Why is there an equation of a line?

The four fundamental subspaces of a matrix are the row space, column space, null space, and left null space.(a) A basis for the row space of A is {{1,2,3}, {2,3,4}}. The row rank of A is 2.(b) A basis for the column space of A is {{1,2}, {2,3}, {3,4}}.

(c) A basis for the null space of A is {{-1,1,0}, {1,-2,1}, {0,1,-1}}. The nullity of A is 3.

(d) A basis for the null space of At is {{1,-1,0}, {-1,1,1}, {0,-1,-1}}. The nullity of At is 3.The four fundamental subspaces of a matrix are the row space, column space, null space, and left null space. The row space is the set of all linear combinations of the rows of the matrix, and its dimension is the row rank. The column space is the set of all linear combinations of the columns of the matrix, and its dimension is the column rank. The null space is the set of all vectors that are solutions to the system of equations Ax = 0, and its dimension is the nullity. The left null space is the set of all vectors that are solutions to the system of equations A^T x = 0, and its dimension is the nullity.

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Answer:

24 divided by 6 equals 4

Step-by-step explanation:

Answer: I think is 4

Step-by-step explanation:

The value of the expression 7/ 9 × 5 2/ 5 is 4 1/5

A fraction can be described as the part of a whole element, number or expression.

There are several types of fractions which includes;

From the information given, we have that;

7/ 9 × 5 2/ 5

Convert the mixed fraction to improper fraction

7/ 9 × 27/ 5

Now, reduce to simpler terms

7/ 1 × 3/ 5

Multiply the values

21/ 5

4 1/5

Hence, the value is 4 1/5

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p = 9

see explanation in image

using law of sines

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

Length of p to the nearest 10th of an inch is 8.9 inches.

Sines law of a triangle defines that the ratio of the side lengths of a triangle to the sine of the opposite angles to the side lengths are equal.

a / sin A = b / sin B = c / sin C

where a, b and c are the sides opposite to A, B and C respectively.

Given is a triangle ΔPQR.

Given, ∠Q = 37° and ∠R = 12°.

Sum of the interior angles of a triangle is 180°.

∠P = 180° - (37° + 12°)

     = 131°

Using the sine law,

p / sin P = q / sin Q

p / sin (131°) = 7.1 / sin (37°)

p = (7.1 / sin (37°)) × (sin (131°))

  = 8.9 inches

Hence the length of p is 8.9 inches.

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Emma and Ryan both have 125/32 pizzas.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given, Emma has [tex]3\frac{1}{8}[/tex]  slices of pizza.

Simplifying to improper fraction;

Emma has 25/8 slices of pizza.

And Ryan has 1/4 x The amount of pizza Emma has, slices of pizza.

That means, Ryan has 1/4 x (25/8) slices of pizza.

Applying multiplication of fraction.

That is, 25/32 slices of pizza.

To find the total amount of pizza;

add the number of pizza,

25/8 + 25/32

To add the number:

First, we take LCM,

25/8 + 25/32

= (100+ 25) / 32

= 125/32

Therefore, they both have 125/32 pizzas.

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Let X be a random variable representing the time until the first sale of a book. Then X has a Poisson distribution with rate a*p per hour.

Let X be a random variable representing the time until the first sale of a book. This random variable is the sum of the times that customers take to arrive and purchase a book. Since customers arrive at a bookstore according to a Poisson process with rate a per hour, the time until the first customer arrives has an exponential distribution with rate a per hour. Moreover, each customer buys a book with probability p, independently of everything else. Thus, the time until the first sale of a book is the sum of the time until the first customer arrives and the time until the first successful purchase. This sum of two independent exponential random variables is a Poisson random variable with rate a*p per hour. Therefore, the distribution of the time until the first sale of a book is a Poisson distribution with rate a*p per hour.

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The standard deviation for the binomial distribution is 3.39

The standard deviation for the binomial distribution is given by,

σ = [tex]\sqrt{n * P(1-P}[/tex]

where n = Number of trials

P = probability of success of an individual trail

If n = 48 and P = 0.6

σ = [tex]\sqrt{48 *0.6(1-0.6})[/tex]

= [tex]\sqrt{48*0.24}[/tex]

=[tex]\sqrt{11.52}[/tex]

=3.39

Therefore, the standard deviation for the binomial distribution will be 3.36.

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fff is a random variable in a game of luck

A random variable is a formula that gives each result in a sample space a numerical value.

There are two types of random variables: discrete and continuous. If a random variable only takes specified values inside an interval, it is said to be discrete. It is continuous if not.

