Practice: Trigonometric Ratios Sides

Therefore, the solution to the given problem of the equation whose factors are (3x - 1)(x + 1).

Examine the equation.

An equation is a mathematical statement that is created by connecting two expressions using the equivalent sign. An example of an equation is 2x - 5 = 15. This equation's solution reveals that the value of the variable x is 5.

According to the given question:

Given : 3x² + 2x - 1

Factorizing using splitting the middle term

= 3x² + 3x - x - 1

= 3x(x + 1) - 1(x + 1)

= (3x - 1)(x + 1)

Therefore , the solution to the given problem of the equation whose factors are (3x - 1)(x + 1) .

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The possible rational zeros of f(x) = [tex]x^{4} + 2x^{3} - 3x^{2} - 4x +20[/tex] are ±1, ±2, ±4, ±5, ±10, ±20.

What is mean of rational zero ?

A rational zero is a rational number, which is a number that can be written as a fraction of two integers. An irrational zero is a number that is not rational, so it has an infinitely non-repeating decimal.

By Rational Zero Theorem,

If P(x) is a polynomial with integer coefficients and if is a zero of P(x) i.e.,(P( ) = 0),

then p is a factor of the constant term of P(x)

q is a factor of the leading coefficient of P(x)

Possible value of rational zero is p/q

Have given, f(x) = [tex]x^{4} + 2x^{3} - 3x^{2} - 4x +20[/tex]

Here, constant term, p = +20

Leading coefficient, q = +1

The factors of the constant term +20 are ±1, ±2, ±4, ±5, ±10, ±20.

The factor of the leading coefficient is ±1.

Therefore , The possible rational zeros of f(x) = [tex]x^{4} + 2x^{3} - 3x^{2} - 4x +20[/tex] are ±1, ±2, ±4, ±5, ±10, ±20.

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There are 45 erasers in the box and the total number of writing pencils is 20.

What is a quadratic equation?

Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

We have,

for every 4 pencils, there are 9 erasers and there are 25 more erasers than pencils in a box

erasers are in the box:

pencil/erasers = pencil/erasers

Let's consider x for pencils and y for the erasers

4/9 = x/25 + x

9x = 100 + 4x

5x = 100

x = 100/5

x = 20

there are 25 more erasers than pencils in a box

so, 25 + x = 25 + 20 = 45

there are 45 erasers in the box

Hence, there are 45 erasers in the box and the total number of writing pencils is 20.

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The connection that will have the same constant of proportionality will likewise have a slope of 3, and the constant of proportionality is 3.

We must first obtain the equation of the line before we can get the proportionality constant for the given graph.

Y = mx + b is the standard equation for a line.

With reference to the coordinates (0, 0) and (2, 6)

Get the "m" slope.

[tex]m = \frac{(6 -0)}{2-0} \\\\m = \frac{6}{2} \\\\m= 2[/tex]

The y-intercept is 0 since the line traveled through the origin.

Obtain the necessary equation:

y = mx + b

y = 3x + 0

y = 3x

The proportionality constant is determined by the equation to be 3. The slope of the connection, which will have the same proportionality constant, will be 3.

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The shift in the line's y coordinate relative to its x coordinate is known as the slope of a line. The slope of the given line graph is 3.

The slope of a line is defines as the change in the y coordinate of the line to the x-coordinate. Mathematically, the slope of a line is expressed according to the formula below:

Slope = y₂-y₁/x₂-x₁

Using the following coordinate from the given graph (0, 0) and (1, 3), we will substitute the coordinates into the formula to have:

Slope = 3-0/1-0

Simplify to have:

Slope = 1/3

Slope = 3

Hence the slope of the given line graph is 3.

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The graph of Y > -2x + 4 can be drawn by plotting points on a coordinate plane and connecting them with a dashed line. The dashed line should be above the line Y=-2x+4.

A sample graph is shown below:

[Graph of Y > -2x + 4]

(0,4), (1,1), (2,-2), (3,-5), (4,-8)

To graph Y > -2x + 4, you need to plot points on a coordinate plane. Start by finding the intersection point of the line Y=-2x+4 and the x-axis, which will be (0,4). From there, you can calculate the coordinates of the other points by substituting x values into the equation and solving for y. For example, when x=1, y=-2x+4=-2+4=2, so the point (1,2) would be plotted. Then, plot the other points (2,-2), (3,-5), and (4,-8). Finally, connect the points with a dashed line to represent Y > -2x+4.

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The answers to each part is mentioned below.

Given is the tabular data as shown in the image.

[A] - The equation {3} represents exponential relationship.

[B] - In an exponential relationship, the values of [y] first increases very slowly and than it increases very fast or the instantaneous rate of change  is very very fast.

