how do i solve this equation using factoring method?
x² - 14x + 9 = 0 ​

Answer:

hope this might help you!!

A​ T-shirt is launched with an initial upward velocity of 78 feet per second, the T-shirt will reach its maximum height in approximately 2.44 seconds.

The height of the T-shirt is given by the function h(t) = -16t^2 + 78t + 5, where h is the height in feet and t is the time in seconds.

To find the time it takes for the T-shirt to reach its maximum height, we need to find the vertex of the parabolic function.

The vertex occurs at the time t = -b/2a, where a = -16 and b = 78 are the coefficients of the quadratic function.

t = -b/2a = -78/(2*(-16)) = 2.4375

Therefore, the T-shirt will reach its maximum height in approximately 2.44 seconds.

To find the maximum height, we substitute this value of t into the equation for h:

h(2.4375) = -16(2.4375)^2 + 78(2.4375) + 5 ≈ 97.19 feet

Therefore, the maximum height of the T-shirt is approximately 97.19 feet.

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Okay, let's analyze the r^2 values for the 4 options:

a. y=16.5839•1.0185^x

r^2 is undefined, as this is an exponential model. We cannot determine how well it fits the data based only on r^2.

b. y=0.985515x-2.81333

This is a linear model, so r^2 would be between 0 and 1. Without knowing the actual r^2 value, we cannot determine how good the fit is.

c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667

This is a 3rd order polynomial model. Again, without the r^2 value, we cannot determine the quality of fit. It could be a good or poor fit.

d. y=0.00182197x^2+0.785098x+1.195

If this model has the highest r^2 value (closest to 1), it would indicate the best fit to the data of the options.

In summary, without seeing the actual r^2 values calculated from the data for each model, we cannot definitively say which option is the "best fit". The model with the r^2 closest to 1 would likely be the best, but r^2 only tells part of the story. Other factors like complexity, interpretability, and residual analysis also matter. But based solely on r^2, the quadratic model d seems the most likely to be the best fit, as long as its r^2 value is high.

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a)Traveled 0.3 miles in 1 hour.

b) The fraction representation is 3/10 miles per hour.

a) To find out how many miles the person traveled in 1 hour, we need to divide the distance traveled by the time taken.

Distance traveled = 1/5 miles

Time taken = 3/2 hours

To make it easier to divide, we can convert the time taken to a fraction with a common denominator of 10:

3/2 = 15/10

Now we can divide the distance by the time:

1/5 ÷ 15/10 = 1/5 x 10/15 = 2/15

This tells us that the person traveled 2/15 miles in one-tenth of an hour (i.e., 6 minutes).

To find out how many miles per hour they traveled, we can convert the fraction to a rate by multiplying it by the reciprocal of the time fraction (i.e., 10/3):

2/15 x 10/3 = 2/9

Therefore, the person traveled 2/9 miles per hour.

b) To write this as a model fraction representation, we can express it as a single fraction:

2/9 = 3/10 (rounded to the nearest tenth)

So the person traveled at a rate of 3/10 miles per hour.

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Step-by-step explanation:

This function has two pieces, each of which is the absolute value of a linear expression. We need to consider the function separately for different ranges of x.

When -5 < x < 0, then x + 5 is negative and x - 5 is also negative. Therefore, we have:

y = -(x - 5) - (x + 5) = -2x

When 0 ≤ x < 5, then x + 5 is positive and x - 5 is negative. Therefore, we have:

y = (x - 5) + (x + 5) = 2x

So the function y = |x - 5| + |x + 5| can be written as:

y =

-2x if -5 < x < 0

2x if 0 ≤ x < 5

Notice that the function is not defined for x ≤ -5 or x ≥ 5.

Answer:

B represents a function.

The proportion of eligible voters who would support the businesswoman is less than or equal to 0.6, and the proportion of eligible voters who would support the businesswoman is greater than 0.6.

