Why are the values for sine and cosine equal at 45?.

A polynomial equation can be written in a particular format by using its standard form. A polynomial equation is written in its standard form when the terms are written in descending order of their exponents and the leading coefficient, or the coefficient of the term with the highest exponent, is 1, as in the example above.

   The term with the highest exponent in the equation Y = -5x3 is x3, which has a coefficient of -5. The entire equation must be divided by -5 in order to be written in standard form, which will set the coefficient of the x3 term to 1 and convert the equation to standard form.

  The zero coefficients have been included in the equation when written in this form, however when the equation is read, we only take the term for the non-zero coefficients into account.

  So, the standard form of Y = -5x^3 is -5x^3 + 0x^2 + 0x + 0 = 0.

   Therefore ,the answer is  Y = -5x^3 is -5x^3 + 0x^2 + 0x + 0 = 0.

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The standard form of Y = -5x^3 is -5x^3 + 0x^2 + 0x + 0 = 0.

The term with the highest exponent in the equation Y = -5x3 is x3, which has a coefficient of -5. The entire equation must be divided by -5 in order to be written in standard form, which will set the coefficient of the x3 term to 1 and convert the equation to standard form.

 The zero coefficients have been included in the equation when written in this form, however when the equation is read, we only take the term for the non-zero coefficients into account.

So, the standard form of Y = -5x^3 is -5x^3 + 0x^2 + 0x + 0 = 0.

Therefore ,the answer is  Y = -5x^3 is -5x^3 + 0x^2 + 0x + 0 = 0.

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Step-by-step explanation:

the average rate of change is

(h(interval end) - h(interval begin)) /

(interval end - interval begin)

in our case this is

(h(8) - h(-1)) / (8 - -1) = (108 - 9) / 9 = 99/9 = 11/1 = 11

Answer: The area of a rectangular room is 750 square feet and the width of the room is 5 feet less than the length of the room.

Three equations that can be used to solve for y, the length of the room are:

y(y + 5) = 750: This equation uses the formula for the area of a rectangle, which is length x width. Since the width is 5 feet less than the length, we can substitute y-5 for the width.

750 – y(y – 5) = 0: This equation uses the same method as the first equation, but it is rearranged to solve for y.

(y + 25)(y – 30) = 0: This equation uses the quadratic formula to solve for the length of the room, this equation is also useful when the length is an irrational number.

Note that the fourth equation y(y – 5) + 750 = 0 is not valid because it is not possible to have negative area, hence y(y-5) should not be added to 750.

The fifth equation (y+25)(y-30)=0 is also not valid because it gives y = -25 and y = 30 as solutions but the length of the room can't be negative.

Step-by-step explanation:

The equation y = -2 is represented on the graph as shown below :

Use the slope-intercept form to find the slope and y-intercept.

The slope, m, represents the steepness of a line. The slope of the line is also termed as gradient, sometimes. The y-intercept, b, of a line, represents the y-coordinate of the point where the graph of the line intersects the y-axis.

The slope-intercept form is

y = mx + b, where m is the slope and b is the y-intercept.

y = mx + b

Find the values of m and b, using the slope-intercept equation.

y = -2

m = 0, b = -2.

The slope of this line = m = 0

The y-intercept = -2, therefore a point on the line = (0,-2)

Finding two points on the line:

(0,-2), (1,-2)

Thus, the equation y = -2 on graph is shown below.

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To find the solution set for the inequality 2 - 3x > 17, we can start by solving for x:

2 - 3x > 17

3x < 15

x < 5

So, the solution set for the inequality is all values of x that are less than 5.

Of the options given, only the set C, x = -9, -8, -7, -6, contains only numbers that are less than 5. Therefore, the set of numbers that contains only solutions to the inequality is C, x = -9, -8, -7, -6.

We have expresses 53 Kobo as a decimal of 0.52 Naira.

A number that is not a whole is written using decimals. Between whole numbers are decimal numbers. 12.5, a decimal number that falls between 12 and 13, serves as an illustration of this. It is less than 13, but it is greater than 12. It's crucial to remember that fractions and decimal numbers are equivalent; the only difference is how they are expressed.

