Maria buys some soft drinks for her friends. she buys a total of 13 drinks for a total of $32. if medium drinks, m, cost $3 and small, s, drinks $2, write a system of equations which can be used to find how many small drinks and medium drinks she bought.

The solution for the given system of equations would be (6, 6).

What is the system of equations?

A system of equations is a set of two or more equations that are solved simultaneously. Each equation in the system contains one or more variables, and the goal is to find the values of the variables that satisfy all the equations in the system.

y = -1/6x + 7

y = 2x - 6

To graph the equations y = -1/6x + 7 and y = 2x - 6, we can follow these steps:

Plot the y-intercepts of the equations: The y-intercept is the point where the line crosses the y-axis. For the equation y = -1/6x + 7, the y-intercept is (0,7), and for the equation y = 2x - 6, the y-intercept is (0,-6).

Draw the lines: Starting from the y-intercepts, use the slope of the lines to draw the lines. The slope of the first equation is -1/6 and the slope of the second equation is 2.

Find the x-intercept: The x-intercept is the point where the line crosses the x-axis. For the equation y = -1/6x + 7, the x-intercept is (-42,0) and for the equation y = 2x - 6, the x-intercept is (-3,0)

Locate the point of intersection: The point of intersection of the two lines is the solution of the system of equations. The point of intersection for the given equation is (3,1).

Label the axes and the lines: Label the x- and y-axes, and give the lines descriptive names or equations.

Now draw the graph, we get

Hence, the solution for the given system of equations would be (6, 6).

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Answer:

2145

Step-by-step explanation:

Here is the formula for the sum of the first n terms.

[tex]S_n=\frac{n}{2}(2a_1+(n-1)d)[/tex]

Here is the formula for the nth term.

[tex]a_n=a_1+(n-1)d[/tex]

We are given

[tex]a_6=13[/tex]

[tex]S_{40}=3420[/tex]

[tex]3420=\frac{40}{2}(2a_1+(40-1)d)[/tex]

[tex]13=a_1+(6-1)d[/tex]

We don't have a lot to work with but we can get it done.

Lets solve for [tex]a_1[/tex] in [tex]S_n=\frac{n}{2}(2a_1+(n-1)d)[/tex].

Multiply each term by [tex]\frac{2}{n}[/tex].

[tex]\frac{n}{2}(2a_1+(n-1)d)\frac{2}{n} =S_n\frac{2}{n}[/tex]

Simplify.

[tex]\frac{n}{2}*(2a_1+nd-d)\frac{2}{n} =S_n\frac{2}{n}[/tex]

Apply the distributive property.

[tex][\frac{n}{2} (2a_1)+\frac{n}{2} (nd)+\frac{n}{2} (-d)]\frac{2}{n} =S_n\frac{2}{n}[/tex]

Simplify.

[tex](2\frac{n}{2}a_1+\frac{n^2d}{2} -\frac{n}{2}d)\frac{2}{n} =S_n\frac{2}{n}[/tex]

[tex](na_1+\frac{n^2d}{2} -\frac{n}{2}d)\frac{2}{n} =S_n\frac{2}{n}[/tex]

[tex](na_1+\frac{n^2d}{2} -\frac{dn}{2})\frac{2}{n} =S_n\frac{2}{n}[/tex]

[tex]\frac{(na_1+\frac{n^2d}{2} -\frac{dn}{2})*2 }{n}=S_n\frac{2}{n}[/tex]

[tex]\frac{n(2a_1+nd-d)}{n} =S_n\frac{2}{n}[/tex]

[tex]2a_1+nd-d=S_n\frac{2}{n}[/tex]

[tex]2a_1+nd-d=\frac{2S_n}{n}[/tex]

[tex]2a_1=\frac{2S_n}{n}-nd+n[/tex]

Divide each term by 2.

[tex]\frac{2a_1}{2}=\frac{\frac{2S_n}{n} }{2} +\frac{-nd}{2} +\frac{d}{2}[/tex]

Simplify.