In statistics, a hypothesis is a statement or assumption about a population parameter that is being tested for its truthfulness based on sample data. It is a tentative explanation for an observation or phenomenon and is used to make predictions about the outcome of an experiment or study. Hypotheses can be either null hypotheses, which state that there is no significant difference or relationship between variables, or alternative hypotheses, which propose that there is a significant difference or relationship.

(a) The hypotheses that the businesswoman should test are:

H0: The proportion of eligible voters who would support the businesswoman is less than or equal to 0.6.

Ha: The proportion of eligible voters who would support the businesswoman is greater than 0.6.

(b) The p-value is greater than the significance level of 0.05, which suggests that the results are not statistically significant. Therefore, the businesswoman should not run for office. There is not enough evidence she has enough supporters.

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The number line where we plotted 1 1/4 and 5/2 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

-1 1/4 and 5/2

To start with, we convert both numbers to the same form

i.e. decimal or fraction

When converted to fractions, we have

-5/4 and 5/2

Rewrite the denominators of the fractions

So, we have

-5/4 and 10/4

This means that we can plot -5/4 at -5 and 10/4 at point 10 where the difference in each interval is 1/4

Using the above as a guide, we have the following:

The number line is attached

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Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=2 and x=0 making it (0,2)

the coordinates of the point that represents the number of snowballs needed to make 2 snowmen should be option C. which is (2,6)

1. Distribute. Everything. 2x - 2 + 3x + 3 = 4x + 16.
2. Add your like terms. (must be on the same side) 5x + 1 = 4x + 16
3. Single out x by subtracting 1. 5x = 4x + 16 - 1.
4. Simplify. 5x = 4x + 15
5. Subtract 4x from both sides to combine like terms. 5x - 4x = 15.
6. Simplify. 1x = 15.

That means your final answer would be x = 15. If you were to input 15 into every x, it would simplify to 76 = 76, which means x is definitely 15.

1. Distribute. Everything. 2x - 2 + 3x + 3 = 4x + 16.
2. Add your like terms. (must be on the same side) 5x + 1 = 4x + 16
3. Single out x by subtracting 1. 5x = 4x + 16 - 1.
4. Simplify. 5x = 4x + 15
5. Subtract 4x from both sides to combine like terms. 5x - 4x = 15.
6. Simplify. 1x = 15.

That means your final answer would be x = 15. If you were to input 15 into every x, it would simplify to 76 = 76, which means x is definitely 15.

Answer:

x = 15

Step-by-step explanation:

Simplifying the expression:

Add the numbers:

Combine like terms:

Subtract 1 from both sides:

Subtract 4x from both sides:

Answer:

x = 15

Step-by-step explanation:

Simplifying the expression:

Add the numbers:

Combine like terms:

Subtract 1 from both sides:

Subtract 4x from both sides:

When 14,277s is converted to hr, min and hr, it gives 3 hours, 57 minutes, 7 seconds.

Conversion is the process of changing the value of one form to another. It is also the conversion between different units of measurement for the same quantity.

How to determine this

When 60 seconds makes 1 minute

60 minutes makes 1 hour

14,277 seconds to minutes

When 60 seconds = 1 minute

14,277 seconds = x

x = 14,277/60 minutes

x = 237 minutes 7 seconds

By converting 237 minutes to hour

When 60 minutes = 1 hour

237 minutes = x

x = 237/60 hours

x = 3 hours 57 minutes.

Therefore, the conversion is 3 hours 57 minutes 7 seconds

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Okay, here are the steps to solve this:

* The recipe calls for 1 teaspoon of cinnamon for every 4 cups of granola mix.

* We are making 12 cups of granola.

* So to make 12 cups, we need 12 / 4 = 3 times as much cinnamon.

* Since each 4 cups uses 1 teaspoon, 12 cups will need 3 teaspoons.

Therefore, for 12 cups of granola mix, the recipe will call for 3 teaspoons of cinnamon.

The amount of fudge the student gives to her sister, which is (1/2) of her remaining fudge, calculated using fractions is 16 ounces

A fraction is a representation of a part of a whole, by setting the quantity representing the part as the numerator and the quantity representing the whole as the denominator with both quantities separated by the fraction bar.

