Evaluate the following expression
x2 + 2(x + y) – 2x2
when x= -1 and y= 5

Answer: √58 or about 7.6

Step-by-step explanation:

use the distance formula: √((x1 - x2)² + (y1 - y2)²)

√((3 - 0)² + (7 - 0)²)

√((3)² + (7)²)

√(9 + 49)

√58

hope this helps!

Answer:

about 7.6

Step-by-step explanation:

right on edge 2021

Answer:

it makes the goals easier to reach

Step-by-step explanation:

you dont want to say you need 1,000 dollars.. you would want to say you are going to save 5 dollars a week till you reach it.

5 benefits of breaking down ones periodic savings have been listed below.

Breaking down the amount one will need to save on a daily, weekly or monthly basis is simply called budgeting.

Now, budgeting is very important because it helps to do the following;

- Helps to ensure you spend money appropriately on things that you really need and not just wants.

- Helps you to effectively monitor your spending habits/patterns.

- Helps you to meet your financial goals.

- Helps you to make good decisions on things that involve finance.

- Helps you to monitor your progress in savings or interest as the case may be.

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Answer:\(\frac{X1-X2}{Y1-Y2}\)

Step-by-step explanation: \(\frac{0-(-4)}{0-0}\)   = (4,0)

Answer: $12

Step-by-step explanation: Divide $48 by 4

Option D. 1 + 1/s is the correct choice for a PI controller that has the minimum impact on the root loci of the system.

To minimize the impact of a proportional plus integral (PI) controller on the root loci of a system, the controller should introduce a pole at the origin (s=0) and a zero at a distant location from the origin.

Among the given options, the controller that fits this purpose is D. 1 + 1/s.

The PI controller in option D has a constant term of 1, which introduces a pole at the origin (s=0). It also has a term of 1/s, which introduces a zero at s=infinity, which is a distant location from the origin.

By having a pole at the origin and a zero at a distant location, the PI controller in option D minimizes the impact on the root loci of the system. This configuration ensures stability and avoids significant changes in the system's dynamic behavior.

Therefore, option D. 1 + 1/s is the correct choice for a PI controller that has the minimum impact on the root loci of the system.

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In the theater, that have 1,464 seats.

1426 seats are in "regular" sections

38 seats are  "premium" front-row section

The seat arrangement is solved by division. In this case the 62 equal spaced is the divisor while the number of seats is the in each row is the quotient

The division is as follows

1464 / 62

= 23 19/31

The number of seats in the regular section is 23 * 62 = 1426

The remainder will be arranged in premium front row

using equivalent fractions

19 / 31 = 38 / 62

the remainder is 38 and this is the seat for the premium front row section

OR 1464 - 1426 = 38 seats

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The measure of one of its angle is 150°

A Polygon is a two-dimensional closed figure made up of line segments (not curves). Polygon is a combination of two words, poly (which means many) and gon (which means shape) (means sides). To create a closed figure, at least three line segments must be connected end to end.

Given that

12 sided regular polygon

We can use the following formula to calculate the total number of degrees in any shape:

(n−2)⋅180

[Where n = number of sides]

(12−2)⋅180

(10)⋅180

=1800

So a 12-sided polygon has 1800 degrees. To calculate the measure of one angle, divide the total number of degrees (1800) by the number of sides, n.

(1800/12) = 150°

Therefore the measure of one of its angle is 150°

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Answer: Root 16 = 4, 4*1/2= 2

5/9*1/2= 5/18

Root 3 = 1.73205...*1/2= 0.866025...

Root 3 is the answer

The probability that none of the ten freshmen graduates from the local community college is approximately 0.006 or 0.6%.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

Assuming that the probability of each freshman graduating is independent of the others, the probability that none of the ten freshmen graduates is -

\(P = (0.6)^{10}\)

= 0.0060466176

Here, we are using the fact that the probability of a freshman not graduating is 1 - 0.4 = 0.6.

So, the probability value is obtained as 0.006 or 0.6%.

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9514 1404 393

Answer:

  (1, 7)

Step-by-step explanation:

Fill in x=1 and do the arithmetic.

  h(1) = 4(1) +3 = 7

The coordinate pair is ...

  (x, h(x)) = (1, h(1)) = (1, 7)

Probability of people less than 19 year old = 0.5343

Probability of people greater than 10 year old = 0.8116

What is probability?

Mathematical descriptions of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the probability of an event, with 0 roughly denoting impossibility and 1 denoting certainty.

