Which of these strategies would eliminate a variable in the system of equations?

When charging $15 for a key chain, it is discovered that his maximum profit is $75 using the vertex of the quadratic function.

The vertex of a quadratic equation,

A quadratic equation is given by, [tex]ax^{2} +bx +c[/tex]

The vertex is given by [tex]A (x_{1} ,y_{1} )[/tex]

[tex]x_{1} = \frac{-b}{2a}\\ \\y_{1} = \frac{-b^{2} +4ac }{4a}[/tex]

Considering the coefficient a, we have that:

If a < 0, the vertex is a maximum point.

If a > 0, it will be a minimum point.

The function given is (x -10 ) (60 -3x)

f(x) = (x -10 ) (60 -3x)  = 60x -3[tex]x^{2}[/tex] -600 +30x = -3[tex]x^{2}[/tex] +90x -600

So, here a = -3, b = 90 and c = -600

So,

[tex]x_{1} = \frac{-b}{2a}\\ \\x_{1} = \frac{-90}{2*(-3)} = 15[/tex]

[tex]y_{1} = \frac{-b^{2} +4ac }{4a} = \frac{(-90)^{2} + 4*(-3)*(-600) }{4*(-3)} = 75[/tex]

Hence, He can make up to $75 in profit when he charges $15 for a key chain.

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The number 74.9963 would round down to 70

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

We need to round  74.9963 to the nearest 10

We can see that the 74.9963 is below 75 so it goes down, and it rounds down to 74.9963 instead of, 74.9 then that would round up to the decimal is higher than 70.

The answer would be 70

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The correct statement regarding the proportional relationships is given as follows:

Boat A travels at a faster rate than Boat B.

A proportional relationship is a special case of a linear function with intercept zero in which the output variable is given by the multiplication of the input variable and the constant of proportionality, in the case of a direct relationship, as follows:

y = kx

The function for boat A is:

d = 10.5t.

Hence the rate is:

10.5 miles per hour.

From the graph, the rate for boat B is obtained as follows:

k = 90/10 = 9 miles per hour.

A higher constant means a faster rate, 10.5 is greater than 9, hence boat A travels faster.

The problem is given by the image shown at the end of the answer.

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The first four terms in the sequence are 30, 90, 270 and 810 respectively.

We have that the nth term of the sequence is expressed as;

U = 10 × 3 ^n

Where;

n = number of terms

To determine the first terms, let's substitute the value of n as 1, we get;

U = 10 × 3^1

Multiply the values

U₁ = 30

The second terms, n = 2

U₂ = 10 × 3²

U₂ =  10 × 9

Multiply through

U₂ = 90

The third year, n = 3

U₃ = 10 × 3³

Find the cube of the value and multiply the values

U₃ = 270

The fourth year, n = 4

U₄ = 10 × 3^4

U₄ = 10 × 81

Multiply through

U₄ = 810

Thus, the numbers are 30, 90, 270, 810

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Answer:

The absolute difference is 1050

The relative percentage is 32.3076%

Step-by-step explanation:

We are given

The population of a town increased from 3,250 in 2008 to 4,300 in 2010

In 2008:

In 2010:

Absolute difference:

we know that

absolute difference =

absolute difference =

absolute difference is 1050

Relative increase:

we know that

Relative percentage is

now, we can plug values

=32.3076

So, the relative percentage is 32.3076%

The relationship between height and vertical jump is High positive correlation.

What is a correlation?

A statistical indicator of the relationship between the relative motions of two variables is the correlation. If the variables are correlated, a line or curve will be formed by the points. The points will touch the line more closely the better the correlation.

Main body:

To find the relation we need to draw a line passing closely to all the points , if we are able to draw such line , it has high positive correlation.

If the line doesn't pass through all points it has low positive correlation.

hence this has high positive correlation .

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Answer:

-positive

-linear

-strong

-no.

Step-by-step explanation:

edge 2023

The amount you pay for the items is C. $41.42.

The amount that the customer pays for the two items is determined by first discounting the second item by 60%.

The result after the discount is added to the cost of the first item before the sales tax is added to get the final cost of the items.

