What are the x- and y- coordinates of point p on the directed line segment from k to j such that p is three-fifths the length of the line segment from k to j? x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 y = (startfraction m over m n endfraction) (y 2 minus y 1) y 1 (40, 96) (85, 105) (80, 104) (96, 72)

The average value of the given function is [tex]f_{avg} = \frac{-2a^{2} + 6a + 6 }{6}[/tex].

According to the statement

we have given that the function f(x) and we have to find the average value of that function.

So, For this purpose, we know that the

The given function f(x) is

[tex]f(x) = -x^{2} + 2x +1[/tex]

And now integrate this function with the limit 0 to a then

[tex]f_{avg} = \frac{1}{b - a} \int\limits^a_0 {f(x)} \, dx = -x^{2} + 2x +1[/tex]

Now integrate this then

[tex]f_{avg} = \frac{1}{a} \int\limits^a_0 {-x^{2} + 2x +1} \, dx[/tex]

Then the value becomes according to the integration rules is:

[tex]f_{avg} = \frac{1}{a} \int\limits^a_0 {-\frac{x^{3} }{3} + \frac{2x^{2} }{2} +x} \,[/tex]

Now put the limits then answer will become as output is:

[tex]f_{avg} = \frac{1}{a} [ {-\frac{a^{3} }{3} + \frac{2a^{2} }{2} +a} \,][/tex]

Now solve this equation then

[tex]f_{avg} = [ {-\frac{a^{2} }{3} + \frac{2a }{2} +1} \,][/tex]

Now

[tex]f_{avg} = \frac{-2a^{2} + 6a + 6 }{6}[/tex]

This is the value which represent the average of the given function in the statement.

So, The average value of the given function is [tex]f_{avg} = \frac{-2a^{2} + 6a + 6 }{6}[/tex].

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The given graph doesn't represent a function, as it has two values of y for a single value of x ( that is : for x = 3 it has two solutions, -3 and -6 )

therefore it can't be considered as a function ~

Answer:

B

Step-by-step explanation:

because i said so

The resulting equation on completing the square is (x+19/2)^2 = 39 + (19/2)^2

Quadratic equation are equations that has a leading degree of 2. Most quadratic equations have 3 terms.

Given the quadratic equation x^2-19x-39 = 0

Add 39 to both sides to have:

x^2 - 19x - 39 + 39 = 0 + 39

x^2 -19x = 39

Complete the square of the resulting

x^2-19x+(19/2)^2 = 39 + (19/2)^2
(x+19/2)^2 = 39 + (19/2)^2

x + 19/2 = ±√39 + (19/2)^2

x = ±√39 + (19/2)^2 - 19/2

Hence the resulting equation on completing the square is (x+19/2)^2 = 39 + (19/2)^2

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Answer:

OA=95

Step-by-step explanation:

JL = 19Z = OA = 4Z+75

19Z = 4Z+75

19Z-4Z=75

15Z=75

Z=75÷15

Z=5

OA=4(5)+75

OA=95

btw, u stan blackpink? i cant wait for their next comeback "BORN PINK"

Answer:

a. triangle DEF's lines are all 3 times more than triangle ABC

b. triangle DEF's lines are all 3 times more than triangle ABC

c. 2.5 times 2 = 5

I hope u can elaborate a bit more :)

Let [tex]X(s)[/tex] and [tex]Y(s)[/tex] denote the Laplace transforms of [tex]x(t)[/tex] and [tex]y(t)[/tex].

Taking the Laplace transform of both sides of both equations, we have

[tex]\dfrac{dx}{dt} + 3x + \dfrac{dy}{dt} = 1 \implies \left(sX(s) - x(0)\right) + 3X(s) + \left(sY(s) - y(0)\right) = \dfrac1s \\\\ \implies (s+3) X(s) + s Y(s) = \dfrac1s[/tex]

[tex]\dfrac{dx}{dt} - x + \dfrac{dy}{dt} = e^t \implies \left(sX(s) - x(0)\right) - X(s) + \left(sY(s) - y(0)\right) = \dfrac1{s-1} \\\\ \implies (s-1) X(s) + s Y(s) = \dfrac1{s-1}[/tex]

Eliminating [tex]Y(s)[/tex], we get

[tex]\left((s+3) X(s) + s Y(s)\right) - \left((s-1) X(s) + s Y(s)\right) = \dfrac1s - \dfrac1{s-1} \\\\ \implies X(s) = \dfrac14 \left(\dfrac1s - \dfrac1{s-1}\right)[/tex]

Take the inverse transform of both sides to solve for [tex]x(t)[/tex].

[tex]\boxed{x(t) = \dfrac14 (1 - e^t)}[/tex]

Solve for [tex]Y(s)[/tex].

