Write the expression in radical form.
x 5/4

Answer:

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If the point (-9,2) is a solution to a linear equation, the point (2,-9) will be a solution to it's inverse is false.

If the point (-9,2) is a solution to a linear equation, it means that when you substitute x = -9 and y = 2 into the equation, it satisfies the equation and makes it true.

However, the point (2,-9) will not necessarily be a solution to the inverse of that equation.

To find the inverse of a linear equation, you need to switch the x and y variables and solve for the new y.

So if the original equation is in the form y = mx + b, the inverse will be in the form x = my + b.

Therefore, the point (2,-9) will only be a solution to the inverse equation if substituting x = 2 and y = -9 into the inverse equation makes it true.

It cannot be determined just based on the fact that (-9,2) is a solution to the original equation.

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The total weight of Rice that Mark buys is given as follows:

2.5 pounds.

The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.

The weight of each bag is given as follows:

5/8 pounds = 0.625 pounds.

The number of bags is given as follows:

4 bags.

Hence the total weight of Rice that Mark buys is given as follows:

4 x 0.625 = 2.5 pounds.

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Angle D measures 81 degrees in quadrilateral ABCD.

We have,

To find the measure of angle D in quadrilateral ABCD, we can use the fact that the sum of the angles in any quadrilateral is always 360 degrees.

Let's denote angle D as x. Given that angle A is 72 degrees, angle B is 94 degrees, and angle C is 113 degrees, we can set up the equation:

72 + 94 + 113 + x = 360

Combining the known angle measures:

279 + x = 360

To solve for x, we can subtract 279 from both sides of the equation:

x = 360 - 279

x = 81

Therefore,

Angle D measures 81 degrees in quadrilateral ABCD.

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As per the given details, the value of ff.ds over the region V bounded by the planes x = 0, y = 0, z = 0, z = 4, and the surface of the cylinder x² + y² = 9 in the first octant, where F = xî + xyj + 2k, is 81π.

The divergence theorem relates a flux fundamental across a closed floor S to a triple crucial over strong E enclosed by way of the surface.

It states that for a vector field F and a closed floor S that encloses a solid area E, the outward flux of F across S is equal to the triple necessary of the divergence of F over E.

Mathematically, the divergence theorem can be written as:

∫∫ F · dS = ∭ div(F) dV

To examine ff.Ds over the vicinity V bounded by using the planes x = zero, y = zero, z = zero, z = 4, and the floor of the cylinder x² + y² = 9 within the first octant, in which F = xî + xyj + 2k, we can use the divergence theorem. The first step is to locate the divergence of F:

div(F) = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z

= 1 + x

Next, we want to discover the volume enclosed via the surface. The cylinder x² + y² = 9 inside the first octant is a round cylinder with radius 3 and top 4. Therefore, the volume enclosed with the aid of the floor is:

V = ∫∫R (4 - z) dA

= ∫0^3 ∫0^(2π) (4 - z) r dr dθ

= 18π

So,

∫∫S F · dS = ∭V div(F) dV

= ∭V (1 + x) dV

= ∫0^4 ∫0^3 ∫0^(2π) (1 + x) r dθ dz dr

= 81π

Therefore, the value of ff.Ds over the place V bounded through the planes x = 0, y = 0, z = zero, z = four, and the surface of the cylinder x² + y² = 9 inside the first octant, where F = xî + xyj + 2k, is 81π.

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Answer:

(x - 8)² + (y - 5)² = 400

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r the radius

the radius is the distance from the centre to a point on the circle

use the distance formula to calculate r

r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (8, 5 ) and (x₂, y₂ ) = (- 4, 21 )

r = [tex]\sqrt{(-4-8)^2+(21-5)^2}[/tex]

 = [tex]\sqrt{(-12)^2+16^2}[/tex]

 = [tex]\sqrt{144+256}[/tex]

 = [tex]\sqrt{400}[/tex]

 = 20

then with (h, k ) = (8, 5 ) and r = 20, the equation of the circle is

(x - 8)² + (y - 5)² = 20² , that is

(x - 8)² + (y - 5)² = 400

Answer:

[tex](x-8)^2+(y-5)^2=400[/tex]

Step-by-step explanation:

The standard equation of a circle is:

[tex]\boxed{(x-h)^2+(y-k)^2=r^2}[/tex]

where:

The given center of the circle is (8, 5).

To find the value of r², substitute the circle and the given point (-4, 21) into the equation and solve for r².

