Write an equation in Point Slope Form that has a slope
of -2 and passes through the point (5,7)

If a is an m x n matrix with m pivot columns, the linear transformation represented by A is a one-to-one mapping if and only if the number of pivot columns is equal to n.

To determine if the linear transformation represented by the matrix A is a one-to-one mapping, we need to examine the relationship between the columns of A and the null space of A.

First, let's define the linear transformation T: R^n → R^m represented by the matrix A. For any vector x in R^n, T(x) is given by the matrix-vector multiplication T(x) = Ax.

If a is an m x n matrix with m pivot columns, it means that the matrix A has m linearly independent columns. This implies that the columns of A span a subspace of dimension m in R^m. In other words, the column space of A has dimension m.

Now, let's consider the null space of A, denoted by N(A). The null space consists of all vectors x in R^n such that Ax = 0. Since A has n columns, the null space N(A) is a subspace of R^n.

If the number of pivot columns in A is equal to n, which means every column of A is a pivot column, then the null space N(A) contains only the zero vector, i.e., N(A) = {0}. In this case, the linear transformation T is one-to-one, because for any two distinct vectors x₁ and x₂ in R^n, T(x₁) = Ax₁ and T(x₂) = Ax₂ will also be distinct.

However, if the number of pivot columns in A is less than n, then the null space N(A) will contain non-zero vectors, indicating that there are vectors x₁ and x₂ in R^n such that x₁ ≠ x₂ but T(x₁) = T(x₂) = Ax₁ = Ax₂. This violates the definition of a one-to-one mapping, as multiple inputs map to the same output.

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Answer:

y intercept = (0,4)

Answer:

0,4 i think

(sorry if i am wrong)

To check if y = 3cos(3t) + 4sin(3t) is a solution by differentiation, we will differentiate y with respect to t and use the chain rule.
y = 3cos(3t) + 4sin(3t)
dy/dt = -9sin(3t) + 12cos(3t)
The differentiation confirms that the given function y = 3cos(3t) + 4sin(3t) is a valid solution, as we were able to compute its derivative with respect to t without encountering any issues.

To check whether y = 3cos3t 4sin3t is a solution, we need to differentiate it with respect to t and see if it satisfies the differential equation.
y = 3cos3t 4sin3t
dy/dt = -9sin3t + 12cos3t

Now, we substitute y and dy/dt into the differential equation:

d^2y/dt^2 + 9y = 0
(d/dt)(dy/dt) + 9y = 0
(-9sin3t + 12cos3t) + 9(3cos3t 4sin3t) = 0
-27sin3t + 36cos3t + 36cos3t + 27sin3t = 0
As we can see, the equation simplifies to 0=0, which means that y = 3cos3t 4sin3t is indeed a solution to the differential equation.

Therefore, we can conclude that y = 3cos3t 4sin3t satisfies the differential equation and is a valid solution.

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The product is less than 67,124 because the number 50,343 is less that the number 67,124.

The product is greater than 12,400 because the number 14,800 is greater than 12,400.

What is product?

A mathematical expression that specifies the objects to be multiplied, known as a factor, produces a product. For instance, the product of x and is c dot, and the product of 6 and 5 is 30.

First to multiply 67124 x 3/4

Here 67124 x 3 = 201372

⇒201372/4 = 50343

Hence, the product is less than 67,124 because the number 50,343 is less that the number 67,124.

Now to multiply 12,400 x 1 1/5

First to convert \(1\frac{1}{5}\) into a fraction.

\(1\frac{1}{5} = \frac{5+1}{5} = \frac{6}{5}\)

Now,

12,400 x 6/5 = 74,400/5 = 14800

Hence, the product is greater than 12,400 because the number 14,800 is greater than 12,400.

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Answer:

x     y

0    28

1     24

2    20

3    16

4    12

5     8

6     4

7     0

8     -4

9     -8

10    -12

Step-by-step explanation:

Not sure how many you needed, but I graphed it out here is the table from 1-10 on it.

Joule per meter second is the unit of measurement for momentum flux or power per unit area. It is commonly used in physics and engineering to quantify the rate of energy transfer or momentum flow per unit area.

Joule per meter second (J/m^2s) is not the correct unit for momentum flux or power per unit area. The correct unit for momentum flux is Newton per square meter (N/m^2), also known as Pascal (Pa), while the correct unit for power per unit area is watt per square meter (W/m^2). The joule per meter second (J/m^2s) is actually the unit for volumetric energy dissipation rate, which measures the rate at which energy is being dissipated within a fluid volume per unit volume. It is used in the study of fluid dynamics and turbulence.

