Question 1
Simplify the rational expression, if possible.

15y^3/5y^2

State the excluded value.

Answer: 8

Step-by-step explanation:

2 x 2 = 4        2 x 4 = 8

Three images are formed when two plane mirrors are placed at 120.

assuming an angle of x between the mirror and the object. The previous graphic makes it evident that, regardless of the value of x assumed, the angle of the fourth picture will be more than 180 degrees. A mirror's reflection of the object in question produces a mirror image. The mirror image is what an object seems to be when it is placed in front of a mirror. The reality is quite different from what appears to be the case. No, some messages contain both mirror images and real photographs.

We know that angle = 120

number of images = 360/120

number of images = 3.

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Algebra is a branch of mathematics that deals with mathematical statements and relationships in which symbols (such as x, y, and z) represent numbers or other unknown values. Harry has 62 quarters and 38 nickels.

How many of each coin does he have?

To find out how many of each coin Harry has, we need to use algebra. Let x be the number of quarters and y be the number of nickels. We know that:

x + y = 100 (because Harry collected 100 coins in total)

0.25x + 0.05y = 17.40 (because that's the total value of the quarters and nickels in dollars)

We can use the first equation to solve for one of the variables in terms of the other. For example, we can subtract y from both sides to get:

x = 100 - y

Then we can substitute this value of x into the second equation and solve for y:

0.25(100 - y) + 0.05y = 17.40

25 - 0.25y + 0.05y = 17.40

25 = 17.40 + 0.20y

0.20y = 7.60

y = 38 (the number of nickels)

Now that we know the value of y, we can use the first equation to find the value of x:

x + 38 = 100

x = 62 (the number of quarters)

So Harry has 62 quarters and 38 nickels.

These symbols are used to represent quantities, and the operations and relationships between them are studied through the use of mathematical laws and rules.

Algebraic equations and formulas allow one to solve a wide variety of problems, including problems in physics, engineering, and other sciences, as well as in everyday life.

Algebraic concepts include variables, expressions, equations, and functions. It is the study of mathematical symbols and the rules for manipulating these symbols. Algebra is a powerful tool for solving problems by using mathematical models.

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2 feet : 5/12 minutes has unit less than 1

A rate is a comparison between two separate measurement units.

18 bucks

one hour

A rate with a unit rate has 1 as the bottom number (also called a single-unit rate). Any rate can be converted into a unit rate. To accomplish this, divide both the top and bottom numbers by the bottom one. Of course, the denominator is the figure at the bottom.

18 dollars and 30 minutes = 0.6 dollars and 1 minute

Consider that a 5 ounce can of soup costs $1.25. What is the price of one ounce?

1.25 US dollars

5 ounces times 5 times 5 is 0.25 dollars.

1 ounce

Therefore, each ounce costs $0.25, or 25 cents! This is referred to as the soup unit price.

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Answer:239.583

Step-by-step explanation:

First you have to divide 83500 by 12 because there is 12 months in a year which gives you 6958.3

Second you have to divide 6958.3 by 4 because there is 4 weeks in a month and that gives you 1739.583

Finally you have to subtract 1739.583 by 1500 giving you 239.583

The simplified expression of the ∛4x / 5 is ∛4x / ∛5

Index laws are the rules for simplifying expressions involving powers of the same base number, these laws are also called Laws of indices.

Laws of indices provide us with rules for simplifying calculations or expressions involving powers of the same base. The indices are also known as powers or exponents.

It is represented in the form:

am = a × a × a ×……× a (m times)

we have the  law of indices formula:

[tex]\sqrt[a]{b}=b^\frac{1}{a}[/tex]

∛4x / 5 = (4x/5)^1/3

Therefore,

∛4x / 5 = ∛4x / ∛5

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Answer:

See below

Step-by-step explanation:

Given a line segment consisting of endpoints [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], the midpoint of the line segment is [tex]\displaystyle \biggr(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\biggr)[/tex].

Answer: B $2:00

I Just took it

The statements that are true regarding the area of circle D include the following:

A. The area of the circle depends on the square of the radius.

C. The area of circle D is 324π centimeters squared.

Mathematically, the area of a circle can be calculated by using this formula:

Area = πr²

Where:

r represents the radius of a circle.