[tex]a_1=\frac{S_n}{n} -\frac{nd}{2} +\frac{d}{2}[/tex]

Insert our answer for [tex]a_1[/tex] into [tex]a_n=a_1+(n-1)d[/tex]

[tex]a_n=\frac{S_n}{n_{40} } -\frac{n_{40} d}{2} +\frac{d}{2}+(n_6-1)d\\[/tex]

I continued my work on paper. I will attach it below.

Using the slope and y - intercept, the linear function that models this problem is y = -33.333x + 68.32

A system of linear equation is a set of at least two linear equations containing the same set of variables. Linear equations use only polynomial coefficients and the operations of addition, subtraction, multiplication and division. The solutions to a linear equation system are the values of the variables which make all the equations true.

To solve this problem, we have to define our variables and set our system of linear equations.

Let;

Using the data given, we can find the slope and y - intercept of a linear function that represents this.

slope (m) = y₂ - y₁ / x₂ - x₁

m = 64.99 - 59.99 / 0.10 - 0.25

m = -33.333

Using the slope in the slope-intercept form of a linear equation

y = mx + c

Taking one point;

59.99 = -33.333(0.25) + c

c = 68.32

The linear equation can be written as;

y = -33.33x + 68.32

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On the other hand, it is not impossible for an equation to have only one solution, an infinite number of solutions, or none at all. Any value for the variable would make the equation true, but an equation with infinite solutions suggests that there is no answer to the equation.

What is  infinite solution?

Both sides of an infinite solution are equal. As an illustration, 6x + 2y - 8 = 12x + 4y - 16 Using a formula or method for infinite solutions, you can simplify the equation and make both sides to equal one another, making it an infinite solution. The concept of infinite connotes boundlessness or infinity. Typically, it is denoted by the symbol "".

What is an infinite number?

There are an unlimited number of numbers in a series. a collection of infinitely many natural integers, as an illustration. The initial value 0, and the initial value infinite, are represented by the logarithms and +, respectively.

                    The original values 0 and infinity are similarly treated when we consider both of the conceivable values and + as a single infinity.

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Given that segment BD bisects segment AC, the value of x is 5.8 units.

If the corresponding sides and/ or internal angles of two shapes have some  common properties, then it can be said that the shapes are similar. Though similarity does not mean congruency.

Given that segment BD bisects segment AC, the value of x can be determined by comparing the sides of triangles ABD and BCD.

Thus, we have;

x/ 7 = 14/ 17

17x = 7 * 14

     = 98

17x = 98

x = 98/ 17

  = 5.76

x = 5.8 units

Thus to the nearest tenth, the value of x is 5.8 units.

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The expression that is an element of AxBxB is (1,2,3)

The given data is A= (a, b}, B = {1,2,3}

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. If both A and B are square matrices of the same order, then both AB and BA are defined.

[tex]& \ A \times B=\left\{\begin{array}{c}(a, 1),(a, 2),(a, 3),(b, 1) \\(b, 2),(b, 3)\end{array}\right. \\[/tex]

[tex]& A \times B \times B=\left\{\begin{array}{l}(a, 1,1),(a, 1,2),(a, 1,3), \\(a, 2,1),(a, 2,2),(a, 2,3),\end{array}\right. \\& (a, 3,1),(a, 3,2),(a, 3,3) \\ & (b, 1,1),(b, 1,2),(b, 1,3) \\& \left.\begin{array}{l}(b, 2,1),(b, 2,2),(b, 2,3) \\(b, 3,1),(b, 2),(b, 3,3)\end{array}\right\} \\[/tex]

[tex]& \therefore(b, 2,3) \in D \times B \times B \\\\& (a, a, 1) \notin A \times B \times B \\\\& \left(b, 2^2\right) \quad \forall A \times B \times B \\\\& (2,1,1) \notin A \times B \times B \\\\&=(b, 2,3) \in \cap \times B \times B \\&\end{aligned}[/tex]

The union of two sets X and Y is equal to the set of elements that are present in set X, in set Y, or in both the sets X and Y.

