Could someone help me with this? Do I have to get the inverse?

The value of x, y and z in the system equation is (1, 2, 3).

The solution of the equation can be determined by using Cramer's rule as follows;

[-5    -6      0] = [ -17]

[-3     -5     5]    [2   ]

[-6    -5      1]     [-13 ]

The determinant of the matrix is calculate as;

Δ = -5 (-5 + 25) + 6(-3 + 30) + 0(15 + 30)

Δ = 62

The x-determinant of the matrix is calculated as follows;

Δx = -17(-5 + 25) + 6(2 + 65) + 0

Δx = 62

The y-determinant of the matrix is calculated as follows;

Δy = -5(2 + 65) + 17(-3 + 30) + 0

Δy = 124

The z-determinant of the matrix is calculated as follows;

Δz = -5(65 + 10) + 6 (39 + 12) - 17(15 - 30)

Δz =  186

The value of x, y and z is calculated as follows;

x = Δx/Δ = 62/62 = 1

y = Δy/Δ = 124/62 = 2

z = Δz/Δ = 186/62 = 3

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Answer:

Part A

The amplitude of a cosine function is the distance between its highest and lowest points. In this case, the highest point is 8 feet and the lowest point is 8 - 12 = -4 feet, so the amplitude is 8 - (-4) = 12 feet.

The period of a cosine function is the time it takes for the function to complete one cycle of its movement. In this case, the bird completes one cycle of its movement every 16 seconds, so the period is 16 seconds.

Part B

The cosine function that could represent the situation is:

y = 6 cos(2πt / 16) + 8

This function has an amplitude of 6 feet and a period of 16 seconds. It also passes through the point (0, 8) when t = 0, which is the condition given in the problem.

Part C

The bird will reach its lowest height when the cosine function is equal to -6. This happens when 2πt / 16 = π / 2, or t = 4 seconds.

Here is a graph of the function:

[Image of a cosine function with an amplitude of 6 feet and a period of 16 seconds. The graph reaches its lowest point at t = 4 seconds.]

I hope this helps! Let me know if you have any other questions.

Step-by-step explanation:

Hello !

Answer:

[tex] \boxed{h = 6}[/tex]

Step-by-step explanation:

He has grown :

We also know that in total, he has grown 11 vegetables.

We will have to solve an equation !

[tex]h + 2h + 5 = 11[/tex]

[tex] \iff3h + 5 = 11[/tex]

We want to isolate h.

[tex]3h + 5 - 5= 11 - 5 \\ \iff3h = 6 \\ \iff \frac{3h}{3} = \frac{6}{3} = 2[/tex]

The value of h is 2.

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Answer:

35

Step-by-step explanation:

The median is the measurement that is the same for Charles and Jermod.

In a dot plot, the median represents the middle value when the data points are arranged in ascending or descending order.

From the given dot plots, we can see that both Charles and Jermod have their median values at 35 minutes per day.

Therefore, the median is the measurement that is the same for Charles and Jermod.

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The vertex and the range of the quadratic function in this problem are given as follows:

The quadratic function in the context of this problem is defined as follows:

y = x² + 4x  + 5.

The coefficients are given as follows:

a = 1, b = 4, c = 5.

Hence the x-coordinate of the vertex is given as follows:

x = -b/2a

x = -4/2

x = -2.

Then the y-coordinate of the vertex is given as follows:

y = (-2)² + 4(-2) + 5

y = 1.

As a > 0, the vertex (-2, 1) is the minimum value of the function, hence the range is given as follows:

1 ≤ y < ∞.

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The integral of the given function is determined as (4²ˣ) / ln4    +  C.

option B.

The integral of the function is calculated by applying exponent rule of integration as follows;

The given integration ∫ 4²ˣ4⁻⁴

The given integral function is simplified as follows;

4²ˣ4⁻⁴ = ( 4² )ˣ 4⁻⁴ = 16ˣ4⁻⁴

The simplified expression is integrated as follows;

∫16ˣ4⁻⁴ = [ 16ˣ / ln 4 ] + C

where;

The integral of the given function is determined as;

∫ 4²ˣ4⁻⁴ = [ 16ˣ / ln 4 ] + C = (4²ˣ) / ln4    +  C

so option B is the correct answer.

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The Chillan earthquake had an intensity about 5 times greater than the Taiwan earthquake.

