Simon is making a frame for a photo that measures 6 inches by 8 inches. He wants the frame to be the same width all the way around and the total area of the frame and photo to be 120 square inches. Which quadratic equation represents the area of the picture and frame?​

Answer:

linear equations produce straight lines when graphed, and their rate of change remains constant

Nonlinear equations do not produce straight lines when graphed.

To determine whether its linear or nonlinear, you can graph it and see if it produces a straight line, or check if it can be written in the form y= Mx+b

Step-by-step explanation:

The expressions 10x-7 and 7-10x represent the statement "seven less than ten times a number".

The verbal expression "seven less than ten times a number" can be written mathematically in different ways, depending on the intended meaning. One possible expression is:

10x - 7

In this expression, "10x" represents ten times a number, and "-7" represents seven less than that quantity. Thus, the entire expression represents the result of subtracting 7 from the product of 10 and the number x.

Another possible expression is 7 - 10x

In this expression, "10x" represents ten times a number, and "7 - 10x" represents seven less than that quantity. Thus, the entire expression represents the result of subtracting the product of 10 and the number x from 7.

If the focus is on finding the result of subtracting 7 from ten times a number, the first expression is more appropriate. If the focus is on finding the result of subtracting the product of 10 and a number from 7, the second expression is more appropriate.

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From the given information provided, the 12th term of the geometric sequence 7, -35, 175 is -341,796,875.

To find the 12th term of the geometric sequence 7, -35, 175, we can use the formula for the nth term of a geometric sequence:

an = a₁ × r⁽ⁿ⁻¹⁾

where aₙ is the nth term, a₁ is the first term, r is the common ratio, and n is the term number we want to find.

First, we need to find the common ratio (r) between any two consecutive terms. We can do this by dividing any term by its preceding term:

r = (-35) / 7 = -5

Now, we can use the formula to find the 12th term:

a₁₂ = 7 × (-5)⁽¹²⁻¹⁾

a₁₂ = 7 × (-5)¹¹

a₁₂ = 7 × (-48828125)

a₁₂ = -341,796,875

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The upper and lower 3-sigma control chart limits for this DNA sample data are UCL = 18.53 and LCL = 0

When we are given data on the DNA samples taken over the past 10 days, we can calculate the upper and lower 3-sigma control chart limits. The sample size is 100, and the defective number of DNA samples is given for each of the ten days.

The 3-sigma control limits for a process control chart can be calculated using the following formula: Upper control limit (UCL) = Mean + (3 × Standard Deviation) and Lower control limit (LCL) = Mean - (3 × Standard Deviation),where the mean is the average value of the data, and the standard deviation is the spread of the data around the mean.

Here, we need to calculate the mean and standard deviation of the defective samples for the past 10 days. The average number of defectives per day (mean) is (7+9+9+11+7+8+0+11+13+2) / 10 = 77 / 10 = 7.7

To calculate the standard deviation, firstly, calculate the variance: variance = sum of the squared differences from the mean divided by the number of samples = [tex][(7-7.7)^2 + (9-7.7)^2 + ... + (2-7.7)^2] / 10[/tex]  ≈ 13.01 2.. Now, take the square root of the variance which gives standard deviation. So, standard deviation = [tex]\sqrt{13.01\\}[/tex] ≈ 3.61

Using the 3-sigma rule UCL = Mean + (3 * Standard Deviation) = 7.7 + (3 * 3.61) ≈ 18.53    and   LCL = Mean - (3 * Standard Deviation) = 7.7 - (3 * 3.61) ≈ -3.13. However, since the LCL cannot be negative, we set it to 0 in this context. So, the upper and lower 3-sigma control chart limits are: UCL = 18.53 LCL = 0

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Using L'Hopital's rule, verified that Lim_x→0 (4^(2 x) - 1)/(7 x) = (2 log(4))/7

To solve the limit, we can use L'Hopital's rule. First, let's rewrite the limit as

lim_x→0 [(4^(2x) - 1)/x]/(7/2)

Now, we can apply L'Hopital's rule to the numerator

lim_x→0 [(4^(2x) - 1)/x] = lim_x→0 [8x*4^(2x-1)] = 0

So we get:

lim_x→0 [(4^(2x) - 1)/x]/(7/2) = (0)/(7/2) = 0

Therefore, the limit is 0.

