Find the slope and the y-intercept of the line y=x+6

Answers

Answer 1

Answer:

slope = 1 , y- intercept = 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x + 6 ← is in slope- intercept form

with slope m = 1 and y- intercept c = 6

Answer 2

The answers are:

slope = 1 ; y intercept = 6

Work/explanation:

In slope intercept equations, such as this one, the slope is the number that appears before x.

When we don't see a number before x, it means that the slope is 1.

So slope = 1. As for the y intercept, it's the constant, which is 6.

So the y-intercept = 6

Related Questions

The starting numbers for the patterns for x and y are shown in the table below.
The blanks in the table represent the next four terms for each of the patterns.
• The rule for the x-values is add 3.
•The rule for the y-values is add 6.
X
y
0
0
Which graph represents the ordered pairs of the first five terms of the patterns
from the table?

Answers

The graph that represents the ordered pairs of the first five terms of the patterns from the table is the line graph.

The graph that represents the ordered pairs of the first five terms of the patterns from the table is the **line graph**.

The x-values in the table are increasing by 3 each time, while the y-values are increasing by 6 each time. This means that the ordered pairs are forming a straight line. The line graph is the only graph that shows a straight line.

The other graphs are either curves or not straight lines. The **scatter plot** shows a cloud of points that are not evenly distributed. The **bar graph** shows a series of vertical bars that are not evenly spaced. The **histogram** shows a series of horizontal bars that are not evenly spaced.

Here is a table of the first five terms of the patterns from the table, along with the corresponding ordered pairs:

X | Y | Ordered Pair

-- | -- | --

0 | 0 | (0, 0)

3 | 6 | (3, 6)

6 | 12 | (6, 12)

9 | 18 | (9, 18)

12 | 24 | (12, 24)

As you can see, the ordered pairs form a straight line.

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If a bike wheel covers a total of 69. 08 inches


after one complete rotation,what is the approximate radius of the bike wheel?

Answers

The approximate radius of the bike wheel is 11.0 inches.

If a bike wheel covers a total of 69.08 inches after one complete rotation, we can use the formula for the circumference of a circle to find the approximate radius of the bike wheel.

Circumference = 2piradius

where pi is approximately 3.14.

We are given that the circumference is 69.08 inches, so we can plug in these values and solve for the radius:

69.08 = 23.14radius

Dividing both sides by 2*pi, we get:

radius = 69.08 / (2*3.14) ≈ 11.0 inches

Therefore, the approximate radius of the bike wheel is 11.0 inches.

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Gunther used 3 3/5 pints of blue paint and 2 1/10 pints of yellow paint to make a mural.


How many pints of blue paint and yellow paint did Gunther use in all?



Simplify your answer if needed.


Explain your thinking using 3-5 complete sentences.

Answers

To solve the given problem we have to add the quantities of blue and yellow paint that were used by Gunther to make the mural.We are given that:Gunther used 3 3/5 pints of blue paint and 2 1/10 pints of yellow paint to make a mural.To add these two quantities we need to find a common denominator.

Here, the common denominator is 10.As such, we have to convert the mixed numbers to improper fractions.3 3/5 = (3 × 5 + 3)/5 = 18/5 2 1/10 = (2 × 10 + 1)/10 = 21/10Now, we can add the two fractions to get the total amount of paint used:18/5 + 21/10 = (36 + 21)/10 = 57/10 Therefore, Gunther used a total of 57/10 pints of paint to make the mural.Now, let's simplify this answer.

We can simplify the fraction by dividing both the numerator and denominator by the greatest common factor of 57 and 10, which is 1.57/10 = 5.7Thus, Gunther used 5.7 pints of paint to make the mural.In conclusion, Gunther used 3 3/5 pints of blue paint and 2 1/10 pints of yellow paint, or a total of 5.7 pints of paint to make the mural.

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Tre is helping his mom buy soil and plants for her small garden. Soil costs $3 per bag and plants


cost $12 each. Tre's mom wants at least 5 plants in her garden, but Tre can spend no more than $120.