People under age 10 = 253

People between the age of 10-18 = 466

People between the age of 19-30 = 174

People above the age of 30 = 450

Total no. of people = 1343

a) people less than 19 years old = 253+466 = 719

probability of people<19 year old = P(age<19) = 719/1343 = 0.5354

b) people of age greater than 10 = 466+174+450 = 1090

probability of people >10 year old = P(age>10) = 1090/1343 = 0.8116

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The algebraic expression for the sum of (k) and (l) divided by the sum of (d) and (e) is: (k + I) / (d + e) =

To solve this problem, we have to state the equation using the information of the problem:

Algebraic Expression:

"the sum of (k) and (l) divided by the sum of (d) and (e)"

(k + I) / (d + e) =

We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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4.92*10^5 times the annual flow of the Mississippi River fit in the Atlantic Ocean

Given that,

Volume of the Atlantic Ocean = 3.1*10^17cubicmetres

Annual flow of the Mississippi River = 6.3*10^11cubicmeters

Now, we have to find how many times the annual flow of the Mississippi River fit in the Atlantic Ocean

So,

= Volume of the Atlantic Ocean / Annual flow of the Mississippi River

= 3.1*10^17 / 6.3*10^11

= 0.4921*10^6 (Approximately)

=4.92*10^5

Therefore,

It takes 4.92*10^5 times for the Mississippi River to fit into the Atlantic Ocean.

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Answer:

(0,3)

Step-by-step explanation:

Question:

Solution:

The diagram of a triangle ABC, where C is the right angle is:

Now, by definition and according to the data of the problem, we get that:

that is:

now, to find the cos(B), first, we must find the missing side of the triangle. To do that, we can apply the Pythagorean theorem:

now, with respect to angle B, we obtain that:

So that, we can conclude that the correct answer is:

Answer:

the coefficient of 0 indicates that there is no relationship between the two values

The height of a randomly selected giraffe is a continuous random variable.

Question: Determine whether the value is a discrete random variable, continuous random variable, or not a random variable: the height of a randomly selected giraffe.

Response: The height of a randomly selected giraffe can be considered a continuous random variable.

A random variable is a variable whose value is determined by the outcome of a random event. In this case, the random event is selecting a giraffe, and the variable is the height of that giraffe.

A discrete random variable can only take on a countable number of distinct values. For example, the number of students in a class or the number of cars passing through a toll booth in an hour.

On the other hand, a continuous random variable can take on any value within a certain range. In this case, the height of a giraffe can vary continuously, as there are no specific height values that it can only take.

For example, a giraffe can be 4.2 meters tall, or it can be 4.201 meters tall, or even 4.200001 meters tall. The height can be measured to any level of precision, and there are no specific intervals or distinct values that the height must fall into.

Therefore, the height of a randomly selected giraffe is a continuous random variable.

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Answer: c=-1,b=5,a=-5

Step-by-step explanation: If c=-1, substitute it into the second equation first. The second equation becomes -2b-1=-11, simplify it becomes -2b=-10, divide by 2 it becomes -b=-5, so b=5. Then you substitute b and c into the first equation. The first equation becomes a+5+-(-4)=4, simplify it becomes a+5+4=4, Simplify again it becomes a=-5.

The total distance traveled by the particle over the time interval [1, 5] is 12 units.

To find the total distance traveled, we need to consider both the magnitude and direction of the velocity function. Since the velocity function given is in meters per second (m/sec), the total distance traveled will be measured in meters.

To calculate the total distance, we need to consider the intervals where the velocity function changes its sign. In this case, the velocity function is linear and increasing, starting at t = 1 with a velocity of 3 m/sec. From t = 1 to t = 3, the particle moves in the positive direction, covering a distance of (3t - 9) × (t - 1) = 12 units. From t = 3 to t = 5, the particle moves in the negative direction with the same magnitude, covering a distance of (-1) × (3t - 9) × (t - 3) = 12 unit

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The equation of line that passes through the points (6, 5) and

(0, -7) is y = 2x - 7.

What is point slope form of line?

The equation of a straight line that passes through a given point and is inclined at a specific angle to the x-axis can be found using the point slope form.

One of the formulas used to determine a line's equation is the point slope formula. According to the point slope formula, y - y1 = m (x - x1) is the equation for a line with slope "m" and the points (x, y1) on it.

We have to find the equation of line that passes through the points (6, 5) and (0, -7).