Discount on second item = 60%

The price of the first item purchased = $30

The price of the second item purchased = $20

Discounted price on the second = $8 ($30 x (1 - 60%)

Total cost before sales tax = $38 ($30 + $8)

Sales tax = 9%

Total cost after sales tax = $41.42 ($38 x 1.09)

Thus, after discounting the second item by 60% and adding the sales tax of 9%, the customer will pay $41.42 for the items.

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Answer:

c. 41.42 my teacher told me the answer

Step-by-step explanation:

Answer: the answer would be 2

Step-by-step explanation: f(x) means that for every x you are going to multiply it by the value it gives you in this case it is 3.

2x3=6-4=2

The domain of the function d(t)=1/2t+6 is (-∞, ∞) and the range of the function is (-∞, ∞).

Similar to how we input different numbers into functions, we also receive new numbers as the outcome. The two main characteristics of functions are domain and range.

A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A  → B exists that maps every element of A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R. The set of images is the function's range.

The domain of the function d(t)=1/2t+6 is given by

Domain: (-∞, ∞), {x|x ∈ R}

The range of the function is given by

Domain: (-∞, ∞) , {y|y ∈ R}

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The principle investment necessary to obtain a total sum of $400.00 from simple interest at an annual rate of 8% for 8 years is $243.90.

Arithmetic operations is a field of mathematics that studies numbers and the operations on numbers that are helpful in all other disciplines of mathematics. It consists mostly of operations like addition, subtraction, multiplication, and division. Arithmetic Operator is used to conduct mathematical operations on the supplied operands such as addition, subtraction, multiplication, division, modulus, and so on.

Here,

First, converting R percent to r a decimal

r = R/100 = 8%/100 = 0.08 per year.

Solving our equation:

P = 400 / ( 1 + (0.08 × 8)) = 243.90243902439

P = $243.90

The principal investment required to get a total amount, principal plus interest, of $400.00 from simple interest at a rate of 8% per year for 8 years is $243.90.

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Answer:  [tex](g \circ f)(x)=9\text{x}^2-36\text{x}+50\\\\[/tex]

=====================================================

Explanation:

The notation (g∘f)(x) is the same as g(f(x))

We'll start with the outer function g(x). Then replace each x with f(x). Afterward plug in f(x) = -3x+5 for the right hand side only.

This is what the steps look like

[tex]g(\text{x})=\text{x}^2+2\text{x}+15\\\\g(f(\text{x}))=(f(\text{x}))^2+2f(\text{x})+15\\\\g(f(\text{x}))=(-3\text{x}+5)^2+2(-3\text{x}+5)+15\\\\g(f(\text{x}))=9\text{x}^2-30\text{x}+25-6\text{x}+10+15\\\\g(f(\text{x}))=9\text{x}^2-36\text{x}+50\\\\[/tex]

Therefore,

[tex](g \circ f)(x)=9\text{x}^2-36\text{x}+50\\\\[/tex]

You can use tools like WolframAlpha, GeoGebra, and Desmos as ways to confirm the answer.

The probability that the student takes statistics given that he or she is a business major is 0.04.

The probability that an event will occur is determined by the probability formula. The ratio of positive outcomes to all possible outcomes is used as the formula to determine an event's probability. Probabilities are always in the 0 to 1 range. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.

Given,

The probability that a student takes statistics and is a business major is 0.036. the probability that a student takes statistics is 0.9. the probability that a student is a business major is 0.12

Students who have taken both:

P( statistics ∩ business) = 0.036

Only a statistics major:

P( statistics/ business) = 0.9

P( student is business major)

P ( statistics / business) ÷ P( statistics/ business)

0.036/0.9

0.04

The probability that the student takes statistics given that he or she is a business major is 0.04.

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Answer:

the answer Is 6 .........

The number of groups formed is 10 if we consider 5 cars in groups of 3.

Given, 5 cars in groups of 3, we can use the formula,

(5 3) = 5! / 3! × 2!

= 10

Permutation and combination are the various ways in which one can form a set that may be selected without any replacement. When the selection of a subset is where we use the permutation and when the ordering of the subset is there we use a combination.

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Answer:

(2,1)

Step-by-step explanation:

The x-value stays the same since we are only moving up/down and the y-value becomes the opposite

(x,y)--> (x,-y)

So the point becomes (2,1)

Answer:

(2,-1) hope this helps you understand

Answer:

Answer is: 8 2/3 but improper is 26/3

g(x) = (x+2-3) + 4 = (x-1)+4

Given that the signal gets larger than 210 microvolts, there is a 2.335 % chance that it is also larger than 240 microvolts.

As, per the given question.

Gaussian random variable n (200, 256)

Part a: Probability that signal will exceed 240 micro volts.

P(x > 240) = 1 - P(x ≤ 240)

P(x > 240) = 1 - P(240 - 200)/16

P(x > 240) = 1 - P(2.5)

See p value for z = 2.5

P(x > 240) = 0.00621

Thus, Probability that signal will exceed 240 micro volts is 0.00621.

Part b:  larger than 210 micro volts.

P(x ≥ 240) | x ≥ 210) = P(x ≥ 240) / P(x ≥ 210)

P(x ≥ 240) | x ≥ 210) = 1 - P(240 - 200)/16 /  1 - P(210 - 200)/16

P(x ≥ 240) | x ≥ 210) = 0.00621 / 0.26599

P(x ≥ 240) | x ≥ 210) = 0.02335

Thus, for the signal gets larger than 210 microvolts, there is a 0.02335 percent chance that it is also larger than 240 microvolts.

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Answer: 4x+10

simplified: 2x+5

Step-by-step explanation:

Answer: 4x+10

You multiply 2 by (2x) = 4x

You multiply 2 by (5) = 10

Reflection in geometry means the type of transformation that flips a shape in a mirror line.

What is reflection ?

Reflection is a type of transformation that flips a shape in a mirror line so that each point is the same distance from the mirror line as its reflected point.

Let us suppose that the triangle with one coordinate  [tex](3,-5)[/tex] and the other two are unknown and we do not even want to know them but it would be better if we do know them:-

And we have a graph.

Let us draw a line [tex]y=-2[/tex] on the graph and draw the triangle

Now the coordinates [tex](3,-5)[/tex] are three boxes away from the line [tex]y=-2[/tex], so we plot this coordinate three boxes up from the line [tex]y=-2[/tex] and do the same for other coordinates so [tex](x,y)[/tex] is one box up from the line [tex]y=-2[/tex] so we plot the coordinates one box up from the line [tex]y=-2[/tex]

Hence, the image is located at [tex]G[/tex] is plotted above.

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Answer:

X = 2, Y = 0

Step-by-step explanation:

Add the two equations together to cancel out -4y and +4y

leaving you with:

8x = 16

8x = 16

divide both sides of the equation by 8 to get x on its own (8x/8 = x, 16/8 =2)

leaving you with:

x = 2

substitute the value of x back into the equation to calculate y (it can be either equation, top or bottom):

8(2) - 4 y = 16

8 x 2 = 16

leaving you with:

16 - 4y = 16

subtract 16 from both sides to get 4y on its own

leaving you with:

-4y = 0

so y = 0, and x = 2

The area of the figure created by Brianna is  [tex]33\frac{3}{4}[/tex] square feet.

Explain area in mathematics.

Area is a mathematical concept that expresses the size of a region on a planar or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area or, it can be simply defined as the total amount of space occupied by a flat (2-D) surface or an object's shape.

Solution Explained:

A square with a side of 4 1/2 feet and two parallelograms with bases of 4 1/2 feet and heights of 1 1/2 feet make up the figure.

Therefore, the total area of the figure is
Area of Square + 2 X Area of Parallelogram
= (side)^2 + 2(b X h)
= (4 1/2)^2 + 2(4 1/2 X 1 1/2)
= 81/4 + 27/2    
=  135/4
= [tex]33\frac{3}{4}[/tex] square feet

Area of the figure is [tex]33\frac{3}{4}[/tex] square feet.

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The number of student like at least one kind of ice cream is given by (d) 275.