Write a System Of Inequalities and Write Two Possible Solutions

Answers

The System Of Inequalities are : $3s + $12p ≤ $120

How to Write a System Of Inequalities and Write Two Possible Solutions

Let's represent the number of bags of soil as 's' and the number of plants as 'p'.

The given information can be translated into the following system of inequalities:

1. Cost inequality: $3s + $12p ≤ $120

  (The total cost of soil bags and plants should be less than or equal to $120.)

2. Plant requirement: p ≥ 5

  (Tre's mom wants at least 5 plants in her garden.)

Now, let's find two possible solutions that satisfy the given conditions:

Solution 1:

- Let's consider Tre purchasing 8 bags of soil (s = 8).

- Then, he can buy 5 plants (p = 5).

  (8 bags of soil cost $24, and 5 plants cost $60, which sums up to $84.)

Solution 2:

- Let's consider Tre purchasing 10 bags of soil (s = 10).

- Then, he can buy 6 plants (p = 6).

  (10 bags of soil cost $30, and 6 plants cost $72, which sums up to $102.)

These two solutions satisfy the conditions of at least 5 plants and a total cost of $120 or less.

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Jonas is conducting an experiment using a 10-sided die. He determines that the theoretical probability of rolling a 3 is StartFraction 1 over 10 EndFraction. He rolls the die 20 times. Four of those rolls result in a 3. Which adjustment can Jonas make to his experiment so the theoretical and experimental probabilities are likely to be closer?.

Answers

To make the theoretical and experimental probabilities closer, Jonas can increase the sample size by conducting more rolls of the 10-sided die. This will provide a more accurate representation of the theoretical probability.

By increasing the sample size, Jonas can gather more data points, which can help to reduce the impact of random variations and provide a more accurate representation of the theoretical probability. As the number of rolls increases, the experimental probability is more likely to approach the theoretical probability.

In this case, Jonas can conduct more rolls of the 10-sided die beyond the initial 20 rolls. The larger the number of rolls, the better the experimental probability will reflect the theoretical probability of rolling a 3. By increasing the sample size, Jonas can minimize the impact of outliers or chance occurrences that may have influenced the results in the initial 20 rolls, resulting in a closer alignment between the theoretical and experimental probabilities.

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Let ​​ f(x)=−32x and ​ g(x)=(12)x−1. Graph the functions on the same coordinate plane. What are the solutions to the equation f(x)=g(x) ? Enter your answers in the boxes. X = or x =.

Answers

The solutions to the equation f(x) = g(x) are x = 1/65. Hence, this is our final answer.

We have the following functions to graph:f(x)=−32x and ​g(x)=(12)x−1.Similarly, to graph the above functions we would require a table of values. For this we set x = −2, −1, 0, 1, 2 and solve for f(x) and g(x):x -2 -1 0 1 2f(x) 192 96 0 −32 −64g(x) 0.25 0.5 1 2 4Once we get the table of values, we can then graph the functions on the same coordinate plane.

We have the graph as below:Graph of f(x) = −32x and g(x) = (1/2)x−1Now to get the solutions to the equation f(x) = g(x), we equate the two expressions:−32x = (1/2)x−1Multiplying both sides by 2, we get:-64x = x - 1Collecting like terms, we get:-65x = -1Dividing both sides by -65, we get:x = 1/65

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An 85kg man stands on a scale inside an elevator. What is the weight in Newtons that the scale reads when the elevator is 


a.  at rest?


b.  moving upward at a constant speed of 5m/s?


c.   moving downward at a constant speed of 8m/s?


d.  moving with an upward acceleration of 3 m/s2


e.  moving with a downward acceleration of 4 m/s2

Answers

The weight in Newtons that the scale reads when the elevator is in different scenarios can be calculated using the formula W = mg, where W = weight, m=  mass, and g = the acceleration due to gravity.

a. When the elevator is at rest, there is no acceleration, so the weight will be equal to the gravitational force acting on the person. The weight can be calculated as W = mg, where m is the mass of the person (85 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Thus, the weight is W = 85 kg * 9.8 m/s^2.

