You are looking for a way to improve reading glasses by adding mineral to the glass. It is known that without additives, people who use glasses, on average, read 25 pages per day
with a standard deviation of 2.4 pages per day. Now you are wondering if the addition of the mineral increases the number of pages read. You select 30 people for research and give them glasses with a mineral supplement. As you go through your research, you find that these thirty people read an average of 25.5 pages per day. Using z-test for a mean, with a 5% significance level, is it possible to conclude from
this result that the addition of the mineral is effective?Justify your answer by stating what is
(a) the null hypothesis and alternative hypothesis. Explain what test (left-tailed, right-tailed or two-tailed)
you are using. Also find
(b) critical z-value (not the p-value!)
(c) test value



SteSteAnswerAnswer:

x = 3/4 and -2

Step-by-step explanation:

If x²+ 5/4x = 3/2, x²+ 5/4x - 3/2 = 0

Multiply by 4 to get 4x²+ 5x - 6 = 0

Factor it to get (4x - 3)(x + 2) = 0

anything times 0 = 0, so x = 3/4 and -2

Using ratios, Carl will receive 24 oranges, while Dina will get 40 oranges, and Eva will receive 36 oranges.

A ratio shows the relative size of one quantity compared to another quantity or value.

Ratios are expressed in standard ratio forms using the colon (:), in decimals, fractions, or percentages.

The total number of oranges shared between Carl, Dina, and Eva = 100

The ratio Carl's oranges to Dina's oranges = 3:5

The ratio Carl's oranges to Eva's oranges = 2:3

Based on the above ratios, for every 2 oranges that Carl receives, Eva receives 3.

For Carl to receive 3 oranges, Eva will receive 4.5 oranges (3 x 3/2)

The ratios among the three friends are 3: 5: 4.5

The sum of ratios = 12.5 (3 + 5 + 4.5)

Carl's share = 24 (3/12.5 x 100)

Dina's share = 40 (5/12.5 x 100)

Eva's share = 36 (4.5/12.5 x 100)

Thus, based on the ratios, the number of oranges Carl receives is 24.

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The system of equations- 4x-22=0

26y-2=0.

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for

When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

Hence, The system of equations- 4x-22=0,

26y-2=0.

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Step-by-step explanation:

Take the derivative of this function using the power rule

[tex] \frac{d}{dx} ( {x}^{n} ) = nx {}^{n - 1} [/tex]

Since the terms are serpated using addition or subtraction we can take the derivative of this function separately

So our derivative end up becoming

[tex]6x - 7[/tex]

Plug in x=2

[tex]6(2) - 7 = 5[/tex]

So the gradient of the tangent line at 2,-7 is 5

The value of the ratio of baking soda to salt is 3/4 : 1.

A fraction is a number that represents a portion of a whole or a ratio of two quantities.  It consists of two integers arranged one above the other and divided by a horizontal line known as a vinculum or fraction bar.The ratio of baking soda to salt in the recipe can be written as:

Baking soda : Salt = 3/4 : 3

To simplify the ratio, we can first convert the fraction 3/4 to an equivalent fraction with a denominator of 12  

3/4 = 9/12

So the ratio becomes:

Baking soda : Salt = 9/12 : 3

We can simplify this ratio further by dividing both the numerator and denominator of the first fraction by 3:

Baking soda : Salt = 3/4 : 1

Therefore, the value of the ratio of baking soda to salt = 3/4 : 1.

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If tan ⁡θ = - 1, a possible value of θ is C. 135 degrees.

If tanθ = -1, we are looking for an angle where the ratio of the opposite side to the adjacent side is -1. This occurs in the second and fourth quadrants, where either the opposite side is positive and the adjacent side is negative or vice versa.

In the second quadrant, the angle would be (180 - 45)° = 135° or (3π/4) radians.

In the fourth quadrant, the angle would be (360 - 45)° = 315° or (7π/4) radians. Both of these angles have a tangent of -1.

