Ava and Wyatt are reading the same book. At the beginning of the month, Ava was on
page 10 and Wyatt was on page 30. Ava will read 20 pages per day and Wyatt will
read 15 pages per day. Let A represent the page of the book that Ava is on at the end
of t days into the month, and let W represent the page of the book that Wyatt is on at
the end of t days into the month. Graph each function and determine after how many
days, t, Ava and Wyatt will be on the same page of the book.

I'll assume you need to find the equation of the line that passes through those points.

Answer:

\(\displaystyle y-2=\frac{1}{4}(x+4)\)

Step-by-step explanation:

Equation of a Line:

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

\(\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)

The given points are (-4,2) and (12,6), thus:

\(\displaystyle y-2=\frac{6-2}{12+4}(x+4)\)

Operating:

\(\displaystyle y-2=\frac{4}{16}(x+4)\)

Simplifying, the equation in point-slope form is:

\(\mathbf{\displaystyle y-2=\frac{1}{4}(x+4)}\)

The given function f, with the provided set of ordered pairs, has a domain of {10, 17, 45, 51} and a range of {-6, 1, 5}.

The domain of a function refers to the set of all possible input values or x-values for which the function is defined. In this case, the given set of ordered pairs determines the domain. Looking at the x-values in the set {10, 17, 45, 51}, these are the unique inputs for which the function f is defined. Hence, the domain of f is {10, 17, 45, 51}.
On the other hand, the range of a function refers to the set of all possible output values or y-values that the function can take. By examining the y-values in the set {-6, 1, 5}, we can observe the distinct outputs generated by the function f. Thus, the range of f is {-6, 1, 5}.
In summary, the domain of the function f is {10, 17, 45, 51}, and the range of f is {-6, 1, 5}.

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Answer:

2/-2

Step-by-step explanation:

X-axis is first and Y-axis

Answer:

Slope: \(m=-\frac{1}{2}\)

y-intercept: \((0,-1)\)

Equation: \(y=-\frac{1}{2}x-1\)

Step-by-step explanation:

Slope-intercept form of an equation is written as \(y=mx+b\), where \(m\) is the slope and \(b\) is the y-intercept.

The slope of a line that passes through the points \((x_1,\: y_1)\) and \((x_2, \: y_2)\) is \(m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}\). Using the coordinates \((-2, 0)\) and \((2,-2)\) as given in the problem, we have slope of this line to be:

\(m=\frac{-2-0}{2-(-2)}=\frac{-2}{4}=-\frac{1}{2}\).

Now using this slope we've found and any point the line passes through, we can find the y-intercept of this equation:

\(0=-\frac{1}{2}(-2)+b, \\ b=-1\)

Therefore, the equation of this line in slope-intercept form is \(\fbox{$y=-\frac{1}{2}x-1$}\).

The y-intercept occurs when \(x=0\):

\(y=-\frac{1}{2}(0)-1, \\\\y=1\)

Thus, the y-intercept is

\((0, -1)\)

Answer:

x² + 34x + 104 = 0

x² + 34x = -104

x² + 34x + ((1/2)(34))² = -104 + ((1/2)(34))²

x² + 34x + 17² = -104 + 17²

x² + 34x + 289 = 185

(x + 17)² = 185

x + 17 = +√185

x = -17 + √185

The slope of the secant line passing through the points (2, f(2)) and (4, f(4)) for the given function is 24.

To determine the slope of the secant line, we need two points on the function. Let's say the function is f(x) and the given points are (x1, f(x1)) and (x2, f(x2)).

slope = (f(x2) - f(x1)) / (x2 - x1)

This formula represents the change in the function's values divided by the change in the x-values between the two points.

To find the slope, substitute the function values and x-values into the formula and simplify. Remember to use parentheses to clearly indicate which values belong to which point.