b. the weight will remain the same as the gravitational force, which is calculated using the formula W = mg.  c. The acceleration is still zero, and the weight will be the same as the gravitational force, calculated using the formula W = mg.

d. We need to consider the net force acting on the person. The net force will be the sum of the gravitational force and the force due to the acceleration. The weight can be calculated as W = mg + ma, where m is the mass of the person (85 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and a is the upward acceleration (3 m/s^2).

e. We calculate the weight similarly to case d. The weight is W = mg + ma, where m is the mass of the person (85 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and a is the downward acceleration (-4 m/s^2) since it acts in the opposite direction.

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Suppose a 5-minute overseas call costs $5.91 and a 10-minute call costs $10.86. The cost of the call and the length of the call are related. The cost of each minute is constant.


A. What is the cost, c, ofa call of m minutes duration?


B. How long can you talk on the phone if you have $12 to spend?

Answers

The cost of a call of m minutes duration, given the cost of the calls would be c = 0. 05 + 0. 99m

If you have $ 12 to spend, the time you can spend is 10.15 minutes.

How to find the cost per minute ?

The cost per minute would be :

= Difference between 5 and 10 minute call / Number of minutes

= ( 10. 86 - 5. 91 ) / 5

= $ 0.99

The cost per minute is therefore:

= 0. 99 x number of minutes

= 0. 99m

The initial cost is :

=  5 - 0. 99 x 5

= $ 0. 05

The number of minutes with $12 is:

= ( 12 - 0.05 ) / 0. 99

= 12. 1 minutes

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A dice is rolled 50 times. It lands on six 37 times. what is the relative frequency of the dice landing on a six.

Answers

The relative frequency of the dice landing on a six is 0.74 or 74%.

1. Given that a dice is rolled 50 times and it lands on six 37 times.

2. Use the formula for relative frequency: Relative Frequency = (Number of times the dice lands on a six) ÷ (Total number of times the dice is rolled).

3. Substitute the values into the formula: Relative Frequency of dice landing on six = 37/50 = 0.74 or 74%.

Conclusion: In summary, when a dice is rolled 50 times and it lands on six 37 times, the relative frequency of the dice landing on a six is calculated to be 0.74 or 74%.

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what is the answer to this problem 2 ft 5 in + 9 in =

Answers

The problem requires adding two measurements in different units, 2 ft 5 in and 9 in. We need to determine the sum of these measurements.

To add the given measurements, we should first convert them to a consistent unit. In this case, we will convert everything to inches since the second measurement is already in inches.

1 foot is equal to 12 inches, so 2 ft is equal to 2 * 12 = 24 inches. Therefore, 2 ft 5 in can be written as 24 in + 5 in. Adding 24 in and 5 in, we get 29 in. Thus, the sum of 2 ft 5 in and 9 in is 29 inches. In conclusion, when we add 2 ft 5 in and 9 in, the result is 29 inches.

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Jordan's pet grooming business has a monthly cost function of C - $12p+ $2100. His Revenue is given by the function R - $62p, where Cis the total cost


per month, R is the total revenue he receives each month and x is the number of pets he grooms in a month. How many pets must he groom each month


to break even?

Answers

Jordan's pet grooming business has a monthly cost function of C - $12p+ $2100. The monthly cost function for Jordan's pet-grooming company is C - $12p+ $2100.

His Revenue is given by the function R - $62p, where C is the total costper month, R is the total revenue he receives each month and x is the number of pets he grooms in a month. We need to find out how many pets must he groom each month to break even.Let's set revenue equal to costs, and solve for p.R = C62p = 12p + 2100p = (12p + 2100) / 62p = 0.1935p ≈ 19.35 petsJordan must groom approximately 19.35 pets each month to break even. The nearest whole number is 19.

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A scooter rental store charges a $4 rental fee plus $1. 50 for each hour a scooter is rented. What are the slope and y- intercept that represent this situation

Answers

Answer:

y = 1.5x + 4

The slope is 1.5, and the y-intercept is 4.