In this context, we can reasonably infer and logically deduce that the area of any circle is directly proportional to the square of its radius.

Substituting the given radius into the formula for the area of a circle, we have the following;

Area of circle = π × 18²

Area of circle = 324π centimeters squared.

Based on the calculations, we can reasonably infer and logically conclude that the area of circle D in terms of pie (π) is equal to 324π centimeters squared.

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Which statements are true regarding the area of circle D? Select two options.

The area of the circle depends on the square of the radius.

The area of circle D is 36π centimeters squared.

The area of circle D is 324π centimeters squared

The area of the circle depends on the square of π.

The area of the circle depends on the central angle.

The inequality used to determine the domain of the function is greater than equal to and the domain is [10, ∞).

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. The values in this set

Hence, once we input an x value, the function returns. The y values are those.

The given expression is:

[tex]\sqrt{x- 10} + 3\\[/tex]

The value in the square root must be greater than or equal to 0 to ensure that the number is real.

[tex]\sqrt{x - 10} \geq 0[/tex]

Taking squares on both sides of the equation:

x - 10 ≥ 0

x ≥ 10

The domain of the given inequality is [10 , ∞).

Hence, the inequality used to determine the domain of the function is greater than equal to and the domain is [10, ∞).

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The expression is equivalent to the given expression is 5x²+12x-7: Option C

You should understand that  simplification means making an expression more simpler for better understanding

The given expression is

-2x²+8x-9+4x+7x²+2

The first thing to do is to rearrange the expression in the following ways by collecting the like terms

7x²-2x²+8x+4x-9+2

This implies that

5x²+12x-7

Conclusively the simplest form of the expression is 5x²+12x-7

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angle of elevation = 17.5 degrees

shadow length = 4

To compute the tree height using the given formula, you would need to use the inverse tangent function (arctan) to find the angle of elevation in radians, and then multiply that value by the shadow length.

In this example:

angle of elevation = 17.5 degrees

shadow length = 4

tree height = tan⁻¹ (17.5) × 4

From this, the final output will be 7.398881327917831.

The formula states that the ratio of the tree's height to the shadow's length is equal to the tangent of the angle of elevation. So, by measuring the shadow length and the angle of elevation, we can use the tangent function to calculate the tree's height.

The inverse tangent function (arctan) is used to find the angle of elevation in radians, and then the result is multiplied by the shadow length to get the tree height.

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Answer:

answer for the first is "Obtuse", answer for the second is "acute", answer for the third is a=right, b=obtuse, c=obtuse, d=acute

Step-by-step explanation:

The value of x is 15.25 inches

Subtraction is one of the four arithmetic operation along with addition, multiplication and division. Subtraction is an operation that represents removal of objects from a collection. For example, in the adjacent picture, there are 5 − 2 peaches, this means that 5 peaches with 2 taken away, resulting in a total of 3 peaches.

The frame is place in the Middle of the wall. The space left after the frame is hanged is calculated as 48inches - 17.5 inches = 30.5 inches.

Since the frame is at the middle of the wall , the space (x) at both sides is equal

therefore x+x = 30.5

2x = 30.5

divide both sides by 2

x = 30.5/2 = 15.25 inches

therefore the value of x is 15.25 inches.

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Answer:

The y-intercept is -58

The equation is y=7x-58

Step-by-step explanation:

We'll look for an equation of the form y=mx+b, where m is the slope and b the y-intercept (the value of y when x is 0).

We are given the slope and one point on a line.  The slope, m, of 7 leads us to:

    y=7x+b

We need a value for b that will force the line to go through point (4,-30).  Enter that point in the above equation and solve for b:

  y = 7x+b

  -30 = 7(4)+b  for point (4,-30)

  -30 =  28 + b

      b = -58  [b is the y-intercept]

The equation is y = 7x-58

See the attached graph.

Answer: 21 cm

Step-by-step explanation: The formula for the perimeter of an equilateral is 3 x side.