For example, let's say the points are (2, f(2)) and (4, f(4)), and the function is f(x) = 3x^2 + 2x - 1. Plugging these values into the formula, we get:

slope = (f(4) - f(2)) / (4 - 2)
slope = ((3*4^2 + 2*4 - 1) - (3*2^2 + 2*2 - 1)) / (4 - 2)
slope = (57 - 9) / 2
slope = 48 / 2
slope = 24

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Complete question :

Two trains leave towns 1180 kilometers apart at the same time and travel toward each other. One train travels 19km/hr slower than the other. If they meet in 4 hours, what is the rate of each train

Answer:

138 km/hr ; 157 km/hr

Step-by-step explanation:

Distance apart, d = 1180

Let :

Speed of A = x

Speed of A, = x - 19

Meeting time = 4 hours

Distance covered by A + Distance covered by B = total distance

Distance = speed * time

4 * (x - 19) + (4 * x) = 1180

4x - 76 + 4x = 1180

8x = 1180 + 76

8x = 1256

x = 1256 / 8

x = 157 km/hr

Speed of other train : (x - 19) = 157 - 19 = 138 km/hr

Answer:

17

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

x - 3y

y = 5, x = 32

Step 2: Evaluate

Using the elimination method, the price of one t-shirt is $30 and one key-chain is $11.

In the given question, Elizabeth's family went to NYC for their vacation.

At the gift shop on Liberty Island, Valerie bought three t-shirts and four key chains for $134, and Jennifer bought four t-shirts and five key chains for $175.

We have to find the price of each item.

Let the price of one t-shirt = $x

Let the price of one Key chain = $y

According to question

Price of three t-shirts and four key chains = $134

So the equation is

3x + 4y = $134……………….(1)

Also,

Price of four-shirts and five Key chains = $175

So the equation is

4x+5y = $175……………………..(2)

Now solving the equation using the elimination method.

Multiply Equation (1) by 5 and Equation (2) by 4, we get

15x+20y = 670....................(3)

16x+20y = 700......................(4)

Subtract equation 4 and 3, we get

x = 30

Now put the value of x in equation 1,

3*30 + 4y = $134

90+4y=$134

Subtract 90 on both side, we get;

4y = 44

Divide by 4 on both side, we get;

y = 11

Hence, the price of one t-shirt is $30 and one key-chain is $11.

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1.The machine will have no value after 48 months. 2.The graph of the machine's value over time will be a straight line. 3.The slope of the graph represents the rate of depreciation per month. 4.The intercepts of the graph indicate the initial value and zero value. 5.The expression V = -750x + 28,000 represents the value of the machine. 6.The machine has no value when x = 37 according to the expression. 7.The answer obtained using the expression differs from the answer in 8.question 1 due to possible rounding errors or calculation variations.

To determine when the machine has no value, we observe the pattern of depreciation. Based on the given data, the machine depreciates by $3,500 every 6 months. Therefore, it will take 48 months (8 cycles of 6 months) for the machine to have no value.

The table shows a consistent decrease in value over time with equal intervals of 6 months. This indicates a linear relationship between the number of months and the value. A linear relationship is represented by a straight line on a graph.

The slope of the graph can be determined by calculating the change in value divided by the change in time. In this case, the slope is (-750), meaning the value decreases by $750 per month. It represents the rate of depreciation per month.

The intercepts of the graph are obtained by determining the value of the machine at the start (initial value intercept) and when it reaches zero (zero value intercept). The initial value intercept is $28,000, which represents the starting value of the machine. The zero value intercept occurs when the machine has no value.

The expression V = -750x + 28,000 represents the value of the machine. The coefficient of x (-750) represents the rate of depreciation per month, while the constant term (28,000) represents the initial value.

Using the expression, when x = 37, the machine has no value. This differs from the answer in question 1 (48 months). The discrepancy could be due to rounding errors or variations in the method used to calculate the exact point at which the value reaches zero.

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a)

A rectangle is a quadrilateral

A trapezoid is a quadrilateral

Both of them have 4 sides

b)

In the parallelogram, every two opposite sides are equal and parallel

In the trapezoid, only two opposite sides are parallel but not equal

c)

In the square, diagonals are perpendicular

In the rhombus, diagonals are perpendicular

Both of them have perpendicular diagonals

d)

In the rectangle, diagonals are equal

In the rhombus, diagonals are not equal

The measurement of AB is given as follows:

AB = 16.23.

The three trigonometric ratios are defined as follows:

For the angle of 52º, we have that:

Hence the measurement of AB is obtained as follows:

cos(52º) = 10/AB

AB = 10/cos(52º)

AB = 10/0.616

AB = 16.23.