[tex](s - 1) X(s) + s Y(s) = \dfrac1{s-1} \implies -\dfrac1{4s} + s Y(s) = \dfrac1{s-1} \\\\ \implies s Y(s) = \dfrac1{s-1} + \dfrac1{4s} \\\\ \implies Y(s) = \dfrac1{s(s-1)} + \dfrac1{4s^2} \\\\ \implies Y(s) = \dfrac1{s-1} - \dfrac1s + \dfrac1{4s^2}[/tex]

Taking the inverse transform of both sides, we get

[tex]\boxed{y(t) = e^t - 1 + \dfrac14 t}[/tex]

Answer:

[tex]\Large\boxed{1)~6x+7}[/tex]

[tex]\Large\boxed{2)~-7x+5y+8}[/tex]

Step-by-step explanation:

Given expression

4x + 7 + 2x

Move like terms together

= 4x + 2x + 7

= (4x + 2x) + 7

Combine like terms

[tex]\Large\boxed{=6x+7}[/tex]

Given expression

-4x + 3y - 3x + 8 + 2y

Move like terms together

= -4x - 3x + 3y + 2y + 8

= (-4x - 3x) + (3y + 2y) + 8

Combine like terms

[tex]\Large\boxed{=-7x+5y+8}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

3x + 16 + 30/x - 13

Step-by-step explanation:

[tex] \sf \blue{True✅}[/tex]

Yes, it's true sometimes we don't use negative value of 'x'.

So, we conclude it's True.

The numeric value of the expression -a² - 2bc - |c| for a = -3, b = -5 and c = 2 is of 9.

The numeric value of an expression is found replacing each letter by it's attributed value.

In this problem, the expression is:

-a² - 2bc - |c|

The attributed values are:

a = -3, b = -5 and c = 2

Hence the numeric value will be given by:

-a² - 2bc - |c| = -(-3)² - 2(-5)(2) - |2| = -(9) + 20 - 2 = -9 + 18 = 9.

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Answer:

A. (3x + 4)(x-7)

Step-by-step explanation:

3x times x = 3x^2

3x times -7 = -21x

4 times x = 4x

4 times -7 = -28

-21x + 4x = -17x

3x^2 - 17x - 28

Answer:

300

Step-by-step explanation:

375 divided by 5=75

Each “1”=75

4x75=300

There are 300 boys.

Hope this makes sense

Answer:

300 boys

Step-by-step explanation:

Let the number of boys = x

Girls: 375

boys : girls = 4 : 5

total in the ratio is 9

girls are 5/9 of total, and are 375

boys are 4/9 of total

5/9 x = 375

x = 375 × 9/5

x = 675

Boys are 4/9 of total.

4/9 × 675 = 300

Answer:

By definition, angles A and 1 are corresponding angles and angles B and 1 are consecutive angles. By the corresponding angles postulate, angles A and 1 are congruent, and by the consecutive angles theorem, angles B and 1 are supplementary. By the definition of supplementary angles, measures of angle B and 1 add up to 180 degrees (m<B + m<1 = 180). By definition of congruent angles, angles A and 1 have same measurement (m<A = m<1). By substitution property of equality, measures of angles A and B add up to 180 degrees (m<A + m<B = 180). By definition of supplementary angles, angles A and B are supplementary.

The answer is y = -5.5x - 52.

First, let's find the slope of the line.

m = Δy/Δx

Now, substitute the slope and one of the given points in the point slope equation.

y - y₁ = m (x - x₁)

Answer: y=-5,5x-52.

Step-by-step explanation:

                        Equation of a straight line

                               [tex]\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]

[tex](-10;3)\ \ \ \ \ (-8;-8).\\\displaystyle\frac{x-(-10)}{-8-(-10)} =\frac{y-3}{-8-3}\\ \frac{x+10}{-8+10}=\frac{y-3}{-11} \\ \frac{x+10}{2}=\frac{y-3}{-11} \\-11*(x+10)=2*(y-3)\\-11x-110=2y-6\\2y=-11x-104\ |:2\\y=-5,5x-52.[/tex]

The value of A such that cos A = 0.7715 is 39.5 degrees

The equation is given as:

cos A = 0.7715

Where the angle is in degrees

There are several ways to solve this equation, some of which include:

In this case, we make use of the first option; using a scientific calculator

Recall that the equation is represented as:

cos A = 0.7715

Next, we take the arccos (or anti cosine) of the above equation.