We typically use capital letters, such X and Y, to designate the random variables

A random variable must be measured in order to be able to assign probabilities to a set of potential values. It is evident that the outcomes depend on a number of unpredictable physical elements.

According to the question,

In a game of luck, a turn consists of a player rolling 777 six-sided dice and counting how many of the dice show a 555. Let fff be the number of dice showing a 555 in a turn.

Here, fff is a Random variable.

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The rate the level in the tank falling when the height of the syrup level is 3 feet is 8/π feet per minute. The result is obtained by using the rate of change concept.

A conical tank containing syrup is draining.

Find the rate of syrup level falling (dh/dt) when h = 3 ft!

See the picture in the attachment!

By the similar triangles, we get

r/h = 2/6

r/h = 1/3

r = 1/3 h

Find the volume of the syrup left at a certain height.

V = 1/3 πr²h

V = 1/3 π(1/3 h)²h

V = 1/3 π(1/9) h² h

V = 1/27 πh³

The rate of syrup level falling is

dV/dt = dV/dh . dh/dt

dV/dt = d/dt [1/27 πh³] . dh/dt

dV/dt = 1/27 π 3h² dh/dt

8 = 1/27 π 3(3)² dh/dt

8 =  π dh/dt

dh/dt = 8/π ft/min

Hence, the rate of syrup level falling is 8/π feet per minute.

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Answer:

175 yards

Step-by-step explanation:

70/2 = 35

35 x 5 = 175

The linear function relating the variables C and S is given as follows:

C(S) = 5000 + 200S.

The graph of the linear function is given by the image at the end of the answer.

The linear function in this problem is defined in the slope-intercept as follows:

y = mx + b.

In which the coefficients of the function are defined as follows:

In the context of this problem, the variables are given as follows:

It will cost $5000 to rent trucks, hence the intercept is of:

b = 5000.

It will cost an additional $200 for each ton of sugar transported, hence the slope is of:

m = 200.

Then the equation is defined as follows:

C(S) = 5000 + 200S.

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The limit of a constant times a function is equal to the constant times the limit of the function. lim x →a(c f(x)) = c lim x →a f(x).

limit of a function

The limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input.

the right-hand limit of a function is the value of the function approaches when the variable approaches its limit from the right. The left-hand limit of a function is the value of the function approaches when the variable approaches its limit from the left.

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Answer:

To find the equation of the line through the two given points, we can use the slope-intercept form of the equation of a line, which is $y = mx + b$, where $m$ is the slope of the line and $b$ is the $y$-intercept (the point where the line crosses the $y$-axis).

We can find the slope of the line by using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the two given points. In this case, the slope is

$$m = \frac{(-3) - 5}{3 - (-6)} = \frac{-8}{9} = -\frac{4}{3}.$$

To find the $y$-intercept, we can plug the coordinates of one of the points and the slope into the equation of a line, so we have $y = -\frac{4}{3} x + b$. If we plug in the coordinates of the first point, we get

$$5 = -\frac{4}{3} (-6) + b \Rightarrow b = -\frac{4}{3} (-6) + 5 = \frac{28}{3}.$$

Therefore, the equation of the line through the two given points is

$$y = -\frac{4}{3} x + \frac{28}{3} = -\frac{4}{3} x + \frac{28}{3}.$$

Answer:

Step-by-step explanation:

(-6,5)     (3,-3)

The equation of the line:    

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

x₁=-6      x₂=3     y₁=5     y₂=-3

Hence,

[tex]\displaystyle\\\frac{x-(-6)}{3-(-6)} =\frac{y-5}{-3-5} \\\\\frac{x+6}{3+6}=\frac{y-5}{-8} \\\\\frac{x+6}{9} =\frac{y-5}{-8} \\\\[/tex]

Multiply both parts of the equation by -72:

[tex]-8(x+6)=9(y-5)\\\\-8x-48=9y-45\\\\-8x-48+45=9y-45+45\\\\-8x-3=9y\\\\[/tex]

Divide both parts of the equation by 9:

[tex]\displaystyle\\-\frac{8}{9} x-\frac{1}{3} =y\\\\Thus,\ y=-\frac{8}{9}x-\frac{1}{3}[/tex]

Answer:

Step-by-step explanation:

urmom

Answer:

31%

Step-by-step explanation:

total number of candy bars in the beginning =  28

number of milkyway bars in the beginning = 9

probability = 9/28 x 100 = 32% (rounded)

number of candy bars after = 27

number of milkway bars after = 8

probablity = 8/27 x 100 = 30 (rounded)

total probablity = (30+32)/200 x 100 = 31

Option-B is correct that is exponential growth. The new Malthusians fear that a lack of food will result from the population's exponential growth.