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Answer:

x = 6

Step-by-step explanation:

"Six times the quantity, x-2, is 24" can be rewritten symbolically as

6(x - 2) = 24.  We are to solve this for x.

To do that, divide both sides of the above equation by 6, to isolate x - 2:

x - 2 = 4

Adding 2 to both sides isolates x:  x = 6

Answer:

\(2\frac{1}{5}\)

Step-by-step explanation:

The 11 gals of water are equally split up into 5 tanks, so divide 11 by 5.

\(\frac{11}{5}\) then simplifies into \(2\frac{1}{5}\)

Answer:

2/3 ft

Step-by-step explanation:

area of triangle =base*height/2

2/5=base*6/5/2

2/5 *2 =base * 6/5

4/5 =base*6/5

4/5÷6/5=base

4/5 * 5/6=base

20/30=base

2/3=base

therefore base=2/3 ft

Answer:

-4,6

Step-by-step explanation:

6 horizontally and -4 vertically

ANSWER

Step-by-step explanation:

DEGREE =2

Given:

The equation is,

Explanation:

Simplify the equation for y.

So answer is, -2w + 10

In the coordinate plane, if a line is drawn to connect two points (4, 2), and (8, 6), then the coordinates of the midpoint of the line joining these two points are ({4 + 8}/2, {2 + 6}/2) = (12/2, 8/2) = (6, 4).

Midpoint refers to a point that is in the middle of the line joining two points. The two reference points are the endpoints of a line, and the midpoint is lying in between the two points. The midpoint divides the line joining these two points into two equal halves. Further, if a line is drawn to bisect the line joining these two points, the line passes through the midpoint.

The midpoint formula is used to find the midpoint between two points whose coordinates are known to us. The midpoint formula is also used to find the coordinates of the endpoint if we know the coordinates of the other endpoint and the midpoint. In the coordinate plane, if a line is drawn to connect two points (4, 2), and (8, 6), then the coordinates of the midpoint of the line joining these two points are ({4 + 8}/2, {2 + 6}/2) = (12/2, 8/2) = (6, 4). Let us learn more about the formula of the midpoint, and different methods to find the midpoint of a line.

(3, 8 )

given 2 points (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

(x+x /2  ,y+y/2  )

here (x₁, y₁ ) = P (1, 6 ) and (x₂, y₂ ) = Q (5, 10 ) , then

midpoint = (1+5/2 ,++10/2  ) = ( 6/2 , 16/2 ) = (3, 8 )

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The Newton-Raphson algorithm is used to find the root of the equation \(e^{-x^2}\) - \(x^3\) = 0. Three iterations are performed from the starting point x₀ = 1. The estimated root is 0.806553.

The Newton-Raphson algorithm is an iterative method used to find the root of an equation. It involves repeatedly improving an initial guess by using the formula:

xᵢ₊₁ = xᵢ - f(xᵢ)/f'(xᵢ),

where xᵢ is the current approximation, f(xᵢ) is the function value at xᵢ, and f'(xᵢ) is the derivative of the function at xᵢ.

To apply the algorithm to the equation \(e^{-x^2}\) - \(x^3\)= 0, we need to find the derivative of the function. Taking the derivative of \(e^{-x^2}\) gives -2x *\(e^{-x^2}\), and the derivative of \(x^3\) is 3\(x^{2}\).

Starting from x₀ = 1, we can perform three iterations of the Newton-Raphson algorithm to approximate the root. After each iteration, we update the value of x based on the formula mentioned above.

After three iterations, we find that the estimated root is approximately 0.806553.

To estimate the error, we can calculate the difference between the estimated root and the actual root. In this case, the actual root is given as 0.806553. The error can be obtained by taking the absolute value of the difference between the estimated root and the actual root.

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If your PCR product size was 172 and there were 130 base pairs next to a 14 base pair repeat, then there are 3 repeats.

Given that the newly used primer amplifies 130 base pairs that are near

(a) 14 base pair and

(b) the size of the pcr product is 172

Size = (number of base pairs * number of repetitions) + Initial/Primer Amplicon Value

172 = (14 * x) + 130

172 -130 = 14x

42 = 14x

3 = x

Therefore, we can say that the PCR product has 3 repeats.