Steve determines that sides DK and BC are congruent. He also measures

Answers

Therefore, the measure of the angle BDK is 62.5°.

Given: Steve determines that sides DK and BC are congruent. Therefore, DK ≅ BC.

He also measures the angle DBK to be 55°. Therefore, ∠DBK = 55°.

To find the measure of the angle BDK, we can use the fact that the sum of the angles in a triangle is 180°.

∠BDK = 180° - ∠DBK - ∠BKD

Since DK ≅ BC, ∠BDK = ∠BCD.

∴ ∠BDK = ∠BCD = (125° - ∠BCD)

Simplifying the equation, we get:

2∠BCD = 125°

∠BCD = 62.5°

Therefore, the measure of the angle BDK is 62.5°.

Hence, option D is correct.

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Given \small \Delta ABC\sim\Delta DEC, could you use the proportion \small \frac{9}{10}=\frac{8.75}{EC} to determine the measure of EC? If yes, type yes and solve for EC. (Must type yes and give value of EC) If no, type no and rewrite the proportion and then solve for EC. (Must type no, give the correct proportion, and the value of EC)

Answers

Yes, In order to determine the measure of EC, we need a proportion that relates the corresponding sides of similar triangles. we can use the proportion 9/10 = 8.75/EC to determine the measure of EC

The proportion is,

To solve for EC, we can cross-multiply and then solve for EC.

9/10 = 8.75/EC

9×EC=10×8.75

Simplifying we get,

EC = 9.72

Therefore, the measure of EC is approximately 9.72 units.

Please provide the correct proportion relating the corresponding sides of

ΔABC and ΔDEC, and I'll be happy to help you solve for EC.

Hence, the correct answer is:Yes, EC ≈ 9.7222.

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¿Cuál es la asignatura que más requiere atención? *


2 puntos


a) Historia.


b) Ciencias Naturales.


c) Cívica y Ética.


d) Geografía

Answers

The subject that most requires attention would be Natural Sciences.

Option B is the correct answer.

We have,

It is subjective to determine which subject requires the most attention, as it depends on various factors such as educational goals, societal needs, and individual interests.

However, if we were to assign points based on general importance:

a) History - 1 point

b) Natural Sciences - 2 points

c) Civic and Ethical - 1 point

d) Geography - 1 point

Based on this allocation, the subject that most require attention would be Natural Sciences.

Thus,

The subject that most requires attention would be Natural Sciences.

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The complete question:

What is the subject that most require attention? *

2 points

a) History.

b) Natural Sciences.

c) Civic and Ethical.

d) Geography




One link in a chain was made from a cylinder that has a radius of 2. 5 cm and a height of 22 cm. How much plastic coating would be needed to coat the surface of the chain link? Use


3 14 for TT


O2512 cm


O 314 cm?


O 345 4 cm


O 471 cm

Answers

The plastic coating would be needed to coat the surface of the chain is 345.4 cm². Hence option 3 is true.

A cylinder's surface area is the overall area or region that the shape's surface covers. A cylinder's total surface area comprises both the area of the curved surface and the area of the two flat surfaces since there are two flat surfaces and one curved surface.

The formula for a particular cylinder's total surface area is as follows:

TSA = 2πr (h + r)

Given that;

One link in a chain was made from a cylinder that has a radius of 2.5 cm and a height of 22 cm.

Hence, The plastic coating would be needed to coat the surface of the chain is,

2 × 3.14 × 2.5 × 22

= 345.4 cm²

So, The plastic coating would be needed to coat the surface of the chain is 345.4 cm². Hence option 3 is true.

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Write log12 in four different ways. Name each you use and explain your process

Answers

The logarithm base 12 can be expressed as log12 or in exponential form as 12^x = y, where x is the exponent and y is the result.

The logarithm function is the inverse of exponentiation. It represents the exponent to which a given base (in this case, 12) must be raised to obtain a certain value. There are four different ways to express log12:

Logarithmic form: log12(y) - This notation indicates that the logarithm base 12 is being applied to a value y.

