3s + a = 38 and 3s + 2a =52

Answer: 157.5

Step-by-step explanation:

The quadrilateral's new coordinates will be J(4, 4), K(3, 4), L(1, 1), and M (4,1) when the procedure is applied.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given coordinates of a quadrilateral J(-4, 4), K(-3, 4), L(-1, 1), M(-4,1)

Reflect in the x-axis

Since,

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).

thus new coordinates will be,

J(-4, -4), K(-3, -4), L(-1, -1), M(-4,-1)

Rotate 180 degrees about the origin

Since,

When we rotate a figure of 180 degrees about the origin either in the clockwise or counterclockwise direction, each point of the given figure has to be changed from (x, y) to (-x, -y) and graph the rotated figure.

Thus new coordinates will be

J(4, 4), K(3, 4), L(1, 1), M(4,1)

Therefore, After applying the given operation the new coordinates of the quadrilateral will be  J(4, 4), K(3, 4), L(1, 1), and M(4,1).

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Answer: The solution of the equation is x = 48. The equation is 20 = x - 28.

Step-by-step explanation:

-20 is like having -20 dollars, and you want to know how much you have to add to it to get to 28 dollars. So we add 20 to -28 and we get the number x = 48, so 48 dollars is what we need to add to -20 dollars to get to 28 dollars.

Answer:

what is this i do not know sorry so no 30 points right

Answer:

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation: I'm not 100% if this is it because it's been awhile but I believe that you write 2x+2=4x-4 to solve for x since they're both y=mx+b equations. After solving it you would get 3

Answer:

The answer is option A.

Step-by-step explanation:

To find the rate at which the questions were answered correctly on the first try, we can divide the number of questions answered correctly by the total number of questions.

Let's call the rate of correct answers on the first try as R

R = (number of questions answered correctly) / (total number of questions)

Substituting the given values:

R = 67 / 74

R = 0.905

So, the rate of correct answers on the first try is 0.905.

Answer:

Step-by-step explanation:

The question answered correctly in fraction will be 67/74.

67/74 equals 67÷74, which is 0.9054054054...

0.9054054054... round to the nearest thousand is 0.905.

So the answer is A, 0.905.

Answer:

y = 5x - 4

Step-by-step explanation:

1. Parallel have the same slope (equation)

- Standard form of an equation of a line: y=mx + b

m = slope

x = x-coordinate

b = y-intercept

y = y-coordinate

SLOPE = [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1}}[/tex]

Given that x-2y = 5

and the line has the point:

(-3,-1)

We need to find another point to find the slope

x - 2y = 5

Let's say x = 7 and y = 1

(7, 1)

Now plug it into the slope equation

[tex]\frac{-3-7}{-1-1} = \frac{-10}{-2} = 5[/tex]

Plug the slope into the standard form of an equation of a line

y = 5x + b

Plug in (7,1)

1 = 5 + b

b = -4

The answer is: y = 5x - 4

Hope this helps :)

Have a great day!

Answer:

y = 5/4x - 8

Step-by-step explanation:

first you convert the equation to y = mx + b

then you add the the -8 into the x and the 2 into the y and solve for b

b = -8 and since it is parallel same slope.

hope this helps :)

[tex]P(t)=3400e^{0.04t}\implies 68000=3400e^{0.04t}\implies \cfrac{68000}{3400}=e^{0.04t} \\\\\\ 20=e^{0.04t}\implies \log_e(20)=\log_e(e^{0.04t})\implies \log_e(20)=0.04t \\\\\\ \ln(20)=0.04t\implies \cfrac{\ln(20)}{0.04}=t\implies 74.89\approx t[/tex]

that's about 74 years and 325 days more or less.

based on the exponential equation which is really a continuously compounding equation with an initial value of 34000 in 1994, so 74 years later that'd be 1994 + 74 = 2068, then we add the 325 days to that, well, that's pretty much in November in 2069.

The linear equation for this situation is ax + y = Total cost, where is no. of ticket, x = $32.5, is cost of ticket and y = $11.9 is processing fee.

A linear equation is an algebraic equation where the highest exponent of the variable is one. There are linear equations with one, two, or three variables, but not all linear systems have three equations. Typically, a system of linear equations has a single solution, but occasionally there is no solution or an infinite number of solutions.

A relationship in which the value of one variable, say "x," depends on the value of the other variable, say "y," is described by a two variables linear equation. A linear equation's graph will be a straight line if there are only two variables.