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Answer: yes but... i might be wrong so i think no cause i had a question like this and it was no

Step-by-step explanation:

1. Considering the equation \(z^{16}\) = −1−i.The value of z which satisfies this equation and which has the second smallest positive argument θ, 0<θ<2π as z=r\(e^{i\theta}\) where r = \(\underline{2^{1/32}}\) and θ = 13π/64.

2. Considering the equation \(z^{13}=(-1+\sqrt{3i})\). The value of z which satisfies this equation and which has the second smallest positive argument θ,0<θ<2π as z=r\(e^{i\theta}\) where r = \(\underline{2^{1/13}}\) and θ = 8π/39.

1. The equation is z^{16} = -1 - i.

We have express our answer in the form of

\(\; z = re^{i\theta }\)

When we enter it into the first equation, we obtain,

\(r^{16}e^{16i\theta }=-1-i\; \; \; \; \; \; \; \; \; \; \; \;\)--(2)

Using the modulus of both sides, we obtain,

\(\left |r^{16} \right |\: \: \left | e^{16i\theta } \right |=\sqrt{\left ( -1 \right )^{2}+\left ( -1 \right )^{2}}\)

Simplifying

\(\; \; \; \; \; r^{16}=\sqrt{2}\)

Taking root of 16 on both side, we get

\(r=2^{1/32}\)

Plugging this value of 'r' back in equation (2), we get,

\(\sqrt{2}\; \; e^{16i\theta }=-1-i\)

Divide by √2 on both side, we get

\(e^{16i\theta }=-\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}i\)

We can write \(e^{16i\theta }\) as

\(\; \; \; \;cos16\theta +isin16\theta =-\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}i\)

On comparing, we get

\(\; \; \; \;cos16\theta=-\frac{1}{\sqrt{2}}\;, \; \; \; \; \; \; \; sin16\theta =-\frac{1}{\sqrt{2}}\)

Angle must therefore be in the third quadrant.

\(16\theta=\pi +\frac{\pi }{4}=\frac{5\pi }{4}\; \; \; \; \; \; \; \; ,\; \; \; \; \; \; \; \;16\theta=\frac{5\pi }{4}+2\pi =\frac{13\pi }{4}\)

\(\theta=\frac{5\pi }{64}\; \; \; \; \; \; \; \; ,\; \; \; \; \; \; \; \;\theta=\frac{13\pi }{64}\)

So, second smallest positive argument = 13π/64.

2) The equation is \(z^{13} = -1 +\sqrt{3i}\).

We have express our answer in the form of

\(\; z = re^{i\theta }\)

When we enter it into the first equation, we obtain,

\(r^{13}e^{13i\theta }=-1+\sqrt{3}i\; \; \; \; \; \; \; \; \; \; \; \;\)

Using the modulus of both sides, we obtain,

\(\left |r^{13} \right |\: \: \left | e^{13i\theta } \right |=\sqrt{\left ( -1 \right )^{2}+\left ( \sqrt{3} \right )^{2}}\)

Simplifying

\(r^{13}=2\)

Taking root of 13 on both side, we get

\(r=2^{1/13}\)

Reintroducing this 'r' value into the equation from \(r^{13}e^{13i\theta }=-1+\sqrt{3}\), we get,

\(2e^{13i\theta }=-1+\sqrt{3}i\)

Divide 2 on both side, we get

\(e^{13i\theta }=-\frac{1}{2}+\frac{\sqrt{3}}{2}i\)

We can write \(e^{13i\theta }\) as

\(\; \; \; \;cos13\theta +isin13\theta =-\frac{1}{2}+\frac{\sqrt{3}}{2}i\)

\(\; \; \; \;cos13\theta=-\frac{1}{2}\;, \; \; \; \; \; \; \; sin13\theta =\frac{\sqrt{3}}{2}\)

Angle must therefore be in the second quadrant.

\(13\theta=\pi -\frac{\pi }{3}=\frac{2\pi }{3}\; \; \; \; \; \; \; \; ,\; \; \; \; \; \; \; \;13\theta=\frac{2\pi }{3}+2\pi =\frac{8\pi }{3}\)

\(\theta=\frac{2\pi }{39}\; \; \; \; \; \; \; \; ,\; \; \; \; \; \; \; \;\theta=\frac{8\pi }{39}\)

So, second smallest positive argument = 8π/39.