Given that,

The new Malthusians worry that ______ of the population will lead to a scarcity of food.

We have to fill the blank.

We know that,

A pattern of data that exhibits larger increases over time, forming the curve of an exponential function, is said to exhibit exponential growth.

The formula for the exponential growth is

V=S×(1+R[tex])^{T}[/tex]

The starting value, S, of an initial starting point subject to exponential growth can be multiplied by the sum of one plus the interest rate, R, raised to the power of T, or the number of periods that have passed, to get the current value, V.

Therefore, Option-B is correct that is exponential growth. The new Malthusians fear that a lack of food will result from the population's exponential growth.

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Answer:

34

Step-by-step explanation:

First you arrange the data in an ascending order and the median is the middle value. if the number of values is an even number, then the median will be the average of the two middle numbers. In this case, the median is 34.

The point is located (d) outside the target in relation to the target

From the question, we have the following parameters that can be used in our computation:

This means that we substitute (-1,-6) for x and y in the circle equation = (x + 5)² + (y + 5)² = 16.

So, we have the following representation

(x + 5)² + (y + 5)² = 16.

Substitute the known values in the above equation, so, we have the following representation

(-1 + 5)² + (-6 + 5)² = 16.

Evaluate the sum

(4)² + (-1)² = 16.

Evaluate the exponent

16 + 1 = 16.

Evaluate the sum

17 = 16

17 is greater than 16

Hence, the point is not in the target

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The Total Square Footage of the House is 780 sq. ft.

What is Area?

The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.

Solution:

Area of Living Room = 20*15 = 300 sq. ft.

Area of Kitchen = 12*10 = 120 sq. ft.

Area of Bedroom 1 = 12*12 = 144 sq. ft.

Area of Bedroom 2 = 12*10 = 120 sq. ft.

Area of Bathroom = 8*12 = 96 sq. ft.

Total Area is 300 + 120 + 144 + 120 + 96 = 780 sq. ft.

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The inequality formed is x + 6 > 20 and Julie will sell more than 14 items after the first Week

A relationship between two expressions or values that is not equal to one another is referred to as "inequality" in mathematics.

According to the given information

Let x be the more items that Julie will sell after First week

Number of items soled in First week = 6

So

The inequality formed will be

x + 6 > 20

Solving the inequality is

x > 20 - 6

x > 14

So

The inequality formed is x + 6 > 20 and Julie will sell more than 14 items after the first Week

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The steps of the perpendicular bisector construction in order from 1 to 4 are;

1) Open the compass

2) Draw arcs above and below the segment to be bisected

3) Draw arcs from the other endpoint of the segment to be bisected

4) Join the intersection of the arcs with a line

A perpendicular bisector is a line, that is perpendicular to another line, and which divides the other line into two congruent segments.

The steps of a perpendicular bisector construction includes;

1) Opening the compass to a radius that is more than half the length of the segment to be bisected

2) With the radius of the compass opening in step 1, place the compass at one endpoint of the segment to be bisected and draw arcs above and below the the segment to be bisected

3) With the same radius of the compass from step 1, place the compass at the other endpoint and draw arcs above and below the segment to be bisected to intersect the arcs drawn in step 2

4) With a straightedge, draw a straight line joining the point of intersection of the arcs in step 3. The line is the perpendicular bisector of the segment.

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The examples of functions in real life situation is given below .

In the question,

we have to give few examples for functions in real life .

the term Function is defined as as a relationship between two variables where for every input variable there is one output variable.

the examples are :

Example 1 :

Suppose that a car is driving at a constant speed of 30 mph.

the total distance "d" is equal to the rate, 30 times the time "t" ,that we drive for . the function for the relationship between our distance, d, and the time for driving is

d = f(t) =30 × t  .

Example 2:

Suppose that the cost for 1 bag is $9 , then the function for the cost of "x" bags can be written as

Cost = f(x) = 9x .

Therefore , the real life situations examples are shown above.

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Answer:

(-4,-7)

Step-by-step explanation:

Multiply both sides of the first equation by-5 or 2 (I'll use 5) and both sides of the second equation by - 2 or 3 (I'll use -2).

3x - 2y = 2

5(3x-2y)= 5(2)

-15x - 10y = 10

2x - 5y = 27

-2(2x - 5y) = -2(27)

-4x + 10y = -54

Now you see that the absolute values of the y-values of the 2 equations match up . They are still the same equations but scaled up.

-15x + 10y = 10

-4x - 10y = -54

Add to eliminate y.

-11x = 44

Divide both sides by -11.

[tex]\frac{-11x}{-11} = \frac{44}{-11}[/tex]

x = -4

Plug back in to either equation to solve. I'll use the first equation.