Now let's verify the given answer using logarithmic properties

(4^(2x) - 1)/(7x) = (2 log(4))/7

Multiplying both sides by 7x

4^(2x) - 1 = 2x log(4)

Using the identity a^2 - b^2 = (a+b)(a-b), we can rewrite the left-hand side as:

(4^x + 1)(4^x - 1) = 2x log(4)

Dividing both sides by (4^x - 1)

4^x + 1 = (2x log(4))/(4^x - 1)

Now, taking the limit as x approaches 0, we get:

lim_x→0 [(2x log(4))/(4^x - 1)] = lim_x→0 [(2 log(4))/(ln(4) × 4^x)] = (2 log(4))/7

Therefore, the given answer is verified.

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The true statements for the graph of y=(x+2)²2+4 are:, The vertex of the parabola is at the point (-2, 4)., The graph opens upwards, since the coefficient of the squared term is positive., The y-intercept of the graph is at the point (0, 9)., The x-coordinate of the vertex is -2, which is also the axis of symmetry of the parabola., The graph is a parabola, which is a U-shaped curve.

What is graph?

In mathematics, a graph is a visual representation of a set of points, called vertices or nodes, that are connected by lines or curves, called edges. Graphs are used to model relationships between objects or to represent data in a visual way.

In the context of coordinate geometry, a graph is a visual representation of a function or relation, which shows the relationship between the input values (x-axis) and output values (y-axis). The graph is typically a set of points plotted on a Cartesian plane, where each point represents a unique input-output pair.

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Complete Question:

Select the statements that are true for the graph of y = (x+2)²2 + 4.

a) The vertex of the parabola is (-2, 4).

b) The parabola opens upward.

c) The y-intercept of the parabola is 4.

d) The x-intercepts of the parabola are (-4, 0) and (0, 0).

e) The axis of symmetry of the parabola is a vertical line through x = -2.

The average total lung capacity (TLC) of an average man is around 6 liters. However, the average total lung capacity of a man like Tom Sietas cannot be determined precisely as it depends on factors like height, weight, age, and physical condition.

What is lung capacity? Lung capacity refers to the total amount of air that your lungs can hold. Lung capacity is measured by a spirometer, a machine that measures the amount of air that you can breathe in and out. The total lung capacity (TLC) is the sum of four different volumes that include the tidal volume, inspiratory reserve volume, expiratory reserve volume, and residual volume.What is Tom Sietas’ total lung capacity?Tom Sietas is a German freediver who set a world record for holding his breath for 22 minutes and 22 seconds underwater in 2012. He is known for his exceptional lung capacity and has been reported to have a total lung capacity of 14 liters, which is more than double the average TLC of an average man. However, this figure may vary depending on several factors like height, weight, age, and physical condition.

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Answer:

43 seashells

Step-by-step explanation:

x = 26

x + 31 - 14

(26) + 31 - 14

57 - 14

= 43

The value of x in this equation is -¼ so, the approximate solution to the equation "-1+3=12x+5" is (x = -¼).

As equation given is -1+3=12x+5

Thus, 2 = 12x+5

12x = -3

x = -3/12

x = -¼

Hence the value of x in this equation is -¼.

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable. As a result, this equation has a single solution, x = 5/2. A linear equation with two variables, however, has two solutions.

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Answer:

Answer B

Step-by-step explanation:

you want the answer or not i dont need to explain myself

In order to calculate the expected revenue of a toll bridge during a particular daytime period, we need to know how many passenger cars and other vehicles are expected to pass through the bridge, as well as the toll charges for each type of vehicle.Let's say that X is the number of passenger cars and Y is the number of other vehicles. Then, we can use the following formula to calculate the expected revenue of the toll bridge:h[tex](X, Y) = 1.00X + 2.50Y[/tex]This formula takes into account the toll charges for each type of vehicle and multiplies them by the number of vehicles that are expected to pass through the toll bridge during the daytime period.