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The full question is:

If tan⁡ θ = - 1, a possible value of θ is:

Answer:

Step-by-step explanation:

After answering the provided question, we can conclude that Therefore, the simplified expression is [tex](y / x) * (1 / z^5)[/tex] and the value of the exponent for y is 1.

An expression in mathematics is a collection of manifestations, digits, and transnational corporations that resemble a significant correlation or regimen. A square root, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, pervasiveness, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

To simplify the expression,

[tex]x^0xy^2z(^-3) = xy^2z(^-3)\\xy^2z(^-3) / x^2yz^2\\= (xy^2 / x^2y) * (1 / z^5)\\= (y / x) * (1 / z^5)[/tex]

Therefore, the simplified expression is [tex](y / x) * (1 / z^5)[/tex] and the value of the exponent for y is 1.

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Answer:

(-5, -7)

Step-by-step explanation:

To rotate a point (x,y) by 180 degrees about the origin, we can multiply its coordinates by the matrix:

-1  0

0 -1

So, to rotate the triangle JKL by 180 degrees about the origin, we can apply this transformation to each of its vertices. We have:

J(3,1)  ->  J^`(−3,−1)

K(7,−5) ->  K^`(−7,5)

L(5,7)  ->  L^`(−5,−7)

Therefore, the coordinates of the vertex L^(`) after the triangle is rotated by 180 degrees clockwise about the origin are (-5, -7).

Therefore, the long dimension of the quilt is (26x + 60)/(x + 6) cm longer than the short dimension.

Area is the measure of the extent of a 2-dimensional surface or region, usually measured in square units such as square meters (m²), square feet (ft²), or square centimeters (cm²). It is the amount of space inside the boundary of a flat shape or the surface of an object.

Here,

The area of the original square is x^2 cm². Maria adds some fabric to one side of the square, which increases the length of the rectangle by a certain amount, and adds a different amount of fabric to the adjacent side, which increases the width of the rectangle by a certain amount. Let's say Maria adds y cm of fabric to one side and z cm of fabric to the other side. Then the length of the rectangle is x + y cm and the width is x + z cm. The area of the rectangle is given by:

(x + y)(x + z) = x^2 + xy + xz + yz

We know that the area of the rectangle is x² + 13x + 30 cm². So we can set these two expressions equal to each other:

x² + xy + xz + yz = x² + 13x + 30

Simplifying this equation, we get:

xy + xz + yz = 13x + 30

We want to find the difference between the length and the width of the rectangle, which is (x + y) - (x + z) = y - z. To solve for y - z, we need to express yz in terms of y - z. We can do this by factoring the left side of the equation above:

xy + xz + yz = y(x + z) + xz = (y - z)(x + y + z)

Substituting this expression for yz in the equation above, we get:

(y - z)(x + y + z) = 13x + 30

We want to solve for y - z, so let's focus on the left side of the equation:

(y - z)(x + y + z) = y(x + y + z) - z(x + y + z)

= xy + y² + yz - xz - z² - yz

= y² - z² + xy - xz

Substituting the expression we found earlier for xy - xz, we get:

(y - z)(x + y + z) = y² - z² + (y - z)(x + z)

(y - z)[x + y + z - (x + z)] = y² - z²

y - z = (y² - z²)/(y - z) = y + z

= (13x + 30)/(x + 6)

So the difference between the length and the width of the rectangle is:

y - z = (13x + 30)/(x + 6)

Therefore, the long dimension of the quilt is (x + y) = x + (13x + 30)/(x + 6) cm, and the short dimension is (x + z) = x + (30 - 13x)/(x + 6) cm. The difference between the long and short dimensions is:

[x + (13x + 30)/(x + 6)] - [x + (30 - 13x)/(x + 6)]

= (13x + 30)/(x + 6) - (30 - 13x)/(x + 6)

= (26x + 60)/(x + 6)