Given that cost for 5 tickets is $174.45

Let x be the cost of each ticket and y be the processing fee

5x + y = 174.45

And for the cost for 8 tickets is $271.95

8x + y = 271.95

Subtract the terms

 8x + y = 271.95

- 5x + y = 174.45

 3x + 0 = 97.5

If 3x = 97.5

Then,

x = 97.5/3

x = 32.5

Each ticket costs $32.5 then processing fees

5(32.5) + y = 174.45

y = 174.45 - 162.5

y = 11.95

8(32.5) + y = 271.95

y = 271.95 - 260

y = 11.95

Thus, The linear equation for this situation is ax + y = Total cost, where is no. of ticket, x = $32.5, is cost of ticket and y = $11.9 is processing fee.

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When the function, m ( x)  = x + 1 is graphed, the result is shown attached.

When graphing a function, you need to remember that x is the independent variable. This means that you need to come up with the values of x and then use these values to come up with the corresponding values of y or m (x ) using the function.

Assuming you have values of x which are -3, -2, -1, 0, 1, 2, 3, the values of y would be:

x = - 3:
= x + 1

= - 3 + 1

= -2

x = - 2

= - 2 + 1

= - 1

x = - 1

= - 1 + 1

= 0

x = 0:

= 0 + 1

= 1

x = 1 :

= 1 + 1

= 2

x = 2 :

= 2 + 1

= 3

x = 3 :

= 3 + 1

= 4

The points would then be:
( - 3, - 2) , ( - 2, - 1) , ( - 1 , 0 ) ( 0, 1 ) ( 1, 2 ) ( 2, 3 ) ( 3, 4 )

The graph would be shown as attached.

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The value of the expression - 9(18 - 9 + 12) + 12(- 9 + 18 + 18) is 135.

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Let, The rectangle be x, the triangle by y, and the star be z.

Therefore,The three linear equations are,

x + 3y + z = 57...(i)

12x + 5y = 234...(ii)

8x - 6x + 3x = 60...(iii)

5x = 60.

x = 12.

Putting the value of x in eqn(ii) we have,

12(12) + 5y = 234.

144 + 5y = 234.

5y = 90.

y = 18.

Now, Putting the value of x and y in eqn(i) we have,

12 + 3(18) + z = 57.

12 + 54 + z = 57.

z = - 9.

So, The value of the expression z(y + z + x) + x(z + y + y) is,

= - 9(18 - 9 + 12) + 12(- 9 + 18 + 18).

= - 9(21) + 12(27).

= - 189 + 324.

= 135.

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Answer: x = 2

Step-by-step explanation:

Multiply each term between the parentheses by 2 1/3.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2\frac{1}{3}(2x-3)=2\frac{1}{3} \iff \ 2\frac{1}{3}\times2x+2\frac{1}{3}\times(-3)=2\frac{1}{3} } \end{gathered}$} }[/tex]

We calculate the expression of the multiplication.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2\frac{1}{3}\times2x+2\frac{1}{3}\times(-3)=2\frac{1}{3} \iff \ \frac{14x}{3}+2\frac{1}{3}\times(-3)=2\frac{1}{3} } \end{gathered}$} }[/tex]

We calculate the multiplication and division of rational numbers.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{14x}{3}+2\frac{1}{3}\times(-3)=2\frac{1}{3} \iff \frac{14x}{3}-7=2\frac{1}{3} } \end{gathered}$} }[/tex]

We convert the mixed fraction to improper.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{14x}{3}-7=2\frac{1}{3} \iff \dfrac{14x}{3}-7=\dfrac{7}{3} } \end{gathered}$} }[/tex]

We eliminate the fractions by multiplying by the least common multiple of the denominators of both sides.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\dfrac{14x}{3}-7=\dfrac{7}{3} \iff \ 14x-21=7} \end{gathered}$} }[/tex]

We move the constant to the right side and change the direction of the sign.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{14x-21=7 \iff 14x=7+21=28, and \ remains \ 14x=28} \end{gathered}$} }[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{14x=28 \iff \ we \ divided \ x=\frac{28}{14}=x; \Rightarrow x=2. } \end{gathered}$} }[/tex]

The number of quarters Dalton has is 5.

Dalton has $3.05 in dimes and quarters. He has 13 more dimes than quarters. Therefore, the number of quarters he has can be calculated as follows:

Hence, using system of equation,

Therefore,

let

x = number of quarters

y = number of dimes

y = x + 13

0.25x + 0.1y = 3.05

using substitution method,

0.25x + 0.1(x + 13) = 3.05

0.25x + 0.1x + 1.3  = 3.05

0.35x = 3.05 - 1.3

0.35x = 1.75

x = 1.75 / 0.35

x = 5

Therefore,

number of quarters = 5

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Answer:

improper fraction

Step-by-step explanation:

A mixed number has a whole number and a fraction.

An improper fraction is a fraction with a numerator bigger than the denominator.

Since 17 > 4 and there is no whole number,  this is an improper fraction.