For example, if we expect 100 passenger cars and 50 other vehicles to pass through the toll bridge during the daytime period, then the expected revenue of the toll bridge would be[tex]:h(100, 50) = 1.00(100) + 2.50(50) = 100 + 125 = $225[/tex]

Therefore, the expected revenue of the toll bridge during the particular daytime period would be $225.

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A system loses 640 J of potential energy. In the process, it does 660 J of work on the environment and the thermal energy increases by 120 J .  Change in kinetic energy is -1420 J.

Solution:

To find the change in kinetic energy, we can use the conservation of energy principle. In this case, the loss of potential energy is converted into work done on the environment and an increase in thermal energy, as well as the change in kinetic energy.

The equation for this would be:

Loss of Potential Energy = Work Done + Increase in Thermal Energy + Change in Kinetic Energy

Let's plug in the values:
-640 J (loss of potential energy) = 660 J (work done) + 120 J (increase in thermal energy) + Change in Kinetic Energy

Now, solve for the change in kinetic energy:
-640 J = 660 J + 120 J + Change in Kinetic Energy
-640 J = 780 J + Change in Kinetic Energy

Change in Kinetic Energy = -640 J - 780 J
Change in Kinetic Energy = -1420 J

So, the change in kinetic energy is -1420 J.

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Answer:

Trina is 56 years old

Explanation:

If Duane is 6 years older than his brother, who just turned 14, we are adding 14+6, which is 20.

If trina is 4 years less than TRIPLE Duanes' age, then we first find triple of Duanes' age 20 x 3, which is 60. Then we find 4 less than 60, which is 56.

There are a few different reasons why certain categorical variables may not be allowed in a linear regression model:

Some software packages require categorical variables to be converted to numerical variables before they can be included in a linear regression model. This is typically done using one-hot encoding, where each category is represented by a binary variable indicating whether or not it is present.

If the number of categories for a given variable is very large, this can create a very large number of new variables, which may exceed the capacity of the software or the memory available on the computer running the analysis.

Some software packages may not allow categorical variables with a very large number of categories, again because of the potential computational demands of encoding these variables as binary variables.

If a categorical variable has a large number of categories relative to the sample size, it may not be possible to estimate the coefficients for each category with enough precision to be useful. Some software packages may not allow categorical variables with missing values, unless those missing values are explicitly coded as a category.

Overall, the decision to include or exclude categorical variables from a linear regression model will depend on a variety of factors, including the number of categories, the software being used, the size of the dataset, and the research question being addressed.

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The ratio of the surface area to the volume of the cylinder is 2/r + 1/9.

Mathematically, the surface area (SA) of a cylinder can be calculated by using this formula:

SA = 2πrh + 2πr²

Where:

By substituting the given parameters into the formula for the surface area of a cylinder, we have;

Surface area (SA) of cylinder = (2 × π × r × 18) + 2πr²

Surface area (SA) of cylinder = 36πr + 2πr²

For the volume, we have:

Volume of cylinder = πr²h

Volume of cylinder = πr²(18)

Volume of cylinder = 18πr²

Now, we can determine the ratio;

Ratio = (36πr + 2πr²)/18πr²

Ratio = 2/r + 1/9

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Answer:

0.0593, or 5.93%

Step-by-step explanation:

There are a total of 8 x 8 = 64 one-foot tiles in the foyer. Since two of them are cracked, there are 62 tiles that are not cracked.

To find the probability that the two cracked tiles share a common edge, we need to first determine the total number of pairs of adjacent tiles in the 62 remaining tiles. Each tile has four adjacent tiles (unless it is a tile on the edge of the foyer), so the total number of pairs of adjacent tiles is:

4 x (62 - 14) + 3 x 8 = 220

We subtracted 14 from 62 because there are 14 tiles on the edges of the foyer that only have three adjacent tiles, and we added 3 x 8 to account for the eight corner tiles that only have two adjacent tiles.