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Regarding the graphs of the functions \(h(x) = x^2 - 4\) and \(g(x) = (x - 4)^2,\) the following statements are true:

The vertex of the graph of h(x) is located at (0, -4), while the vertex of the graph of g(x) is located at (4, 0).

The vertex represents the minimum or maximum point of the parabola.

The graph of h(x) opens upwards, indicating a positive coefficient for the \(x^2\)  term, while the graph of g(x) also opens upwards due to the positive coefficient of the squared term \((x - 4)^2.\)

The graph of h(x) intersects the x-axis at x = -2 and x = 2, indicating the solutions to the equation \(x^2 - 4 = 0.\)

On the other hand, the graph of g(x) intersects the x-axis at x = 4, representing the solution to the equation \((x - 4)^2 = 0.\)

It's important to note that the graph of h(x) is a standard quadratic function, while the graph of g(x) is a quadratic function with a horizontal shift of 4 units to the right.

The differences in their vertex, x-intercepts, and shape indicate these variations between the two functions.

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Answer:

Zero!!

Zero can't be divided and when multiplied, will result 0.

Answer:

answer in picture

Step-by-step explanation:

According to the information, we can infer that the histograms indicate that female students tend to have a higher frequency of studying times compared to male students during the week prior to their AP tests.

By comparing the histograms, we can observe that the frequency of studying times for female students is generally higher across all time intervals compared to male students. Female students have a higher frequency in each category, indicating that they spend more time studying than male students during the week before the AP tests.

To further analyze the distributions, we can also consider the measures of center and variation. The measures of center, such as the mean or median, would provide insights into the typical studying time for each group. Additionally, measures of variation, such as the standard deviation or interquartile range, would indicate the spread or variability of studying times within each group.

Accoding to the above, based on the provided frequency distributions, it can be concluded that female students tend to dedicate more time to studying during the week prior to their AP tests compared to male students.

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Answer:

27:1

Step-by-step explanation:

If the dimensions of the original pyramid are tripled then the ration between the new, larger pyramid and the old one would be 27:1 . This can be calculated by first calculating the volume of a pyramid and then doing the same but with dimensions 3 times the old one. Then divide the volume of the new one with that of the old one.

Volume of Pyramid = \(\frac{length * width * height}{3}\)

Volume Pyramid 1 = \(\frac{3*3*3}{3}\) = 9

Volume Pyramid 2 = \(\frac{9 * 9 * 9}{3}\) = 243

243/9  =  27/1 or  27:1

Answer:

The new volume is 27 times the original volume.

Edgenuty

Answer:

Step-by-step explanation:

This expression is a binomial; it has two terms.

Answer:

x less 21.5

Step-by-step explanation:

Given : the algebraic expression x - 21.5

a. 21.5 decreased by x

the expression becomes 21.5 - x

b. x more than 21.5

more than means we add , so expression becomes 21.5 +x

c. 21.5 minus x

For minus we use subtraction symbol,

so the expression becomes 21.5 -x

d. x less 21.5

x less 21.5 , we subtract 21.5

so the expression becomes x - 21.5 . that is the given expression

The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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Answer:

\(\boxed{\mathrm{view \: explanation}}\)

Step-by-step explanation:

1. Relations are the set of y (output) and x (input) values that are related. A function is when each input has a relation with one output.

2. The mathematical formula is the formula of Pythagoras theorem. Where the length c (hypotenuse) is equal to the square root of the sum of the legs squared.

A(7,10) and B(9,-3) are separated by 13.1 units.

How to calculate distance between two points?
The separation between two points the coordinates of two points in space are used in the formula. In coordinate geometry, a two-dimensional or three-dimensional space can be used to calculate the distance between two points using the distance formula. The Pythagoras theorem is sometimes used to calculate the distance between two places.
The distance between two locations on a plane is the length of the line segment connecting them. The following equation is frequently used to determine the separation between two points:
d = √[(x₂-x₁)² + (y₂-y₁)²] -- (i)

Given, the two points are A≡(7,10) and (9,-3)
On comparing A and B with (x₁, y₁) and (x₂, y₂) respectively, we get
x₁ = 7, y₁ = 10,  x₂ = 9, y₂ = -3
Therefore using the formula in (i), we get
Distance between A & B = √[(9-7)²+(-3-10)²] = √173 = 13.15 = 13.1 units

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