this is a partially decoupled system. solve for v(t) first by separation of variables. then substitute into the second equation and solve for y(t). if c1 is the constant that is in the general solution for v(t), and c2 is the constant that appears when solving for y(t), what is the value of c2?

The vertices of the image of triangle ABC after the transformations are given as follows:

A'(4,-2), B'(4,2), C'(0,-1).

The vertices of triangle ABC are given as follows:

A(1,1), B(1,5), C(5,2).

The first transformation is the translation defined as follows:

(x,y) -> (x - 5, y - 3).

Hence the translated vertices are given as follows:

A'(-4, -2), B'(-4, 2), C'(0, -1).

The second transformation is the reflection over the x-axis, hence the rule is:

(x,y) -> (x, -y).

Then the vertices of the translated and reflected triangle are given as follows:

A'(-4, 2), B'(-4,-2), C'(0,1).

The final transformation is the rotation of 180º clockwise around the origin, for which the rule is of:

(x,y) -> (-x,-y).

Then the vertices of the image, after all the transformations, are given as follows:

A'(4,-2), B'(4,2), C'(0,-1).

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The amounts of each substance are given as follows:

The graphic solution of a system of equations is given by the point of intersection of the equations that compose the system.

The variables that define the system in this problem are given as follows:

Yaritza sold a total of 75 pounds of peaches and grapes, hence:

x + y = 75.

Each pound of peaches sell for $2.50 and each pound of grapes sells for $3.75, and she made $225, hence:

2.5x + 3.75y = 225.

As given by the image at the end of the answer, the intersection of these two equations in the graph is given as follows:

(45, 30).

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The measurement of <B is 121 degree.

The sum of a triangle's three internal angles is 180 degrees, as stated by the angle sum Property of a triangle.

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees.

Given:

let the measure of <A be x.

So, m<G= x- 9

and, m<B = 4x- 15

Using Angle Sum Property

m<A+ m<B+ m<G= 180

x+ 4x- 15 + x- 9 = 180

6x - 24 = 180

6x = 180+ 24

x= 204/6

x= 34

So, m<A = 34

m<B= 4(34) - 15 = 121

and, m<G = 34 - 9= 25 degree.

Hence, the measure of <B is 121 degree.

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Answer:

1.25 hours  (1 and 1/4 hours)

Step-by-step explanation:

Kiran;s aunt bikes at an average rate of 8 miles/hr.  Assuming it is an average day, we can determine the time it will take her to bike 10 miles by dividng the miles by her average speed:

  (10 miles)/(8 miles/hr)

The miles cancel and the hr comes to the top:

 (10/8) hours or 1.25 hours  1 and 1/4 hours

Kiran's aunt takes 1.25 hours to cover the distance of 10 miles at the average speed of 8 miles per hour.

In unit time, the distance covered by any object is called speed.

In mathematical term, Speed is express as S = D/T,

where S=speed, D=distance, T= time.

Given that,

Distance that Kiran's aunt plans to bike = 10 miles.

The average speed of bike = 8 miles per hour.

To find the time taken by Kiran' aunt to cover 10 miles distance,

Use Formula

Time = Distance / speed

Time = 10 / 8

Time = 1.25

The time taken by Kiran's aunt to cover 10 miles distance is 1.25 hours.

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68.26% of students out of 500 would score between 68 and 82  if the mean is 75 and standard deviation is 7.

A low standard deviation suggests that values are often close to the mean (also known as the anticipated value) of the collection, whereas a large standard deviation suggests that values are dispersed over a wider range.

Standard deviation, often known as SD, is most frequently represented in mathematical texts and equations by the lower case Greek letter (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.

Given,

Mean μ=75

σ=7

By using normal distribution,

P(68<x<82)=P(((68-μ)/σ)<z<((82-75)/7))

P(-1<z<1)

P(z<1)-P(z< -1)

By using z-table, we get

=0.8413-0.1587

=0.6826

P(68<x<82)=0.6826≈68.26

P(68<x<82)=68.26%

Therefore, 68.26% of students out of 500 would score between 68 and 82 if the mean is 75 and standard deviation is 7.