[tex]\begin{aligned}(-4-8)^2+(21-5)^2&=r^2\\(-12)^2+(16)^2&=r^2\\144+256&=r^2\\400&=r^2\end{aligned}[/tex]

Finally, substitute the center and r² into the formula to create an equation of the circle with the given parameters:

[tex]\boxed{(x-8)^2+(y-5)^2=400}[/tex]

The value of [tex]\(r\)[/tex] is [tex]\(r = -2\)[/tex], according to the given cartesian points.

To find the value of [tex]\(r\)[/tex], we can use the slope-intercept form of a linear equation, [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] represents the slope of the line. Given that the line has a slope of [tex]\(-10\)[/tex] and passes through the cartesian points [tex]\((4, 8)\)[/tex]and \[tex]((5, r)\)[/tex], we can calculate the slope as follows:

[tex]\[m = \frac{{y_2 - y_1}}{{x_2 - x_1}} = \frac{{r - 8}}{{5 - 4}} = r - 8\][/tex]

Since the slope is [tex]\(-10\)[/tex], we can equate it to the calculated slope and solve for [tex]\(r\)[/tex]:

[tex]\[-10 = r - 8\][/tex]

Simplifying the equation, we have:

[tex]\[r - 8 = -10\][/tex]

Adding [tex]\(8\)[/tex] to both sides, we get:

[tex]\[r = -10 + 8\][/tex]

Therefore, the value of [tex]\(r\)[/tex] is [tex]\(r = -2\)[/tex].

In conclusion, the value of [tex]\(r\)[/tex] in the line with a slope of [tex]-10[/tex] passing through the points [tex](4, 8)[/tex] and [tex](5, \(r\))[/tex] is [tex]\(r = -2\)[/tex]. This satisfies the equation and represents the y-coordinate of the second point. This value of [tex]r[/tex] indicates that the second point lies on the line with a slope of -[tex]10[/tex] passing through ([tex]4,8[/tex]).

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Car A is 2 times Faster than Car B during the first hour.

The graph of Car A is a straight line, indicating that it is traveling at a constant speed.

The graph shows that Car A is traveling 100 miles in 2 hour .The table of Car B shows that it travels 50 miles in 1 hour, 100 miles in 2 hours, and 150 miles in 3 hours. Thus, the rate of Car B is increasing, as it travels at a faster speed during each hour compared to the previous hour.To find the rate of each car, we need to divide the distance by the time. For Car A, rate = distance ÷ time = 100 miles ÷ 2 hours = 50 miles per hour.

For Car B, we can find the average rate for each hour by dividing the distance traveled during that hour by the time. Thus, the rates are: First hour: 50 miles per hour Second hour: 50 miles ÷ 1 hour = 50 miles per hour Third hour: 50 miles ÷ 1 hour = 50 miles per hour By comparing the rates, we see that both cars are traveling at the same speed during the second and third hours. However, during the first hour, Car A is traveling faster than Car B.

Thus, Car A has the greatest speed.To determine how many times faster Car A is compared to Car B during the first hour, we can divide their rates. The rate of Car A is 50 miles per hour, while the rate of Car B is 50 miles per hour. Therefore, Car A is traveling at the same speed as Car B during the second and third hours. During the first hour, Car A is traveling twice as fast as Car B. Thus, Car A is 2 times faster than Car B during the first hour.

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Note that the roots of the equation Unequal and rational (Option D)

The roots of the equation   (x - 3)² = 4 can be found by taking the square root of both sidesof the equation.

x - 3 = ±√4

⇒ x - 3 = ±2

Solve for x

For the positive square root.

x - 3 = 2

x = 2 + 3

x = 5

For the negative square root.

x - 3 = -2

x = -2 + 3

x = 1

Since the equation has two roots, x = 5 and x = 1. These roots are unequal and rational. (Option D)

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Full Question:

Although part of your question is missing, you might be referring to this full question:

The roots of the equation (x - 3)² = 4 are

A.Unequal and irrational.

B.Equal and rational.

C.  Equal and irrational.

D.  Unequal and rational.

Answer:

 (b)  f(x) = -1/x⁹ and g(x) = -8x +4

  (d)  f(x) = x⁹ and g(x) = -1/(-8x +4) . . . . . alternate solution

Step-by-step explanation:

You want to decompose h(x) = -1/(-8x +4)⁹ into f(x) and g(x) such that h(x) = f(g(x)).