The intersection of sets can be denoted using the symbol ‘∩’. As defined above, the intersection of two sets A and B is the set of all those elements which are common to both A and B. Symbolically, we can represent the intersection of A and B as A ∩ B.

Therefore, the expression that is an element of AxBxB is (1,2,3).

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The median age of the presidents at their death is 69.

The median is the value that is exactly in the middle of a dataset when it is arranged in order. It is a measure of central tendency which separates the lowest 50% from the highest 50% of values.

The median formula is {(n + 1) / 2}th, where “n” is the number of items in the set and “th” means the (n)th number. To find the median, first arrange the data points from smallest to largest.

The steps for finding the median differ depending on whether we have an odd or an even number of data points. If the number of data points is odd, the median is the middle data point in the list. If the number of data points is even, the median is the average of the two middle data points in the list.

In this case, the number of data points is even, that is 38. So, the median is:

= {(n + 1) / 2}th

= {(38 + 1) / 2}th

= 19,5th

Thus, it means the median is the average of the 19th and 20th in the data points. So, it will be:

Median = (68 + 70) / 2

Median = 138 / 2

Median = 69

Hence, the median age of the presidents at their death is 69.

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Although part of your question is missing, you might be referring to this full question: This list shows the age at which 38 U.S. Presidents died.

46 58 64 68 73 80 90

49 60 65 70 74 81 93

53 60 66 71 77 83

56 63 67 71 78 85

56 63 67 71 78 88

57 64 67 72 79 90

What is the median age of the presidents at their death?

A. 69

C. 68

b. 67.5

d. 70

The domain of a function is the set of all possible input values for which the function produces a valid output.

The domain of a function is the set of all possible input values for which the function produces a valid output. To find the domain of a specific function, you will need to look at the equation and determine what values are acceptable for the inputs. For example, if the equation is y = x2 + 5, then the domain of the function would be all real numbers, since any real number can be plugged in for x and the equation will produce a valid output.

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The measure of the alternate exterior angle made by the intersection of road B and road C is 77 degrees.

The pair of angles known as alternate exterior angles are those that are formed on the opposite side of the transversal from the parallel lines' outer side.

According to the alternate exterior angle theorem, alternate exterior angles are regarded as congruent angles or angles of equal measure when two parallel lines are intersected by a transversal.

In this case, two roads, A and B, run parallel to each other. A third road, C, passes through both A and B. Road C creates an exterior angle of 77 with road A. Therefore, the angle will also be equal to 77°.

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The response to claim A and Claim B on potential energy being stored in  a magnet in terms of the given options is that;

Claim A; I think So

Claim B; Definitely Not

Claim A; This claim is true because If we move a magnet against the magnetic force of a stronger magnet, the motion will make the magnetic field lines to be compressed and this would lead to an increase in potential energy since the magnetic force lines will now be compressed.

Thus, the claim is correct that there is more potential energy that can be stored by moving against the magnetic force of a stronger magnet.

Claim B; Unlike claim A where the magnets were being moved from each other, in this case they are moved closer to each other and therefore this causes a greater compression of space which will lead to a loss in potential energy. Therefore this claim is not true.

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Complete question

Claim A: More potential energy can be stored by moving against the magnetic force of a stronger magnet.

definitely

I think so

I don't know

I don't think so

definitely not

Explain why, using evidence from the activities you have done.

Do you agree with Claim B, More potential energy can be stored by moving against the magnetic force closer to a magnet?

definitely

I think so

I don't know

I don't think so

definitely not

Explain why, using evidence from the activities you have done.

Answer:

no the points shown would not be part of y =0.5x

Answer:

840 quarts could be made in 12 hours. The rate per day is 1680 quarts could be made per day.

Step-by-step explanation:

140/2=x/12

reduce/simplify 140/2 to 70

so 70/1=x/12.

cross product

70*12=1*x

840=x

One day has 24 hours,

so we multiply 2 by 12 to get 24,

thus 840*2=1680.