[C] - The bacterial growth is represented by the equation : y = f(x) = A(B)ˣ, which is a exponential relationship. So, the bacterial growth is represented by equation 3.

[D] - Amount of water leaking from a leaky faucet can be given by a linear relationship. So, equation 2 will represent the situation.

Therefore, the answers to each part is mentioned above.

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The degree of the variable that appears in the polynomial has the most power. The leading term is the one with the highest degree or the one with the highest power of the variable. The coefficient of the leading term is the leading coefficient.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.

For instance, the polynomial 2x+5 has an exponent of 1.

A polynomial is not an expression with a variable that has fractional or negative exponents, divides by a variable, or is contained inside a radical.

The biggest power of the variable that occurs in the polynomial is its degree.

The term with the highest degree—i.e., the term with the largest power of the variable—is the leading term.

The leading coefficient is the leading term's coefficient.

Therefore, the degree of the variable that appears in the polynomial has the most power. The leading term is the one with the highest degree or the one with the highest power of the variable. The coefficient of the leading term is the leading coefficient.

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According to this graph of supply and demand schedules, the current cost of the good is:

A demand schedule in economics is a table that displays the quantity demanded of an item or service at various price points. On a graph where the X-axis is quantity and the Y-axis is price, a demand schedule can be represented as a continuous demand curve.

A demand schedule, also known as a tabular representation or statement, displays the various quantities of goods that are wanted at various price points throughout a given time period. The precise quantity of goods and services that will be purchased at each price will be shown on a demand schedule.

The complete question is : Which statement best describes the current price for the good shown in this graph of supply and demand schedules? A. The current price should be raised to reflect lower supply. B. The current price reflects the point where supply and demand are balanced. C. The current price should be lowered to reflect higher supply. D. The current price should be lowered to reflect lower demand.​

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Answer:

[tex]10.5\%[/tex]

Step-by-step explanation:

[tex]\% \: error = \frac{absolute \: error}{actual \: value} \times 100[/tex]

actual value = 38ml, measurement error = 42ml

absolute error = actual value - measurement error (where actual value > measurement error) OR measurement error - actual value (where actual value < measurement error)

(Note: absolute error is different from measurement error. Absolute error is the distance between the actual value and the measurement error, while measurement error is the error made in measurement).

Therefore, absolute error = 42 - 38 = 4

[tex]\% \: error = \frac{4}{38} \times 100[/tex]

[tex]\% \: error = 10.52[/tex]

Therefore: % error = 10.5 (to the nearest tenth)

In the Logarithm prompt above, note that the value of In x when In x = e to the power -x is x = 1/e.

The above assertion is right because the definition of the natural logarithm denoted as In x or ln x, is that it is the inverse function of the exponential function, denoted as e to the power x or ex.

This means that if we have an equation of the form In x = ex, then we can find the value of x by simply taking the inverse of both sides of the equation.

So, if we take the inverse of both sides of the equation In x = ex, we get x = In (ex) = In e to the power x = 1/e.

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As per the integral value of the closed path, the magnitude of I3 is 3.597

The term magnitude in math refers a measure of the size of a mathematical entity.

Here we have the value of the line integral around the closed path 1.96 x 10⁻⁵.

Now, we have to find the value of the magnitude I3,

Here we have also know that the value of I1 and I2 are 18A and 12 A respectively.

Now, as per the line integral of the magnetic field is written as,

=> 1.96 x 10⁻⁵ = 4π⋅10⁻⁷ (I3 + 12)

When we simplify this one then we get,

=> 1.96 x 10²/4π = I3 + 12

=> 15.597 = I3 + 12

Then the value of the magnitude is calculated as

=> I3 = 3.597

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Occupation is a qualitative variable with a nominal level value, annual salary is a quantitative variable with ratio level value, price of a shirt (in dollars) on clearance rack is quantitative with a ratio level value.

Variables can be divided into quantitative or qualitative (categorical).

Quantitative variables are those variables in which the data measures values or counts and is expressed as amounts or numbers. Qualitative variables are any variables whose data are descriptive rather than numerical.

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The distance traveled by Raven in 1 hour at the given rate is 4 miles.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

We have,

Raven can walk 2 (2/5) miles in 3/5 hours.

so,

2 (2/5) = 0.6 hours.

12/5  = 0.6 hours.

2.4 = 0.6 hours.

then,

if 2.4 = 0.6 hour

for  x = 1 hour

By cross multiplying:

x = 2.4/0.6 miles

= 4 miles

Hence, the distance traveled by Raven in 1 hour at the given rate is 4 miles.

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The exact length of the curve is  7.995.

The function  [tex]y=2+8x^{\frac{3}{2} }[/tex]   is given.