This is represented as

arccos(cos A) = arccos(0.7715)

Evaluate the expression on the left-hand side

A = arccos(0.7715)

Evaluate the expression on the left-hand side using the scientific calculator

A = 39.5112207183

Approximate the above expression

A = 39.5

Hence, the value of A such that cos A = 0.7715 is 39.5 degrees

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Answer:

100

Step-by-step explanation:

Formulate a plan based on the conditions stated: 65/(13/20)

A fraction is divided by multiplying its reciprocal: 65x(20/13)

Remove the connecting element: 5x20

Determine the quotient or product: 100

100 tokens are bought by mark for his daughter.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, Mark bought gift tokens for her daughter, Sally, to use at the state fair. Sally used 13/20 of the tokens on rides.

let "x" be the total token she have

Since, total token she used is 65

Thus,

13/20 * x = 65

x = 100

Therefore, Mark bought for his, daughter 100 Tokens.

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The number of hours spent repairing televisions. after how many hours does he break even is 7 hours

These are equations that contains several equations with unknowns. Given the function that modelled the revenue generated from television repair as;

y = 25 + 30x

where:

x is the number of hours spent repairing televisions.

If his overhead cost, in dollars, is modelled by the equation y=5x^2−10, the company breaks even when;

25 + 30x = 5x^2 -10

Divide through by 5

5 + 6x = x^2 - 2

Equate to zero to have:

x^2 - 6x  -2 - 5 = 0

x^2 - 6x - 7 = 0

x^2 - 7x + x - 7 = 0
x(x-7)+1(x-7) =0

x = -1 and 7

Hence the number of hours spent repairing televisions. after how many hours does he break even is 7 hours

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The definition of the given piecewise function is:

A piecewise function is a function that has different definitions, depending on the input.

In this problem, for x until 2, the function is the cube function shifted down 3 units, hence the definition is:

[tex]y = x^3  - 3, x \leq 2[/tex]

For x greater than 2, the function is the square function shifted up 6 units, hence the definition is:

[tex]y = x^2 + 6, x > 2[/tex]

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There is only one solution for the equation 4z + 2(z -4) = 3z + 11 because the exponent for the power of z is 1.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

A solution is any value of a variable that makes the specified equation true.

According to the given information:

4z + 2(z-4)= 3z+11

Solve the equation,

4z+2z-8=3z+11

6z-3z=11+8

3z =19

z=

Hence,

Number of solution that can be found for the equation 4z + 2(z-4)= 3z+11 is option(2) one

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The two possible positions of point P are:

(3, -5) and (0.6, 5.8)

We know that point P lies on the line:

y = 4 - 3*x

And that the distance between P and the origin is √34, then if the coordinates of point P are (x, y), we have that:

[tex]\sqrt{34} = \sqrt{x^2 + y^2}[/tex]

Now, we can replace "y" in the distance equation by the linear equation, and also remove the square roots:

[tex]34 = x^2 + (4 - 3x)^2[/tex]

Now we can solve the quadratic equation for x:

[tex]34 = x^2 + 9x^2 + 16 - 24x\\\\10x^2 - 24x - 18 = 0\\\\[/tex]

The solutions are:

[tex]x = \frac{24 \pm \sqrt{(-24)^2 - 4*10*(-18)} }{2*10} \\\\x = \frac{24 \pm36}{20}[/tex]

So the two solutions are:

x = (24 + 36)/20 = 3

x = (24 - 36)/20 = -0.6

To get the points, we need to evaluate y on these values:

y = 4 - 3*3 = -5   So we have P = (3, -5)

y = 4 - 3*(-0.6) = 2.2 So we have the point (0.6, 5.8)

There are the two possible positions of point P.

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[tex]denote \: by \: s \: the \: cost \: of \: a \: sweatshirt \\ denote \: by \: t \: the \: cost \: of \: a \: t \: shirt[/tex]

[tex]3t + 7s = 240.5 \\ 6t + 5s = 220[/tex]

[tex] - 6t - 14s = - 481 \\ 6t + 5s = 220[/tex]

[tex] - 9s = - 261 \\ s = \frac{ - 261}{ - 9} = 29 \: dollars[/tex]

[tex]3t + 7(29) = 240.5 \\ [/tex]

3t + 203 = 240.5

3t = 37.5

t = 12.5 dollars

From the two functions function 2 has the highest maximum value.

Given two functions,one is y=-[tex]x^{2} -2x-2[/tex] and f(-2)=1,f(-1)=6,f(0)=9,f(1)=10,f(2)=9,f(3)=6.

We ae required to choose a function which is having highest maximum possible value.

Function is like a relationship between two or more variables expressed in equal to form. Each value of x of a function has some value of y.

The highest value in the second function is 10 which is at x=1. Put the value of x=1 in y=-[tex]x^{2} -2x-2[/tex].

y=-1-2-2

y=-5

So it might not be highest value of this function.So the second function has highest maximum value of 10 at x=1.