In keeping with the previous illustration, the mixed number 12 12 and 12.5 are equivalent numbers. No matter how complex the decimal is, this is true. For instance, 0.75 and 3/4 are equivalent. If you wanted to go even further, you could say that 0.75 is equivalent to 75%.

We know that 1 Kobo = 0.01 naira

Therefore, 52 kobo = 0.01  × 52 naira

                                  = 0.52 naira

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Answer:

Obtuse angle

Step-by-step explanation:

Angles greater than 90 degrees are obtuse angles, angles less than 90 degrees are acute angles, and angles at 90 degrees are right angles.

The scale factor used to produce the second triangle is 5/3.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size. For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.

Given that, a triangle with base length of 3 units is transformed into a second triangle with a base length of 5 units,

Therefore, the scale factor = 3/5

Therefore, to produce Figure 2 from Figure 1 we will multiply it by 5/3

Hence, the scale factor used to produce the second triangle is 5/3.

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Answer:

If ur options are  one sixth

6

one half

2

then the correct answer is 2

Step-by-step explanation:

I took the quiz and got it right.

The formula for a circle's arc length is L = r * θ, where L is the arc length, r is the circle's radius, and θ is the arc's central angle, expressed in radians.

We can calculate the radius of the circle by dividing the arc length by the central angle because we know the value of L (7 cm) and that can be calculated from the arc's measure (degrees or radians):

r = L / θ

It is crucial to keep in mind that in order to calculate the radius, you must first know the arc's central angle's measurement in radians.

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The sum of the polynomial is obtained by adding the terms with the same power and variable together.

The steps to determine the sum of the polynomial :

Step 1: Arrange each polynomial with the term with the highest degree first then

in decreasing order of degree.

Step 2: Group the like terms : Like terms are defined as the terms whose variables and exponents are the same. For example 2x² and 3x² are like terms.

Step 3: Simplify by combining like terms.

For example, (2x² + 6x +5) +(-2x + 3x²- 1)

and we have determine sum of polynomial. Follows the above steps :

=> (2x² + 6x +5) + ( 3x²– 2x – 1)

2x² + 3x² + 6x – 2x + 5 -1

= 2x² + 3x² + 6x – 2x + 5 -1

= 5x² + 4x + 4

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Answer:

[tex]x\le \cfrac{6}{5}[/tex]

Step-by-step explanation:

[tex]10x+2\le \:14[/tex]

[tex]10x\le \:12[/tex]

[tex]\cfrac{10x}{10}\le \cfrac{12}{10}[/tex]

[tex]x\le \cfrac{6}{5}[/tex]

The relation between mean, median and mode the difference between mean and mode is equal to three times the difference between the mean and median.

The average of a set of numerical data is referred to as the arithmetic mean. Either a weighted average or a basic average is possible. Adding up all the data from the data set, we divide it by the total frequency to get the simple average.

When a data set is ordered in either a descending or an ascending order, the median is the number that falls in the middle of the range. Because it removes the outliers, the median is far more useful than the mean.

The most frequent number in a dataset is referred to as the mode. There could be one mode, several modes, or none at all for a given collection of integers.

(Mean - Median) = 1/3 (Mean - Mode).

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The GCD is 30 and the LCM is 13860 for the numbers 420, 630, and 330 .

The highest factor among two or more numbers is the greatest common denominator (GCD).

The lowest common multiple (LCM) is another name for the least common multiple in mathematics. The least common multiple of two or more numbers is the smallest of all the common multiples of the numbers provided.

Take all three numbers and their factors to determine the greatest common divisor.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420 are the factors for 420.

The factors for 630 are as follows: 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630, and 330 are as follows: 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330.

Of the three, 30 is the common factor with the highest value.

Take all three numbers and their prime factors to determine the lowest common multiple.

The prime factors for 420 = 2 × 2 × 3 × 5 × 7

The prime factors for 630 = 2 × 3 × 3 × 5 × 7

The prime factors for 330 = 2 × 3 × 5 × 11

The LCM of 420,630,330 = 2 × 2 × 3 × 3 × 5 × 7 × 11 = 13860.

Therefore, the GCD and LCM is 30 and 13860 respectively.