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The equation of the line that passes through (1,2) and is perpendicular to the given line is y = -x + 3 with slope 2.

Given line: y = 2x - 1

We know that two lines are perpendicular if their slopes are negative reciprocals of each other.

The provided line's slope is m1 = 2.

Therefore, slope of the line that passes through (1,2) and is perpendicular to the given line = m2 = -1/2

Now, we can use the point-slope equation of a line to find the equation of the line:

y = -x + 3

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Answer:

skewed to the right

40.1

49.9

Step-by-step explanation:

the largest possible range is the largest number from the largest margin minus the smallest number from the smallest margin

(49.9-0=49.9

the smallest possible range is the smallest number from the largest margin minus the largest number from the smallest margin

(45.0-4.9=40.1)

The slope and y-intercept of a graph can be determined by examining the equation of the line.

The slope is the coefficient of the x-term (the number next to x in the equation) and the y-intercept is the number that the line crosses the y-axis (the constant in the equation). For example, if the equation of a line is y = 2x + 5, then the slope is 2 and the y-intercept is 5. To graph the line, you can use the slope and y-intercept. Start at the y-intercept and move up or down the number of units indicated by the slope. For example, if the slope is 2, move two units up or two units down and plot a point. Repeat this process until the graph is complete.

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The equation of the line is y = 4x + 9

Given,

The points; (x₁, y₁) = (1, 5)

The line is parallel to, y = 4x - 2

Here,

The line given is in the Slope Intercept Form

y = mx + b

y = 4x - 2

Parallel Lines have the same slope

So,

Slope, m = 4

Then,

y = 4x + b

Since it passes through point p(1, 5) we can use these coordinates to solve for b

5 = -4 + b

Solve for b

9 = b

Therefore, the equation of the line;

y = 4x + 9

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The probability that in the resulting coloring, no two adjacent edges have the same color is 1/24.

It is given that the edges of a regular pentagon are colored res, blue or green at random, so that each edge has an equally likely chance of being painted with any color.

So you can't have 0 reds.

You can have 1 red and there are 2 scenarios for that.

You can have 2 reds and there are 8 scenarios for that.

You can't have 3+ reds.

In total there are 10 scenarios that work.

Therefore there are 3⁵ - 3 total cases.

i.e there are 240 total cases.

So the probability that no two adjacent edges have the same color is,

total scenarios/total cases = 10/240 = 1/24.

Therefore the probability that no two adjacent edges have the same color is 1/24.

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Answer: -8 and 4 or 16 and 2

Step-by-step explanation:

A pair of integers that satisfies the given conditions is -8 and 4.

When multiplied, the product of -8 and 4 is -32. When added, the sum of -8 and 4 is -4. Therefore, -8 and 4 are a pair of integers that satisfies the given conditions.

To verify this solution, we can multiply -8 and 4 to get -32, and then add -8 and 4 to get -4. This confirms that -8 and 4 are a valid solution to the problem.

It is also possible to find other pairs of integers that satisfy the given conditions. For example, another pair of integers that satisfies the given conditions is -16 and 2. When multiplied, the product of -16 and 2 is -32. When added, the sum of -16 and 2 is -4. Therefore, -16 and 2 are another pair of integers that satisfies the given conditions.

The percentage of defective panels from the two plants was 6% number of panels produced by plant are 6000.

Let x be the quantity of tv panels that the Company B produced. It is said on this object that 10% of those panels are faulty.