0 ≤ x ≤ 1

Differentiating given function with respect to x.

[tex]\frac{dy}{dx}= \frac{d}{dx}2+8x^{\frac{3}{2} }[/tex]

[tex]\frac{dy}{dx}= 12x^{\frac{1}{2} }[/tex]

Length of arc, L = [tex]\int\limits^a_b {\sqrt{1+(\frac{dy}{dx} )^{2} } } \, dx[/tex]

Putting the values,

L = [tex]\int\limits^1_0 {\sqrt{1+144x } } \, dx[/tex]

Let 1 + 144x = z

         144dx = dz

When we plug in "z" and "dz" values to the equation above, we get:

L = [tex]\int\limits^1_0\frac{z^{1/2} }{144} \, dx[/tex]

  = [tex][\frac{z^{3/2} }{144(3/2)} ]^{1} _{0}[/tex]

 = [tex]\frac{1}{216}[z^{3/2} ]^{144} _{1}[/tex]

 = [tex]\frac{1}{216}[144^{3/2}-1^{3/2} ][/tex]

 = [tex]\frac{1}{216}[1728-1][/tex]

 = 1727/216

 = 7.995

Hence, the exact length of the curve is  7.995.

Correct Question :

Find the exact length of the curve,   [tex]y=2+8x^{\frac{3}{2} }[/tex], 0 ≤ x ≤ 1.

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The letter "I" represents the symbol of the current.

Electric current is defined as the rate at which a given flow of electrons passes through a point in a complete electrical circuit or flow of charge.

The electric current is defined with the capital letter I being its symbolism, and its unit of expression is the Ampere (A).

It is important to know that if we keep relation of the "i" as a complex number to give values of current is also valid, since the current or the flow of charge describes sinusoidal and cosine wave, and these are studied more easily with these complex numbers of the form:

e^ i∅     = Cos∅ + iSen∅

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An picture produced through translation, a sort of transformation, has a comparable shape to the pre-image.

Simply said, "translation" indicates motion. Every point in the form must move the same amount and in the same direction during a translation. The size of the Image and the Pre-Image are equal in a translation.

A translation only moves a form up, down, or from side to side; it has no effect on how it appears. An illustration of a transformation is translation. A transformation is a technique for moving or repositioning a shape. Every point in the form is moved in the same direction and by the same amount.

A sort of alteration called translation creates a picture

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Children who are eight years old frequently count up to 1,000 and have mastered skip counting. There are many chances to deepen their comprehension at home using basic math games.

In order to calculate the size of a set, or the number of items in a finite set, one must count. Calculating the amount or total number of items in a collection or group is what is meant when we say we are counting in arithmetic. To count, then, is to speak numbers in sequence while giving each item in a group a value based on a one-to-one correlation. Objects are counted using counting numbers.

Children who are eight  years old frequently count up to 1,000 and have mastered skip counting. There are many chances to deepen their comprehension at home using basic math games.

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The 2 formulas of rectangular prism are Volume = Length x Width x Height cubic units and Surface Area of a rectangular prism = 2 (lh +wh + lw ) Square units.

An item with three dimensions is a rectangular prism. It will therefore have its own volume and surface area. We need to know the dimensions of a prism's sides or edges in order to compute its volume and surface area. Let l, w, and h represent the dimensions of the rectangular prism. Below are the supplied formulas.

The 2 formulas of rectangular prism are

Volume of rectangular prism:

Volume = Length x Width x Height cubic units

Surface area of rectangular prism:

Surface Area of a rectangular prism = 2 (lh +wh + lw ) Square units

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Answer: She can buy a total of 33 packets and have 25 cents leftover.

Step-by-step explanation:

Answer:

she will have $1 left

Step-by-step explanation:

265÷8=33.125 or 33 1/8

she will have $1 left

Step-by-step explanation:

Our straight line has the same gradient as that of the line,

[tex]2y=5x+7[/tex]

Dividing each term by 2,

[tex]y=\dfrac{5}{2}\,x+\dfrac{7}{2}[/tex]

Now this equation is in the form [tex]y=mx+c,[/tex] so the gradient of this line is 5/2.

So the gradient of our straight line is,

[tex]m=\dfrac{5}{2}[/tex]

Given our straight line passes through the point,

[tex](x_1,\ y_1)=(3,\ -2)[/tex]

The equation of a straight line passing through a point [tex](x_1,\ y_1)[/tex] and having gradient [tex]m[/tex] is given by,

[tex]\longrightarrow\large\boxed{\quad y-y_1=m(x-x_1)\quad}[/tex]

This form of equation of a straight line is called point - slope form.

