You swam 4 sets of 200 yards and your friend swam 5 sets of 150 yards. How many more yards did you swim?

The solution is the set of all points (x,y) that satisfy the inequalities:

y < 2x + 4,  y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.

What is the graph of a function?

The graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of the function. In other words, it is a visual representation of the function's rule.

The graph of a function can take many different forms, depending on the function's rule. Linear functions, for example, will produce a straight line on the graph.

i) 2y - 4x < 8 can be solved by adding 4x to both sides and then dividing by 2, giving:

y < 2x + 4.

ii) -4y > -x + 12 can be solved by adding x to both sides and then dividing by -4, giving: y < x/4 - 3.

iii) | x + 3 | = y, you can split this into two cases:

i. x + 3 = y

ii. -(x + 3) = y

iv) |2x – 6| + 2 = y, you can split this into two cases:

i. 2x - 6 + 2 = y

ii. -(2x - 6) + 2 = y

We can use these equations to plot the graph on a coordinate plane.

Hence, the solution is the set of all points (x,y) that satisfy the inequalities:

y < 2x + 4,  y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.

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Answer:

[tex]\mathrm{Factoring}\:4x^3-15x^2-31x+30:\quad \boxed{\left(x+2\right)\left(4x-3\right)\left(x-5\right)}[/tex]

Step-by-step explanation:

This is a particularly tough question. It involves polynomial division(a real laborious process) and solving using quadratic formula.

I presume your school has provided you the resources for both.

Anyways, here goes a brief explanation

To find the roots(zeros) of a polynomial, [tex]f(x)[/tex] , set [tex]f(x) = 0[/tex]  and solve for values of [tex]x[/tex]

In general, if [tex]a[/tex] is a zero of [tex]f(x)[/tex], then [tex]f(x) \div(x-a)[/tex]  will leave no remainder. In other words, it is a factor of the polynomial. It also means [tex]x - a = 0[/tex]

The given polynomial is  [tex]4 x^{3} - 15 x^{2} - 31 x + 30[/tex]

We are given that [tex]- 2[/tex]  is a zero of [tex]f(x)[/tex]. This simply means that [tex]f(-2) = 0[/tex]

Plugging [tex]-2[/tex] into the function gives

[tex]f(-2) = 4(-2)^3 -15(-2)^2 - 31x + 30\\\\ = 0 =4\left(-8\right)-15\cdot \:4-31\left(-2\right)+30[/tex]

Which indeed is 0

Here [tex]a = -2[/tex] , so [tex]x - (-2)[/tex] which is [tex]x + 2[/tex] is a factor of[tex]f(x)[/tex]. It also means that
[tex]x-(-2) = 0 \;or\; x + 2 = 0[/tex]

Steps to factor the polynomial [tex]4 x^{3} - 15 x^{2} - 31 x + 30[/tex] :

Multiplying both sides of the above by [tex]4[/tex] gives [tex]4x -3 = 0.[/tex] So [tex]4x-3[/tex] is the third factor, replacing [tex]x - \dfrac{3}{4}[/tex]

The factors of [tex]4 x^{3} - 15 x^{2} - 31 x + 30[/tex]
are:

[tex]x+2, x-5 \;and \;4x-3[/tex]

Answer:
[tex]\mathrm{Factor}\:4x^3-15x^2-31x+30:\quad \boxed{\left(x+2\right)\left(4x-3\right)\left(x-5\right)}[/tex]

Use a polynomial division calculator which you can find on the web and a quadratic formula calculator (on the we or on your own calculator)

Answer:

C.  f(x) = (x - 3)² + 4

Step-by-step explanation:

Given parent function:

[tex]f(x)=x^2[/tex]

When a graph is translated "a" units right, subtract "a" from the x-value of the function.

Therefore, the translation of the parent function 3 units right is:

[tex]\implies f(x-3)=(x-3)^2[/tex]

When a graph is translated "a" units up, add "a" to the function.

Therefore, the translation of the function 4 units up is:

[tex]\implies f(x-3)+4=(x-3)^2+4[/tex]

Therefore , the solution of  given trigonometric equation has been proved.

