2x+3y=122, x, plus, 3, y, equals, 12
Complete the missing value in the solution to the equation.
((left parenthesis
,8),8)

example:Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3-5 = 3-3 = 1/33 = 1/27.

Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger.

Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology

Understand the connections between proportional relationships, lines, and linear equations.

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Solve linear equations in one variable.

Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Analyze and solve pairs of simultaneous linear equations.

Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

Solve real-world and mathematicl problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line throug

Answer:

The polynomial is 2x^3 - 8x^2 - 24x

And we can factor out a 2x from each of the three terms:

2x(x^2 - 4x - 12)

Lastly, factor the remaining quadratic:

2x(x+(-2))(x+6)

And we have our answer:

a=2

b=-2

c=6

Let me know if this helps!

Answer:

a =2, b =2, and c = -6

Step-by-step explanation:

We factor the polynomial and then see which value corresponds to what.

2x^3-8x^2-24x

As we see it, all terms are factorable by 2x. So if we take out 2x from every term, we get

2x(x^2 - 4x - 12)

Now we factor the quadratic, which we can do mentally to get

2x(x+2)(x-6)

ax(x+b)(x+c)

Comparing that to ax(x+b)(x+c), we can tell that a =2, b =2, and c = -6.

Answer:

260 cities

Step-by-step explanation:

Multiple 5 and 52

James would visit 260 cities in one year.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

1 year = 52 weeks

James visits 5 cities per week.

To find the number of cities in e one year:

Multiply by 52

52 x 5

= 260 cities.

Therefore, he would visit 260 cities.

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The probability that cards are from different suits is \(\frac{39}{51}\)

Probability of an event E represented by P(E) can be defined as (The number of favorable outcomes )/(Total number of outcomes).

There are 4 suits hearts, diamonds, club and spade in a standard deck of 52 cards.

Each of them has 13 cards each .

So when we pick first card from a single suit

we can pick it in 13 ways , now 12 cards are left.

We can pick the 2nd card from the same suit in 12 different ways .

So to pick 2 cards from a single suit we have 13x12 ways.

to pick 2 card from 4 suits = 4x13x12=624 ways

Total ways of choosing 2 cards from the pack of 52 cards is 52 X 51 =2652

probability that the cards are of same suits=\(\frac{624}{2652} =\frac{12}{51}\)

probability that the cards are of different suits=\(1-\frac{12}{51} =\frac{39}{51}\)

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A scatter plot would be the best choice to indicate whether there was a negative relationship between stock and bond returns.

A scatter plot is a type of graph used to display the relationship between two variables. It is also known as a scatter chart or scattergram. The graph consists of a series of points, each representing a single observation or measurement of two variables. The position of each point is determined by its values on the two variables. In a scatter plot, one variable is plotted on the x-axis and the other variable is plotted on the y-axis.

This type of graph would show the relationship between two variables, in this case stock and bond returns, on a single graph. It would provide a visual representation of any negative or positive correlation between the two variables.

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Answer:

A growth function has the following form.

where  = Original amount,

r = annual rate of change,

n = number of periods,

t = time in years

Since the time is in years, we need to convert t into days. We know that 1 year = 365 days. So t years = 365t days.  

So in this case, n = 365, r = 0.0095.

Then the function is rewritten as follows.

The daily growth rate would be  

Step-by-step explanation:

Lets find year wise population for example

\(\\ \sf{:}\longrightarrow P(3)=25,000(1.1023)3^2\)

\(\\ \sf{:}\longrightarrow P(3)=27557.5(9)\)

\(\\ \sf{:}\longrightarrow P(3)=248017.5\)

Answer:

$11.25

Step-by-step explanation:

Let x = pay of regular hour

y = time-and-half rate hour pay

40x + 8y = 585

y = 1.5x

40x + 8(1.5x) = 585

40x + 12x = 585

52x = 585

52x/52 = 585/52

x = 11.25

The graph of the functions f(x) and g(x) shows that f(x) is a straight line that increases as x increases, while g(x) is a parabola that increases as x increases. Therefore, all of the statements given are true.

An asymptote is a straight line or curve that approaches a given curve arbitrarily closely but never meets or crosses it.

