A group of friends collected toys to donate to children in need. After sorting the toys into
boxes, they found they had 6/7 of a box of stuffed animals, 5/7 of a box of board games, and
1/7 of a box of dolls. In total, how many boxes of toys did the friends collect?

An equation to represent the other lengths, X, of the triangle is 2X+7=23.

An isosceles triangle is one that has two equal-length sides in geometry. The term "equilateral triangle" can refer to a shape with either exactly two sides that are the same length or at least two sides that are the same length, with the latter definition containing the equilateral triangle as an exception. The faces of bipyramids and a few Catalan solids are examples of isosceles triangles, as are the isosceles right triangle, the golden triangle, and others.

Isosceles triangles have been the subject of mathematical research since the time of the Babylonians and the Egyptians.

Given,

Perimeter of an isosceles triangle=23 meters

The base of a triangle=7 meters

P=2X+b

2X+7=23

Therefore, an equation to represent the other lengths, X, of the triangle is 2X+7=23.

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Answer: they are complementary

Step-by-step explanation:

they are complementary because they both add up to 90°

From the given 2D graph:

1. It took 20 minutes for Alec to get to his first friend's house.

2. Alec stayed for 40 minutes at his first friend's house.

3. It took 10 minutes for Alec to ride his bike from his first friend's house to his second friend's house.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

4. Alec stayed for 10 minutes longer at his first friend's house than at his second friend's house.

5. In part E of the graph Alec is riding his bike toward his home.

6. In part A of the graph Alec is traveling the fastest.

7. Alec was away from his house for 115 minutes.

1. From the given graph we can observe that part A of the graph is the time taken by Alec to reach his first friend's house which is 20 minutes.

2. From the given graph we can observe that part B of the graph is the time that Alec stayed at his first friend's house.

3.  From the given graph we can observe that part C of the graph is the time that Alec took to ride his bike from his first friend's house to his second friend's house.

4. Alec stayed at his first friend's home for 40 minutes, and he stayed at his second friend's home for 30 minutes, therefore Alec stayed for 10 minutes longer at his first friend's house than at his second friend's house.

5. In part E of the graph Alec is riding his bike toward his home.

6. In part A of the graph Alec is traveling the fastest.

7. Alec was away from his house for part(A+B+C+D+E)=20+40+10+30+15=115 minutes.

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Answer:

Add together

Step-by-step explanation:

Look all you do is add them all together!

Answer:

Step-by-step explanation:

To find KLR, we subtract MLR from KLM. We get left with 2x+14=KLR. With this, we can see that 36 degrees = 2x+14.

Now you just solve.

No, the ordered pair (0, 4) is not a solution of the inequality y ≤ x − 3

The solution of the inequality is checked by substituting the value in the ordered pair

If the given function helps in finding the each of the numbers that makes up the ordered pair then it is a solution

The substitution is as below

y ≤ x − 3

substituting x = 0

y ≤ x − 3

y ≤ 0 − 3

y ≤ -3

y is 4 and 4 is not less than or equal to -3, this means that the ordered pair is not a solution

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The probability that the randomly selected numbers are divisible by 3 is 3/10.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

So, the probability that the randomly selected number is divisible by 3:

Numbers under 20 divisible by 3 are: 3, 6, 9, 12, 15, 18

Total numbers: 20

Probability formula: P(E) = Favourable events/Total events

Now, substitute values and calculate as follows:

P(E) = 6/20

P(E) = 3/10

Therefore, the probability that the randomly selected numbers are divisible by 3 is 3/10.

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Answer:

The two expressions are equivalent, based on a direct numerical comparison (a) and (b) a methematical comparison.

Step-by-step explanation:

a)  The expressions can be shown to be equivalent by entering the numbers into each expression and comparing the results.  This is easy with a spreadsheet program.  Set up a table with the values of x in the left column.  Then enter the 2 equations in the first entry (-2) in each of two subsequent columns.  These expressions can be copied to the other rows by clicking on the first cell and dragging the lower right corner down until all rows are included.  The copied expressions will select the corresponding value of x for both expressions, as shown in the attached table.  It can be seen that both expressions yield the same results.

b)  Prove the equivalence mathematically:

In other words, do the two expressions equal each other?

(12x^2 - 27)/3  = -(-2x+3)(2x+3)   ??

Simplify both sides

(4x^2 - 9)           =   -(-4x^2 + 9)       ?

4x^2 - 9             =   4x^2 - 9            Yes.  They are equivalent

Answer: Because the first washing machine is cheaper

Step-by-step explanation:

Find the first washing machine price by taking 550 times 0.7 = $385

The second machine is first down by 20%, so take 550 times 0.8 =$440

Then 10% off, so take 440 times 0.9 = $396

So the first washing machine is cheaper than the second one $11

g(×)=4x+1 when g(×)=4x​ then we are getting No Solution.

What is system of equations?

Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution. A solution is not assured even then.

[tex]$$\left[\begin{array}{c}g=4 x+1 \\g=4 x\end{array}\right]$$[/tex]

Substitute g=4 x

[4 x=4 x+1]

Refine 4 x=4 x+1

-1=0

-1=0 is false, therefore the system of equations has no solution

No Solution

Complete Question : Find the solution of the given function g(×)=4x+1 when g(×)=4x​.