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Answer:

256

Step-by-step explanation:

*desmos graphing calculator*

Answer:

First number = 5, second number = 3

Step-by-step explanation:

we can write this as x–5y = –10 and x – 2y = –1 so we know now that 3y = 9 so we divide both by 3 to get: y = 3

now that we know the second number we can multiply it by 2 to get 6 and now we just have to figure out what – 6 is –1 which would be 5

The decreased numbers are first number is 2. and the second number is -9.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

Given that, there are two numbers, first of two numbers decreased by five times the second number equals -10. The first number decreased by two times the second number equals -1.

x - y = 0

The first number decreased 5 times

-5 -y = -10

-y = -10 + 5

-y = -5

y = 5

The second number decreased 2 times

x - (-2) = -1

x + 2 = -1

x = -1 -2

x = -3

Now,

the first number is

-3 - 5 = -10

-8 = -10

10-8 = 0

2 = 0

the second number is

-3 - 5 =-1

-8 = -1

-8 +1 =0

-9 = 0

Hence, the answer is 2, -9.

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A parallelogram is created when two congruent triangles with the same orientation are connected along equal sides.

When two congruent triangles with different orientations are joined along equal sides, they can be used to make a kite or a dart.

Here, ABC and ACD, two triangles that are mirror reflections of one another, combine to make a dart.

Darts and kites both feature two adjacent pairs of equal sides. The sole distinction is that darts are concave whereas kites are convex.

A quadrilateral can be produced if there are more than two congruent triangles. At least two of the sides of such a quadrilateral will be equal if each of its sides is one of the sides of the triangles.

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Answer:

  2

Step-by-step explanation:

You want the largest possible greatest common divisor of consecutive terms of the sequence an = n! +n.

The sequence starts off 2, 4, 9, 28, 125, ...

The first two terms have a GCD of 2. The remaining pairs of terms have a GCD of 1.

The maximum possible GCD of adjacent terms is 2.

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The equation modeled on the number line represents "c. 7/8 - 1/4 = 5/8".

What is algebraic equation ?

An algebraic equation is a mathematical statement that uses mathematical symbols (such as numbers, variables and mathematical operations) to express the equality of two expressions. It is used to represent mathematical relationships and to find solutions to problems. The most common operations used in algebraic equations are addition, subtraction, multiplication, and division.

This is an algebraic equation and it represents the mathematical relationship between different values.

The equation is , 7/8 - 1/4 = 5/8

This equation states that if we subtract 1/4 from 7/8 we get 5/8.

It can be verified by solving the equation:

7/8 - 1/4 = (7/8) - (1/4) = (74/84) - (18/48) = 28/32 - 8/32 = 20/32 = 5/8

So, the equation modeled on the number line represents "c. 7/8 - 1/4 = 5/8".

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The equation is , 7/8 - 1/4 = 5/8

This equation states that if we subtract 1/4 from 7/8 we get 5/8.

It can be verified by solving the equation:

7/8 - 1/4 = (7/8) - (1/4) = (74/84) - (18/48) = 28/32 - 8/32 = 20/32 = 5/8

So, the equation modeled on the number line represents "c. 7/8 - 1/4 = 5/8".

The condition for two lines to be perpendicular lines :

the two lines meet each other at the right angle

We know that the two lines are perpendicular to each other if they intersects and these two lines are inclined at angle 90°

Since these lines are inclined at 90° to each other, hence they create right angles.

This means, the condition for two lines to be perpendicular lines is that the two lines must meet each other at the right angle

This property of lines is said to be perpendicularity.

Mathematically, the perpendicular lines are represented by the symbol, ‘⊥‘.

For example, if two lines l₁ and l₂ are perpendicular to each other then they are represented as l₁ ⊥ l₂.

The product of slopes of perpendicular lines is always -1.

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The experimental probability of spinning red and spinning blue is 4 and 2.8.

What is the experimental probability?

Experimental probability is a type of probability that is determined by conducting an experiment and observing the outcomes. It is also known as empirical probability.

It is calculated by counting the number of times an event occurs in a set of trials and then dividing that number by the total number of trials.

The experimental probability of spinning red.

P(red) = 20/5 = 4

The experimental probability of spinning blue

P(red) = 20/7 = 2.8

Hence, The experimental probability of spinning red and spinning blue is 4 and 2.8.

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The side length of square C is given as follows:

5 ft.