Exponential form: 12^x = y - In this form, the base 12 is raised to an exponent x to produce a value y.

Fractional exponent form: y^(1/12) - The fractional exponent represents the root of y with a base of 12. It is equivalent to log12(y).

Common logarithm form: log(y) / log(12) - If the logarithm base 12 function is not directly available, we can use the common logarithm (base 10) or any other logarithmic base and apply the change of base formula. The result is the logarithm of y divided by the logarithm of 12.

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Given the general form for linear systems: a1x b1y = c1 a2x b2y = c2 What is the correct solution using determinants, in terms of a, b and c?.

Answers

The solution to the linear system of equations in terms of a, b, and c is given by the values of x and y obtained from the determinants.

To solve the linear system of equations using determinants, we can use Cramer's Rule, which relies on the concept of determinants. The determinants involved in Cramer's Rule are the coefficient determinant (D), the x-determinant (Dx), and the y-determinant (Dy).

The general form of the linear system of equations is:

a1x + b1y = c1

a2x + b2y = c2

To find the solution using determinants, we first calculate the coefficient determinant (D):

D = | a1 b1 |

| a2 b2 |

The coefficient determinant D represents the determinant of the matrix formed by the coefficients of x and y.

Next, we calculate the x-determinant (Dx):

Dx = | c1 b1 |

| c2 b2 |

The x-determinant Dx is obtained by replacing the x-coefficients in the coefficient determinant D with the constants c1 and c2.

Similarly, we calculate the y-determinant (Dy):

Dy = | a1 c1 |

| a2 c2 |

The y-determinant Dy is obtained by replacing the y-coefficients in the coefficient determinant D with the constants c1 and c2.

Now, we can find the values of x and y using the determinants:

x = Dx / D

y = Dy / D

It's important to note that this method using determinants applies specifically to linear systems with two variables. For larger systems, the method becomes more complex and involves calculating determinants for higher-order matrices.

In summary, to find the solution using determinants, we calculate the coefficient determinant (D), the x-determinant (Dx), and the y-determinant (Dy) based on the given linear system of equations. Then, we find the values of x and y using the determinants. The solution is expressed in terms of a, b, and c.

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find the side of the triangle if two of its sides are equal the third side is 1 1/3 cm longer than the others and its perimeter is 5 2/5cm

Answers

The lengths of the sides of the triangle are approximately:

The two equal sides: 61/45 cm

The third side: 1089/405 cm

Let's assume that the two equal sides of the triangle are represented by "x" cm each. According to the given information, the third side is 1 1/3 cm longer than the other two sides.

So, the length of the third side can be represented as "x + 1 1/3" cm.

The perimeter of a triangle is the sum of all its sides. In this case, the perimeter is given as 5 2/5 cm.

Using this information, we can write the equation:

2x + (x + 1 1/3) = 5 2/5

To solve this equation, let's convert the mixed number 1 1/3 to an improper fraction.

1 1/3 = (3× 1 + 1) / 3 = 4/3

Substituting the value, we have:

2x + (x + 4/3) = 5 2/5

To simplify the equation, let's convert the mixed number 5 2/5 to an improper fraction.

5 2/5 = (5 ×5 + 2) / 5 = 27/5

Now, the equation becomes:

2x + (x + 4/3) = 27/5

Combining like terms, we have:

3x + 4/3 = 27/5

To eliminate the fractions, let's multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 15:

15 × (3x + 4/3) = 15 ×(27/5)

45x + 20 = 81

Subtracting 20 from both sides:

45x = 61

Dividing both sides by 45:

x = 61/45

So, the value of x is 61/45 cm. This represents the length of the two equal sides of the triangle.

Now, to find the length of the third side, we substitute x back into the expression:

x + 1 1/3 = (61/45) + 4/3

To add these fractions, we need to find a common denominator. The LCM of 45 and 3 is 45:

[(61/45) × (3/3)] + (4/3) = (183/135) + (4/3)

Now, we can add the fractions:

(183/135) + (4/3) = (549/405) + (540/405) = 1089/405

So, the length of the third side is 1089/405 cm.