By this point - slope form, the equation of our straight line will be given by,

[tex]\longrightarrow y-(-2)=\dfrac{5}{2}\,(x-3)[/tex]

[tex]\longrightarrow y+2=\dfrac{5}{2}\,(x-3)[/tex]

[tex]\longrightarrow2(y+2)=5(x-3)[/tex]

[tex]\longrightarrow2y+4=5x-15[/tex]

[tex]\longrightarrow\underline{\underline{5x-2y-19=0}}[/tex]

This is the equation of our straight line, written in the form [tex]Ax+By+C=0.[/tex]

Answer:

Step-by-step explanation:

7.89 is about 8 so we can multiply 215*8 to get 1720 dollars

Answer:

$1696.35

Step-by-step explanation:

$7.89 × 215 = $1696.35

A linear equation in one variable can have one, no, or an infinite number of solutions.

A linear equation in one variable is an equation that can be written in the form ax + b = 0, where a and b are constants, and x is the variable. Depending on the values of a and b, a linear equation can have one, no, or an infinite number of solutions.

If a = 0 and b = 0, then the equation is 0 = 0, which is true for all values of x. In this case, the equation has an infinite number of solutions.

If a = 0 and b ≠ 0 then the equation 0x + b = 0 has no solution, as 0x = 0 for all values of x and b ≠ 0.

If a ≠ 0 and b = 0, then the equation ax + 0 = 0 can be written as ax = 0 and has one solution, x = 0.

If a ≠ 0 and b ≠ 0, then the equation ax + b = 0 can be solved by subtracting b from both sides of the equation and dividing by a. This will yield one solution, x = -b/a.

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The average of all values is mean and the middle of all values is the median.

Mean is the average taken of the all the values in the data. It is calculated by -

x = (x1+x2+x3+...+xn)/n = ∑ [tex]\frac{Xn}{n}[/tex]

i.e. the sum of all data values divided by the number of data values.

It is used in situations when we need to get an idea of the data.

For ex - the mean of data values 1,2,3,4,5 is given by -

(1+2+3+4+5)/5 = 3.

The median is the middle of the data values. It is calculated differently for both odd and even no. of observations.

For example, the median of 1,2,3,4,5 is 3 as it is the value in the middle.

So, the average of observations is mean and their middle value is median.

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Answer:

a. 234 ft

b. 102 ft

Step-by-step explanation:

a. Checkpoint 1 = -179

-179 + 413 =   ==> get the height of the top of the hill by adding 413 to  

                            checkpoint 1

413 - 179 = 234 ft

b. -77 - (-179) =  ==> get the difference between checkpoint 4 = -77 and  

                             checkpoint 1 = -179

-77 + 179 =  ==> subtracting a negative number is equivalent to adding a

                         positive number

179 - 77 = 102 ft

To make expressions in mathematics we must set a variable value that varies according to the conditions of our problem.

Let's define what a mathematical expression is:

Algebraic expressions are expressions composed of numbers and letters, where the letters are called variables and each of them adopts a specific value according to the process in which it is used.

To make an expression in mathematics you must set a variable, since an expression is a numerical solution of a process, and by having a variable we will have the result on it, for example:

I have a business and every day I earn 2 times more than the previous day:

expression:

x = 2n

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When there are two arguments, the first one is used as a starting value rather than 0; when there are three arguments, the third one is used as an increment rather than the implied default of 1.

The statistical range is the range of values between the highest and lowest for a particular data collection. Another way to represent the range is the difference between the highest and lowest observation. The sample interval is determined by subtracting the largest number from the lowest. For continuous variables, the sample range is a critical measure of variability.

here

Basically, the range function in Python takes three inputs.

Start: An integer designating the range object's beginning.

Stop: An integer that represents the object at the end of the range.

Step: An integer that represents the increment following each value.

When there are two arguments, the first one is used as a starting value rather than 0 .

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y = (-1/2)x + 4 is the equation for the linear function with an x-intercept of 8 and a y-intercept of 4.

We are aware that lines might have several kinds of equations; the typical form is

The equation of a line in slope-intercept form is Ax + By + c = 0, and

y = mx + b.

m is the slope, and b is the y-intercept.

The y-intercept, or (0,b), is the point where the line crosses the y-axis at x = 0. The slope represents the rate of change of the y-axis relative to the x-axis.

Given, An x-intercept for a linear function is 8, and a y-intercept is 4.

The two points on the line are therefore (8, 0) and (0, 4).

Slope(m) is now equal to (4 - 0)/(0 - 8).

m slope = 4/8.

slope(m) equals -1/2.

With a y-intercept of 4, it represents the value of b in the equation y = mx + b.

Consequently, the equation is y = (-1/2)x + 4 is linear.

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Answer:16

Step-by-step explanation: 4 x 4 because a square has 4 sides and each side is 4cm because each side is the same measurements