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A 95% confidence interval on the difference in the towels' mean absorbency produced by the two processes is between -295.36 and -104.64

We can use the two-sample t-test formula to find the confidence interval for the difference in means:

t = (x1 - x2 - d) / √(s1²/n1 + s2²/n2)

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, d is the hypothesized difference in means (usually 0 in a two-sided test), and t follows a t-distribution with degrees of freedom given by:

df = (s1^2/n1 + s2^2/n2)^2 / (s1^4/n1^2(n1-1) + s2^4/n2^2(n2-1))

Plugging in the given values, we have:

x1 = 130, s1 = 15, n1 = 10

x2 = 310, s2 = 50, n2 = 4

d = 0 (since we are testing for a difference of means)

t(0.025, df) = 2.306 (using a t-table or calculator)

Substituting these values into the formula, we get:

t = (130 - 310 - 0) / sqrt(15^2/10 + 50^2/4) = -4.156

df = (15^2/10 + 50^2/4)^2 / (15^4/10^2(10-1) + 50^4/4^2(4-1)) = 7.38 (rounded to 2 decimal places)

The 95% confidence interval for the difference in means is given by:

(x1 - x2) ± t(0.025, df) * sqrt(s1^2/n1 + s2^2/n2)

= (130 - 310) ± 2.306 * sqrt(15^2/10 + 50^2/4)

= (-200 ± 95.36)

= (-295.36, -104.64)

Therefore, we can be 95% confident that the true difference in mean absorbency between the two processes is between -295.36 and -104.64. Since the interval does not contain 0, we can conclude that the means are significantly different at the 5% level.

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Step-by-step explanation:

vertex             vertical angles

The caffeine is leaving Bree's body at a rate of approximately 11.96 mg per hour.

What is the rate?

Rate is a measurement of the speed of change or the amount of change that occurs per unit of time or per unit of some other quantity. It is a ratio between two different measurements, typically expressed in units of distance, time, weight, volume, or currency.

The caffeine in Bree's system is decreasing linearly over the course of 6 hours (from 8am to 2pm).

We can use the information given to find the hourly decreasing rate by calculating the slope of the line connecting the two data points.

The change in caffeine over 6 hours is:

100 mg - 28.24 mg = 71.76 mg

So the hourly decreasing rate can be calculated as:

Hourly decreasing rate = Change in caffeine / Time

Hourly decreasing rate = 71.76 mg / 6 hours

Hourly decreasing rate = 11.96 mg/hour (rounded to two decimal places)

Therefore, the caffeine is leaving Bree's body at a rate of approximately 11.96 mg per hour.

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The cost of operating the dryer for a month is $6.

An electric clothes dryer has a power rating of 4000W. Assume that a family does five loads of laundry each week for 4 weeks. Further assume that each load takes one hour. A. Find the energy used in both J and kWh.

1J = 1W.s

Energy used = Power x time= 4000W x (5 x 4) x 1h= 80000Wh= 80 kWh

Thus, the energy used in kWh is 80 kWh.1kWh = 1000Wh

1kWh = 3.6 x 10^6 J

Thus, the energy used in J is 80 x 3.6 x 10^6 = 288 x 10^6 J.B. If the cost of electricity is $.075/kWh, find the cost of operating the dryer for a month (4 weeks).

The energy used by the dryer for a month is 80 kWh.

Cost of operating the dryer for a month = Energy used x Cost per kWh= 80 kWh x $0.075/kWh= $6

Therefore, the cost of operating the dryer for a month is $6.