A trigonometric equation is one that contains one or more ratios of unknown trigonometric angles. The ratios of sine, cosine, tangent, cotangent, secant, and cosecant angles are used to express it. A trigonometric equation is cos2 x + 5 sin x = 0, for instance.

Here,

Given :

Cosec A cosec²A cot A+ cot² A

LHS=(1+cot2A)2- (1 + cot2 A)

=1+2cot2A+cot A-1- cot2 A

= cot2A+ cot1A

= RHS

Hence, Cosec1A- cosec² A = cot ⁴A-cot ²A

Therefore , the solution of  given trigonometric equation  comes out to be it has been proved

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The given points lies in the following quadrant :

Point P ( 2,3 ) lies in first quadrant and point Q( -3,2 ) lies in the second quadrant.

As given in the question,

Given points are as follow:

Coordinates of point P are ( 2, 3)

Coordinates of point Q are ( -3, 2)

Sign of coordinates in each quadrant of the coordinate plane:

Let ( x, y) be the coordinates.

First quadrant : ( x , y) both are positive

Second quadrant : ( -x , y)

Third quadrant : ( -x , -y )

Fourth quadrant : ( x , -y )

Point P( 2,3) represent both are positive:

Point P lies in the first quadrant.

Point Q(-3,2) represent (-x ,y).

Point Q lies in the second quadrant.

Therefore, point P (2,3) lies in the first quadrant and point Q(-3,2) lies in the second quadrant.

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The answer is l = 3.75 and l = 11.25.

Given the length l and width w of a rectangle, its perimeter is:

                                    P=2(l+w)

This formula can be used to form an equation as we already know the value of P.

So, Let the width be w. The length will be 3w. As the perimeter is 30 inches, the width can be found as follows.

                               2(w+3w)=30

                                        4w=15

                                          w=3.75

Thus, the width is 3.75 inches. The length will be 3*3.75=11.25 inches.

Steps:

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Answer:

Step-by-step explanation:

The expressions that are equivalent to 4/9 x 7 are 28/9,  3¹/₉ and 3.11

As no options are included, I will include the expression that is equivalent to 4/9 x 7 in both fractions and decimal.

In fractions:

= 4/9 x 7

= 28/9

or,

= 3¹/₉

In decimals:

= 4/9 x 7

= 28/9

= 28 ÷ 9

= 3.11

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Answer:

1, 2, 5 and 10

Step-by-step explanation:

Step-by-step explanation:

1x10

2x5

4x5

.................

Answer:

[tex]1386 in^2[/tex]

r: radius

Circumference:  [tex]2\pi r[/tex]

Area: [tex]\pi r^2\\[/tex]

In this case, we are using 22/7 as an estimation for pi.

Plug into the area formula.

22/7 * (21)^2

22/7 * 441

[tex]1386 in^2[/tex]

Based on the information provided, the area in Nina's garden is 0.26 square meters.

The word area refers to the space occupied by a surface, in this case, the space of the garden. In a rectangle, this area can be calculated with the following formula,  although for other shapes the formula might be different:

area = length x width

To make this process easier, let's convert the fractions into regular numbers

4 1/5 = 4.2 (1/5 = 0.2)

3/10 = 0.3

4.2 x 0.3 = 1.26 square meters

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An inequality is defined as an unfair comparison between two numbers or other mathematical expressions. When comparing the sizes of two numbers on a number line, it is most commonly used. The graph for each inequality or equation is included in the attachment.

A graph is a visual representation of statistical data or a functional relationship between variables. Graphs are useful for forecasting because they can highlight broad trends in the quantitative behaviour of data. However, as mere approximations, they can be inaccurate and occasionally deceptive.

Most graphs have two axes: one for a set of independent variables and one for a set of dependent variables. The most common type of graph is a broken-line graph, with time serving as the independent variable.