The Richter scale is logarithmic, meaning that a difference of 1 on the scale corresponds to a tenfold difference in the amplitude of the seismic waves. Therefore, we can calculate the difference in intensity between the two earthquakes using the formula:

difference in intensity

= 1[tex]0^{((magnitude of earthquake 1) - (magnitude of earthquake 2))[/tex]

For the Chillan earthquake:

magnitude = 8.3

difference in magnitude = 8.3 - 7.6 = 0.7

For the Taiwan earthquake:

magnitude = 7.6

Plugging these values into the formula, we get:

difference in intensity = 10^(0.7) = 5.01187

This means that the Chillan earthquake had an intensity about 5 times greater than the Taiwan earthquake.

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The second number line has a point that is equivalent to point P = 32.

Given information:

There are four choices of number lines given.

The first line has an open dot at 32, the second line has a closed dot at 32, the third line has a closed dot, and moving towards greater than 32, the third line has a closed dot at 31.

And we have to find at P = 32.

The first line has an open dot at 32, indicating that 32 is not included in the set of numbers on the line. The second line has a closed dot at 32, indicating that 32 is included in the set of numbers on the line. Therefore, the second line has a point that is equivalent to point P = 32.

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The complete question:

Which number line has a point that is equivalent to point P = 32?

The first line has an open dot at 32, the second line has a closed dot at 32, the third line has a closed dot, and moving towards greater than 32, the third line has a closed dot at 31.

The final coordinates of the transformed figure are A"(-12,-8), B"(0,-16) and C"(-16,-16)

To translate the figure by <6,4>:

Add 6 to the x-coordinate of each point to get the new x-coordinate

Add 4 to the y-coordinate of each point to get the new y-coordinate

New coordinates:

A'(-3+6,-2+4) = (3,2)

C'(-4+6,-4+4) = (2,0)

B'(0+6,-4+4) = (6,0)

To dilate the figure K=4:

The coordinates x and y are multiplied by 4.

New coordinates:

A"(-34,-24) = (-12,-8)

C"(-44,-44) = (-16,-16)

B"(04,-44) = (0,-16)

Hence, the final coordinates of the transformed figure are A"(-12,-8), B"(0,-16) and C"(-16,-16)

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The federal government spends slightly more on defense than Social Security.

We have,

The federal government spends different amounts of money on different programs and services every year, so there is no fixed answer to this question.

However, based on recent data, we can make some general statements about federal spending on defense and Social Security.

In the United States, defense spending typically makes up a significant portion of the federal budget, usually around 15-20%.

Social Security spending is also a major component of the federal budget, making up about 24% of total federal spending in recent years.

Thus,

Based on these figures, we can say that the federal government spends slightly more on Social Security than on defense.

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The time needed to pay the compound interest of Rs 6,305 is given as follows:

3 years.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters for this problem are given as follows:

P = 40000, A(t) = 40000 + 6305 = 46305, n = 1, r = 0.05.

Hence the time is obtained as follows:

[tex]40000(1.05)^t = 46305[/tex]

[tex](1.05)^t = \frac{46305}{40000}[/tex]

[tex]t = \log{\left(\frac{46305}{40000}\right)}{\log{1.05}}[/tex]

t = 3 years.

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Upon performing polynomial long division, we find that the width is (x - 7). So, the dimensions of the rectangle are length (x - 5) and width (x - 7).

Given that the area of a rectangle is equal to its length multiplied by its width, we can set up the equation as follows:

Area = Length × Width

In this case, the area is given as (x^2 - 12x + 35), and the length is (x - 5). We are asked to find the width.

So, we can rewrite the equation as:

(x^2 - 12x + 35) = (x - 5) × Width

To find the width, we need to divide the area by the length:

Width = (x^2 - 12x + 35) ÷ (x - 5)

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Answer:

C

Step-by-step explanation:

x=base angle

2x+130=180

2x=50

x=25

base angle = 25

Answer:

The scale of the drawing is 1 cm to 90 m. This means that every 1 cm on the drawing represents 90 m in real life. The length of the field is 450 m, so the length of the drawing will be 450 m / 90 m = 5 cm.

Therefore, the length of the dam drawing is 5 cm.

Step-by-step explanation:

The Absolute value function takes the same value for positive and negative values of its argument.

The graph of the absolute value function y = -|x + 6|, we first need to understand the properties of an absolute value function.

The absolute value of a number is its distance from 0 on the number line. Thus, the absolute value function |x| will always return a non-negative value, regardless of the sign of x. When the absolute value function is multiplied by -1, as in -|x|, the function reflects the graph over the x-axis and makes it negative.