Next, we need to determine the number of ways that the two cracked tiles can be placed such that they share a common edge. There are 60 possible locations for the first cracked tile, and once it is placed, there are only 3 possible locations for the second cracked tile (it can only be placed in one of the three tiles adjacent to the first cracked tile). Therefore, the total number of ways that the two cracked tiles can be placed next to each other is:

60 x 3 = 180

Finally, we can calculate the probability by dividing the number of favorable outcomes (i.e., the number of ways that the cracked tiles can be placed next to each other) by the total number of possible outcomes (i.e., the total number of ways that the two cracked tiles can be placed):

P = 180/ (62 choose 2) = 180/ (62 x 61/2) = 0.0593 (approximately)

Therefore, the probability that the two cracked tiles share a common edge is approximately 0.0593, or 5.93%.

Answer:

The height of the water increases 2 inches per minute.

Step-by-step explanation:

The slope is the rate at which the pool is being filled.

A slope of 2 means a filling rate of 2 inches per minute.

Answer: The height of the water increases 2 inches per minute.

Let (x1, y1) = (9,7) and (x2, y2) = (6,3)

By distance formula,

d = (x2 - x1)² + (y2 - y1)²

d = (6 - 9)² + (3 - 7)²

d = (-3)² + (-4)²

d = 9 + 16

d = 25 units

The balance after 6 years when the interest is compounded monthly is $7289.60

To find the balance after 6 years when the interest is compounded monthly, we can use the formula:

A = P(1 + r/n)^(nt)

where:

In this case, P = $5000, r = 6.3% = 0.063 (annual interest rate as a decimal), n = 12 (since interest is compounded monthly), and t = 6.

Plugging in these values, we get:

A = $5000(1 + 0.063/12)^(12*6)

Evaluate

A = $7289.60

Therefore, the balance after 6 years when the interest is compounded monthly is $7289.60

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Answer: y = 17x + 114

Step-by-step explanation:

The equation for the slope-intercept form is y = mx + b.

Arrange the equation so that it resembles y = mx + b.

You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.

y + 5 = 17(x + 7)

y + 5 = 17x + 119

y + 5 - 5 = 17x + 119 - 5

y = 17x + 114

Answer:

Y = 17x + 114

Step-by-step explanation:

1. Y + 5 = 17 (x+7)

2. Y + 5 = 17x + 119   [Multiply the numbers in parenthesis by 17.]

3. Y = 17x + 114.     [To keep the balance and move the 5 over, subtract it from 119.]

Answer: 85%

Step-by-step explanation:

percentage increase/decrease formula: new-old/old x 100

122914-66440/66440x100=85

The answer of the given question based on the  the volume of the terrarium will be 70 cubic feet to  solve for x the answer is the terrarium is 7 ft long, 5 ft wide, and 2 ft tall.

A formula is mathematical expression that shows relationship between different variables or quantities. It can be used to calculate value based on given inputs or to derive  mathematical result from  set of conditions or assumptions.

To find the value of x, we can use the formula for the volume of a rectangular prism, which is:

Volume = Length x Width x Height

We are given the dimensions of the terrarium in terms of x, so we can substitute them into the formula:

Volume = (x) * (x-2) * (x-5)

We know that the volume of the terrarium is 70 cubic feet, so we can set the equation equal to 70 and solve for x:

(x) * (x-2) * (x-5) = 70

Expanding left side of equation we get:

x^3 - 7x^2 + 10x = 70

We can simplify this equation by subtracting 70 from both sides:

x^3 - 7x^2 + 10x - 70 = 0

In this case, the constant term is -70 and the leading coefficient is 1, so the possible rational roots are:

±1,±2,±5,±7,±10,±14,±35,±70

We can use synthetic division to simplify the calculation. After testing all the possible roots, we find that the only rational root is x = 7.

This means that the dimensions of the terrarium are:

Length = x = 7 feet

Width = x - 2 = 5 feet

Height = x - 5 = 2 feet

Therefore, the terrarium is 7 ft long, 5 ft wide, and 2 ft tall.

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Answer:

$25.96

Step-by-step explanation:

Since the tip is 18% of the fare, he pays 118% of the fare.