The composition h(x) = f(g(x)) means that the function g(x) will replace x in the definition of f(x).

It is often convenient to look at the order of operations when asked to decompose a function like this. Here, the parenthetical expression (-8x+4) is raised to the 9th power and its opposite reciprocal is found. This suggests that f(x) can be a function that finds the opposite reciprocal of a 9th power,  matching choice B. Thus, a reasonable choice is ...

  (b)  f(x) = -1/x⁹ and g(x) = -8x +4

We note that the reciprocal of a 9th power is also the 9th power of a reciprocal. A negative sign is preserved by the odd power. This means that another reasonable choice for the decomposition is ...

  (d)  f(x) = x⁹ and g(x) = -1/(-8x +4)

__

Additional comment

We list choice B first because that one is probably the one you're supposed to claim as the answer. However, this question has two correct decompositions among those listed. You may want to discuss this with your teacher.

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The equation of the line parallel to 2x + 4y = 1 and passing through the point (1, 1) is y = (-1/2)x + 3/2.

For finding the equation of a line parallel to the given line and passing through the point (1, 1), we need to determine the slope of the given line and use it to construct the equation.

The given line has the equation 2x + 4y = 1. To determine its slope, we can rewrite the equation in slope-intercept form (y = mx + b), where m represents the slope. Rearranging the equation, we have:

4y = -2x + 1

y = (-2/4)x + (1/4)

y = (-1/2)x + 1/4

Comparing this equation to the slope-intercept form (y = mx + b), we can see that the slope of the given line is -1/2.

The line we're trying to find is parallel to this line, it will also have a slope of -1/2. We can now use the point-slope form of a line to construct the equation. The point-slope form is given by:

y - y₁ = m(x - x₁)where (x₁, y₁) represents the coordinates of the point through which the line passes, and m is the slope.

Substituting the values of (x₁, y₁) = (1, 1) and m = -1/2 into the point-slope form, we get:

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

Expanding and simplifying the equation:

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

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

y = (-1/2)x + 3/2

The equation of the line parallel to 2x + 4y = 1 and passing through the point (1, 1) is y = (-1/2)x + 3/2.

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The correlation coefficient for each scatter plot displayed is

The correlation coefficient gives the strength and direction of relationship between variables using values between -1 and 1 .

plot A has a very perfect association, hence the value 0.999 , Plot D also depicts a strong association with a well defined trendline . For plot B, the slope is negative, hence, the negative value in the coefficient.

Therefore, the type of correlation can be visually inferred from the graph.

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The sum of angles ∠D and ∠F in quadrilateral DEFG, inscribed in circle P, is equal to 180∘.

To prove that m∠D + m∠F = 180∘, we can use the property of angles inscribed in a circle.

In a circle, an inscribed angle is equal to half the measure of its intercepted arc. Therefore, if we can show that arc DE + arc FG = 360∘, we can conclude that m∠D + m∠F = 180∘.

Let's start the proof:

1. Quadrilateral DEFG is inscribed in circle P. This means that all the vertices of the quadrilateral lie on the circumference of the circle.

2. Let's consider arc DE and arc FG. These arcs are intercepted by angles ∠D and ∠F, respectively.

3. By the property of angles inscribed in a circle, we know that the measure of an inscribed angle is equal to half the measure of its intercepted arc.

4. Therefore, m∠D = 1/2(arc DE) and m∠F = 1/2(arc FG).

5. We want to prove that m∠D + m∠F = 180∘. This is equivalent to showing that 1/2(arc DE) + 1/2(arc FG) = 180∘.

6. Combining the fractions, we have 1/2(arc DE + arc FG) = 180∘.

7. Now, we need to show that arc DE + arc FG = 360∘.

8. Since quadrilateral DEFG is inscribed in circle P, the sum of the measures of all the arcs intercepted by the sides of the quadrilateral is equal to 360∘.

9. This means that arc DE + arc EF + arc FG + arc GD = 360∘.

10. However, we can observe that arc EF and arc GD are opposite sides of the same chord, so they have equal measures. Therefore, arc EF = arc GD.

11. Substituting arc GD with arc EF in the equation from step 9, we have arc DE + arc EF + arc FG + arc EF = 360∘.

12. Simplifying the equation, we get 2(arc DE + arc EF + arc FG) = 360∘.

13. Dividing both sides by 2, we have arc DE + arc EF + arc FG = 180∘.

14. Comparing this result with step 7, we can conclude that arc DE + arc FG = 180∘.

15. Finally, going back to our initial goal, we can now substitute arc DE + arc FG with 180∘ in the equation from step 6: 1/2(180∘) = 180∘.