Applying these principles to the given function y = -|x + 6|, we can start by identifying the vertex, which is the point where the absolute value term inside the function equals 0. In this case, the vertex is at x = -6.

Next, we can plot some points to get a sense of the shape of the graph. We can choose values of x that are greater than or less than -6, and use the fact that the function is negative to find the corresponding y-values. For example:

- When x = -7, y = -|(-7) + 6| = -1

- When x = -5, y = -|(-5) + 6| = -1

We can see that the graph has a "V" shape, with the vertex at (-6,0). The line of symmetry is the vertical line passing through the vertex, which is the equation x = -6. The graph approaches the x-axis on either side of the vertex, but never touches it. The negative sign in front of the absolute value term causes the graph to be reflected over the x-axis.

since the absolute value function takes the same value for positive and negative values of its argument.

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Spinning a spinner with four equal sized sections and assigning a novel to each section.

Spinning a spinner with four equal-sized sections and assigning a novel to each section is the correct option to stimulate randomly choosing a novel. The spinner can be designed with each section representing one of the four novels

The spinner is spun to randomly select one of the novels. Since each section is equal-sized, each novel has an equal probability of being selected.

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The complete question Members of a book club have 4 different novels to choose from each time they meet. Which of the following could be used to stimulate randomly choosing a novel?

(a) Placing 6 marbles in a bag (3 red and 3 blue) and drawing one ball from the bag

(b) spinning a spinner with four equal sized sections and assigning a novel to each section

(c)Tossing a fair coin, where each of the outcomes represents a novel

(d) Rolling a number cube labeled 1-6, where each book is represented by 2 numbers

Answer: 62.8

Step-by-step explanation:

20x3.14=62.8

Answer:

#4. 62.83

#5. 314.16

Step-by-step explanation: READ THIS IS IF YOU ARE HAVING TROUBLE LIKE I DID!! Anytime you are trying to find the circumference of a circle, you multiply the radius (the 20 ft part) by 3.14, 3.14 is a number known as Pi. Number five should be 314.16, you take the radius and put it to the power of Pi. Use this formula for the area: 3.14 X half of the length of the circle (radius) then put it to the power of 2. I hope this helped.

Rule for the first transformation : (x, y) → (2.5x, 2.5y)

Rule for the second transformation : (x, y) → [(x - 4), (y + 1)]

Transformations of a figure:

If a figure is dilated by a scale factor 'k', rule defining the dilation will be,       If a point (x, y) is shifted 'a' units left and 'b' units upwards,

         Rule defining the translation will be,

         (x, y) → (x - a, y + b)

we have,

Radius of image circle = 2.5 units

Radius of pre image circle = 1 unit

Scale factor 'k' = 2.5/1

                        = 2.5

Since, image circle (blue) is shifted to the left and upwards, rule for the translation will be,

(x, y) → [(x - a), (y + b)]

Following the rule, coordinates of the image circle will be,

(0, 0) → [(0 - a), (0 + b)]

        → (-a, b)  

Coordinates of the image circle from the picture → (-4, 1)

Therefore, -a = -4 ⇒ a = 4

                  b = 1

         First transformation: (x, y) → (2.5x, 2.5y)

         Second transformation : (x, y) → [(x - 4), (y + 1)]

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complete question:

Write an algebraic description for the sequence of transformations that will map the preimage onto the image, to show that the two circles are similar.

Answer:

[tex]\frac{8}{52}[/tex]

Step-by-step explanation:

given

[tex]\frac{2}{13}[/tex]

to obtain a denominator of 52 multiply the original denominator of 13 by 4 , that is 13 × 4 = 52

the numerator must also be multiplied by 4, then

[tex]\frac{2}{13}[/tex] = [tex]\frac{2(4)}{13(4)}[/tex] = [tex]\frac{8}{52}[/tex]

Answer:

x = -1, -7

Step-by-step explanation:

(2x + 14) (x + 1) = 0

2x + 14 = 0, 2x = -14, x = -7.

x + 1 = 0, x = -1.