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Having sides that are parallel to one another, a parallelogram is a two-dimensional geometric shape. It is a sort of four-sided polygon (sometimes known as a quadrilateral) where each parallel pair of sides is the same length.

In addition, AB = CD and AD = BC.

A = C & B = D are also true.

Therefore,

∠A + ∠D = 180

∠B + ∠C = 180

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The data set of favorite sports among 9th graders is univariate and numerical.

Univariate data just has one variable. Since there is only one variable that varies, univariate data analysis is the most straightforward type of analysis.

In bivariate two different variables in this kind of data. The analysis of this kind of data focuses on linkages and causes, and it seeks to understand the causal connection between the two variables.

Given, A set of data of the favorite sports among 9th graders.

Baseball or Softball, Basketball, Lacrosse, Soccer and Field hockey

and the percentage of 9th graders who plays a certain type of sport.

This is a univariate and numerical type of data set not bivariate,

An example of bivariate data is temperature and ice cream sales in the summer season as the sales of ice cream must be related to the temperature.

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Answer:

yes, because there is a constant of proportionality

Step-by-step explanation:

pages = 4h

If h = 1 ; pages = 4

if h = 2 ; pages = 8

4 / 1 = 4

8 / 2 = 4

The address of element 0 is T₂₁ in the given matrix.

What are Matrices?

Matrices, the plural form of a matrix, are the arrangements of numbers, variables, symbols, or expressions in a rectangular table that contains various numbers of rows and columns. They are rectangular-shaped arrays, for which different operations like addition, multiplication, and transposition are defined. The numbers or entries in the matrix are known as its elements. Horizontal entries of matrices are called rows and vertical entries are known as columns.

We have given,

the matrix:

[tex]T = \left[\begin{array}{cc}4&2\\5&0\\11&-1\\8&3\end{array}\right][/tex]

To find the denotation of the element 0,

so,

A matrix is the arrangement of numbers in rows and columns in order to form an array.

The horizontal arrangement is called a row and the vertical arrangement is called a column.

If the matrix is denoted as  [tex][T]_{m \times n}[/tex] it means that the matrix T has m rows and n columns and the order of the matrix is m × n.

Each number in the matrix is called an element and the position of the element is represented as [tex]a_{mn}[/tex].

Representation of the standard matrix is:

[tex]A = \left[\begin{array}{ccc}a_{11}&a_{12}&........ a_{1n}\\a_{21}&a_{22}&........a_{2n}\\\\a_{m1}&a_{m2} &........a_{mn}\end{array}\right]_{m \times n}[/tex]

from the above information, we can say that the address of element 0 is

T₂₁.

Hence, the address of element 0 is T₂₁ in the given matrix.

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The equation of the line passing through points (5, 18) and (8, 9) will be y = - 3x + 33.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The points are given below.

(5, 18) and (8, 9)

The points (5, 18) and (8, 9) will satisfy the equation y = mx + c, then the equations are given as,

18 = 5m + c          ...1

9 = 8m + c           ...2

From equations 1 and 2, then we have

18 - 9 = 5m - 8m

3m = - 9

m = -3

Then the value of 'c' is given as,

9 = 8(-3) + c

9 = - 24 + c

c = 33

The equation is written as y = -3x + 33.

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The domain of the given graph will be equal to -4≤ x ≤ 4. The correct option is A.

The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f. (x).

A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value.

The values that we can put in the function of the given graph images vary from -4 to 4.

In the y-axis, the value of x varies from -4 to 4.

Therefore, the domain of the given graph will be equal to -4≤ x ≤ 4. The correct option is A.

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Answer:

I think its these:

(0,3)

(1,4)

(2,5)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

h = 6.2w + 4.5

using forth week

h = 6.2(4) + 4.5

h = 24.8 + 4.5

h = 29.3

gives a close value

Answer:

1:2

1 to 2

These are the other notations for 1/2

Answer:

39.512195122

Step-by-step explanation:

You divide 162 by 4.1, you can use a calculator to help solve. If needed to be rounded it is 40

The graph of f(x) = x in a straight line passing through the origin (0,0) and  at an angle of 45 degrees to the x axis. It increases from left to right.

What is graph?

In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other forms of graphs.

A simple graph is one in which no two vertices are connected by more than one edge, and no edge begins or finishes at the same vertex. In other terms, a simple graph is one that doesn't have loops or many edges.

Reflection in the x axis  will convert all positive values of f(x) to negative values of f(x)  and vice versa.  

g(x)  = - x     and is a straight line passing through origin  at angle of 45 degrees but the slope descends from left to right.

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The number of students travelled by bus and train are 38.