16. 2y – 4x < 8

=  2y < 4x + 8

= y < 2x + 4

17. -4y > -x + 12

= y > x/4 + -3

18. | x + 3 |= y

y = | x + 3 |

19.  |2x – 6| + 2 = y

y = |2x – 6| + 2

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The formula for a triangular method is: (x1 + x2 + x3) / 3

1. The triangular method is the average of three different values: x1, x2, and x3.

2. To calculate the average, add the three values together and divide by three.

3. The formula for a triangular method is therefore (x1 + x2 + x3) / 3.

The triangular method is a method used to calculate an average of three different values. This method is most useful when there is not enough information available to calculate a more accurate average. To calculate an average using the triangular method, the three values (x1, x2, and x3) are added together and then divided by three. The formula for a triangular method is (x1 + x2 + x3) / 3. This method is useful for finding an average when a more accurate average cannot be calculated due to a lack of data. It is also used when data points are not necessarily related, as the triangular method is less affected by outliers than other methods of calculating an average. The triangular method is a quick and easy way to find an average when more complex calculations are not possible.

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Answer:

3x+7

Step-by-step explanation:

You need to combine like terms. Add 2x + x. It is 3x add the six and the one to make seven \

Hope this helps

Answer:

3x+7

Step-by-step explanation:

First, you want to group the variables, which in this case, is x. You take the 2x and x and make it 3x.

3x+1+6

Now that you have this done, you want to group the numbers, by making the 1+6 to 7.

3x+7

This is your answer, 3x+7.

The area of the circle is 1962.5cm²

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr², (Pi r-squared) where r is the radius of the circle.

The length of the wire will be the diameter of the circle. Therefore the radius of the circle = 50/2 = 25 cm

Area of a circle is given as = πr²

A = 3.14×25×25

A= 1962.5 cm²

Therefore the area of the circle when a length 50cm of wire is bent into circle is 1962.5cm²

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A table of numbers is a collection of numbers arranged in a specific format, usually in rows and columns.

The numbers in the table can represent various types of data, such as measurements, counts, or statistical values. Tables of numbers can be used to organize, compare, and analyze data in a clear and easy-to-read format. They are often used in fields such as math, statistics, and data analysis. Tables can be created using spreadsheet software, or they can be created manually using a pen and paper. The table can be used to represent a function, a data set, a matrix or a multiplication table, etc

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Complete question is: What is table of numbers?

[tex]x^2-2px+2p^2 \\ \\ =(x^2-2px+p^2)+p^2 \\ \\ =(x-p)^2+p^2[/tex]

Assuming [tex]p \in \mathbb{R}[/tex], [tex](x-p)^2 \geq 0[/tex] and [tex]p^2 \geq 0[/tex], meaning that [tex](x-p)^2+p^2 =x^2-2px+2p^2 \geq 0 \forall x \in \mathbb{R}[/tex]

The right angled triangle's side measures 19, its hypotenuse is approximately 8100.25.

Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners.

given

Let's say we don't know the triangle's hypotenuse and that angle A is approximately 33.56.

Cos and Cos-1 are available. Make sure it is set to degrees.

Cos(33.56)=6750/h

h=8100.25

The right angled triangle's side measures 19, its hypotenuse is approximately 8100.25.

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The width of a similar photo will be 2 inches.

As per the given problem,

Width of original photo = 4 inches

Height of original photo = 6 inches

After scaling the photo,

Height of new photo = 3 inches.

Let’s understand about scale factor.

An amount that multiplies (or "scales") a quantity is called a scale factor.

Scale factor = height of the sized image/size of the original image.

Scale factor = 3/6 = 1/2.

Therefore, the scaled image's width = scale factor *the size of the original image.

The width of the scaled photo = (½)*4 = 2.

Hence, the width of a comparable image measures 2 inches.

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The area occupied by the garden is 185 square feet.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Given:

Base = 10 feet, height = 8 feet

First, Area of Garden without patio

= 15 x 15

= 225 square feet.

Now, The patio is in the shape of a triangle which has a height of 8 feet and a base length of 10 feet.

So, Area of triangular patio

= 0.5 x 8 x 10

= 0.5 x 80

= 40 square feet.

Then, Actual Area of garden

= area of garden without patio - area of patio

= 225 square feet - 40 square feet

= 185 square feet.