The correct answers are 1, 2, 3, 4, 5, 6, 7 and 8.

The graph of the functions f(x) and g(x) shows that f(x) is a straight line that increases as x increases, while g(x) is a parabola that increases as x increases.

From the table and graph, it is clear that both functions go to positive and negative infinity as x approaches positive and negative infinity, respectively, so there is no maximum or minimum value for either function.

Additionally, both functions have a horizontal asymptote at y=0 and y=1 for x values greater than zero but not going to positive infinity.

This means that the minimum for g(x) is almost at 0 and the minimum for f(x) is almost at 1. Therefore, all of the statements given are true.

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Step-by-step explanation:

4×10×2=80

20×10×1=200

20×8×1=160

20×10×1=200

2×20×1=40

10×2×2=40

80+200+160+200+40+40=720

The standard form of the given polynomial is x⁶ + 53x⁵ + 2x⁴ - 2 which has a highest degree of 6 while the leading coefficient is 1. This polynomial is called a quadrinomial because it has 4 terms

A polynomial is an equation that only uses addition, subtraction, multiplication, and non-negative integer exponents of variables and consists of variables (also known as indeterminates) and coefficients. Algebra, calculus, and numerical analysis are just a few of the mathematics and scientific disciplines that use polynomials.

In the presented problem, we must determine the terms, variables, coefficients, and other properties of the polynomial f(x).

f(x) = 2x⁴ + 53x⁵ - 2 + x⁶

The standard form of this polynomial is x⁶ + 53x⁵ + 2x⁴ - 2

The degree of the polynomial is 6

The leading coefficient is 1 which is the coefficient of the degree of the polynomial

This is called a Quadrinomial because it has 4 terms

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Answer: Option B.

Step-by-step explanation:

A linear function can be written as:

y = a*x + b

where a is the slope and b is the y-intercept.

if the line passes through the points (ax, ay) and (bx, by) then the slope is:

a = (bx - ax)/(by - ay)

In this case, we can see that the line passes through the points:

(1, 3) and (2, 1)

Then the slope is:

a = (1 - 3)/(2 - 1) = -2

y = -2*x + b

In the graph we also can see that the line intersects the y-axis at y = 5, then b = 5.

The line is:

y = f(x) = -2*x + 5.

the inverse function is such that:

g( f(x)) = x

to find the inverse function of a linear equation, we just could isolate x.

y - 5 = -2x

-y/2 + 2.5 = x

Then we could write the inverse function as:

g(x)  = - x/2 + 2.5

Now we need to see which pairs belong to this line. I just will evaluate the function g(x) in different values of x, and see which points belong to the line.

g(9) = -9/2 + 2.5 = -4.5 + 2.5 = -2

(9, -2) belongs to the line.

g(7) = -7/2 + 2.5 = -3.5 + 2.5 = -1

Then (7, -1) belongs to this line.

g(5) = -5/2 + 2.5 = 0

Then the point (5, 0) belong to this line.

We can already see that all these points are in option B, then option B is the correct one.

Answer:

A: 6 and 4x

B: SEE BELOW

C: 20 and X

Step-by-step explanation:

A: becuase of the 5 on the outside of the parentheses you would multiply both by 5 making the factors 6 and 4x

B: I just answered it in A

C 5*4x = 20x

20 is the coefficient and X is the variable

Answer:

8b

Step-by-step explanation:

You can factor the b-term out since b-term exists for all terms in the expression. By factoring out, you are basically dividing the factored term off and put it outside of the bracket, thus:

\(\displaystyle{16b-8b=\left(16-8\right)b}\)

Then evaluate and simplify:

\(\displaystyle{\left(16-8\right)b=8\cdot b}\\\\\displaystyle{=8b}\)

We diagree with Marco because

and

where, in the first expression, we factorized x and got

and in the second one, we got

In summary, the first expression is equal to x and the second one is equal to zero, so they are different expressions.

Answer: The solution of these inequalities are similar because they begin at two, however they are different because in the first inequality two cannot be an answer hence the open circle ⭕️, but the second inequality can have two as a solution hence the closed circle.

Step-by-step explanation:

The total annual cost of the machine is $25,312.50.