Given that, the Marching Band is traveling from Minnesota to Florida to perform in a national competition

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let x = Students traveling by train

Let y = Students traveling by bus

Now equations to represent the situation is

150x+120y=4,800 and 15x+20y=720

30(5x+4y)=4,800

5x+4y=160 ----------(I)

15x+20y=720

3x+4y=144 ----------(II)

Subtract equation (II) from (I), we get

5x+4y-(3x+4y)=160-144

⇒ 2x=16

⇒ x=8

Substitute x=8 in equation (I), we get

5(8)+4y=160

⇒ 4y=120

⇒ y=30

Number of students =38

Therefore, the number of students travelled by bus and train are 38.

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Answer:

Step-by-step explanation:

Answer: CLICK TO VIEW

16x^3+5x?

Answer:

x = 2, y = 3

Step-by-step explanation:

Solve the following system:

{-2 y + 3 x = 0 | (equation 1)

{-2 y + x = -4 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:

{3 x - 2 y = 0 | (equation 1)

{0 x - (4 y)/3 = -4 | (equation 2)

Multiply equation 2 by -3/4:

{3 x - 2 y = 0 | (equation 1)

{0 x + y = 3 | (equation 2)

Add 2 × (equation 2) to equation 1:

{3 x + 0 y = 6 | (equation 1)

{0 x + y = 3 | (equation 2)

Divide equation 1 by 3:

{x + 0 y = 2 | (equation 1)

0 x + y = 3 | (equation 2)

Collect results:

Answer: {x = 2, y = 3

Answer:

2x=4 x=2

Step-by-step explanation:

3x-x=2x

-2y-(-2y)=0

0-(-4)=4

2x=4

x=2

If x=2,3(2)-2y=0

When  (a, b) appears on a graph, it is said to be symmetric around the x-axis if (a ,b) also appears there at the same time. A graph that is symmetric around the x-axis is shown in the following illustration. A graph is said to be symmetric around the y-axis if and only if (a ,b) and (a, b) are both present on it.

We replace all the x's with -x and check to see if we get an equivalent formula to determine algebraically whether a graph is symmetric with regard to the y axis. Example: A) To make y = x2 symmetric with regard to the y axis, we substitute y = (-x)2 = x2 for y = x2.

Ordered pairs (x, y) and and exist in equations or functions that are symmetric to the origin (-x, y). The original equation is symmetric with respect to the origin if you swap -x for x and -y for y in the equation and simplify.

If we reflect a function's graph about the y-axis, we will get the same graph since some functions might be symmetrical about the y-axis. We may reflect various functions about the x- and y-axis and obtain the same graph. These two symmetry kinds are known as even and odd functions.

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The completed reasons that justify the statements in the solution to the equation consisting of an algebraic expression are presented as follows;

Statements        [tex]{}[/tex]                             Reasons

1. (1/2)·x - 5 = 10                        [tex]{}[/tex]     1. Given

2. 2·((1/2)·x - 5) = 20   [tex]{}[/tex]                   2. Multiplication property

3. x - 10 = 20                                 4. Distributive property

4. x = 30                                        5. Additive property

An algebraic equation consists of a statement that sets two expressions, that (at least one) consists of algebraic term, as being equivalent or the same.

The details of the reasons used to justify the steps are presented as follows;

Multiplication property

The multiplication property of equality states both sides of an equation remain equal following the multiplication of both sides of the equation by the same property.

Distributive property

The distributive property states that the multiplication of the sum of two numbers by a specified number has equivalent result as multiplying the individual numbers in the addend by the number

Mathematically; a·(b + c)  = a·b + a·c

Additive property

The additive property states that the equality of both sides of an equation is still true following the addition of the same quantity to both sides of the equation.

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Answer:they all end in the same number

Step-by-step explanation:

if you look at the ending of each number they are the same

The value of divisor and the dividend for the synthetic division problem will be;

⇒ (x + 3) and 2x³ + 4x² - 4x + 6

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The synthetic division problem is,

⇒ - 3/ 2 4 -4 6

Now,

Since, The synthetic division problem is,

⇒ - 3/ 2 4 -4 6

Hence, The divisor of the synthetic division problem is,

⇒ x - (- 3) = x + 3

And, There are four leading coefficient.

Hence, The dividend of the polynomial must be degree of 3.

So, By the leading coefficient are;

⇒ 2, 4, - 4, 6

Hence, We get;

⇒ 2x³ + 4x² - 4x + 6

Thus, The value of divisor and the dividend for the synthetic division problem will be;

⇒ (x + 3) and 2x³ + 4x² - 4x + 6

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45 be the number of scoops of ice cream sold and 73 be the number of salads sold that day.

Two or more expressions with an Equal sign is called as Equation.

Given,

Salad 'n Scoops is a food truck that sells salads for $4 and scoops of ice cream for $2

On a hot July day, they had 118 customers and earned $326.

Let x be the number of scoops of ice cream sold and y be the number of salads sold that day.

From the given information

4x+2y=$326...(1)

x+y=118

x=118-y..(2)

Substitute 2 in 1

4(118-y)+2y=326

472-4y+2y=326

472-2y=326

Subtract 472 on both sides

-2y=-146

Divide both sides by 2

y=73

Plug in y value in equation 2'

x+y=118

x+73=118

x=118-73

x=45

Hence, 45 be the number of scoops of ice cream sold and 73 be the number of salads sold that day.

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