An inverse function or  anti function is defined as a function, in which the graph can be  reverse into another function. hence commonly , if any type of function “f” takes x to y then, the inverse of “f”  function will take y to x.  hence  the function is represented as ‘f’ or ‘F’, then the inverse function is denoted by [tex]f^{-1} and F^{-1}[/tex].

let us assume that  f and g are inverse functions, then the condition for  f(x) = y if and only if g(y) = x

when the graph is represented in an original function which has to be  one-to-one function in order  to assure that its inverse is an function. A function is said to be a one to one function only if  function of every second element corresponds to the first value .

The graph of function is  the inverse of a function which  reflects two things, that is , one represents the  function and second represents the inverse of the function, over the line y = x. This line in the graph passes through the origin and which  has slope value  equal to 1 and represented as;

y = f-1(x)     which is equal to     x = f(y)

This relation is basically  similar to y = f(x), which tells that  graph of f but the part of x and y are reversed here. So if we have to draw the graph of f-1, then we have to manipulate the positions of x and y in coordinate axes.

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Answer:

he has 86.36% percent out of 100

Answer: The first graph

Step-by-step explanation:

Graph the absolute value using the vertex and a few selected points.

Hope this helps !

A. The quotient is given as follows: 60.9 miles / 3.5 hours.

B. The exact distance that she rode in one hour is of: 17.4 miles.

The measures in this problem are obtained considering the relation between velocity, distance and time.

The relation between velocity, distance and time states that the velocity is obtained by the quotient of the distance by the time, as follows:

v = d/t.

In which:

The parameters for this problem are obtained as follows:

Hence the average velocity is obtained as follows:

v = d/t

v = 60.9/3.5

v = 17.4 miles per hour.

This means that the exact distance that she rode in one hour is obtained as follows:

17.4 = d/1

d = 17.4 miles.

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Answer:

80 %

Step-by-step explanation:

Christine enjoyed 44 out of the 55 movies she watched.

This can be represented as

44/55 movies. This fraction simplified is 4/5 or 80 %

The three various steps of problem-solving methods are.

A problem must be defined, its root cause must be found, then there must be a search for, ranking, and selection of potential solutions, followed by their implementation. the actions taken to fix issues.

Clarifying:

Ideating:

Developing:

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Karmyn has 56 tablespoons of vinegar for a salad dressing recipe.

In mathematics, Multiplication operations perform Multiplying values on either side of the operator.

For example 4×2 = 8

Karmyn is making a salad dressing using vinegar. She has three and a half glasses of vinegar. She understands that one cup contains 16 tablespoons.

First, we need to convert the 3 1/2 cups of vinegar to tablespoons.

We know that there are 16 tablespoons in 1 cup, so we can multiply the number of cups by the number of tablespoons per cup to convert the measurement.

3 1/2 cups × 16 tablespoons/cup = 56 tablespoons.

Therefore, she has 56 tablespoons of vinegar.

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The statements that are true about rhombus MNPQ include A. and B.

A quadrilateral with a diamond shape is a rhombus. It has four equal sides with the opposite sides running parallel to one another. It resembles a square that is skewed.

A rhombus is a quadrilateral with four equal-length sides in plane Euclidean geometry. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.

Based on the diagram, it should be noted that NR equals QR as they are the same.

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Answer: 22.5

Step-by-step explanation: To get a percentage of a number you multiply the number you want the percentage of (125), and multiply it by your percent in decimal form. So basically the equation went like this: 125 x 0.18 = 22.5. Another example of this would be if you wanted to find 60 percent of 20. You would just take 60 and put it in decimal form and multiply. 20 x 0.60 = 12. Hope this helps!

Graph of g(x) = (1/2)ˣ i.e. Graph of f(x) = 2x reflected over the y-axis is drawn below.

A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B. A relation f from a set A (the domain of the function) to another set B (the co-domain of the function) is called a function in math.

f = {(a, b)| for all a ∈ A, b ∈ B}.

Given, the function

f(x) = (2)ˣ

g(x) = (1/2)ˣ

g(x) is the graph of f(x) reflected over y- axis.

The rule of reflection over y-axis:

(x, y) → (-x, y)

Thus, when a graph gets reflected over y-axis it means that horizontal components are additive inverse of the original horizontal components.