Therefore, the lengths of the sides of the triangle are approximately:

The two equal sides: 61/45 cm

The third side: 1089/405 cm

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A man uses a rod of length 5. 0m to lift a 700 kg marble. The fulcrum is 0. 50m from the end of the bar that is under the marble. Calculate the mechanical advantage and minimum effort required to lift the load. If the efficiency of this system is 90% determine it's velocity ratio

Answers

The velocity ratio of the system is 9. To calculate the mechanical advantage of the system, we can use the formula Mechanical Advantage (MA) = Length of Effort Arm / Length of Load Arm

In this case, the length of the effort arm is the distance from the fulcrum to the end of the bar that the man applies effort, which is 0.50m. The length of the load arm is the distance from the fulcrum to the marble, which is 5.0m - 0.50m = 4.50m.

Therefore, the mechanical advantage is:

MA = 0.50m / 4.50m = 1/9

The minimum effort required to lift the load can be calculated using the formula:

Effort = Load / MA

In this case, the load is the weight of the marble, which is 700 kg, and the mechanical advantage is 1/9.

Therefore, the minimum effort required is:

Effort = 700 kg / (1/9) = 6300 N

Now, let's calculate the velocity ratio. Efficiency is defined as the ratio of useful work output to the total work input. Since the efficiency is given as 90%, the efficiency can be expressed as:

Efficiency = (Useful Work Output / Total Work Input) * 100%

In this case, the useful work output is the work done in lifting the load, which is the weight of the marble multiplied by the height it is lifted. The total work input is the effort applied multiplied by the distance it moves.

Let's assume the marble is lifted vertically by a height h.

Useful Work Output = Weight of Marble * Height Lifted = 700 kg * g * h

Total Work Input = Effort * Distance Moved = 6300 N * h

Efficiency = (700 kg * g * h / (6300 N * h)) * 100% = (700 / 6300) * 100% = 11.11%

The velocity ratio can be calculated as the reciprocal of the efficiency:

Velocity Ratio = 1 / Efficiency = 1 / 0.1111 = 9

Therefore, the velocity ratio of the system is 9.

In summary, the mechanical advantage of the system is 1/9, the minimum effort required to lift the load is 6300 N, and the velocity ratio is 9.

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Reflect the triangle across the y-axis, and then translate the image 5 units down. The final image is the same as which of the following transformations? Translate 5 units down, and then reflect over the x-axis. Translate 5 units down, and then reflect over the y-axis. Rotate 180° about the origin. Reflect over the x-axis, and then translate 5 units left.

Answers

The final image obtained after reflecting the triangle across the y-axis and translating it 5 units down is equivalent to reflecting the original triangle over the x-axis and then translating it 5 units down.

When we reflect the triangle across the y-axis, each point's x-coordinate is negated while the y-coordinate remains unchanged. This reflection essentially flips the triangle horizontally.

After reflecting the triangle, we then translate it 5 units down. This translation involves shifting each point of the triangle downward by 5 units along the y-axis.

Now let's consider the second transformation: reflecting the original triangle over the x-axis and then translating it 5 units down.

Reflecting the triangle over the x-axis means that each point's y-coordinate is negated while the x-coordinate remains unchanged. This reflection flips the triangle vertically.

After reflecting the triangle, we translate it 5 units down, which involves shifting each point of the triangle downward by 5 units along the y-axis.

By comparing the two sequences of transformations, we can see that they result in the same final image. First, we horizontally flip the triangle and then shift it downward, which is equivalent to first vertically flipping the triangle and then shifting it downward.

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Answer:

B. Translate 5 units down, and then reflect over the y-axis.

Step-by-step explanation:

The total salamander population on the island is represented by the expression 3,000 (1.035) t, where t is the time in years. what is the equivalent exponential expression rewritten to identify the weekly growth rate of the population?