It can be changed to a mixed number by dividing the numerator by the denominator

17 ÷4 = 4 and there is a remainder of 1.  The remainder goes over the denominator

4  1/4

Answer: It's an improper fraction

Step-by-step explanation: It's an improper fraction because an improper fraction is a fraction where the numerator is greater than the denominator, whereas a proper fraction is the opposite. A mixed number is when there is a whole number and then a regular (proper) fraction beside it. Here's an example:

[tex]5\frac{1}{7}[/tex]

Since 17 is greater than 4, 17/4 is an improper fraction. Now, if you wanted to find 17/4 as a fraction, you would divide the 17 by the 4, so the  whole number (4 in this case) would be the whole number, and the faction would be 1/4

So, [tex]\frac{17}{4}[/tex]= [tex]4\frac{1}{4}[/tex]

To check, you can multiply the 4 by the 4, which is 16, and add the numerator (1) to it, which would be 17/4. I hope this helps.

The cost of a candy bar is equal to $1.61.

In order to write an equation that model this situation, we would assign variables to the cost of candy bars and the cost of soda respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation based on the fact that three (3) candy bars and one (1) soda costs $5.63 as follows;

3x + y = 5.63   ...equation 1.

Additionally, one candy bar and four sodas cost $4.81 at the same price;

x + 4y = 4.81 ...equation 2.

x + 4(5.63 - 3x) = 4.81

x + 22.52 - 12x = 4.81

11x = 22.52 - 4.81

x = 17.71/11

x = $1.61

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The new coordinates after dialting using scale factor are , A ' ( -21, 14 ) ,

B ' ( 28, 14 ) and C ' ( -7, -7 ) .

What is a graph ?

Graph can be defined as the visual representation which is used to represent the data.

The scale factor is k = 7. This tells us to multiply each coordinate, of each point, by the scale factor to get the dilated points.

For example, point A is at (-3, 2) and moves to A ' (-21, 14) after multiplying the x,y coordinates by 7. The same applies for points B and C as well.

The dilation rule can be written as (x, y) -> (7x, 7y)

As a result of the dilation, triangle A'B'C' has sides that are 7 times longer compared to the corresponding sides of triangle ABC.

Example: side AB = 7 units, side A'B' = 49 units

Hence, The new coordinates after dialting using scale factor are , A ' ( -21, 14 ) , B ' ( 28, 14 ) and C ' ( -7, -7 ) .

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Answer:

a) To determine an equation for the revenue, y, when x packages of batteries are sold, we need to know the price of each package of batteries.

Since the price of a package of batteries is $5.00, the revenue, y, when x packages of batteries are sold is given by y = 5x, where x is the number of packages of batteries sold and y is the revenue in dollars.

b) To find the maximum daily revenue that Rahj can expect from battery sales, we need to find the value of x that maximizes y = 5x.

Given that for every increase of 10¢ in the price A of a package of batteries, sales decrease by 10 packages per day. And the store normally sells 700 packages of batteries per day, at $5.00 per package.

It means that the store will sell a maximum number of batteries when the price is at $5.00

And the maximum daily revenue will be $5 * 700 = $3500.

So the maximum daily revenue that Rahj can expect from battery sales is $3500. And the number of packages of batteries sold when the revenue is at a maximum is 700.

The equation is y = 5x, where x is the number of packages of batteries sold and y is the revenue in dollars.

The zeroes of the equation are the points at which the function crosses the x and y-axis.

The x-intercept is the point at which the function crosses the x-axis. It happens when y = 0. So the x-intercept of this equation is (0,0)

The y-intercept is the point at which the function crosses the y-axis. It happens when x = 0. So the y-intercept of this equation is (0,0)

Step-by-step explanation:

Answer:

C, E and F

Step-by-step explanation:

Area of figure 1 is 468 cm² and figure 2 is 45 cm².

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

In these given figure for calculating the area of them we need to divide them into two or more shape like rectangle, triangle or square. For example, I will take Figure 1 and 2

For figure 1

Length of base = 16 + 14 =  30 cm

Length of right rectangle whose side is 14 and 14(smaller one)

Thus, its area = 14 * 14 = 196

Area of left rectangle whose side is 16 and 17 = 16 * 17 = 272

Total area of the figure = 272 + 196 = 468 square cm

For figure 2

If we split them into two shape they will become a square and a triangle

Area of triangle = 1/2 base * height = 1/2 * 6 *3 = 9

Area of square = side * side = 6*6 = 36

Thus, total area = 9 + 36 = 45 square cm

Therefore, Area of these given figures(in unit square) are:

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Answer:

the circuit a1 and a3 are parallel to each other

rest of them must be in series

The quotient of these two expressions is not a finite value.

A quotient is a result obtained by dividing one quantity by another. It is the number that results from dividing one number by another.