Here is the formula:

P= 3 x side

P= 3 x 7

P= 21 cm

On solving the provided question, we can say that angle are given a 9n - 3 + 8n +9 = 60; angle 1 = 24 and angle 2 = 33

In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays can generate an angle that is in the plane where the rays are located. The meeting of two planes also creates an angle. They are referred to as dihedral angles. An angle is the shape created by two rays or lines that have a shared termination in plane geometry. The Latin word "angulus," which meaning "horn," is the source of the English term "angle." The vertex is the common terminal of the two rays, which are referred to as the sides of the angle.

here,

angle are given as

9n - 3 + 8n +9 = 60

17n = 60-6

17n = 54

n = 3.1764705882 = 3

n = 3

angle 1 = 24

angle 2 = 33

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If the equations be y = 6.9x + 4.3, y = 4.7x + 8 then the solution of the system is 2.14.

A system of equations, usually referred to as an equation system or a set of simultaneous equations, is a finite set of equations for which common solutions are sought.

Multiple equations in algebra must be solved concurrently (i.e., the solution must satisfy all the equations in the system). There must be an equal number of equations and unknowns for a system to have a singular solution. As was said earlier, a system of equations is a group of equations that attempt to find a common solution for all of the variables.

Let the system of equations be

y = 6.9x + 4.3

y = 4.7x + 8

then the solution of the system be 2.14.

Therefore, the correct answer is option C. 2.14.

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Answer: there

Step-by-step explanation:

0.16666666666

d).  A ball with radius r, lying inside a glass described by the function y = x^2, has its center at (0, F(r)) units above the bottom of the glass. f(2) - f(1/4)=4.

To solve this problem, we first need to find the function F(r). We can do this by finding the y-coordinate of the center of the ball when its radius is r.

Since the ball lies inside the glass described by the function y = x2, the y-coordinate of the center of the ball when its radius is r is equal to the y-coordinate of the point (r,r2).

Thus, the function F(r) is given by F(r) = r2. Now, we can calculate f(2) - f(1/4) = F(2) - F(1/4) = 22 - (1/4)2 = 4 - 1/16 = 4 - 0.0625 = 3.9375 ≈ 2. Therefore, f(2) - f(1/4) = 2.

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The Propositions from the given data are All Statements except Statement A.

(a) What time is dinner? This is not a proposition because it is a question and does not have a definite truth value.

(b) It is not the case that π is not a rational number. This is a proposition and its truth value is True because pi is not a rational number.

(c) x / 2 is a rational number. This is not a proposition because it is a statement about a variable, and the truth value depends on the value of x.

(d) 2x + 3y is a real number. This is not a proposition because it is a statement about variables, and the truth value depends on the values of x and y.

(e) Either π is rational and 17 is a prime, or 7 < 13 and 81 is a perfect square. This is a proposition and its truth value is False, because neither pi is rational nor 17 is prime.

(f) Either 2 is rational and π is irrational, or 2π is rational. This is a proposition and its truth value is False, 2 is rational and π is irrational.

(g) Either 5π is rational and 4.9 is rational, or there are exactly four primes less than 10. This is a proposition and its truth value is False because 5π is not rational and 4.9 is not rational and also there are four primes less than 10.

(h) −3.7 is rational, and either 3π < 10 or 3π > 15. This is a proposition and its truth value is False because −3.7 is not rational.

(i) It is not the case that 39 is prime, or that 64 is a power of 2. This is a proposition and its truth value is True because 39 is not a prime and 64 is a power of 2.

(j) There are more than three false statements in this book, and this statement is one of them. This is a proposition and its truth value is False because it is self-referential and also it's not true that there are more than three false statements in this book.

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The function is given by: h(x) = -2(x³ - 2x² - 5x + 6).

The factor theorem in algebra connects a polynomial's components and zeros. The polynomial remainder theorem has this particular special instance. A polynomial f(x) has a factor if and only if f=0, according to the factor theorem.

The Factor Theorem states that a polynomial function with roots [tex]$x_1, x_2, x_n$[/tex] is given by:

[tex]$$f(x)=a\left(x-x_1\right)\left(x-x_2\right) \cdots\left(x-x_n\right)$$[/tex]

In which a is the leading coefficient.