A.) 3000(1.035⁵²)t
B.) 3000(1.035) t/⁵²
C.) 3000(1.035 ¹/⁵²)t
D.) 3000(1.035 ¹/⁵²)⁵²t​

Answers

Answer:

The correct answer is:

C.) 3000(1.035^(1/52))^t

This expression represents the equivalent exponential expression that identifies the weekly growth rate of the population. The exponent 1/52 represents the conversion from years to weeks, as there are 52 weeks in a year.

Step-by-step explanation:

Nicholas scoops a few gumballs into his bag. When he weighs it, he finds that he scooped 0.76 pounds.

Answers

Nicholas scooped a few gumballs into his bag and found that it weighed 0.76 pounds.

Nicholas's bag of gumballs weighs 0.76 pounds. This weight includes the combined mass of the gumballs and the bag itself. The weight measurement indicates the force exerted by the bag due to the gravitational pull of the Earth. To determine the weight of just the gumballs, Nicholas would need to subtract the weight of the bag from the total weight.

To find the weight of the bag, Nicholas could use a scale or balance to measure an empty bag of the same type. Once he knows the weight of the empty bag, he can subtract that weight from the total weight of the bag with the gumballs. The result will give him the weight of the gumballs alone.

It's important to note that the weight of the gumballs may vary depending on their size, density, and the material of the bag. Different types of gumballs may have different weights. To get an accurate measurement, Nicholas should use a precise weighing instrument and account for any external factors that could affect the weight, such as moisture or contaminants.

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30% of the members of a tennis club are pensioners. 36 members are pensioners


a) how many members there in total ?


b) how many members are not pensioners

Answers

Answer

there's 120 members in total

84 not pensioners

Explaination

36÷30% = 120

70% are not pensioners

so 70% × 120 = 84

or you could minus the pensioners from the total 120-36=84

A rectangular box has width (x), length (5x - 1), and height (2x + 3). The area is 29,946 in. Find X

I need help please

Answers

To find the value of x in the given problem, we can start by calculating the area of the rectangular box. The area of a rectangular box is given by the formula A = 2lw + 2lh + 2wh, where l represents the length, w represents the width, and h represents the height. In this case, the area is given as 29,946 in².

The first step is to substitute the given values into the formula:

29,946 = 2(x)(5x - 1) + 2(x)(2x + 3) + 2(5x - 1)(2x + 3).

Next, we simplify the equation and distribute the terms:

29,946 = 2(5x² - x) + 2(2x² + 3x) + 2(10x² + 15x - 2x - 3).

After combining like terms, we have:

29,946 = 10x² - 2x + 4x² + 6x + 20x² + 30x - 4x - 6.

Combining similar terms further, we get:

29,946 = 34x² + 40x - 6.

Now, we can rearrange the equation and set it equal to zero:

34x² + 40x - 29,946 = 0.

To solve this quadratic equation, we can either factor it or use the quadratic formula. However, since the equation is not easily factorable, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a).

By substituting the values a = 34, b = 40, and c = -29,946 into the quadratic formula, we can find the two possible values of x. However, since we are looking for a real-world length, we can discard any negative or non-real solutions.

After solving the equation, we find that x is approximately equal to 24.4 or x ≈ -29.36. Since negative values are not meaningful in the context of length, we can conclude that the value of x for which the rectangular box has the given area of 29,946 in² is approximately 24.4 inches.

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Lincoln's monthly bank statement showed the following deposits and withdrawals: − −$28. 51, − −$41. 34, $90. 95, − −$88. 95, $11. 16 If Lincoln's balance in the account was $19. 96 at the beginning of the month, what was the account balance at the end of the month?

Answers

After considering the deposits and withdrawals, the account balance at the end of the month is $64.23.

To calculate the account balance at the end of the month, we need to add up all the deposits and withdrawals. The negative values represent withdrawals, while the positive values represent deposits.

Starting with an initial balance of $19.96, we can calculate the final balance by adding the amounts of the deposits and subtracting the amounts of the withdrawals.

Starting balance: $19.96

Deposits: $90.95, $11.16

Withdrawals: -$28.51, -$41.34, -$88.95

Adding the deposits: $19.96 + $90.95 + $11.16 = $122.07

Subtracting the withdrawals: $122.07 - $28.51 - $41.34 - $88.95 = $64.23

Therefore, the account balance at the end of the month is $64.23.