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The solution of the system of equations y = -3x - 2 and 5x + 2y = 15 is (-19, 55)

The first equation is

y = -3x - 2

The second equation is

5x + 2y = 15

To solve this problem we have to use the substitution method

Substitute the value of y = -3x - 2 in the second equation 5x + 2y = 15

5x + 2(-3x -2) = 15

5x - 6x - 4 = 15

-x - 4 = 15

-x = 15 + 4

-x = 19

x = -19

Substitute the value of x in the first equation

y = -3x - 2

y = -3(-19) - 2

= 57 - 2

= 55

Therefore, the solution of the system of equation is (-19, 55)

I have solved the question in general, as the given question is incomplete

The complete question  is

What is the solution to the system of equations

y = -3x - 2 and 5x + 2y = 15

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Answer:

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

Let the number of miles be x.

Then we have the following equation:

Solve it for x:

In a shipment of 3500 tomatoes can be expected to weight from 0.32 lb to 0.92 lb is 3340. When A vegetable distributor knows that during the month of august, the weights of its tomatoes are normally distributed with a mean Of 0.62 lb and a standard deviation of 0.15.

A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. In contrast, a high or low standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean. The standard deviation measures the degree of dispersion of a set of data. Each data point is compared to the average of all the data points, and standard deviation gives a determined value that indicates whether the data points are clustered together or dispersed. The standard deviation of a normal distribution indicates how far values deviate from the mean.

Given,

A vegetable distributor knows that during the month of august, the weights of its tomatoes are normally distributed with a mean Of 0.62 lb and a standard deviation of 0.15.

Normal variable of x = 0.32

Z = X - mean/ standard deviation

Z = 0.32 - 0.62/0.15

Z = -2

Now, normal variable of x = 0.92

Z1 = X - mean/ Standard deviation

Z1 = 0.92 - 0.62/ 0.15

Z1 = 2

Required area,

P(-2 ≤ z ≤ 2)

2P(0 ≤ z ≤2 )

2 × 0.4772

0.9542

Weight of 3500 tomatoes

3500 × 0.9542

3340

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Answer:

x = −1 and y = 3

Multiply the second equation by -1, then add the equations together.

(−x−7y=−20)

−1(−6x−7y=−15)

Becomes:

−x−7y=−20

6x+7y=15

Add these equations to eliminate y:

5x=−5

Then solve5x=−5for x:

5x=−5

5x/5 = -5/5

x = -1

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

−x−7y=−20

Substitute−1 for x in −x −7y = −20:

−(−1)−7y=−20

−7y+1=−20(Simplify both sides of the equation)

−7y+1+−1=−20+−1(Add -1 to both sides)

7y = -21

-7y/-7 = -21/-7

y=3

The solution is Option B.

The value of y of the equation 4x + 7y = 11 is y equals the quantity negative 4 times x plus 11 end quantity over 7

y = ( -4x + 11 ) / 7

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by

4x + 7y = 11   be equation (1)

On simplifying the equation to solve for y , we get

Subtract 4x on both sides of the equation , we get

7y = 11 - 4x

Divide by 7 on both sides of the equation , we get

y = ( 11 - 4x ) / 7

So , on simplifying the equation , we get

y = ( -4x + 11 ) / 7

Therefore , the value of y is ( -4x + 11 ) / 7

And , y equals the quantity negative 4 times x plus 11 end quantity over 7

Hence , The value of y of the equation 4x + 7y = 11 is y equals the quantity negative 4 times x plus 11 end quantity over 7

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Answer:

To solve for the value of x that makes the equation 52(x−2)=4 true, we need to first isolate the x term on one side of the equation. We can do this by dividing both sides of the equation by 52 to get rid of the coefficient in front of the x term.

Dividing both sides of the equation by 52, we get:

52(x−2) = 4

(x−2) = 4/52

(x−2) = 1/13

Next, we can add 2 to both sides of the equation to isolate the x term on the left side of the equation.

(x−2) + 2 = 1/13 + 2

x = 1/13 + 2

x = (1/13) + (2/1)

x = (13+26)/13

x = 39/13

Therefore, the value of x that makes the equation 52(x−2)=4 true is x = 39/13.

Step-by-step explanation:

We choose an infinitive in a sentence; It is "to + 1st form of verb" in the case of the infinitive, "1st form of the verb + -ing", and "1st form of the verb + both the first and third form of the verb" in the case of gerunds.