The area of a square of side length is given as follows:

A = s².

Hence the side length of A and B are given as follows:

Then the side length of square C is the hypotenuse of a right triangle, and applying the Pythagorean Theorem, it's length is obtained as follows:

C² = 3² + 4²

C² = 25

C = 5 ft.

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The approximate distance from Town A to Town C is 12.5 miles.

What is the midpoint?

The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.

To find the midpoint of Town A and Town B, you need to find the average of the x-coordinates and the average of the y-coordinates.

The x-coordinate of Town A is -8 and the x-coordinate of Town B is 10, so the average is (10 - (-8))/2 = 9/2 = 4.5.

The y-coordinate of Town A is 2 and the y-coordinate of Town B is 8, so the average is (8 - 2)/2 = 6/2 = 3.

Therefore, Town C is located at (4.5, 3).

To find the distance from Town A to Town C, you can use the distance formula, which is the square root of the difference in x-coordinates squared plus the difference in y-coordinates squared.

The distance from Town A to Town C = √((4.5 - (-8))^2 + (3 - 2)^2) = √(12.5^2 + 1^2) = √(156.25 + 1) = √(157.25) = 12.5 miles

Hence, the approximate distance from Town A to Town C is 12.5 miles.

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The standard deviation of 4:

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

In descriptive statistics, the standard deviation measures how widely the data points vary from the mean. It describes how values are distributed throughout the data sample and measures how widely apart data points are from the mean. The square root of the variance is used to calculate the standard deviation of a sample, statistical population, random variable, data collection, or probability distribution.

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The inverse of a relation is a relation obtained by interchanging or swapping the elements or coordinates of each ordered pair in the relation.

Let R be a relation from a set A to another set B. Then R is of the form. The inverse relationship of R is denoted by R-1 and its formula is R-1 ={(y, x): y∈B and x∈A}.

The first element of each ordered pair of R = the second element of the corresponding ordered pair of R-1 and

The second element of each ordered pair of R = the first element of the corresponding ordered pair of R-1.

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The 4 laws of logarithms are product rule, division rule, power rule and change of base rule.

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Write a logarithmic expression in the form [tex]log_{b}M[/tex] = N.

In an exponential equation, the variable is expressed as an exponent. A logarithmic equation uses the logarithm of an expression including a variable to solve the problem. Check to determine if you can write both sides of an exponential equation as powers of the same number before attempting to solve it. If you can't, use property after taking the common logarithm of both sides of the equation.

Use the properties of logarithms to express the equation in the form  [tex]log_{b}M[/tex] = N, then convert it to exponential form, M = [tex]b^{N}[/tex], to solve an equation requiring logarithms.

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The answer for the Daffynition Decoder is 7.

The formula is O3 - M2 = 7. The calculation is to take the ozone (O3) and subtract the mistletoe (M2). O3 stands for ozone, which is composed of three atoms of oxygen and is represented by the number 3. M2 stands for mistletoe, which is composed of two atoms of oxygen and is represented by the number 2. The formula used to calculate the answer is m = 2o + 1, where m is the number of mistletoes and o is the number of ozones. The calculation is as follows: if there are 2 ozones, then the number of mistletoes is 2(2) + 1 = 5. Therefore, the answer is 7 (5 mistletoes and 2 ozones). This formula is useful for quickly calculating the total number of items when you know the number of each type of item.Therefore, if we subtract the mistletoe from the ozone, we get the answer of 7. In summary, O3 - M2 = 7.

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The measure in degrees of the angle, the 1/360 of a circle is equals to one degree.

First note the following information: Degrees is an angular unit. The One rotation around the circle is equals to the 360 degrees. Angles measured in degrees always require the unit "degrees" after either a number or the degree symbol °. For example, 90 degrees = 90°. Rotation is 360 degrees, so angles greater than 360 degrees indicate more than a full rotation. The resulting direction that, when plotted on a circle, makes the endpoint of that angle the same as any other angle between 0 and 360 degrees. These angles are called coends. The arc should be proportional to the angle. The circle should be 360 degrees. Therefore, the degree of the angle is = 1/360 ( 360°) = 1 degree. From this we can conclude that the degree of the angle is 1 degree.

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Complete question:

How many degrees is a circle of 1/360?.