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Complete steps 2 and 3 to solve the system of equations.


y = 4x – 5,

Answers

The solution of the given system of equations is (2, -10).

The given system of equations is:

y = 4x - 5

We need to solve the system of equations given by

Step 1: We need to substitute

y = 4x - 5 into the second equation.

4x - y = 5 becomes

4x - (4x - 5) = 5

Simplifying the above equation will give us:-

y + 4x - 4x = 5 + 5y = -10

Hence, the solution of the given system of equations is

(x, y) = (2, -10).

Steps 2 and 3 to solve the system of equations are:

Step 2: Substitute

y = 4x - 5 into the second equation. This gives us:

4x - (4x - 5) = 5

Simplifying the above equation will give us:-

y + 4x - 4x = 5 + 5

Step 3: Solve the simplified equation to get the value of y.-

y = 10y = -10

Thus, the solution of the given system of equations is (2, -10).

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6. Walking path BE intersects two sides of a park at their midpoints. You start your walk at point D and then


proceed to points E, B, C and then back to D. How many yards did you walk? Show your work

Answers

When you start your walk at point D and then proceed to points E, B, C, and then back to D the the total distance traveled is 72 yards.

In the figure above, walking path BE intersects two sides of a park at their midpoints. One of the vertices of the rectangle is point D.

Starting at point D, walking path BE intersects two sides of the park at their midpoints. Then proceed to points E, B, C and back to D.

The rectangle has two sets of sides with equal length, and BD is a diagonal of the rectangle, so triangle ABD is a 45°-45°-90° right triangle.

As a result,

              AD = BD = 12 yards.

Likewise, triangle BDC is a 45°-45°-90° right triangle, so

            CD = BD

                    = 12 yards.

Therefore, the total distance traveled is 12 + 4 + 12 + 8 + 12 + 4 + 12 + 8 = 72 yards.

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The equation shows the relationship between x and y: y = 7x 2 What is the slope of the equation? −7 −5 2 7.

Answers

The slope of the equation y = 7x^2 is 14x, not one of the given options.

The slope of a quadratic equation can be determined by finding its derivative with respect to x. In this case, we have y = 7x^2. To find the derivative, we apply the power rule of differentiation. The power rule states that if we have a term of the form ax^n, the derivative is given by nx^(n-1).

Applying the power rule to y = 7x^2, we get dy/dx = 2 * 7x^(2-1) = 14x. The slope of the equation is represented by the derivative, which in this case is 14x. It is important to note that the slope of a quadratic equation varies depending on the value of x. Therefore, the slope is not a constant value like the options given (-7, -5, 2, or 7). Instead, the slope is expressed as a function of x, which is 14x in this case.

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Use the coordinates to find the length of each side of the rectangle. Then find the perimeter. M(1,1) N(1,9) P(7. 9) Q(7,1)

Answers

The length of each side of the rectangle can be found by calculating the distance between the given coordinates.

The side lengths are 8 units and 6 units, respectively. The perimeter of the rectangle is the sum of all four side lengths, which is 28 units.

To find the length of each side of the rectangle, we calculate the distance between the given coordinates. Let's consider the coordinates M(1,1), N(1,9), P(7,9), and Q(7,1).

The side MN has coordinates (1,1) and (1,9). The vertical distance between these two points is 9 - 1 = 8 units.

The side NP has coordinates (1,9) and (7,9). The horizontal distance between these two points is 7 - 1 = 6 units.

The side PQ has coordinates (7,9) and (7,1). The vertical distance between these two points is 9 - 1 = 8 units.

The side QM has coordinates (7,1) and (1,1). The horizontal distance between these two points is 7 - 1 = 6 units.

Therefore, the length of each side of the rectangle is 8 units and 6 units.

The perimeter of a rectangle is the sum of all four side lengths. In this case, the perimeter is 8 + 6 + 8 + 6 = 28 units.

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