Looking at the table, considering the values of x when h(x)=0, the roots of h(x) are given as follows:

[tex]$$x_1=-2, x_2=1, x_3=3$$[/tex]

Then the rule is:

h(x) = a(x + 2)(x - 1)(x - 3)

h(x) = a(x² + x - 2)(x - 3)

h(x) = a(x³ - 2x² - 5x + 6)

The h-intercept is of -12, as when x = 0, h = -12, hence this is used to find a as follows:

6a = -12

simplifying the above equation, we get

a = -12/6

a = -2.

Therefore, the function is given by: h(x) = -2(x³ - 2x² - 5x + 6).

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The slope-intercept form of the given linear equation 2x + y = 10 is y = -2x + 10.

If we draw the graph of the linear equation y = mx + c. The result is a line with m as the slope, and c as the y-intercept. This form of the linear equation y = mx + c is called the slope-intercept form, and the values of m and c are real numbers.

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

Now, change the given equation to slope-intercept form, y = mx + c, where m is the slope and c is the y-intercept.

2x + y = 10

Subtract 2x from both sides of the above equation, we get

y = -2x + 10

This is the required slope-intercept form of the given linear equation.

-- The given question is incorrect, the correct form of equation is

"What is the slope-intercept form the linear equation  2x + y = 10?" --

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Answer:

median = 4

Step-by-step explanation:

On the box plot the median is represented by the vertical line inside the box.

That is the median = 4

JL has a length of 5.

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees.

At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

For instance, if the length of one side of a rectangle is 20 cm, the opposing side will also be 20 cm.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle.

It is also known as an equiangular quadrilateral for this reason.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

According to our question-

3x + 4 = 4x - 1

-3x         -3x

4 = x - 1

+1      +1

5 = x

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Antonio's budget line has shifted upwards due to a 50 percent increase in the price of new books and a 20 percent increase in the price of used books. His new budget line equation is y = 110x.

Upper L1: y = 80x

Upper L2: y = 110x

Antonio's original budget line (Upper L1) is represented by the equation y = 80x. This equation means that for every x amount of textbook Antonio buys, he will spend 80y in total.

Antonio's new budget line (Upper L2) is represented by the equation y = 110x. This equation means that for every x amount of textbook Antonio buys, he will spend 110y in total.

As a result, Antonio's budget line has shifted upwards due to the increase in both the price of new and used books. Antonio's budget line has shifted upwards due to a 50 percent increase in the price of new books and a 20 percent increase in the price of used books. His new budget line equation is y = 110x.

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The points A(3,-2), B(-3, 8), C(-5, -1) and D(2,16) would form a parallelogram.

How to plot points on graph?

In mathematics, points on a graph are typically plotted on a coordinate plane. The x-coordinate and y-coordinate of each point determine its location on the plane. To plot a point, you will need to know its coordinates (x, y).

To plot the points A(3,-2), B(-3, 8), C(-5, -1) on the coordinate axes, we can start by drawing the x-axis and y-axis, where the x-axis is the horizontal line and y-axis is the vertical line.

We can then locate point A by starting at the origin (0,0) and moving 3 units to the right on the x-axis and 2 units down on the y-axis. Point B can be located by starting at the origin and moving 3 units to the left on the x-axis and 8 units up on the y-axis. Point C can be located by starting at the origin and moving 5 units to the left on the x-axis and 1 unit down on the y-axis.

To form a parallelogram, point D must be opposite of point B and have the same distance from point C and point A. Since a translation of a vector is a linear transformation, D is the translation of vector AB to point C.

The coordinates of point D would be (2,16), which is the translation of point B by the vector (2,8) to point C.

So the points A(3,-2), B(-3, 8), C(-5, -1) and D(2,16) would form a parallelogram.

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The amount charged by the boutique for each item is given as follows:

The price of each item is obtained considering a system of equations, for which the variables are given as follows:

From the description, the equations are given as follows:

Simplifying the first equation by 11, we have that:

3.272727x + y = 299.5454

y = 299.5454 - 3.272727x

Replacing on the second equation, the cost of a wallet is given as follows:

91x + 10(299.5454 - 3.272727x) = 7599

58.2728x = 4603.5455

x = 4603.5455/58.2728

x = 79.

Then the cost of a belt is obtained as follows:

y = 299.5454 - 3.272727(79)

y = $41.

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