Hence the second function has highest value.

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Answer: the area of the triangle is 5.

Step-by-step explanation:

[tex]A(0;0) \ \ \ \ B(1;3) \ \ \ \ C(4;2) \ \ \ \ S_{ABC}=?\\Use \ the\ formula:\\\displaystyle\\\boxed{S=\frac{1}{2}*|[(x_A-x_C)*(y_B-y_C)-(x_B-x_C)*(y_A-y_c)] |}\\x_A=0\ \ \ \ x_B=1\ \ \ \ x_C=4\ \ \ \ y_A=0\ \ \ \ \ y_B=3\ \ \ \ \ y_C=2.\\S=\frac{1}{2}*|[(0-4)*(3-2)-(1-4)*(0-2)]|\\S=\frac{1}{2}*| [(-4)*1-(-3)*(-2)]|=\\ S=\frac{1}{2}*| (-4-6)|\\S=\frac{1}{2}*|(-10)|\\S= \frac{1}{2} *10\\S=5.[/tex]

Answer:

-8

Step-by-step explanation:

y=(1/3)x

4 = (1/3)12

y=(1/3)(-24)

y= -8

Answer:

x^2

Step-by-step explanation:

So there's very two obvious ones we can elimination immediately, that's f(x) = x, and f(x) = |x|. The reason for this is because we can just look at the first ordered pair of (-2, 4). If it was f(x) = x, then the ordered pair would be (-2, -2), but it isn't. Very similar reasoning for f(x) = |x|, except for this function each ordered pair should have the same magnitude or absolute value. So the f(-2) should output 2, since it's the absolute value, but of course this isn't the case since it's 4.

So let's look at 2^x

[tex]2^{-2} = \frac{1}{2^2} = \frac{1}{4}[/tex]

Since the y value is 4 and not 1/4, this is not the parent function

It should be the second option (x^2), and we can double check

(-2)^2 = 4

(-1)^2 = 1

(0)^2 = 0

(1)^2 = 1

(2)^2 = 4

It outputs the same y-values as the table so this is the parent function

The solutions to the questions are given below

a)

sample(n) word length sample mean

1                    5,4,4,2    3.75

2                    3,2,3,6     3.5

3                         5,6,3,3    4.25

b)R =0.75

c)

The table below shows sample means in the table.

sample(n) word length sample mean

1                    5,4,4,2    3.75

2                    3,2,3,6     3.5

3                         5,6,3,3    4.25

b)

Generally, the equation for is  mathematically given as

variation in the sample means

R =maximum -minimum

R=4.25-3.5

R =0.75

c)

In conclusion, In most cases, the mean of many samples will provide a more accurate estimate than the mean of a single sample.

They may have a higher level of confidence in their estimate if the range of the sample means is closer to 0 than it is now.

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Answer:

44°

Step-by-step explanation:

[tex]\frac{134-46}{2}=44[/tex]

.

The 0 = 0 in the solution to the system implies that the system of equations involving the equations 6x - 5y = -8 and 6x - 5y = -8 have infinitely many solutions

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

6x - 5y = -8

6x - 5y = -8

Subtract the equation 6x - 5y = -8 from the equation 6x - 5y = -8

6x - 5y = -8

- 6x - 5y = -8

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

0 = 0

This in other words means that the difference between both equations is 0

When the solution to a system of equation is 0 = 0, it means that the system of equations have infinitely many solutions

Hence, the 0 = 0 in the solution to the system implies that the system of equations involving the equations 6x - 5y = -8 and 6x - 5y = -8 have infinitely many solutions

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Answer: The answer is D for those who don't like to read extra long expert answers (no offense to experts, just shorten answers to the direct answer pls)

Step-by-step explanation: Edge 2022

The average median and mode price is $18. Option C is correct.

Given that certain item is available at 7 stores, three stores sell them for $20, two stores sell them for $15, one store sells them for $13, and one sells them for $16.

The mean is the average of the given numbers and is calculated by dividing the sum of the given numbers by the total number of numbers.

Firstly, we will find the median of the given items by arranging the given numbers in ascending order, we get

13,15,15,16,20,20,20

To find the median use the formula (n+1)/2, where n is the number of values in your dataset.

(7+1)/2=8/2=4

In the ascending order numbers 4th term is 16.

So, median is 16

Mode is the highest repeating term in the set or numbers.

So, here mode is 20

Now, we will calculate the average of median and mode, we get

Average=(median +mode)/2

Average=(16+20)/2

Average=18

Hence, the average (arithmetic mean) of the median price and the mode price where certain item is available at 7 stores, three stores sell it for $20, two stores sell it for $15, one store sells it for $13, and one sells it for $16 is $18.

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