In the given question we have to explain how we choose an infinitive in a sentence.

The verb form called as an infinitive can be used as a noun, adjective, or adverb. They can be helpful when talking about activities without actually performing the activity because they are typically created by adding the word to before the underlying verb.

It is "to + first form of the verb" in the case of the infinitive, "1st form of the verb + -ing" that serves as a noun, and "1st form of the verb + both the 1st and 3rd form of the verb" in the case of gerunds that the first form with –ing. "To do" is the infinitive in this sentence.

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Answer: can you provide the graph so i can give an answer?

Step-by-step explanation:

As per the concept of survey, Nonresponse is the type of bias that happens when individuals with certain characteristics are less likely to respond to surveys than others.

What is the working process of survey?

In general terms, survey refers a set of questions people are asked to gather information or find out their opinions, or the information gathered by asking many people the same questions.

Here we need to find the type of bias occurs when individuals with certain characteristics are less likely to respond to surveys than others.

As we know that, when respondents to a survey question or the entire survey are unable or unwilling to respond, this is known as nonresponse bias. Individuals have many excuses for not responding and a cause of error must be systematic in order to be categorized as biased.

Here the distinction between respondents and non-respondents frequently plays a role in explaining why there was no response.

Therefore,  Non-response bias, also known as participation bias, is sometimes the result of shoddy survey design and poor questionnaire targeting.

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Answer:

a = 2[tex]w^{2}[/tex] + 3w

Step-by-step explanation:

Area = length time width

A= (2w + 3) w

a = 2[tex]w^{2}[/tex] + 3w

Carla's behavior of putting in extra practices to become faster can be seen as an example of (Option A.) compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.

Carla's behavior of putting in extra practices to become faster can be seen as an example of compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.

By engaging in extra practices, Carla is attempting to compensate for her lack of speed and improve her performance. This is different from rationalization, which is the act of making excuses for one's behavior, or from regression, which is the act of reverting to a younger age in response to a stressful situation.

Finally, displacement is the act of redirecting one's emotions or anger onto another person or object.

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Answer:

If the video game that Ethan bought usually costs $39.99, and it was on sale for 20% off, then the discount on the game would be $39.99 x 20/100 = $8.00. To determine the final price of the game after the discount, we can subtract the discount from the original price of the game, which gives us:

Final price = $39.99 - $8.00 = $31.99

Therefore, Ethan paid $31.99 for the video game that was on sale. This can be rounded to the nearest cent to give us a final answer of:

Final price = $31.99 ≈ $32.00.

Therefore, Ethan paid $32.00 for the video game that was on sale.

Step-by-step explanation:

Answer:

-2b - 7/2

Step-by-step explanation:

solve for e: -4b+1=8+2e

-4b + 1 = 8 + 2e

-4b + 1 -8 = 2e

-4b - 7 = 2e

-2b - 7/2 = e

(a) the percent of those  who have a dog also have a cat is  40% .

(b) the percent of those who have a cat also have a dog is  60% .

In the question ,

it is given that ,

the percent of children who have a dog = 45% ,

the percent of children having cat = 30%

the percent of children having dog and cat = 18% ,

Part(a)

the percent of children that have a dog also have a cat is

= (number of children that have dog and cat)/(number of children having dog)

= 18/45

= 0.4 = 40% .

Part(b)

the percent of children that have a cat also have a dog is

= (number of children that have dog and cat)/(number of children having cat)

= 18/30

= 0.6 = 60% .

Therefore , the required percent for part(a) is 40% and part(b) is 60% .

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Answer: 55 square feet

Step-by-step explanation:

To find area:
Length * Width

11 * 5 = 55

Answer: 55 sq. feet

explanation : 5 x 11 is 55, so 55 square feet

Answer:

B

Step-by-step explanation:

Do old total minus the new total to get the difference then divide by old to total.

The correct answer would be (B).

Answer:

-1/2

Step-by-step explanation:

Rise/Run