Helpppp please!!!!!!

Answer:

Step-by-step explanation:

y = (2/3)x + 1

m = 2/3

The slope of the perpendicular line = -1/m

                                         \(Slope = \dfrac{-1}{\dfrac{2}{3}}=-1*\dfrac{3}{2}=\dfrac{-3}{2}\\\\\\(6,-7) ; \ x_{1}= 6 \ ; y_{1} = -7\\\\\\Equation: y-y_{1}=m(x-x_{1})\\\\\\y -[-7] = \dfrac{-3}{2}(x - 6)\\\\\\y + 7 = \dfrac{-3}{2}x - 6*\dfrac{-3}{2}\\\\y +7=\dfrac{-3}{2}x+9\\\\y = \dfrac{-3}{2}x+9-7\\\\y =\dfrac{-3}{2}x+2\)

Answer:

Step-by-step explanation:

Angle ACB is congruent to Angle DCE

Reason 4: SAS- Side Angle Side

Angle ACB is congruent to Angle DCE

Reason 4: SAS- Side Angle Side is the correct answer to the question

Answer:

\(-2(1 - 4x) = 3x + 8\\\\-2 + 8x = 3x + 8\\\\-2 + 5x = 8\\\\5x = -10\\\\x = -2\)

a) The matrix M that transforms the basis vector u into the standard basis is M = [1 0 0; 0 1 0; 0 0 1]

b) The transformation that rotates the plane counterclockwise by θ radians can be represented matrix R = [cos(θ) -sin(θ); sin(θ) cos(θ)]

c) The rotation transformation with respect to the standard basis:

[R]B = [R] = [cos(θ) -sin(θ); sin(θ) cos(θ)]

To find the matrix representation of the transformation that rotates the plane by θ radians counterclockwise with respect to the given basis B = {u}, we'll follow the steps outlined in the question.

(a) Find matrix M that transforms a vector in basis B into a vector in the standard basis:

To find M, we need to express the basis vector u = (1, 2, 17) in the standard basis. We can achieve this by writing u as a linear combination of the standard basis vectors e1, e2, and e3.

u = (1, 2, 17) = x * e1 + y * e2 + z * e3

To determine x, y, and z, we solve the following system of equations:

1 = x

2 = 2y

17 = 17z

From these equations, we find x = 1, y = 1, and z = 1. Therefore, the matrix M that transforms the basis vector u into the standard basis is:

M = [1 0 0; 0 1 0; 0 0 1]

(b) Find the matrix representations of the transformation with respect to the standard basis:

The transformation that rotates the plane can be represented by the following matrix:

R = [cos(θ) -sin(θ); sin(θ) cos(θ)]

(c) Use M and M-1 to convert the matrix representation of the transformation into a representation with respect to basis B:

To find the matrix representation of the transformation with respect to basis B, we use the formula:

\([M]B = [M] * [R] * [M]^-1\)

where [M] is the matrix representation of the basis transformation from basis B to the standard basis, [R] is the matrix representation of the transformation with respect to the standard basis, and \([M]^-1\) is the inverse of [M].

Since we already found M in part (a) as the identity matrix, we have:

\([M] = [M]^-1 = I\)

Therefore, the matrix representation of the transformation with respect to basis B is [R]B = [I] * [R] * [I] = [R]

So the matrix representation of the rotation transformation with respect to basis B is the same as the matrix representation of the rotation transformation with respect to the standard basis:

[R]B = [R] = [cos(θ) -sin(θ); sin(θ) cos(θ)]

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Hey there!

4x - 2 * (3x - 2) + 3x

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

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

= 4x - 6x + 4 + 3x

= -2x + 4 + 3x

= 1x + 4

= x + 4

Therefore, your answer is: x + 4

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Area = 114 m2

Step-by-step explanation:

Area of the Figure = Area of Rectangle ABCD - Area of Rectangle HGFE

Area of the Figure = 12*14 - 9*6 = 168 - 54 = 114

The range of the function f(x) = log5x is (-∞, +∞).The function f(x) = log5x represents the logarithm base 5 of x. To determine the range of this function, we need to consider the possible values that the logarithm can take.