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The standard form of the given linear equation is; -x + 3y = 15

The standard form of a linear equation is expressed in the form;

Ax + By = C

Now, we are given the equation as;

y - 4 = ¹/₃(x + 3)

Multiply through by 3 using multiplication property of equality to get;

3y - 12 = x + 3

Add 12 to both sides to get;

3y = x + 15

Subtract x from both sides to get;

-x + 3y = 15

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Answer:

its the second one: -5<x<2

Step-by-step explanation:

I did out the math

The measure of the larger angle is obtained as follows:

70º

Two angles are defined as complementary is the sum of their measures is of 90º.

The variables that represent each angle in this problem are given as follows:

x and y.

They are complementary angles, hence:

x + y = 90.

The difference between four times the measure of the smaller angle and the measure of the larger angle is 10, hence:

4y - x = 10.

x = 4y - 10.

Hence the value of y is obtained as follows:

4y - 10 + y = 90

5y = 100

y = 100/5

y = 20º.

Hence the measure of the larger angle is given as follows:

x + 20 = 90

x = 70º.

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The absolute value of a complex number is real.

The absolute value of a complex number is also known as its magnitude. It is a non-negative scalar quantity that represents the distance of the complex number from the origin in the complex plane.

The absolute value of a complex number is represented by the symbol "|z|" where z is the complex number.

The absolute value of a complex number is always a real number. For example, the absolute value of the complex number 4 + 3i is 5 (the distance of this point from the origin), which is a real number.

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Yes, y² = 5y - 10 is a quadratic equation.

In algebra, a quadratic equation is that which can be rearranged in standard form as

ax² + bx + c = 0,

where x is an unknown value, and a, b, and c are known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear). Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0.

We have the equation

y² = 5y - 10

y² - 5y + 10 = 0

The highest degree of this equation is 2, therefore it is a quadratic equation.

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

"Is y² = 5y - 10 a quadratic equation justify?" --

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Answer:

Step-by-step explanation:

A and C will both work. 4 goes into 56 evenly and so does 7.

Therefore , the solution of the given problem of unitary method comes out to be 3.5.

One can utilize the unit strategy to solve a problem by first multiplying the value of one unit by the quantity of units required. The unit function, to put it simply, is used to separate a single entity amount from just a given many. 400 pence, or the equivalent of one pen, would buy 40 needles. There might be a common approach to determining this. only one country. Anything has a distinguishing feature. Matrix logic, algebra, and its interpellation & inverse are all comparable terms.

Here,

Given : Josh gathered 2 pounds of plastic while cleaning up the park.

Josh received 1 ¾  times as much money from Sherri.

thus ,

To find the total plastic collected by both of them:

=>  1 ¾ * 2 + 2

=> 7/4 * 2

=> 14/4

=> 7/2

=>3.5

Therefore , the solution of the given problem of unitary method comes out to be 3.5.

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Answer:

The first and third choices

[tex]y = \dfrac{3}{2}x + 3[/tex]

and

[tex]2y-3x=6[/tex]

Step-by-step explanation:

(I cannot properly see the leading negative signs in choices 4 and 5, I copied/pasted your question choices from Brainly post and zoomed)

First understand what x and y intercepts are

The y-intercept is the value of y where the graph of the equation crosses the y-axis, It is the value of y when x = 0

The x-intercept is the value of x where the graph of the equation crosses the x-axis, It is the value of x when y = 0

We are given that the x-intercept is (-2, 0) and y = (0,3)

We can use a process of elimination to get rid of obviously incorrect choices and then work on the possible correct ones depending on whether we come up with the correct values of y first and eliminating those that do not match x =0, y =3 or (0,3) and then see if the x-intercept is (-2,0)

Particularly there is no formula for substitution just insert the given values in the equations.

One of the methods to solve a system of linear equations in two data algebraically is the substitution method. In this method, we find the value of any one of the variables by discordant it on one side and taking every other term on the other side of the equation.

This method is a simple way to resolve a system of linear equations algebraically and find the answer to the variables.

As the name suggests, it involves finding the value of the x-variable in terms of the y-variable from the first equation and then substituting or exchanging the value of the x-variable in the second equation.

The substitution method is one of the algebraic methods to solve coincident linear equations. It concludes by substituting the value of any one of the variables from one equation into the other equation.

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