Therefore the graph of g(x) = (1/2)ˣ is as follows.

Hence, below is the graph of g(x) = (1/2)ˣ that is graph of f(x) reflected over y- axis.

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Answer:

Option D

Step-by-step explanation:

Remember that the sum of all angles in ANY triangle is 180 degrees. Also, remember that an acute triangle has angles that are all less than 90 degrees. So not only do our options have to add up to 180 degrees, but they also have to be less than 90 degrees in order for the triangle to be acute.

We can immediately exclude options A, B, and C because all three options have angles greater than 90 degrees, which means the triangle isn't acute.

Your answer is option D or "70, 80, 30." Since...

70 + 80 + 30 = 180
70 < 90
80 < 90
30 < 90

Hope this helps.

Answer:

I'(-0.5, 0.25), J'(0.5,0.5), K'(0.5, -0.25)[/tex]

Step-by-step explanation:

Assuming the dilation is centered at the origin, it is known that for a dilation of scale factor [tex]k[/tex] centered at the origin, [tex](x,y) \to (kx,ky)[/tex].

The coordinates of the vertices for the figure after the given transformation Dilation of 0.25. is solved to be

I' (-0.5, 0.25)

J' (-1, 1)

K' (1, -0.25)

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

In the given problem the coordinates of the image is solved when r = 0.25

preimage                                       image

I (-2, 1)   → (0.25 * -2, 0.25 * 1) →   I' (-0.5, 0.25)

J (2, 2)   → (0.25 * 2, 0.25 * 2) →   J' (-1, 1)

K (2, -1)   → (0.25 * 2, 0.25 * -1) →   K' (1, -0.25)

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Answer: The relation between the time it will take Rashid to make the trip, t, and the speed at which he slows down, v, can be determined by using the formula:

distance = speed * time

We know that Rashid travels 240 km from Abu Dhabi to Sharjah and that he originally drove at 120 km/h for 2 hours. So, we can write the equation:

240 = 120 * 2

Now, if Rashid slows down by v km/h, then the new speed is (120 - v) km/h and the new time, t, can be determined by substituting the new speed and distance into the equation:

240 = (120 - v) * t

So the relation shows that t = (240 / (120 - v))

This relation shows that the time, t, it will now take Rashid to make the trip is directly proportional to the speed, v, at which he slows down. As Rashid slows down, the time taken to make the trip will increase, and as he speeds up, the time will decrease.

Step-by-step explanation:

Answer:12

Step-by-step explanation:

dive 36 plates by by the amount of plates per stack (3)

The system of equations 12x + 51y = 156 and -8x - 34y = -104 has infinitely many solutions

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Given the equation:

12x + 51y = 156

Dividing by 3:

4x + 17y = 52       (1)

Also:

-8x - 34y = -104

Dividing by 2:

-4x - 17y = -52    (2)

To solve both equation by elimination, add equation 1 and 2:

0 = 0

The equation has infinitely many solutions

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The conventional equation y = ax2 + bx + c yields the vertex (h, k) as h(x-coordinate of the vertex) = -b/2a.

When it comes to geometry, a coordinate system is a technique that uses one or more integers or coordinates to specify the exact location of points or other geometrical objects on a manifold, such as Euclidean space. Locating a point or item on a two-dimensional plane requires the usage of pairs of integer coordinates. Two numbers known as the x and y coordinates serve as a description of a point's location on a 2D plane. a collection of figures that signify exact locations. Most often, the figure contains two numerals. The first number denotes the distance from front to rear, and the second number denotes the distance from top to bottom. In (12.5), for example, there are 12 units below and 5 above.

given

a) the intercepts are (4,0) , (1,9) and (-2 , 0 ) of the given figure

b) The equation for the parabola's axis of symmetry can be found in the vertex's x-coordinate.

(1,9) is the axis of symmetry

c) The conventional equation y = ax2 + bx + c yields the vertex (h, k) as h(x-coordinate of the vertex) = -b/2a.

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