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Answer:

the slope is \(\frac{7}{4}\)

Step-by-step explanation:

Given: 4y - 7x = 10; solve y

4y - 7x = 10; add 7x to both sides to isolate the 4y variable

4y = 7x + 10; now divide by 4

y = \(\frac{7}{4}\)x + \(\frac{10}{4}\); reduce the fraction

y = \(\frac{7}{4}\)x + \(\frac{5}{2}\); the slope is

Answer:

m= 7/4

Step-by-step explanation:

Answer:

I think its 180

Step-by-step explanation:

Answer:

Where is the image to the equations?

Step-by-step explanation:

Answer:

there's no picture???

Step-by-step explanation:

Answer: Degree of Polynomial: 12

Step-by-step explanation:

Answer:

(b) complementary angles

There are 120 different combinations when selecting Christmas presents.

There are 10 available presents in all under a Christmas tree, and

The number of presents chosen to be placed beneath a Christmas tree is 3.

We must determine how many possible combinations there are.

There are a total of three methods by which the 10 gifts can be chosen \(10C_{3}\).

that is

\(nC_{r}=\frac{n!}{r!(n-r)!}\)

\(10C_{r} =\frac{10!}{3!(10-3)!}\)

=120

In order to choose three gifts from a total of ten, there are 120 possible different combinations.

The term "probability" is most commonly used to refer to the likelihood that a specific event (or group of events) will occur, either as a linear scale from 0 (impossibility) to 1 (certainty) or as a percentage between 0 and 100%. Statistics is the study of events subject to probability.

5rdx

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Answer:

whojhuokk

tuhhjhkk

Step-by-step explanation:

kjufig(hgggjkooujjlkhy

Answer:

see explanation

Step-by-step explanation:

A linear pair of angles sum to 180° , then

3x + 10 + 4x - 5 = 180

7x + 5 = 180 ( subtract 5 from both sides )

7x = 175 ( divide both sides by 7 )

x = 25

Then

3x + 10 = 3(25) + 10 = 75 + 10 = 85°

4x - 5 = 4(25) - 5 = 100 - 5 = 95°

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

3x - 3 + 5x + 7 = 180

8x + 4 = 180 ( subtract 4 from both sides )

8x = 176 ( divide both sides by 8 )

x = 22

Then

3x - 3 = 3(22) - 3 = 66 - 3 = 63°

5x + 7 = 5(22) + 7 = 110 + 7 = 117°

Answer:

see explanation

Step-by-step explanation:

A linear pair of angles sum to 180° , then

3x + 10 + 4x - 5 = 180

7x + 5 = 180 ( subtract 5 from both sides )

7x = 175 ( divide both sides by 7 )

x = 25

Then

3x + 10 = 3(25) + 10 = 75 + 10 = 85°

4x - 5 = 4(25) - 5 = 100 - 5 = 95°

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

3x - 3 + 5x + 7 = 180

8x + 4 = 180 ( subtract 4 from both sides )

8x = 176 ( divide both sides by 8 )

x = 22

Then

3x - 3 = 3(22) - 3 = 66 - 3 = 63°

5x + 7 = 5(22) + 7 = 110 + 7 = 117°

The volume flow rate of the water passing through the pipe increases by a factor of 6.

Assuming that the initial cross sectional area of the pipe is A m² and the initial velocity of the water is V m/s, the water flow rate is:

= initial flow rate = area × velocity = AV m³/s

As the water speed doubles (2V m/s) and the pipe cross-sectional area triples (3A m²), the volume flow rate becomes:

Final flow rate = 2V × 3A = 6AV m³/s

As a result, the volume flow rate of the water moving through it multiplies by a ratio of six.

The basic equation for cases like these is

Q=AV,

where Q is the volume flow rate, A is the cross-sectional area occupied by the flowing material, and V is the average velocity of flow.

V is considered an average since not every component of a flowing fluid flows at the same rate. If you monitor the waters of a river moving slowly downstream at a consistent rate of gallons per second, you will see that the surface has slower currents here and faster currents there.

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Answer:

406 percent

Please brainliest me i am begging you for god sake

The expression that is equivalent to 43,450,000 when simplified is 4.345 x 10⁷

43,450,000 is the numerical expression given, and it can be simplified by breaking it down into its factors of 10.