16. Simplifying, we have 90∘ = 180∘, which is a true statement.

17. Therefore, we have proven that m∠D + m∠F = 180∘.

Thus, we have successfully proved that the sum of angles ∠D and ∠F in quadrilateral DEFG, inscribed in circle P, is equal to 180∘.

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The volume of the solid obtained by rotating the region enclosed by the curves [tex]y=\sqrt{x^3}[/tex] and [tex]y = x^2[/tex] about the y-axis is [tex]\pi/14[/tex] . option B

To determine the solid's volume after rotating the area bounded by curves

[tex]y = \sqrt{x^3}[/tex] and [tex]y = x^2[/tex]

We can apply the cylindrical shell approach to the y-axis.

First, let's locate the spots where the two curves intersect:

[tex]\sqrt{x^3} = x^2[/tex]

Squaring both sides:

[tex]x^3 = x^4[/tex]

Rearranging:

[tex]x^4 - x^3 = 0[/tex]

Factorizing [tex]x^3(x - 1) = 0[/tex]

Therefore, the locations of intersection are x = 0 and x = 1.

The integral for the solid's volume must then be set up using cylindrical shells. The following formula determines the volume of a cylindrical shell:

V is equal to 2[a, b] x * h(x). dx where a and b are the integration limits, x is the shell's radius, and h(x) is the height of the shell.

The radius of the shell in this instance is x, while the height of the shell is the ratio of the two curves: [tex]h(x) = \sqrt{x^3} - x^2.[/tex]

Since those are the locations of intersection, the range of integration's bounds is 0 to 1.

The integral then becomes:

∫[tex]V = 2\pi [0, 1] x * (\sqrt{x^3} - x^2) dx[/tex]

We can simplify the formula inside the integral in order to evaluate it:

V = 2π ∫[0, 1] (x^(5/2) - x^3) dx

We can integrate each word by applying the power rule for integration as follows:

[tex]V = 2\pi [(2/7)x^{(7/2)} - (1/4)x^{4}] |[0, 1][/tex]

Calculating the limits of the definite integral:

[tex]V = 2\pi [(2/7)(1^{(7/2))} - (1/4)(1^{4)}] - 2\pi [(2/7)(0^{(7/2})) - (1/4)(0^{4)}][/tex]

Simplifying further:

V = 2π [(2/7) - (1/4)]

V = 2π (8/28 - 7/28)

V = 2π/28

Simplifying the fraction:

V = π/14 ,Therefore, the correct answer is option B.

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Uh I can't explain well so heres the answer

247.75

Answer:kkkkkkkkkkkkkkkkkkkkkkkkkkk mean ok 26 times

The simplified expression is y.

To solve the expression [tex](x^2 y^5 / x^3 y^8) \times (x^5 y^6 / x^4 y^2)[/tex], we can simplify and perform the necessary operation

Let's break it down step by step:

Step 1: Simplify the expression inside the parentheses.

[tex](x^2 y^5 / x^3 y^8) \times (x^5 y^6 / x^4 y^2)[/tex]can be simplified as follows:

= [tex](x^{(2-3)} y^{(5-8)}) \times (x^{(5-4) }y^{(6-2)})[/tex]

= [tex](x^{(-1)} y^{(-3)}) \times (x^1 y^4)[/tex]

= [tex](1/x y^{(-3)}) \times (x y^4)[/tex]

=[tex]x^0 \times y^{(-3+4)[/tex]

= [tex]1 \times y^1[/tex]

= y

Therefore, the simplified expression is y.

The explanation is as follows:

We can simplify the given expression by applying the laws of exponents. In this case, when dividing two terms with the same base (x or y), we subtract their exponents. Additionally, any term raised to the power of 0 is equal to 1.

After simplifying the expression, we find that the answer is y. This means that the original expression[tex](x^2 y^5 / x^3 y^8) \times (x^5 y^6 / x^4 y^2)[/tex]simplifies to just y.

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Answer:

$44

Step-by-step explanation:

Hello!

It said that 7 cameras cost $308, right?

If each camera costs the same, it means that 7 cameras with the same value equal $308.
If we use this in an equation, and if x is a variable we want to solve, it would be:

7x = 308.