Part of the question obtained from a similar question posted online can be presented as follows;

The amount of fudge the student has = 3 pounds

The amount of fudge the student eats = 1 pound of the fudge

Required; The amount of fudge the student has left

The amount of fudge the student has left = 3 - 1 = 2 pounds

The fraction of the remaining fudge the student gives to her sister = (1/2)

Therefore;

The amount of fudge the student gives her sister = (1/2) × 2 pounds = 1 pound

1 pound = 16 ounces

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The radius of this circle with center (8, 2) is equal to 6.71 units.

In Mathematics and Geometry, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given points into the distance formula, the radius of this circle can be calculated as follows;

Distance = √[(14 - 8)² + (-1 - 2)²]

Distance = √[(6)² + (-3)²]

Distance = √[36 + 9]

Distance = √45

Distance = 6.71 units.

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Complete Question:

What is the radius of the circle with Center: (8, 2), Point on Circle: (14,-1)? 2 decimal places

Answer:

a. The probability of getting an O on the first draw can be calculated by dividing the number of O tiles by the total number of tiles in the bag:

```

P(O on first draw) = 3/15 = 0.2

```

Therefore, the probability of getting an O on the first draw is 0.2 or 20%.

b. After removing one O tile, there are 14 tiles left in the bag, of which 2 are U tiles. Therefore, the probability of getting a U if you didn't replace the O is:

```

P(U without replacing O) = 2/14 = 1/7 ≈ 0.143

```

Therefore, the probability of getting a U if you didn't replace the O is approximately 0.143 or 14.3%.

c. The probability of getting O and then U if you don't replace the O can be calculated as follows:

```

P(O and then U) = P(O on first draw) * P(U without replacing O)

               = 3/15 * 2/14

               = 1/35

               ≈ 0.029

```

Therefore, the probability of getting O and then U if you don't replace the O is approximately 0.029 or 2.9%.

Step-by-step explanation:

The company would incur a loss of $14,800,000 if it spends an additional $200,000 on advertising to achieve sales of 35,000 units.

Sales generally refer to the total amount of goods or services that a business sells during a given period of time, typically measured in monetary terms. Sales can also refer to the process of selling products or services, including activities such as prospecting, lead generation, sales presentations, and closing deals.

To calculate the operating profit with sales of 35,000 units and an additional selling expense of $200,000, we need to first calculate the total revenue and the total cost, and then subtract the total cost from the total revenue.

From the table provided, we can see that the selling price per unit is $900 and the variable cost per unit is $600. Therefore, the contribution margin per unit is:

Contribution margin per unit = Selling price per unit - Variable cost per unit

= $900 - $600

= $300

Since the sales target is 35,000 units, the total contribution margin is:

Total contribution margin = Contribution margin per unit x Number of units sold

= $300 x 35,000

= $10,500,000

The total cost can be calculated as follows:

Total cost = Fixed cost + Variable cost

= $3,500,000 + ($600 x 35,000)

= $25,100,000

Adding the additional selling expense of $200,000, the new total cost becomes:

New total cost = $25,100,000 + $200,000

= $25,300,000

Therefore, the operating profit with sales of 35,000 units and an additional selling expense of $200,000 is:

Operating profit = Total revenue - Total cost

= ($900 x 35,000) - $25,300,000

= $10,500,000 - $25,300,000

= -$14,800,000

This indicates that the company would incur a loss of $14,800,000 if it spends an additional $200,000 on advertising to achieve sales of 35,000 units.

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Answer:

Step-by-step explanation:

Given a graph of muffins versus cups of flour, you want to know the constant of proportionality and the equation relating muffins (m) and cups (c).

The slope of the line on the graph is easily found by looking at the "muffins" (y) value for "cups" (x) equal to 1. That point is (c, m) = (1, 4).

The line goes through the origin (0, 0), so the slope is the ratio of y to x.

  m = y/x = 4/1 = 4

This is the constant of proportionality.