The range of the logarithm function y = log5x consists of all real numbers. The logarithm function is defined for positive real numbers, and as x approaches 0 from the positive side, the logarithm approaches negative infinity. As x increases, the logarithm function approaches positive infinity.

The range of the function is the set of all possible output values. In this case, the range consists of all real numbers that can be obtained by evaluating the logarithm

log5(�)log 5 (x) for �>0 x>0.

Since the base of the logarithm is 5, the function log5x will take on all real values from negative infinity to positive infinity. Therefore, the range of the function f(x) = log5x is (-∞, +∞).

In other words, the function can output any real number, ranging from negative infinity to positive infinity. It does not have any restrictions on the possible values of its output.

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Answer: All real numbers

Step-by-step explanation:

Edge

a) The amount of water in the tank will be 0 after 5 minutes.

b) As time increases, the amount of water decreases at a rate of -60 L/min.

Here we can see a graph of a linear function that relates the amount of water in an aquarium (vertical axis) with the time (horizontal axis).

The amount of water in the aquarium will reach the 0 liters mark when the line intercepts the x-axis.

We can see that happens for x =  5 minutes

b) We can see that as we move to the right (time flows to the right in that graph) the line goes downwards. This means that the amount of water on the tank decreases as the time increases.

We can see that in 5 minutes, the amount of water goes from 300 lites to 0 liters, so the rate at which the water comes out of the tank is:

R = 300L/5min = 60 liters per minute.

It should actually be written with a negative sign so we are 100% clear that it means that the water is coming out from the tank, so the rate is:

R = -60 L/min

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We have cut out a total of 29370 squares.

First, let's find the greatest possible square that can be cut from the rectangle. This square will have a side length equal to the width of the rectangle, which is 26 units.

After cutting this square from the rectangle, we are left with a smaller rectangle that measures 90 units by (90-26=) 64 units.\

Now we repeat the process and cut out the largest possible square, which has a side length of 64 units.

After cutting out this square, we are left with a rectangle that measures 64 units by (64-26=) 38 units.

We continue this process until we can no longer cut out any more squares.

The side length of the remaining rectangle will be the length of the last square that we cut out.

Let's call this side length x.

At this point, the length of the rectangle is equal to the width, so:

90 - 26 - 64 - 38 - ... - x = x.

Simplifying this equation, we get:

(90 - 26 - 64 - 38 - ...) + x = x

2x = 90 - 26 - 64 - 38 - ...

2x = 90 - (26 + 64 + 38 + ...)

2x = 90 - (26 + 64 + 38 + 26 + 16 + 4 + 2)

2x = 90 - 176

2x = -86

x = -43

Since x cannot be negative, we know that we cannot cut out any more squares.

Therefore, we have cut out a total of:

\(26^2 + 64^2 + 38^2 + ... + (-43)^2\)

To calculate this sum, we can use the formula for the sum of the squares of the first n natural numbers:

\(1^2 + 2^2 + 3^2 + ... + n^2 = n(n+1)(2n+1)/6.\)

We need to find the value of n such that \(n^2\) is equal to \(43^2\)or the closest perfect square below it, which is \(42^2\).

We have:

\(42^2 = 1764.\)

\(43^2 = 1849\)

So n is equal to 42.

Therefore, the sum of the squares of the squares we have cut out is:

\(26^2 + 64^2 + 38^2 + ... + (-43)^2 = 26^2 + 64^2 + 38^2 + ... + 42^2\)

\(= 1^2 + 2^2 + 3^2 + ... + 42^2 - (1^2 + 2^2 + 3^2 + ... + 25^2)\)

\(= 42(42+1)(242+1)/6 - 25(25+1)(225+1)/6.\)

= 29370.

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Answer:

50.05 cm^2

Step-by-step explanation:

Ok so first lets find the area of the rectangle before finding the attached triangle. You have to imagine a line separating this shape into a triangle and rectangle.

The rectangle's size is 6.5x5.5=35.75 cm^2

The rectangle's size is 11.7-6.5 to get the base length, which is 5.2

The height is 5.5

So it's 5.2*5.5/2=14.3 cm^2

14.3+35.75=50.05 cm^2

Answer:

106.2

Step-by-step explanation:

A 18% increase of a number is the same as multiplying it by 1.18.

If we multiply 90 by 1.18 we get:

90 * 1.18

106.2

Step-by-step explanation:

What is a computer ?♡?×_×7×^××:×::×:+^++^+_+

Answer:

D.  4.5 sec

Step-by-step explanation:

Once the rock is on the ground it has no height (h=0)    

h = -16t² + 320

0 = -16t² + 320

16t² = 320

t² = 20

t² = 20

t = √20

t= √4x5

t = 2√5

around 4.5 seconds

The answer is 48π units³ or 150.72 units³.

To find the volume of the cone, use the formula : 1/3 × πr²h

We are given that r = 6 and h = 4.

Solving :

Answer:

He earns $540

70% of his money went to savings

Step-by-step explanation:

9 weeks x 5 days a week = 45 days

45 days x $12 a day = $540

378 * 100 / 540 =  (378*100) / 540 =  37800/540 = %70

Answer:

20 inches

Step-by-step explanation:

Since there are 480 miles in total, we have to divide it by 12 so we can see how many half inches that would be.

480÷12 = 40

That would mean you can fit forty 12's in 480. Since 12 miles equals 1/2, you would multiply it by 40.

1/2 × 40 =20

This means that the distance between the cities on the map would be 20 inches.

\(Question\)

what is the fraction for 33%and the decimal for 33%?

Answer:

Your Answer Would Be \(\frac{33}{100}\) For your Fraction And For your Decimal It Would Be 0.33

Hope this Helps!

\(xXxAnimexXx\)

Answer:

-2.2

Step-by-step explanation:

Answer:

-19.04 + 38.08 = 19.04

Step-by-step explanation:

To find the height of the rectangular prism, you will need to use the formula for the volume of a rectangular prism, which is:

Volume = Length × Width × Height

In this problem, you have:

Volume = 2,610 cubic inches

Length = 3 inches

Width = 29 inches

You'll need to solve for Height. Using the formula:

2,610 = 3 × 29 × Height

First, multiply the length and width together:

2,610 = 87 × Height

Next, divide both sides by 87 to isolate Height:

Height = 2,610 / 87

Height = 30 inches

So, the height of the rectangular prism is 30 inches.

Answer:

30 inches.

Step-by-step explanation:

Given:
Volume=2610 cubic inches,

length=3 inches

width=29inches

Volume of a rectangular prism is given by.

Volume = length * width * height

We know the volume, length and width. So, we can find the height as follows:

Substituting value

2610=3*29*height

2610=87*height

height=2610/87

height=20 inches

Therefore, the height of the rectangular prism is 30 inches.

Answer:

No, it would not fit because one cup is 8 ounces and if you times 8 and 13 it 104 so it would not fit they would need another container.

Step-by-step explanation:

hope it helps

The general form of the solution is y(x) = ∫ f(x) dx + C If f is continuous for all real numbers dy/dx=f(x) and y(2)=4 then y(x)= 4.

I need to provide concise answers. However, I'll do my best to address your question while incorporating the mentioned terms. Given that f is continuous for all real numbers and dy/dx = f(x), we need to find the function y(x) given the initial condition y(2) = 4.
Since dy/dx = f(x), we can interpret this as a first-order differential equation, where the derivative of y(x) with respect to x is equal to the function f(x). To find y(x), we need to solve this differential equation and apply the initial condition provided.
To do this, we will integrate both sides of the equation with respect to x:
∫ dy = ∫ f(x) dx
y(x) = ∫ f(x) dx + C
where C is the constant of integration. Now, we can use the initial condition y(2) = 4 to determine the value of C:
4 = ∫ f(2) dx + C
Since we don't have an explicit expression for f(x), we cannot determine an exact formula for y(x) or the value of C. However, the general form of the solution to the given problem is:
y(x) = ∫ f(x) dx + C
with the initial condition y(2) = 4. To find the exact solution, we would need more information about the function f(x).

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Answer:

Does the answer help you?

Answer:

k=-27

Step-by-step explanation:

\(\frac{k-7}{-0.4}=85\\\\k-7=85(-0.4)\\\\k=7-34\\\\k=-27\)

John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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In her presentation, Alaina can use a pie chart to show information about how the typical college student spends their day.

A circular chart that has been divided into sectors or "pie slices" to represent numerical proportions is known as a pie chart. Each pie slice symbolises a percentage, and each slice's size is proportional to the percentage it represents.

In this instance, Alaina can separate the pie chart into four segments that stand in for the various activities that college students engage in throughout the day: sleeping, attending classes, studying, and participating in extracurricular activities. She can give each slice a unique colour and a label indicating the proportion it represents.

The pie chart, for instance, might have the following slices:

-30% of people are sleeping (blue).

- 20% of the class (in green)

20% of study time (coloured)

30% of time for socializing

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answer:

it will be rounded to 52

Answer:

Not sure what you are wanting the number to be rounded to, so I'll just put all of the options here:

To the nearest whole number: 52

To the nearest tenth: 51.9

To the nearest one hundredth: 51.89

Answer:

Step-by-step explanation:

The standard from of equation of a line written in slope-intercept format is expressed as y = mx+c where c is the slope of the line and c is the y-intercept.

Given the equation of the line x+3y = 10, to get the slope of the line, we need write he equation in standard from first by making y the subject of the formula as shown;

\(x+3y = 10\\\\subtract\ x \ from \ both \ sides\\\\x+3y-x = 10 -x\\\\3y = -x+10\\\\Divide \ through\ by \ 3\\\\\frac{3y}{3} = -\frac{x}{3} +\frac{10}{3} \\\\\)

\(y = -\frac{1}{3}(x) +\frac{10}{3} \\\)

Comparing the resulting equation with y = mx+c, the slope 'm' of the equation is -1/3

The slope of the line is -1/3.

the correct option is D.

To find the slope of the line given by the equation x + 3y = 10, we need to rewrite it in slope-intercept form, which is y = mx + b, where m represents the slope.

Let's rearrange the equation to solve for y:

x + 3y = 10

3y = -x + 10

y = (-1/3)x + 10/3

Comparing this equation to the slope-intercept form, we can see that the coefficient of x (-1/3) represents the slope.

Therefore, the slope of the line is -1/3.

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The expected value of the product of two independent random variables X and Y is equal to the product of their individual expected values, given that the expected values of X and Y exist.

Let X and Y be two independent random variables. Then, the expected value of the product XY is given by:

E[XY] = ∫∫ xy fX(x) fY(y) dx dy

where fX(x) and fY(y) are the probability density functions of X and Y, respectively. Since X and Y are independent, their joint probability density function is given by:

fXY(x,y) = fX(x) fY(y)

Thus, the expected value of XY can be written as:

E[XY] = ∫∫ xy fX(x) fY(y) dx dy = ∫∫ xy fXY(x,y) dx dy

Now, we can use the linearity of expected value to split up the integral:

E[XY] = ∫∫ xy fXY(x,y) dx dy = ∫∫ x fX(x) y fY(y) dx dy

      = (∫ x fX(x) dx) (∫ y fY(y) dy) = E[X] E[Y]

Therefore, we have shown that E[XY] = E[X] E[Y], given that X and Y are independent and that the expected values of X and Y exist.

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