If 7x = 308, it would be

308/7 =

44.

So, $44 is the answer.

The height of the monument is 30 meters.

We have,

Let's assume the height of the monument is "h" meters.

From the top of the building, the angle of elevation to the top of the monument is equal to the angle of depression to the foot of the monument. This forms a right triangle with the building, the monument, and the ground.

In this triangle, the opposite side of the angle of elevation is the height of the building, which is given as 30 meters.

The opposite side of the angle of depression is the height of the monument, which is "h" meters.

Since the angles of elevation and depression are equal, the triangle is an isosceles triangle.

Therefore, the opposite sides are equal in length.

By setting up the equation:

h = 30

Thus,

The height of the monument is 30 meters.

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The value on the interval [0, 2π) where f(θ) = g(θ) is 3π/2.

To find the value(s) on the interval [0, 2π) where f(θ) = g(θ), we need to set the two functions equal to each other and solve for θ.

Setting f(θ) = g(θ), we have:

4sin(θ) + 3 = cos(2θ)

Now, we can solve this equation. Let's break it down step by step:

Rewrite cos(2θ) using the double-angle identity: cos(2θ) = 1 - 2sin^2(θ)

The equation becomes: 4sin(θ) + 3 = 1 - 2sin^2(θ)

Rearrange the equation:

2sin^2(θ) + 4sin(θ) + 2 = 0

Divide the entire equation by 2:

sin^2(θ) + 2sin(θ) + 1 = 0

Factorize the equation:

(sin(θ) + 1)^2 = 0

Solve for sin(θ):

sin(θ) = -1

The value of sin(θ) is -1 at θ = 3π/2.

As a result, 3π/2 is the value on the interval [0, 2π) where f(θ) = g(θ).

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To find the area of a parallelogram, you need to multiply the base by the height. In this case, the given dimensions are 60ft (base) and 67ft (height), and you need to subtract 52ft from the height.

New height = 67ft - 52ft = 15ft

Area of the parallelogram = Base * Height = 60ft * 15ft = 900 square feet.