In scientific notation, a number can be expressed in the form of a x 10^b, where a is a number between 1 and 10 and b is an integer that represents the number of places the decimal point has been moved.

To simplify 43,450,000, we can write it as

4.345 x 10⁷

This is because we have moved the decimal point seven places to the left.

So, the expression that is equivalent to 43,450,000 when simplified is

4.345 x 10⁷

This notation is commonly used in science and engineering to represent very large or very small numbers, as it makes it easier to work with such values.

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The variance of the sample means that is found in the sample distribution that we have here is 0.3333

This is the measure of dispersion that is used to show the spread of the data that is contained in a data set

The formula that we are to use here is given as

b² - a² / b - a

we have to put the values in this question

(14 - 2)² / 14 - 2

= 144 / 12

= 12

From here we would have to solve for the variance.

The variance = 12 / 35

= 0.3333

Hence the variance that we have in the question is equal to 0.3333

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Answer:

You can by 7 shirts if you wanted

Answer:

175 ÷ 25

=> 7

Therefore, you can only buy 7 shirts.

Step-by-step explanation:

Hoped this helped

Answer:

h ≤ 9

Step-by-step explanation:

Currently, Linda has $26 and needs $80. So, to find how much she needs, you can subtract 80 by 26 to get 54. Since she earns $6 per hour, you need to divide 54 by 6 to get 9, which is the minimum amount of hours she will need to babysit to afford the ski pass.

Answer:

i don't see nothing

Step-by-step explanation:

Answer:

x=1±i√5

Step-by-step explanation:

the quadratic equation is in the form :

y=ax²+bx+c

y= 2x²-4x+12

x=(-b±√b²-4ac)/2a

x=-(-4)±√-4²-4(2)(12)/2a

x=4±√16-96/4

x=4±√-80/4

since the number under the square root then √-80=4i√5 ( assuming possitive numbers)

x=(4±4i√5)/4

x=4(1±i√5)/4

x=1±i√5

Answer:

C

Step-by-step explanation:

The graph is 5x^2. Hence the option C is correct

The required function g(x) is 5x² for the given graph, which is the correct option (C).

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The given function is as follows:

f(x) = x²

Substitute the value of x = 1 in the above equation,

f(1) = 1

As per the given graph, we have

g(1) = 5

Now, we can write the proportion as:

f(x)/g(x) = f(1)/g(1)

Substitute the known values in the above proportion, and solve for g(x):

x²/g(x) = 1/5

Cross-multiplying and we get:

g(x) = 5x²

Therefore, the required function g(x) is 5x².

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Work Shown:

y = 15.6 - 3.8x

y = 15.6 - 3.8*3

y = 4.2

It would be A.15ft

Step-by-step explanation:

(a) 27 outcomes in the sample space are : (1,1,1), (1,1,2), (1,1,3), (1,2,1), (1,2,2), (1,2,3), (1,3,1), (1,3,2), (1,3,3), (2,1,1), (2,1,2), (2,1,3), (2,2,1), (2,2,2), (2,2,3), (2,3,1), (2,3,2), (2,3,3), (3,1,1), (3,1,2), (3,1,3), (3,2,1), (3,2,2), (3,2,3), (3,3,1), (3,3,2), (3,3,3)

(b) All outcomes in the event that all three members go to the same station are : (1,1,1), (2,2,2), (3,3,3)

(a) The 27 outcomes in the sample space can be represented as ordered triples, where each element corresponds to the station that each family member is assigned to. The possible values for each element are 1, 2, and 3. Therefore, the sample space consists of the following 27 outcomes:

(1,1,1), (1,1,2), (1,1,3), (1,2,1), (1,2,2), (1,2,3), (1,3,1), (1,3,2), (1,3,3),

(2,1,1), (2,1,2), (2,1,3), (2,2,1), (2,2,2), (2,2,3), (2,3,1), (2,3,2), (2,3,3),

(3,1,1), (3,1,2), (3,1,3), (3,2,1), (3,2,2), (3,2,3), (3,3,1), (3,3,2), (3,3,3)

(b) The outcomes in the event that all three members go to the same station can be found by examining the 27 outcomes in the sample space and selecting those outcomes where all three elements are the same. Therefore, the outcomes in the event that all three members go to the same station are:

(1,1,1), (2,2,2), (3,3,3)

In these outcomes, all three family members are assigned to the same station. There are three such outcomes, since each family member can be assigned to any one of the three stations.

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