The constant of proportionality is 4, choice A.

The equation of a proportional relationship is ...

  y = kx . . . . . . where k is the constant of proportionality

Here, the independent variable (horizontal axis) is "cups", represented by 'c'. The dependent variable is "muffins", represented by 'm'. Using the above constant of proportionality, the equation is ...

  m = 4c . . . . . choice D

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We number of bags is 10 bags of fertilizer to complete the job.

Algebra is a branch of mathematics that deals with the study of mathematical symbols and their manipulation. It involves the use of letters, symbols, and equations to represent and solve mathematical problems.

In algebra, we use letters and symbols to represent unknown quantities and then use mathematical operations such as addition, subtraction, multiplication, division, and exponentiation to manipulate those quantities and solve equations. We can use algebra to model and solve real-world problems in various fields such as science, engineering, economics, and finance.

The total area of the football field is:

360 feet × 160 feet = 57,600 square feet

To find out how many bags of fertilizer are needed, we need to calculate how many 1000-square-foot areas there are on the field:

57,600 square feet ÷ 1000 square feet/area = 57.6 areas

So there are 57.6 areas on the football field.

We need 8 pounds of fertilizer per 1000 square feet, so to find out how many pounds we need for the whole field, we can multiply by the number of areas:

8 pounds/1000 square feet × 57.6 areas = 460.8 pounds

Therefore, we need 460.8 pounds of fertilizer to cover the football field.

Since the fertilizer comes in 50-pound bags, we can divide the total amount of fertilizer needed by 50 to find out how many bags we need:

460.8 pounds ÷ 50 pounds/bag ≈ 9.22 bags

We can't buy a fraction of a bag, so we need to round up to the nearest whole bag. Therefore, we need 10 bags of fertilizer to complete the job.

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The complete question is:

You are applying fertilizer to a football field. The field is 360 feet long and 160 feet wide. You use 8 pounds of fertilizer per 1000 square feet. The fertilizer comes in 50- pound bags. How many bags of fertilizer will you need to complete this job?

1.

f'(x) = 8 · x^(8-1) = 8·x^7

2.

g'(x) = -4· 4·x^(4-1) = -16·x^3

3.

h(x) = 1/x^5 = x^(-5), so

h'(x) = -5·x^(-5-1) = -5·x^(-6) or -5 / x^6

Answer:

a line graph

Step-by-step explanation:

Okay, let's evaluate each modeling equation candidate based on the r^2 value:

a. y=16.5839•1.0185^x

No r^2 value given, so cannot determine if this is the best fit.

b. y=0.985515x-2.81333

No r^2 value given for this linear model, so cannot determine if it is the best fit.

c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667

This is a 3rd order polynomial model, but no r^2 is given, so cannot determine if it is the best fit.

d. y=0.00182197x^2+0.785098x+1.195

If this model has the highest r^2 value, it would be the best fit.

Based on the information provided, the only option that could potentially be the best fit is choice d, the quadratic model y=0.00182197x^2+0.785098x+1.195, if it has the highest r^2 value. But without the actual r^2 values for each model, a definitive determination cannot be made.

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The domain is all real numbers, and the range is (y ≤ -4.855). (option b)

To sketch the graph of a quadratic equation, you can use a graphing calculator, which is a handy tool that can produce a visual representation of the equation. For instance, let's take the quadratic equation y = -0.5x² + 0.7x - 5.1 and sketch its graph using a graphing calculator.

When we enter this equation into the graphing calculator, we can see a U-shaped curve that is symmetric about the vertical line passing through the vertex. The vertex is the point where the parabola changes direction and is given by the formula x = -b/2a, y = f(x), where f(x) is the value of y at the vertex.

Now let's examine the given options and determine their domain and range based on the graph of the quadratic equation.

all real numbers, R: (y ≤ -4.855)

For this option, we can observe that the parabola opens upward, and the vertex is at (0.7, -5.35).

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Answer:

this is the Pythagorean theorem this is the formula a^2 + b^2 = c^2

Step-by-step explanation:

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