118% of $22 =

= 1.18 × $22

= $25.96

to find 7/8 of 3.5, we multiplied 7/8 and 3.5 together to get 49/16, which we then converted to a mixed number in the simplest form, giving us the answer of 3 1/16.

To find 7/8 of 3.5, we can simply multiply 7/8 and 3.5 together.

7/8 x 3.5 = (7/8) x (7/2) = 49/16

So, the answer is 49/16. However, we need to write the answer as a mixed number in the simplest form.

To convert an improper fraction to a mixed number, we need to divide the numerator by the denominator. In this case, 49 divided by 16 is 3 with a remainder of 1.

So, the mixed number is 3 1/16.

To simplify the mixed number, we need to check if we can reduce the fraction part (1/16) further. 1 is not divisible by any number other than 1 itself, so it is already in its simplest form.

Therefore, the final answer is 3 1/16.

In summary, to find 7/8 of 3.5, we multiplied 7/8 and 3.5 together to get 49/16, which we then converted to a mixed number in the simplest form, giving us the answer of 3 1/16.

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Step-by-step explanation:

Total surface area is 2πr²+2πrh

2× 22/7 × 5/4× 5/4 + 2 × 22/7 × 5/4 × 11/4

continue like this to get your right answer

Answer:

y=-3x+5

Step-by-step explanation:

A line that is parallel to y=-3x-5 will have the same slope, which is -3.

Using the point-slope form, we can write the equation of the line as:

y - 8 = -3(x + 1)

Simplifying:

y - 8 = -3x - 3

Adding 8 to both sides:

y = -3x + 5

Therefore, the equation of the line in slope-intercept form that is parallel to y=-3x-5 and goes through the point (-1,8) is y = -3x + 5.

Answer:  it is a

Step-by-step explanation:

the length of the flower's stem after it was cut is 2/3 of a foot long.

Laura's flower has a stem that is 11/12 of a foot long. If she cuts 3/12 of a foot off the stem, we need to subtract 3/12 from 11/12 to find the length of the remaining stem. To subtract fractions with the same denominator, we simply subtract their numerators and keep the denominator the same. Therefore, we have:

11/12 - 3/12 = 8/12

We can simplify the fraction 8/12 by dividing both the numerator and the denominator by their greatest common factor, which is 4. Therefore, we have:

8/12 = (8 ÷ 4)/(12 ÷ 4) = 2/3

the fraction to show the length of the flower's stem after it was cut

To subtract fractions with the same denominator, we simply subtract their numerators and keep the denominator the same. Therefore, we have:

11/12 - 3/12 = 8/12

Therefore, the length of the flower's stem after it was cut is 2/3 of a foot long.

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To check if the line drawn is diameter it should be intersected at centre and it must be equidistant from the centre of the circle.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

To determine if the line Neil drew is an actual diameter of the circle and not just a smaller chord, he can use the following method -

Extend the line on both sides to create two lines that intersect at a point outside the circle.

Use a compass to draw a circle with the same center as the original circle, and with a radius that is greater than half the length of the line Neil drew.

Check if the two lines intersect the circle at two points that are equidistant from the center of the circle.

If they do, then the line Neil drew is an actual diameter of the circle.

If they do not, then the line Neil drew is just a chord.

This method works because a diameter of a circle is the longest chord that passes through the center of the circle.

By extending the line Neil drew and creating two lines that intersect outside the circle, we can compare the distance from the center of the circle to each of the two intersection points with the radius of the circle we drew.

If the distances are equal, then the line Neil drew must be a diameter of the circle.

Therefore, the method to find the actual diameter is explained.

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The probability that your class of 20 students will have a mean completion time greater than 60 minutes on the unit 5 test is of:

0%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 48, \sigma = 15, n = 20, s = \frac{15}{\sqrt{20}} = 3.354[/tex]

The probability is one subtracted by the p-value of Z when X = 60, considering the standard error calculated with the Central Limit Theorem, hence:

Z = (60 - 48)/3.354

Z = 3.58

Z = 3.58 has a p-value of 1.

1 - 1 = 0.

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