approx22.62^\circ\)<-- You can also use other trig ratios

\(B=180^\circ-(90^\circ+22.62^\circ)=180^\circ-112.62^\circ=67.38^\circ\)

There's no specific order in how to solve for A and B, so there may be more than one way to approach these solutions.

Answer:

Step-by-step explanation:

2π radians = 360°

x  radians · 360°/(2π radians) = (180x/π)°

f(x) = 180x/π

The measure of the angle in degrees would be (180x/π)° and the function would be f(x) = 180x/π which determines the degree measure of an angle in terms of the radian measure of the angle x.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

Given that an angle has a measure of x radians,

So the measure of the angle in degrees

Since 2π radians = 360°

Therefore x  radians · 360°/(2π radians)

= (180x/π)°

A function f represents the degree measure of an angle in terms of the radian measure of the angle, x.

⇒ f(x) = 180x/π

Hence, the measure of the angle in degrees would be (180x/π)° and the function would be f(x) = 180x/π which determines the degree measure of an angle in terms of the radian measure of the angle x.

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If m = -5 or m = 3, the system of linear equations has no solution.

To determine the values of m for which the system of linear equations has no solution, we need to check the determinant of the coefficient matrix, which is:

| 3 m |

| m+2 5 |

The determinant is

=  (3 x 5) - (m x (m+2))

= 15 - m^2 - 2m

= -(m^2 + 2m - 15)

= -(m+5)(m-3)

So, for the system to have no solution, the determinant must be zero, so we have:

-(m+5)(m-3) = 0

This gives us two values of m: m = -5 and m = 3.

Thus, if m = -5 or m = 3, the system of linear equations has no solution.

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Answer:

A, C and G

Step-by-step explanation:

\(\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

From inspection of the given right triangle:

Substitute the values into the trigonometric ratios:

\(\implies \sf \sin(25^{\circ})=\dfrac{a}{c}\)

\(\implies \sf \cos(25^{\circ})=\dfrac{b}{c}\)

\(\implies \sf \tan(25^{\circ})=\dfrac{a}{b}\)

\(\boxed{\begin{minipage}{4 cm}\underline{Trigonometric values} \\\\$\sin(90^{\circ}- \theta)=\cos \theta$\\$\cos(90^{\circ}- \theta)=\sin \theta$\\$\tan(90^{\circ}- \theta)=\cot \theta$\\\end{minipage}}\)

Using trigonometric values and the calculated trigonometric ratios:

\(\begin{aligned} \sf \sin(90^{\circ}- 25^{\circ})&=\sf \cos (25^{\circ})\\\implies \sf \sin(65^{\circ}) &=\sf \dfrac{b}{c}\end{aligned}\)

\(\begin{aligned} \sf \cos(90^{\circ}- 25^{\circ})&= \sf \sin(25^{\circ})\\\implies \sf \cos(65^{\circ}) &=\sf \dfrac{a}{c}\end{aligned}\)

\(\begin{aligned}\sf \tan(90^{\circ}- 25^{\circ})&= \sf \cot(25^{\circ})\\\implies \sf \tan(65^{\circ}) &= \sf \dfrac{1}{\tan(25^{\circ})}\\\implies \sf \tan(65^{\circ}) & = \sf \dfrac{b}{a}\end{aligned}\)

Therefore, the true equations are:

\(\sf A: \quad \cos(25^{\circ})=\dfrac{b}{c}\)

\(\sf C: \quad \sin(65^{\circ})=\dfrac{b}{c}\)

\(\sf G: \quad \sin(25^{\circ})=\cos(65^{\circ})\)

The perimeter of the rug is 36ft

Perimeter is the total length around the outside of a shape. The perimeter can be found by adding all the sides of the shape.

Perimeter of a rectangle is expressed as ;

P = 2(l+w)

The area of the rug is 81ft²

area = l× w

length = 9ft

width of the rug = 81/9 = 9ft

Therefore the perimeter of the rug will be

P = 2(l+w)

P= 2( 9+ 9)

P = 2 × 18

P = 36 ft

therefore the perimeter of the rectangular rug is 36ft

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Answer:

Rate of Change / Slope = 1.75 (or 7/4)

Step-by-step explanation:

Slope is Rise/Run which is (y2-y1)/(x2-x1). When we plug in both ordered pairs, we get (19.25-14)/(11-8)=5.25/3=1.75 as the slope.