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The intersection points between the two lines y > (3x-4) and y > -(1/2)x+3, from the graph is (x, y) = (2, 2)

To graphically solve the system of inequalities, we will first graph the two boundary lines, which are the lines obtained by replacing the inequality symbols with equality symbols in each of the given inequalities:

y > 3x - 4 (red dotted line)

y > -(1/2)x + 3 (blue dotted line)

When we plug (0, 0) into y > 3x - 4, we get:

⇒ 0 > 3(0) - 4

⇒ 0 > -4

This inequality is true, so we shade the half-plane above the solid line,

y = 3x - 4

When we plug (0, 0) into y > -(1/2)x + 3, we get:

⇒ 0 > -(1/2)(0) + 3

⇒ 0 > 3

This inequality is not true, so we shade the half-plane below the dashed line, y = -(1/2)x + 3

The solution set is the region that is shaded in both half-planes, which is the triangular region above the solid line and below the dashed line.

Now, we have to determine the intersection points between the two lines y > (3x-4) and y > -(1/2)x+3, from the graph, we get; (x, y) = (2, 2)

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Graph of the solution-

The ultralight airplane traveled a total of 1350 miles in September while tracking the monarch butterflies migrating to Mexico.

A mile is unit of distance on land in English-speaking countries equal to 5280 feet, or 1760 yards.

The ultralight airplane tracked monarch butterflies migrating to Mexico for 30 days in September, with a flight mile of 45 miles each day. To find the total miles traveled by the ultralight airplane in September, we can do the following:

Multiply flight mile per day by the number of days

= 45 miles/day x 30 days

= 1,350 miles.

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Therefore, the football team scored 4 touchdowns, 2 field goals, and 1 safety in the game.

An equation is a mathematical statement that asserts that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and so on. An equation is often written with an equal sign (=) between the two expressions. The goal of solving an equation is to find the values of the variables that make the equation true. Equations are used extensively in mathematics, physics, engineering, and many other fields to describe relationships between different quantities.

by the question.

Let's denote the number of touchdowns scored by "T", the number of field goals scored by "F", and the number of safeties scored by "S".

From the problem, we know:

[tex]T + F + S = 8 (they scored points 8 times)\\7T + 3F + 2S = 38 (the total score was 38 points)\\T = F + S[/tex] (they scored as many touchdowns as they did field goals and safeties combined)

Substituting the third equation into the first, we get:

[tex]F + S + F + S = 8\\2F + 2S = 8\\F + S = 4[/tex]

We now have a system of three equations:

[tex]T + F + S = 8\\7T + 3F + 2S = 38\\T = F + S[/tex]

Substituting the third equation into the first two, we get:

[tex]7(F + S) + 3F + 2S = 38\\8(F + S) = 21[/tex]

Solving for F + S, we get:

[tex]F + S = 21/8[/tex]

However, we also know that F + S = 4, so there must be a mistake somewhere. Looking back at the problem, we see that the statement "they scored as many touchdowns as they did field goals and safeties combined" implies that T = F + S + 1 (since a touchdown is worth 7 points and a field goal and safety combined are worth 4 points). Substituting this into the first two equations, we get:

[tex](F + S + 1) + F + S = 8\\7(F + S + 1) + 3F + 2S = 38[/tex]

Simplifying, we get:

[tex]2F + 2S = 6\\10F + 9S = 31[/tex]

Solving for F and S, we get:

[tex]F = 2\\S = 1[/tex]

Substituting these values back into the equation T = F + S + 1, we get:

[tex]T = 4[/tex]

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Answer:

options C and D is the answer

The correct order of presentation of sample distribution  should include the introduction, method, results, discussion, and conclusion.

The correct order of presentation for results of an independent samples t-test is as follows:Introduction: Introduction should include the aim of the research, the hypothesis, and the data collection method. Method: The method should include the sample size, the type of sample, the data collection method, and the statistical analysis techniques used. Results: The results should include descriptive statistics for each group, the t-test result, the degree of freedom, and the p-value. Discussion: The discussion should include the interpretation of the results, the significance of the findings, and the limitations of the study.Conclusion: The conclusion should summarize the findings and provide suggestions for future research.

Explanation In research, presenting the findings of an independent samples t-test involves comparing the means of two independent groups to determine if there is a significant difference between the two groups. The independent t-test is used when the data are independent, and it assumes that the samples have a normal distribution with equal variances.The results of the t-test can be presented using tables, graphs, or charts.