Here,

Given : The quotient of

2-√√√8

and

4+√12

is not a finite value.

Explanation:

The square root of 8 is 2, so the first square root is 2, the second one is also 2, the third one is 2 again.

So the expression inside the first square root becomes 8, and the whole first square root becomes 2.

So the final expression would be:

2 - (2) = 0

On the other hand, √12 = √(223) = 2*√3

So the final expression would be:

4+2*√3

Hence, the quotient of these two expressions is not a finite value.

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Answer:

Step-by-step explanation:

3/ B is a salesperson and C is a programmer.

The correct option is: 2/ B is a programmer, and C is a salesperson

Let's analyze the statements and determine what B and C are:

A mumbled a response that the visitor couldn't hear clearly. We don't have any information from A's response.

B said, "A said that he is a salesperson." Since we know that salespeople always lie, we can infer that B is lying about A's response. Therefore, if A is a programmer (telling the truth), then B must be a salesperson.

C said, "Don't believe B; he is lying!" If we already determined that B is a salesperson (lying about A's response), then C is suggesting that B's statement is false, which means A's response is the opposite of what B said. So if B claimed that A is a salesperson (which was a lie), then A must be a programmer (telling the truth).

Based on the above analysis:

A is a programmer.

B is a salesperson.

C is a programmer.

So, the correct option is: 2/ B is a programmer, and C is a salesperson.

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The correct statement is- the square root of the __difference__ of a _the polynomial x²_ and 11 → √x² - 11 the __product__ of _-2x_ times a number and reciprocal of  -11 → -2x/11 the sum_ of the __square root__ of two times a number and 11 → √2x + 11.

Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11

Given here, [tex]\sqrt{x^2-11}[/tex] , This in word phrase can be written the square root of the difference between a square of a number and 11.

-2x/11 can be written as twice the number multiplied by the reciprocal of -11

√2x + 11 can be written as sum of square root of twice the number and 11

Hence, The correct statement is- the square root of the __difference__ of a _the polynomial x²_ and 11 → √x² - 11 the __product__ of _-2x_ times a number and reciprocal of  -11 → -2x/11 the sum_ of the __square root__ of two times a number and 11 → √2x + 11.

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If a textbook store sold a combined total of 447 sociology and math textbooks in a week. The number of  textbooks of each type  that were sold is: 195 Math textbooks, 138  Sociology textbooks.

Let x represent the number of math textbooks

Let y represent the number of sociology

Altogether bookseller sold 447 math and sociology textbooks

Hence,

x + y = 447

Since the number of sociology textbooks sold was 57 less than the number of math books sold.

So:

y = x - 57

Substitute for y in the equation

x + y = 447

x + (x - 57) = 447

2x - 57 = 447

Combine like terms

2x = 447 -57

2x = 390

Divide both side by 2x

x = 390/2

x = 195 (Math textbooks)

y = x - 57

y = 195 -57

y = 138 ( Sociology textbooks)

Therefore 195 and 138 textbooks were sold.

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Answer:

605

Step-by-step explanation:

11x55=605

Answer:

(a) The central 95% of IQ scores in a standardized test would be found in the interval from 85 to 115. This is because a normal distribution is symmetric around the mean, and 95% of the data falls within two standard deviations of the mean. So, the interval would be mean - 2standard deviation to mean + 2standard deviation i.e. 100 - 215 to 100 + 215 = 85 to 115

(b) About 2.5% of people should have IQ scores above 115. This is because the IQ scores follow a normal distribution and IQ scores above 115 are considered to be in the top 2.5% of the distribution.

(c) About 16% of people should have IQ scores between 70 and 85. This is because the IQ scores follow a normal distribution, and IQ scores between 70 and 85 fall within one standard deviation of the mean (85 is one standard deviation below the mean and 70 is one standard deviation below that)

(d) About 0.1% of people should have IQ scores above 130. This is because IQ scores above 130 are considered to be in the top 0.1% of the distribution.

Step-by-step explanation:

It is possible to find out the number of people who attended the event. Hence option B is correct.

What is the system of equations?

System of equations, also known as simultaneous equations, Two or more equations to be solved together in algebra (i.e., the solution must satisfy all the equations in the system). The number of equations must equal the number of unknowns for a system to have a unique solution.

Given that, a total of 24 cases of forks and each case of forks contains 36 packages each containing 12 forks.

Form about information, calculate the number of forks.

A total of 24 cases of spoons and each case of spoons contains 45 packages each containing 12 spoons.

Form about information, calculate the number of spoons.

Given that at the end of the event, 12 forks and 18 spoons were not given out to guests.

Form these we can get information that how many spoon used.

Since each guest will receive 2 forks and 3 spoons at the beginning of the event.

Using this information we can get the number of people who attend the event.

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