The rate of change is the ratio of the rise and the run of the line. Hence, the rate of change of the line is 1.75

Rise = y2 - y1 = (19.25 - 14) = 5.25

Run = x2 - x1 = (11 - 8) = 3

Rate of change = (5.25 / 3) = 1.75

Therefore, the rate of change for the line is 1.75

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Answer:

You have 16 different toppings

Step-by-step explanation:

Given

\(Sameer = 12\)

Required

How many topping at your sundae shop

From the question, we understand that Sameer's is3/4 of your toppings

Mathematically, this is:

\(Sameer = \frac{3}{4} * Y\)

Where

Y represents You

Make Y the subject

\(Y = \frac{4}{3} * Sameer\)

Substitute 12 for Sameer

\(Y = \frac{4}{3} * 12\)

\(Y = 4 * 4\)

\(Y = 16\)

The angles <1, <2, and <3 will not add up to 180 degrees. The angles <1 and <2 are alternate interior angles, and the angles <2 and <3 are also alternate interior angles, AB is parallel to CD.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is always equal to 180 degrees. This means that if you measure the angles inside any triangle and add them up, the result will always be 180 degrees. This property holds true for all types of triangles, whether they are equilateral, isosceles, or scalene.

To understand this property, consider a triangle ABC with interior angles angle A, angle B, and angle C. If we draw a line segment from vertex A to a point D on side BC such that it is parallel to the side AB, then we can see that angle A and angle C are alternate interior angles of the parallel lines AB and CD. Similarly, angle B and angle C are alternate interior angles of the parallel lines BC and AD.

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Answ

Step-by-step explanation:wirugf4

The equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

We have to given that,

A number line is shown in image.

Since,

A number lines are the horizontal straight lines in which the integers are placed in equal intervals.

And, All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.

Now, By given number line,

Point C is two point left from point 8.

Hence, The point C is denoted as,

⇒ C = 8.2

⇒ C = 82/10

⇒ C = 8 2/10

Therefore, the equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

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The transformation was a reflection over the x-axis. This is because \(g(x)=-f(x)\).

Answer:

Average of the draws equals 420

Standard Error = 11.88

Step-by-step explanation:

Given

\(\mu = 420\)

\(\sigma = 84\)

\(n =50\)

Solving (a): The average of the draws

This implies that we calculate the sample mean

This is calculated as:

\(\bar x = \mu\)  --- Sample Mean = Population Mean

So, we have:

\(\bar x = 420\)

Solving (b): The standard error

This is calculated as:

\(SE=\frac{\sigma}{\sqrt n}\)

So, we have:

\(SE=\frac{84}{\sqrt {50}}\)

Using the calculator, we have:

\(SE=11.88\)

Answer:

A=82°

a= 67.4

c = 60.1

Step-by-step explanation:

For A

A+B+C =180°

A= 180-(B+C)

A= 180-(36+62)

A= 189-(98)

A= 82°

For a

a/sinA= b/sinB

a/sin82= 40/sin36

a= (40*sin82)/sin36

a=( 40*0.9903)/0.5878

a=67.39

Approximately = 67.4

For c

c/sinC= b/sinB

c= (sinC*b)/sinB

c= (sin62*40)/sin36

c =(0.8829*40)/0.5878

c = 60.08

Approximately = 60.1

The perimeter of PQRS would depend on the lengths of the tangent segments and the lengths of the intercepted arcs. Without specific measurements, we cannot determine the precise perimeter.

To determine the perimeter of quadrilateral PQRS, we need more information about the lengths of the sides or the relationship between the sides and angles. Without specific measurements or additional details, we cannot calculate the exact perimeter of the quadrilateral.

However, we can provide some general information.Since PQ¯ is tangent to circle R at point Q, it is perpendicular to the radius drawn from the center of the circle to point Q. Similarly, PS¯ is tangent to circle R at point S, so it is perpendicular to the radius drawn to point S.

The quadrilateral PQRS is formed by the tangents PQ¯ and PS¯ along with the two arcs intercepted by these tangents on the circle R.

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Answer:

See below for proof

Step-by-step explanation:

\(\displaystyle \frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{(1-\cos x)(1+\cos x)}\\\\\frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{1-\cos^2 x}\\\\\frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{\sin^2 x}\\\\\frac{\sin x}{1-\cos x}=\frac{1+\cos x}{\sin x}\\\\\frac{\sin x}{1-\cos x}=\frac{1}{\sin x}+\frac{\cos x}{\sin x}\\\\\frac{\sin x}{1-\cos x}=\csc x+\cot x\)

The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2