3x - 2y = 2

x = - 4

3(-4) - 2y = 2

-12 - 2y = 2

Add 12 on both sides.

-12 + 12 - 2y = 2 + 12

- 2y = 14

Divide -2y on both sides.

[tex]\frac{-2y}{-2} = \frac{14}{-2}[/tex]

y = -7

(-4,-7)

The dimensions of the rectangular( length and width) are 14m and 15m.

Here we have to find the dimension of the length and width.

Data given:

Fencing = 58m

Area = 210 m²

Let us assume the length be x

By this, we get the width as:

width = 58 - 2x / 2

         = 29-x

As the area is 210 m²

The formula to find the area of the rectangular is:

Area = length ×width

210 = x ( 29 -x)

x² - 29 x + 210 = 0

Formula to find the value of x from the quadratic equation:

x = -b ±[tex]\sqrt{b^{2} - 4ac }[/tex]

For the general equation ax² + bx + c =0

As the equation is:

x² - 29x + 210 = 0

a = -1

b = -29

c = -210

So,

x = 29 ±[tex]\sqrt{(29)^{2} - 4(-1)(-210) }[/tex] / 2(-1)

  = 29± 1/-2

  = 14, 15

29 - x = 15, 14 (for the value of x = 14 and 15 respectively)

Therefore the dimensions are 14m and 15m.

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Answer:

To divide polynomials, we need to use polynomial long division. First, we divide the first term of the dividend by the first term of the divisor to get the first term of the quotient, which we write above the division bar. In this case, the first term of the dividend is 2x² and the first term of the divisor is x, so the first term of the quotient is 2x. We then multiply the divisor by the quotient and subtract it from the dividend to get the remainder.

Here's how the long division would look:

2x² + 15x + 20
===
x + 5

2x

_______

 15x - 10x

 15x + 20 - 10x - 20

 ___________

    5x - 20

After we perform the polynomial long division, we get the quotient 2x + 5 and the remainder -20. Therefore, the final result of the division is:

(2x² + 15x + 20) ÷ (x + 5) = 2x + 5 + (-20)/(x + 5)

Note that the remainder -20 is written as a fraction with the divisor x + 5 in the denominator. This is the correct way to write the remainder because it tells us that the remainder has a degree that is one less than the degree of the divisor. In this case, the degree of the divisor is 1, so the degree of the remainder is 0.

y=-3/4x-9/2 is the equation of a line that goes through both transformed points.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

we must translate the given point (x,y) into the translation given. We begin with the 90 degree clockwise rotation such that

90 degree clockwise rotation = (x, y) => (y, -x)

we translate the coordinate (y, -x)

2 units to the right such that

(y-4, -x - 2)

So the coordinate of points changed (1,2) and (-4,6) from (-2, -3) and (2, -6)

m=-6-(-3)/2-(-2)

m=-3/4

Now let us find the y intercept.

-3=-3/4(-2)+b

-3=3/2+b

-3-3/2=b

-9/2=b

Hence, y=-3/4x-9/2 is the equation of a line that goes through both transformed points.

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Answer:

it is 9

Step-by-step explanation:

Using the divergence theorem we can compute that the outward flux of the vector field is 16π .

The outward flux of F over the solid cylinder and z = 0 is

∫∫F·ds  = ∫∫∫ DivF dv

F = 2xy² i   +  2x²y j + 2xy k

Div F  =  D/dx (2xy²)  +   D/dy (2x²y )

Div F  =  2y²  +  2x²

In cylindrical coordinates   dV = rdrdθdz and as z = 0 the region is a surface ds = r·dr·dθ

Using the parametric form of the surface equation

x = rcosθ        y =  r sinθ      and z = z

Div F  = 2r² sin²θ  + 2r²cos²θ

∫∫∫ DivF dv  =  ∫∫ [2r²sin²θ  + 2r²cos²θ] × rdrdθ

∫∫ 2r² [sin²θ  + cos²θ] × rdrdθdz   ⇒  ∫∫ 2r³ drdθ

Integration limits

0 < r < 2          0 < θ < 2π

2∫₀² r³ ∫dθ

(2/4) × (2)⁴ × 2π

The divergence theorem, commonly known as Gauss' theorem or Ostrogradsky's theorem, is a theorem that connects the flow of a vector field across a closed surface to the field's divergence in the volume enclosed.

In more detail, the divergence theorem states that the surface integral of a vector field across a closed surface, sometimes referred to as the "flux" through the surface, is equal to the volume integral of the divergence over the region inside the surface.

Therefore the flux is 16π .

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