Therefore, the area of the parallelogram is 900 square feet.

~~~Harsha~~~

Kamryn would save $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

To determine the amount of interest Kamryn will save by raising her credit score from 665 to 680, we need to compare the interest rates associated with each credit score range.

According to the given information, a credit score of 665 falls within the range of 580-669, where the corresponding simple interest rate is 10.358%.

Let's calculate the interest Kamryn would pay on a loan of $13,250.00 at an interest rate of 10.358%.

Interest = Principal * Rate

= $13,250.00 * 0.10358

≈ $1,370.56

Therefore, if Kamryn were to borrow $13,250.00 with a credit score of 665, she would pay approximately $1,370.56 in interest.

Now, let's consider the scenario where Kamryn raises her credit score to 680. A credit score of 680 falls within the range of 670-739, where the corresponding simple interest rate is 9.132%.

Calculating the interest with a credit score of 680:

Interest = Principal * Rate

= $13,250.00 * 0.09132

≈ $1,210.57

Thus, if Kamryn were able to raise her credit score from 665 to 680, she would save approximately $1,370.56 - $1,210.57 = $159.99 in interest.

Therefore, Kamryn would save approximately $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

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Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

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Answer:

There would be 54,307,200 people

Step-by-step explanation:

a. Coefficient matrix A:

A = [[2, 3, 1],

[3, 3, 1],

[2, 4, 1]]

Augmented matrix [AL]:

[A|b] = [[2, 3, 1, -1],

[3, 3, 1, 1],

[2, 4, 1, -2]]

b. The resulting matrix will be [I|A^(-1)], where A^(-1) is the inverse of the coefficient matrix A.

c. The resulting vector [x1, x2, x3] represents the solution set of the system of linear equations.

a. The coefficient matrix A and the augmented matrix [A|b] for the given system of linear equations are as follows:

Coefficient matrix A:

A = [[2, 3, 1],

[3, 3, 1],

[2, 4, 1]]

Augmented matrix [AL]:

[A|b] = [[2, 3, 1, -1],

[3, 3, 1, 1],

[2, 4, 1, -2]]

b. To find the inverse of the coefficient matrix A using the Gauss-Jordan method, we perform elementary row operations until A is transformed into an identity matrix [tex][I|A^{(-1)][/tex].

Gauss-Jordan elimination steps:

Step 1: Perform row operations to convert the first column of A to [1, 0, 0]:

R1' = R1/2

R2' = R2 - (3/2)R1

R3' = R3 - R1

Step 2: Perform row operations to convert the second column of A to [0, 1, 0]:

R2'' = R2''/3

R1'' = R1'' - (3/2)R2''

R3'' = R3'' - (3/2)R2''

Step 3: Perform row operations to convert the third column of A to [0, 0, 1]:

R3''' = R3'''/2

R1''' = R1''' - R3'''

R2''' = R2''' - R3'''

The resulting matrix will be[tex][I|A^{(-1)][/tex], where [tex]A^{(-1)[/tex] is the inverse of the coefficient matrix A.

c. Once we have the inverse matrix A^(-1), we can find the solution set of the system of linear equations by multiplying A^(-1) with the augmented matrix [A|b]:

[A|b] [tex]\times[/tex] [tex]A^{(-1)[/tex] = [x1, x2, x3]

The resulting vector [x1, x2, x3] represents the solution set of the system of linear equations.

Note: To provide the numerical values for the inverse matrix [tex]A^{(-1)[/tex] and the solution set, the calculations need to be performed manually using the given coefficients of the equations.

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The Function  f(g(x)) = g(f(x)) = x + 8.

The functions are: f(x) = x + 4 and g(x) = x + 4. We can find f(g(x)) by substituting g(x) in place of x in f(x).

f(g(x)) = f(x + 4) = (x + 4) + 4 = x + 8

Similarly, we can find g(f(x)) by substituting f(x) in place of x in g(x).g(f(x)) = g(x + 4) = (x + 4) + 4 = x + 8

Thus, we can see that f(g(x)) and g(f(x)) are equal to each other,

which is x + 8.

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The length of segment BC is approximately 10.92 units.

To find the length of segment BC, we can use the properties of a tangent to a circle.

In a circle, a tangent is perpendicular to the radius drawn to the point of tangency. Therefore, triangle ABC is a right triangle with AB as the hypotenuse.

Given that the radius of the circle is 5 units and the tangent AB has a length of 12 units, we can apply the Pythagorean theorem to find the length of segment BC.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AB) is equal to the sum of the squares of the lengths of the other two sides (BC and AC).

Applying the theorem to triangle ABC:

AB^2 = BC^2 + AC^2.

Substituting the given values:

12^2 = BC^2 + 5^2.

144 = BC^2 + 25.

Rearranging the equation:

BC^2 = 144 - 25.

BC^2 = 119.

Taking the square root of both sides:

BC = √119.

Therefore, the length of segment BC is approximately equal to √119 units.

Since it's not possible to represent the square root of 119 exactly as a whole number or fraction, we can leave the answer as √119 or approximate it as a decimal. The decimal approximation for √119 is approximately 10.92.

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The median of the data set are as follows;

Boys: 45. Girls: 110.

The range of the data set are as follows;

Boys: 45. Girls: 110.

The median and range of girls is greater than the median and range of boys.

In Mathematics, a median refers to the middle number (center) of a sorted data set, which is when the data set has either been arranged in a descending order, from the greatest to least or in an ascending order, from the least to greatest.

Based on the information provided in the line plot above, we would determine the median for the data set as follows;

Median of boys = [5th + 6th]/2.

Median of boys = [90 + 90]/2.

Median of boys = 45.

Median of girls = [5th + 6th]/2.

Median of girls = [100 + 120]/2.

Median of girls = 110.

Next, we would determine the range of the data set as follows;

Range = Highest number - Lowest number

Range of boys = 120 - 60

Range of boys = 60.

Range of girls = 120 - 60

Range of girls = 150 - 70.

Range of girls = 80.

In conclusion, we can logically deduce that the median and range for the girls is greater than the median and range of boys.

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Chandler ended up 8 feet below sea level. The negative sign indicates that his final position is below sea level. This means that he has descended further into the lake compared to the starting point on the cliff.

Chandler started on the cliff at 32 feet above sea level. When he jumped for 40 feet, we need to determine the final position in relation to sea level.

Since Chandler jumped down, the distance below sea level will be calculated as a negative value. To find how far below sea level Chandler ended up, we subtract the jump distance (40 feet) from the starting height (32 feet above sea level):

32 feet - 40 feet = -8 feet

It's important to note that negative values are used here to represent the direction and magnitude of Chandler's descent relative to sea level

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Answer:

-8 feet

Step-by-step explanation: