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write the point slope form of the equation of the line through the given point with the given slope
through: (-1, -2) slope =3

The domain of y equals two divided by the quantity x minus three squared all minus one [y = (2)/(x - 3)² - 1] is: all real numbers.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.

This ultimately implies that, a domain is the set of all possible input numerical values or numbers (x-values) to a function and the domain of a graph comprises all the input numerical values which are located on the x-coordinate.

Translating the word problem into an algebraic equation, we have;

y = (2)/(x - 3)² - 1

When x = 3, we have:

y = (2)/(3 - 3)² - 1

y = 2/-1 = -2

When x = 1, we have:

y = (2)/(1 - 3)² - 1

y = 2/3

In conclusion, the domain of this function is all real numbers.

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Answer:hyper bola

Step-by-step explanation:

All you have to do is look up all the answers on images and then pick the one that looks the most similar

Answer: 110°

Step-by-step explanation:

Looks like a bit more than 100°.

The velocity of the sign are given as follows:

a) Relative to the car: 60 kilometers an hour.

b) Relative to the ground: 0 kilometers an hour.

The relative speed of one object towards another is given by the rate of change in the position of each these objects relative to each other in regard to time.

Relative to the car, the sign gets 60 kilometers closer every hour, hence the relative speed of the sign will be of 60 kilometers. an hour.

Now, for the ground, the distance between the sign and the ground will always be the same, that is, there is no change in the distance. Hence, the velocity of the sign relative to the ground is of 0 kilometers and hour.

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Answer:

If two parallel lines are cut by a transversal, then the corresponding angles are congruent.

Answer:

[tex]x=12, y=0[/tex]

Step-by-step explanation:

[tex]22+\frac{1}{5}yi=2x-2 \\ \\ (24-2x)+\frac{1}{5}yi[/tex]=0[/tex]

Setting the real and imaginary parts of the left hand side equal to 0,

[tex]24-2x=0 \implies x=12 \\ \\ \frac{1}{5}y=0 \implies y=0[/tex]

Answer:

See below

Step-by-step explanation:

11x^2 = - 8

x^2  = - 8/11

x = + - i sqrt (8/11)      or  - .727 i   or   .727 i  

By graphing, the solution of the system of equations is: (6, -2).

To solve the system of equations by graphing, plot each of the line of the equations, then find the coordinates of the point where both lines intersect. Where they intersect is the solution to the systems of equations.

Given the following equations:

x + 2y = 2

y = -x + 4

x + 2y = 2 can be rewritten as y = -1/2x + 1. The graph for x + 2y = 2 will intercept the y-axis at 1 and also has a slope of -1/2. (It is the red line in the image below).

The graph of y = -x + 4 will also have a slope of -1 and intercept the y-axis at 4. (It is the blue line in the image below).

The graph of the equations are shown below, and they intersect at (6, -2), which is the solution to the system of equations.

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Answer: Cannot be factored

Step-by-step explanation:

= Factor Y^2x -y^x-20

= Cannot be factored

Answer:

60°

Step-by-step explanation:

As we can conclude from the equal measured side lengths, this is an equilateral triangle so all angles have equal measurement.

Since the sum of interior angles in a triangle is equal to 180 to find the measure of angle V we need to divide 180 by 3:

180 ÷ 3 = 60

The second probability is affected by the first probability. So, we can say that this is a dependent probability.

Given,

Number of white gems = 7

Number of green gems = 5

Number of blue gems = 3

Total number of gems = 7 + 5 + 3 = 15

We have to find the probability when picking a green gem and then another green with out replacement are dependent.

Here,

Probability of choosing the first gem green = Number of green gems / total number of gems

Probability = 5/15 = 1/3

Now,

Number of green gems = 4

Total number of gems = 14

Probability of choosing the second gem green = Number of green gems / Total number of gems

Probability = 4/14 = 2/7

Here,

The second probability is affected by the first probability. So, we can say that this is a dependent probability.

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Answer:

(x+8)(x-9)

Step-by-step explanation:

1. Use the sum-product pattern

x²-x-72

x²+8x-9x-72

2. Find the common factor from the 2 pairs

x²+8x-9x-72

x(x+8)-9(x+8)

3. Rewrite in factored form

x(x+8)-9(x+8)

(x-9)(x+8)

Solution to problem: (x-9)(x+8)

x-intercept is (-250, 0) and y-intercept is (0, 100)

What is  x-intercept and  y-intercept

The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations.

First, find x-intercept

For x-intercept it means y = 0

observe the graph and see the blue line cuts the x-axis when y = 0

We see, x = -250

so, the x-intercept is = (-250, 0)

Now, same thing do to find y-intercept

For y-intercept it means x = 0

observe the graph and see the blue line cuts the y-axis when x = 0

We see, y = 100

so, the y-intercept is = (0, 100)

Therefore, x-intercept is (-250, 0) and y-intercept is (0, 100).

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The set of values for Rents lesser than $700. So, rent 700 <y<0

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The solution of the exponential expression will be a⁹.

Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied.

Given exponential expression is (a⁻¹ x a⁻²)⁻³. The expression will be solved as below,

E = (a⁻¹ x a⁻²)⁻³

The base is the same and the variables are in multiplication with powers then the powers will be added,

E = (a⁻³)⁻³

E = a⁹

Therefore, the solution of the exponential expression will be a⁹.

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If the matrix C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex], then the determinant of the matrix |C| = -12

The given matrix is

C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex]

The matrix is defined as the set of numbers that arranged in rows and columns to form a rectangular array. The numbers in the matrix are called the elements of the matrix.

Here we have to find the determinant of the matrix C

The determinant of the matrix is defined as the scalar value calculated for a given square matrix.

The determinant of C is represented by |C|

Then,

C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex]

|C| = -6×4 - 6×-2

= -24 -(-12)

= -24 + 12

= -12

Hence, if the matrix C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex], then the determinant of the matrix |C| = -12

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Answer:

x=10

Step-by-step explanation:

4x+5x+angle g should equal 180 degrees total.

with this in mind, we can subtract angle g from 180, as it is know,. (180-90)

so 4x+5x=90. 9x=90, x=10.

hope this helps.

Check the picture below.

The function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3

The quadratic function is

f(x) = [tex]-3x^2[/tex] + 18x + 3

The general form of the quadratic function is

y = [tex]ax^2[/tex] + bx + c

If a < 0, the quadratic function has maximum value

Here the value of a = -3

Therefore the function has maximum value.

Maximum value will be at x = -b / 2a

= -18 / 2(-3)

= -18 / -6

= 3

The maximum value of quadratic function will be (4ac - [tex]b^2[/tex]) /4a

Substitute the value in the equation

(4ac - [tex]b^2[/tex]) /4a = (4×-3×3 - 18×18) / 4×-3

= (-36 - 324 / -12

= -360 / -12

= 30

Hence, the function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3

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The given system of equations has no solution.

The given system of equations are A-B =2 and A+2= B.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Here,

A-B =2 --------(I) and A+2= B --------(II)

From equation (II) substitute B=A+2 in the equation (I), we get

A-(A+2)=2

⇒ A-A-2=2

⇒ 0-2=2

Hence, the given system of equations has no solution.

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After ≈16.61 years the population will increased by  times it's original amount.

What do you mean by population?

A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait. A population is the group of people from which a statistical sample is taken in statistics.

Given: If a population doubles every 5  years.

Assume,  'A' is the starting population, and 't' is the passing time in years.

Given the fact that a population doubles every five years, our population is growing exponentially, as per the question.

Here, the equation can be written as follows: [tex]A(t) = A(2)^{\frac{t}{5} }[/tex]                    (1)

We now need to determine when the population will have multiplied by 10 by that time.

Let's substitute [tex]A(t) = 10A[/tex]  in the above equation.

[tex]10A = A(2)^{\frac{t}{5} }[/tex]

[tex]10 = (2)^{\frac{t}{5} }[/tex]

Taking the natural log of both sides we get:

[tex]ln10 = \frac{t}{5} \times ln2[/tex]                        {[tex]ln(a)^n= nln(a)[/tex]}

2.3025 x 5 = t x 0.6931

[tex]t = \frac{2.3025}{0.6931}\\t = 16.6096[/tex]

Therefore, After ≈16.61 years the population will increased by  times it's original amount.

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Answer:

x = 135

Step-by-step explanation:

You need to find the supplementary angle of x.

To find x, use the supplementary angle theorem. (The angles "lie" on a straight line, so they add up to 180°, or a straight line.)

45+x = 180

x = 135

Answer:

1368

Step-by-step explanation:

let 3rd game be x

151+183+x=1702

334+x=1702

x=1702-334

x=1368

The length of the base when the height is 6 cm is 21 cm .

In the question ,

it is given that ,

the length of the base(b) of the triangle varies inversely with the height(h) ,

which is represented as

b ∝ 1/h

b = k/h

where k is the constant of variation

given that when b = 18 , h is = 7

18 = k/7

k = 18 × 7

k = 126

Substituting , the value of k = 126  in the equation b = k/h  ,

we get ,

b = 126/h

So, the length of the Base When h = 6,

b = 126/6

b = 21

Therefore, the length of the base when the height is 6 cm is 21 cm .

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Answer:

  a. 3/2 meters

  b. 15/4 times as great

Step-by-step explanation:

You want the width of a rectangle that is 3/5 m² in area and 2/5 m long. You also want to know the factor by which the length is greater than the width.

The formula for the area of a rectangle is ...

  A = LW

Filling in the known values, we can solve for the length:

  3/5 m² = (2/5 m)·L

  L = (3/5)/(2/5) m = 3/2 m . . . . . . divide by the coefficient of L

The length of the rectangle is 3/2 meters.

The ratio of length to width is ...

  length/width = (3/2 m)/(2/5 m) = (15/10)/(4/10) = 15/4

The length is 15/4 times greater than the width.

The required equation of slope is y = x/2 + 6

Given : y = 3x + 6

this is of the form y = mx + c

thus on comparing we get

the slope or m = 3

And the y intercept = 0, 6

It is also given that we have to find the equation of the slope which passes through the point ( -2, 5 )

thus the two points are:

( -2, 5 )  and ( 0,6 )

Thus the slope or m = y2 - y1/ x2 - x1

=> m = 6 - 5 / - ( -2 )

m = 1/ 2

Thus the equation of the slope is

y - y₁ = m ( x - x₁ )

₁Substituting the value of m from above we get

y - 5 = 1/2 ( x + 2 )

this implies 2y - 10 = x + 2

x - 2y = - 12

or we can also write this as

y = x/2 + 6

Refer to the graph given below for further understanding.

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Answer:

875 square feet.

Step-by-step explanation:

Multiply 350 square feet by 2.5 gallons.

The slope of the line of best fit represents: the expected change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute.

A line of best fit simply refers to a statistical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association between data points.

A slope is also referred to as the rate of change and it's typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or data points.

In this scenario, the slope for the given data is the change in temperature with respect to a unit change in the number of chirps sold.

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