To calculate the total annual cost of the machine, we need to consider the various components:

Capital Cost:

The cost of the machine is $50,000. Since it will be sold after 8000 hours of work for 10% of the purchase price, the capital cost per year is (50,000 * 0.1) / 8000 = $62.50.

Fuel and Minor Repair Cost:

The cost is $15.00 per hour. Considering the estimated working hours of 1400 per year, the annual fuel and minor repair cost is 15 * 1400 = $21,000.

Tire Replacement Cost:

The cost to replace a set of tires is $3500, and the estimated tire life is 2800 hours. So, the cost per hour is 3500 / 2800 = $1.25. Considering the annual working hours of 1400, the annual tire replacement cost is 1.25 * 1400 = $1750.

Opportunity Cost:

The cost of capital rate is 7%. Considering the machine's capital cost of $50,000, the annual opportunity cost is 0.07 * 50,000 = $3500.

Now, we can calculate the total annual cost by adding all the components:

Total Annual Cost = Capital Cost + Fuel and Minor Repair Cost + Tire Replacement Cost + Opportunity Cost

= 62.50 + 21,000 + 1750 + 3500

= $25,312.50

Therefore,  the approximate total annual cost of the machine is $25,312.50.

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The relationship described, where the number of ants in a colony doubles every month, can be modeled by an exponential function.

An exponential function is of the form y = ab^x, where 'a' is the initial value or starting point, 'b' is the growth factor, and 'x' represents the time or number of months in this case.

In the given scenario, the initial number of ants is multiplied by a growth factor of 2 every month. This corresponds to the base 'b' of the exponential function being equal to 2. The exponent 'x' represents the number of months elapsed.

Therefore, the exponential function y = 2^x best models the relationship between the number of ants in the colony and the time, as it reflects the doubling pattern observed in the colony's population over time.

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Answer: D

Step-by-step explanation:

Because 120 is the amount he already has know u need to see what x is and times that by 6 because it’s how many weeks.

Oh and when people send links as answeres there hackers.

Answer:

Step-by-step explanation:

If Sam has 120 dollars in his account and he wants to save the same amount each week

let x be the amount he wants to save each week

the expression will be

120+6x

Answer:

Step-by-step explanation:

(2 + 3) + 4 = 2 + (3 + 4)This expression can be simplified using the associative property of addition, which states that the grouping of the terms in a sum can be changed without changing its value. By rearranging the terms within the parentheses, we can simplify the expression as follows:2 + (3 + 4) = 2 + 7 = 9

Answer:

Step-by-step explanation: (a+b) +c =a +(b+c)

The answer is that the mathematician solved 2k problems on the day he drank coffee.

Let's assume that the mathematician works for x hours a day and can solve y problems per hour. Also, the mathematician drinks some coffee and discovers that he can now solve z problems per hour. So, the mathematician works for n hours that day. We are given that:x*y = number of problems solved in a dayz * n = number of problems solved on the day he drank coffee

Then, we can write the equations:x*y = n * 2*z (he still solves twice as many problems as he would in a normal day)andx = n (he only works for n hours that day)Now, we need to simplify these equations to solve for the number of problems solved on the day he drank coffee. Here is how to do it:$$x*y = n * 2*z$$$$\frac{x*y}{x} = \frac{2*n*z}{x}$$$$y = 2 * \frac{n*z}{x}$$Since x, y, n, and z are all positive integers, we can say that the expression 2*n*z/x is also a positive integer. Therefore, we can write:$$\frac{2*n*z}{x} = k$$$$y = 2k$$where k is a positive integer.

Finally, the number of problems solved on the day he drank coffee is:y = 2k Therefore, the answer is that the mathematician solved 2k problems on the day he drank coffee.

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To determine if the amount of bacteria in carpeted rooms (population 1) is significantly less than the amount in uncarpeted rooms (population 2), a hospital conducted a study using samples from both populations.

The sample of 23 carpeted rooms had an average of 62.1 grams of bacteria per square foot, with a sample standard deviation of 4.5 grams. The sample of 19 uncarpeted rooms had an average of 67.2 grams of bacteria per square foot, with a sample standard deviation of 4.3 grams. The hospital wants to construct an 80% confidence interval for the true difference in means between the two populations.

To construct the confidence interval, we use the formula: (x1 - x2) ± (t * sqrt((s1^2 / n1) + (s2^2 / n2))), where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and t is the critical value from the t-distribution based on the desired confidence level and degrees of freedom.

In this case, since the population standard deviations are unknown, we use the t-distribution. The degrees of freedom are calculated using the formula: df = (s1^2 / n1 + s2^2 / n2)^2 / ((s1^2 / n1)^2 / (n1 - 1) + (s2^2 / n2)^2 / (n2 - 1)).By substituting the given values into the formulas, we can calculate the confidence interval for the difference in means and determine if the amount of bacteria in carpeted rooms is significantly less than in uncarpeted rooms at the 80% confidence level.

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Michael’s child is going to college in 13 years. If he saves $ 7,000 a year at 9% compounded annually. Therefore,  the amount available for Peter's child education will be $147,330.55.

Given that Michael is saving $7,000 per year for his child's education which will occur in 13 years. If the interest rate is 9% compounded annually,

The problem of finding the amount of money Michael will have saved in 13 years is a compound interest problem.

In this case, the formula for calculating the future value of the annuity is: $FV = A[(1 + r)n - 1] / r

where: FV is the future value of the annuity, A is the annual payment,r is the annual interest rate, and n is the number of payments.

Using the above formula; the future value of Michael's savings is:

FV = 7000[(1 + 0.09)^13 - 1] / 0.09= 7000(1.09^13 - 1) / 0.09= 147,330.55

Therefore, the amount available for Peter's child education will be $147,330.55.

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An adiabatic process is one in which the heat transered between a system and its surroundings is equal to zero( q = 0 ). So, option(e) right one.

In thermodynamics, the adiabatic process is a process in which there is no heat or air exchange between the temperature and the environment. It is different from the isothermal heat flow process. Some important properties are :

Hence, option(e) is right answer.

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Answer:

B

Step-by-step explanation:

Divide 323/17 = 19

if you multiply 17 x 19 = 323

The z-score for that condition is 0.38. To be exact, the z-score is 0.38461538461.

First we have to extract mean and standard deviation from x~n(145, 13) where mean (μ) = 145 and standard deviation(б) = 13. As per given corresponding to an observation(x) is directly given = 150 we can start to find the z-score with formula z-score = (x - μ) :  б. So

z = (x - μ) :  б.

z = \(\frac{150-145}{13}\)

z = \(\frac{5}{13}\)

z = 0.38461538461

Normally z written in 2 to 4 digit after decimal, so z-score = 0.38

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If an equation indicates addition in its presentation, in order to solve for the unknown, you must perform the inverse operation, which is subtraction.

Equations typically involve an equality between two expressions, with one or more unknown variables.

To isolate the unknown variable and determine its value, you need to perform operations on both sides of the equation to simplify and solve for the variable.

When an equation shows addition, you can undo that operation by subtracting the same value from both sides of the equation. This ensures that the equation remains balanced and maintains equality.

For example, consider the equation:

x + 5 = 10

To solve for x, you need to eliminate the 5 added to x. To do so, you subtract 5 from both sides of the equation:

x + 5 - 5 = 10 - 5

x = 5

By subtracting 5 from both sides, you isolate the variable x and find that its value is 5.

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Yes, the 5x5 matrix is diagonalizable because it has two eigenvalues with eigenspaces of dimensions 3 and 2.

A matrix is diagonalizable if and only if the sum of the dimensions of its eigenspaces equals its size (the number of rows or columns).

a matrix is a rectangular array of numbers or symbols arranged in rows and columns. Each element in the matrix is

identified by its row and column index. Matrices are commonly used in linear algebra, where they are used to

represent linear transformations and systems of linear equations.

In this case, the three-dimensional eigenspace and the two-dimensional eigenspace have a combined dimension of 5, which is the size of the matrix.

Therefore, the 5x5 matrix is diagonalizable.

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Question

A is a 5 x 5 matrix with two eigenvalues. One eigenspace is three-dimensional, and the other eigenspace is two-dimensional. Is A diagonalizable?