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The equation of a polar curve r^2 = a cos 2θ describes a limaçon, which is a type of polar curve with a loop. When a is positive, the limaçon has an outer loop and an inner loop. When a is negative, the limaçon has a dimple instead of an inner loop.

In this case, a = 81, which is positive, so the limaçon will have an outer loop and an inner loop.

To graph the limaçon, we can start by considering the behavior of the curve at θ = 0, π/4, π/2, 3π/4, and π.

At θ = 0, r^2 = 81cos(2θ) = 81cos(0) = 81, so r = ±9. This means that there are two points on the curve at θ = 0, one at (9, 0) and one at (-9, 0).

At θ = π/4 and 3π/4, cos(2θ) = cos(π/2) = 0, so r^2 = 0 and r = 0. This means that there are two points on the curve at θ = π/4 and two points at θ = 3π/4, all located at the origin.

At θ = π/2, r^2 = 81cos(2θ) = 81cos(π) = -81, which is negative. Since r is always non-negative, there are no points on the curve at θ = π/2.

At θ = π, r^2 = 81cos(2θ) = 81cos(2π) = 81, so r = ±9. This means that there are two points on the curve at θ = π, one at (9, π) and one at (-9, π).

Based on this information, we can sketch the graph of the limaçon as follows:

There are two points on the x-axis, one at (9, 0) and one at (-9, 0).

There are four points at the origin.

There are two points on the line θ = π, one at (9, π) and one at (-9, π).

The curve passes through the origin at θ = π/4, π/2, and 3π/4, and has a loop that encloses the origin.

Overall, the limaçon has a symmetric, flower-like shape with a loop that encloses the origin.

Answer:

an infinity sign

Step-by-step explanation:

Answer: RM 86.40

Step-by-step explanation:

The profit can be calculated as follows:

Selling price = List price + Profit

Profit = (Percentage profit/100) x List price

Discount = (Discount percentage/100) x Selling price

Selling price after discount = Selling price - Discount

Let's plug in the given values into these formulas:

List price = RM 120

Percentage profit = 60%

Profit = (60/100) x 120 = RM 72

Discount percentage = 30%

Selling price = 120 + 72 = RM 192

Discount = (30/100) x 192 = RM 57.60

Selling price after discount = 192 - 57.60 = RM 134.40

To calculate the profit after discount, we need to subtract the cost price from the selling price after discount:

Profit after discount = Selling price after discount - Cost price

Cost price = List price - Profit = 120 - 72 = RM 48

Profit after discount = 134.40 - 48 = RM 86.40

Therefore, the profit after the discount is RM 86.40.

Answer:

1

Step-by-step explanation:

Answer: The answer is 1 tablespoon of vanilla.

Step-by-step explanation:

Based on the given conditions, formulate:

[tex]\frac{1}{6}[/tex]  ÷ [tex]\frac{2}{12}[/tex]

Simplify fraction(s): [tex]\frac{1}{1}[/tex]

Any fraction with a denominator of 1 is equal to its numerator, which is 1.

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The professional set of drawing pencils costs $18.51 more than the basic set. This is a significant difference in price and may be worth the additional cost depending on the user's needs.

First, we need to calculate the difference in price between the professional set and the basic set of drawing pencils. To do this, we will subtract the cost of the basic set ($8.98) from the cost of the professional set ($27.49).

We can write this difference as an equation:

Difference = Professional Set Cost - Basic Set Cost

Difference = 27.49 - 8.98

Next, we can solve for the difference in price by subtracting the two values.

Difference = 18.51

Therefore, the professional set of drawing pencils costs $18.51 more than the basic set. This is a significant difference in price and may be worth the additional cost depending on the user's needs.

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The statements that are true about the quadratic function and its graph include the following:

In Mathematics, the graph of any quadratic function or equation always forms a parabola because it is a u-shaped curve. For the given quadratic function, the graph is a upward parabola because the coefficient of x² is positive i.e when the value of "a" is greater than zero.