Let C be the student who like chocolate ice cream and P be the student who like Pistachio ice cream.

Now given that, n(C) = 145, n(P) = 150

Also given that, 123 students do not like neither chocolate or pistachio ice cream.

So, n(P' and C') = 123

The required number of student like at least one kind of ice cream is given by,

N = 398 - n(P' and C') = 398-123 = 275

Hence the correct option is (d).

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The series expansion for e z 1 z up to z 5 is obtained by multiplying the Maclaurin series for e z and 1 1 z. For |z| 1, this series converges.

The Maclaurin series for e^z is:

e^z = 1 + z + z^2/2! + z^3/3! + z^4/4! + ...

The Maclaurin series for 1/1-z is:

1/(1-z) = 1 + z + z^2 + z^3 + z^4 + ...

Multiplying these two series together gives:

e^z/(1-z) = (1 + z + z^2/2! + z^3/3! + z^4/4! + ...)(1 + z + z^2 + z^3 + z^4 + ...)

= 1 + (1+z) + (z + z^2/2! + z^2) + (z^2/2! + z^3 + z^3/3!) + (z^3/3! + z^4 + z^4/4!) + ...

= 1 + z + 2z^2 + 3z^3 + 5z^4 + ...

This series converges for |z| < 1

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The sum of the geometric progression with the features stated in the text is given as follows:

S = 2.62 x 10^(43).

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

The sum of a finite geometric sequence with n terms is given as follows:

[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]

In this problem, the first term and the common ratio are given as follows:

[tex]a_1 = 2, n = 3[/tex]

Hence the equation is:

[tex]a_n = 2(3)^{n - 1}[/tex]

The nth term is of 1458000, hence the number of terms of the sequence is obtained as follows:

[tex]a_n = 2(3)^{n - 1}[/tex]

[tex]1458000 = 2(3)^{n - 1}[/tex]

[tex]3^{n - 1} = 729000[/tex]

[tex]3^{n - 1} = 3^{90}[/tex]

Then:

n - 1 = 90

n = 91.

Thus the sum of the sequence is given as follows:

[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]

[tex]S_{91} = \frac{2(1 - 3^{91})}{1 - 3}[/tex]

S = 2.62 x 10^(43).

The problem is solvable with an nth term of 1,450,800, not 145,800, as 145,800/2 is not a root of 3.

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The greatest possible number of total points for each of the top three teams is 24.

Given;

Six teams compete against one another twice in a tournament. A team receives three points for a victory, one point for a tie, and no points for a defeat. The top three clubs ended up with the same total number of points when all the games were completed.

After fully understanding the problem, we immediately know that the three top teams, say team A, team B, and team C, must beat the other three teams D, E, F. Therefore, A, B, and C must each obtain (3 + 3 + 3 ) = 9 points. However, they play against each team twice, for a total of 18 points against D, E, and F. For games between A, B, and C, we have 2 cases. There is an equality of points between A, B, and C in the following cases.

Case (I): A team ties the two other teams. For a tie, we have 1 point, so we have (1 + 1) * 2 = 4 points (they play twice).

Therefore, this case brings a total of 4 + 18 = 22 points.

Case (II): A team beats one team while losing to another. This gives equality, as each team wins once and loses once as well. For a win, we have 3 points, so a team gets 3 * 2 = 6 points if they each win a game and lose a game.

This case brings a total of 18 + 6 = 24 points.

Therefore, we use case (II) since it brings the greater amount of points as 24.

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The dimensions of a rectangular box with a square base which has a volume of 12 cubic feet is a = 12^ 1/3, b = 12^ 1/3

Rectangular Box with Square base

Volume v = a²b = 12

S = Surface area = 2a² + 4ab

v = a²b = 12

b = 12/a²

S = 2a² + 4ab = 2a² + 4a(12/a²) =2a² + 48/a

S'(a) = 4a -48/a² = 0

4a³ = 48

a = 12^ 1/3

b = 12/a² = 12/12^ 2/3 = 12^ 1/3

Therefore, the dimensions of a rectangular box with a square base which has a volume of 12 cubic feet is a = 12^ 1/3, b = 12^ 1/3

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