The result of the matrix 4|D| -3|B|

[tex]\left[\begin{array}{ccccc}31&6&36&-14&-57\\-19&-27&-18&18&27\\47&14&-1&-40&9\\10&12&-19&-15&-58\\-14&-23&10&-8&19\end{array}\right][/tex]

To solve the 5 x 5 matrix, we have to multiply and subtract the matrix this way;

4 x 7 - 3 x -1 = 31

4 x -6 - 3 x-10 = 6

4 x 3 - 3 x-8 = 36

4 x -8 - 3 x-6 = -14

4 x -9 - 3 x 7 = -57

Therefore 31, 6, 36, -14, and -57 makes the first role of the matrix 4|D| - 3|B|

4 x 2 - 3 x 9 = -19

4 x -9 - 3 x -3 = -27

4 x -6 - 3 x -2 = -18

4 x 6 - 3 x 2 = 18

4 x 9 - 3 x 3 = 27

Therefore -19, -27, -18, 18, and 27 make the second role of the matrix 4|D| - 3|B|

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The reduced row echelon form of the matrix is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&8\\0&1&0&-2\\0&0&1&-6\end{array}\right][/tex]

The row echelon form of a matrix contains the entire matrix except the last column in the format of an identity matrix, with the last column containing the solution to the system of equations represented by the matrix.

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{cccc}-1&5&-3&6\\0&3&6&-42\\0&-6&-1&18\end{array}\right][/tex]

First we want a value of 1 at line 1, column 1, hence we multiply the first line by -1, that is:

R1 -> -R1.

Hence:

[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&3&6&-42\\0&-6&-1&18\end{array}\right][/tex]

Then we want a value of 1 at line 2 column 2, thus:

R2 -> R2/3.

Hence:

[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&1&2&-14\\0&-6&-1&18\end{array}\right][/tex]

Then we want a value of 0 at line 3, column 2, hence:

L3 -> L3 + 6L2

[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&1&2&-14\\0&0&11&-66\end{array}\right][/tex]

Then the solution to the system of equations is given as follows:

Hence the row echelon form of the matrix is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&8\\0&1&0&-2\\0&0&1&-6\end{array}\right][/tex]

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Answer:

2x

Step-by-step explanation:

hope this helps

Answer:

Subtract the same degrees only.

Step-by-step explanation:

When subtracting polynomials, you can only subtract variables from those with the same degree (like term).

For example:

[tex]x^{2} -x^ = 0[/tex]

You can't subtract as the first x has a degree (exponent) of 2 and the second x has a degree of 1.

However, for example:

[tex]3x^{4} -1x^{4}=0[/tex]

You can subtract this to be [tex]2x^{4}[/tex] as both variables have a degree of 4.

Step-by-step explanation:

5.8 %  means 94.2 % remains after 24 hours    .5 is 1/2 :

.5 = (.942)^n     where n = the number of 24 hour periods (days)

LOG (.5) / LOG(.942) = n = 11.60 days    <==== this is the half life

Answer:

$839.20

Step-by-step explanation:

To find the finance charge, we need to first calculate the total amount financed, which is the price of the snow thrower minus the down payment.

The down payment is 20% of $1,501, which is:

0.20 x $1,501 = $300.20

So the total amount financed is:

$1,501 - $300.20 = $1,200.80

The total amount of the 12 monthly payments is:

12 x $170 = $2,040

The finance charge is the difference between the total amount of the payments and the amount financed:

$2,040 - $1,200.80 = $839.20

Therefore, the finance charge is $839.20.

The solution to the inequality |x − 2| ≥ 5 is x ≤ -3 or x ≥ 7.

We have,

To solve the inequality |x − 2| ≥ 5, we need to consider two cases:

Case 1:

x - 2 is non-negative (i.e., x - 2 ≥ 0)

In this case, the absolute value simplifies to x - 2, so we have:

x - 2 ≥ 5

Adding 2 to both sides, we get:

x ≥ 7

So any value of x that is greater than or equal to 7 satisfies the inequality.

Case 2:

x - 2 is negative (i.e., x - 2 < 0)

In this case, the absolute value simplifies to -(x - 2), so we have:

-(x - 2) ≥ 5

Multiplying both sides by -1, we get:

x - 2 ≤ -5

Adding 2 to both sides, we get:

x ≤ -3

So any value of x that is less than or equal to -3 satisfies the inequality.

Therefore,

The solution to the inequality |x − 2| ≥ 5 is x ≤ -3 or x ≥ 7.

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Answer:

Step-by-step explanation:

4 | x - 6 | ≤ 16

| x - 6 | ≤ 4

-4 ≤ x - 6 ≤ 4

-4 + 6 ≤ x ≤ 4 + 6

2 ≤ x ≤ 10