First to find the slope of the line,

\(m = \frac{y_2-y_1}{x_2-x_1} = \frac{-7-5}{0-6}= \frac{-12}{-6} = 2\)

Now, consider the point slope form of the line

\(y-y_1=m(x-x_1)\)

Plug \(m = 2, (x_1, y_1) = (0, -7)\)

⇒

\(y-(-7)=2(x-0)\\y+7=2x\\y=2x-7\)

Hence, the equation of line that passes through the points (6, 5) and

(0, -7) is y = 2x - 7.

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Answer:

Step-by-step explanation:

m<3=m<7=63

m<6+m<7=180

m<6=180-63

m<6=117

m<7=63

m<6=117

The measurement for ∠6 and ∠7 will be 63° and 117° respectively.

An angle measure is the measurement of the angle created by two rays or arms at a shared vertex in geometry. A protractor is used to measure angles in degrees (°).

As we know the alternate opposite angle of the parallel lines are equal;

∠3 and ∠7 are alternate opposite angles;

So that;

m∠3=m∠7=63°

The sum of the complementary angle is 180°.∠6 and ∠7 are complementary angle

m∠6+m∠7=180

m∠6=180°-63°

m∠6=117

Substitute the value to get ∠7

m∠7=63°

m∠6=117°

Hence the measurement for ∠6 and ∠7 will be 63° and 117°.

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the coordinates of point c is (9/2, -3/2)

The original coordinate = C(6, -2)

scale factor r =3/4

New coordinate (c) = scale factor × the original coordinate

c = 3/4(6, -2)

c = (3/4×6, -2×3/4)

c = (18/4, -6/4)

c = (9/2, -3/2)

Hence, the coordinates of point c is (9/2, -3/2)

Answer:

(90,60)

Step-by-step explanation:

To write the equation in standard form for the circle passing through (–2, 4) centered at the origin, we need to find the radius and the center of the circle.

Since the circle passes through (–2, 4), we can use the distance formula to find the radius, which is the distance from the origin to (–2, 4).

The distance formula is given by:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, x1 = 0, y1 = 0, x2 = –2, and y2 = 4. So, the radius is:

radius = sqrt((-2 - 0)^2 + (4 - 0)^2) = sqrt(20) = 2sqrt(5)

The center of the circle is the origin, since the circle is centered at the origin. Therefore, the equation of the circle in standard form is:

x^2 + y^2 = (2sqrt(5))^2 = 20

So, the equation of the circle passing through (–2, 4) centered at the origin is x^2 + y^2 = 20.

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Answer:

54.1 cm

Step-by-step explanation:

1) Divide the circumference by pi (3.14…)

2) Your quotient (108.2… cm) is now the diameter of the circle. The diameter goes through the circle completely. The radius is half of the diameter, or it goes halfway through the circle. Hence, you would divide the previous answer by 2.

3) 108.2… cm divided by 2 should leave you with about 54.1… cm.

Answer:

3600

Step-by-step explanation:

Reason is because you put the answer in your question.

Answer:

Rs.10800

Step-by-step explanation:

loss of article(L%)=10%

s.p=?

c.p of an article (c.p)=c.p

Now,

s.p=100-L%×c.p

_____

100

= 100-10 ×c.p

_____

100

=90 ×c.p

___

100

=0.9 × c.p

if article sold with Rs. 540 more

Article profit =5%

s.p =c.p + 540 =100+p%×c.p

______

100

or, c.p +540=105×c.p

______

100

or, c.p +540=1.05×c.p

or,c.p +540=1.05c.p

or, 540=1.05c.p-c.p

or,540=0.05c.p

or, 540=c.p

____

0.05

Therefore, c.p =Rs. 10800

Applying the midpoint formula, the coordinates of the other endpoint are: (-9, -13).

The midpoint formula, which can be used in determining the coordinates of the midpoint between two endpoints is usually expressed as: M[(x1 + x2)/2, (y1 + y2)/2].

Given the following coordinates:

Midpoint of GH --> m(-13/2,-6) = (x, y)

One endpoint ---> G(-4, 1) = (x1, y1)

The other endpoint ---> (x2, y2)

Plug in the values into the formula used in calculating the midpoint:

m(-13/2,-6) = [(-4 + x2)/2, (1 + y2)/2]

Solve for x2

-13/2 = (-4 + x2)/2

-13/2 × 2 = -4 + x2

-13 = -4 + x2

-13 + 4 = x2

-9 = x2

x2 = -9

Solve for y2

-6 = (1 + y2)/2

2(-6) = 1 + y2

-12 = 1 + y2

-12 - 1 = y2

-13 = y2

y2 = -13

Thus, using the midpoint formula, the coordinates of the other endpoint are: (-9, -13).

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