Next, we would determine the statements about the quadratic function and its graph that are true:

At point (-10, 82), we have:

[tex]f(x) = \dfrac{1}{5} \ x^2 - 5x + 12[/tex]

[tex]f(x) = x^2/5 - 5x + 12[/tex]

[tex]f(-10) = -10^2/5 - 5(-10) + 12[/tex]

[tex]f(-10) = 82[/tex]

At point (20, -8), we have:

[tex]f(x) = \dfrac{1}{5} \ x^2 - 5x + 12[/tex]

[tex]f(x) = x^2/5 - 5x + 12[/tex]

[tex]f(20) = 20^2/5 - 5(20) + 12[/tex]

[tex]f(20) = -8[/tex]

In conclusion, the graph of this quadratic function does not contain the point (0, 0) as shown in the image attached below.

Answer:21

Step-by-step explanation:

The slope of the line is 2/5 and to represent the "rise" and "run" on the line, a vertical line and a horizontal line are drawn to show the change in y and x, respectively.

To find the slope of the line, we can choose two points on the line and use the formula:

slope = (change in y)/(change in x)

Let's choose the points (-2, 3) and (3, 5) on the line. The "rise" is the change in y and the "run" is the change in x between these two points:

Rise = change in y = 5 - 3 = 2

Run = change in x = 3 - (-2) = 5

So the slope of the line is:

slope = (change in y)/(change in x) = 2/5

Therefore, the slope of the line in simplest form is 2/5.

To represent the "rise and run" on the line, we can draw a vertical line going from the point (-2, 3) to the point (-2, 5) to represent the "rise" of 2 units, and a horizontal line going from the point (-2, 5) to the point (3, 5) to represent the "run" of 5 units.

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The longest fish caught needs to grow an additional 4 inches in order to reach the maximum length of 23 inches.

The longest fish caught needs to grow an additional 4 inches in order to reach the maximum length of 23 inches. This can be calculated using the formula:

Maximum length - Current length = Amount of growth required

In this case, we substitute the values as follows:

23 inches - 19 inches = 4 inches

Therefore, the longest fish caught needs to grow an additional 4 inches in order to reach the maximum length.

To help visualize this, we can consider the scales of the fish. To reach the maximum length, the longest fish caught would need to add 4 scales, which is a relatively small amount. This is conceivable, as the fish can continue to grow as long as it has access to enough food and a suitable environment.

In summary, the longest fish caught needs to grow an additional 4 inches in order to reach the maximum length of 23 inches. This can be calculated using the formula: Maximum length - Current length = Amount of growth required. To help visualize this, the fish needs to add 4 scales which is a relatively small amount.

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By answering the presented question, we may conclude that Because equation both of these answers are real values, the solution to the equation x2 - 9 = 0 is that it has two real solutions.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation [tex]"x^2 + 2x - 3 = 0,"[/tex]for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

(x-3)(x+3) = 0 is a rewrite of the equation [tex]x^2 - 9 = 0.[/tex] This suggests that the equation's solutions are x = 3 and x = -3.

Because both of these answers are real values, the solution to the equation x² - 9 = 0 is that it has two real solutions.

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The point of intersection of the graph (2,9), means that at 2 minutes, the altitude was 9 thousand feet.

The y-axis in the presented graph denotes altitude in thousand feet, while the x-axis in the graph denotes time in minutes. The point of intersection, (2,9), indicates that the height was 9000 feet at 2 minutes.

The moment when the height was 9000 feet is indicated by the x-value, which in this instance is 2. It identifies the precise point in time when the height was displayed on the graph as 9000 feet.

It is crucial to understand the x-value of the point of contact because it enables precise computations and predictions about the height at various times.For example, if we want to know the altitude at 5 minutes, we can use the slope of the graph and the point of intersection to determine the altitude accurately.

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