Complete the square to solve 0=x^(2)+9x+16.25 and determine the roots. Then sketch the parabola y=x^(2)+9x+16.25 and state the coordinates of the x intercepts and the vertex.

For matrix g : \(\displaystyle g^{-1}=\frac{1}{\left| g \right|}\left[\begin{array}{ccc}6 & 1 & -3 \\ -8 & -3 & 2 \\ 3 & -1 & -3\end{array}\right] \)
For matrix h : \(\displaystyle h^{-1}=\frac{1}{\left| h \right|}\left[\begin{array}{ccc}1 & 0 & -1 \\ 1 & -1 & 1 \\ 0 & 1 & -1\end{array}\right] \)

For matrix g, the inverse can be found using the following equation:

\(\displaystyle g^{-1}=\frac{1}{\left| g \right|}\left[\begin{array}{ccc}6 & 1 & -3 \\ -8 & -3 & 2 \\ 3 & -1 & -3\end{array}\right] \)



For matrix h, the inverse can be found using the following equation:

\(\displaystyle h^{-1}=\frac{1}{\left| h \right|}\left[\begin{array}{ccc}1 & 0 & -1 \\ 1 & -1 & 1 \\ 0 & 1 & -1\end{array}\right] \)



Where \(\left| g \right|\) is the determinant of the matrix g and \(\left| h \right|\) is the determinant of the matrix h.

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The dimensions that would produce the maximum enclosed area are 350ft x 350ft, which will cut off 3 equal size rectangle regions in the yard.

To understand why this is the case, let's consider the problem step-by-step. If Alex wants to cut off three equal size rectangle regions in the yard, he will need to divide the lawn into four equal size rectangles. Let's call the dimensions of two of these rectangles "x" and "y".

To maximize the enclosed area, we want to maximize the area of the lawn that is left over after the three rectangles are cut out. This area can be represented by the equation A = (350-x)(350-y). We know that the total length of the piping is 1400 ft, so the perimeter of the enclosed area (the sum of all four sides) is 1400 ft. This means that 2x + 2y + 1400 = 1400, or 2x + 2y = 0.

Solving for y, we get y = -x + 700. Substituting this equation into the area equation, we get A = (350-x)(350-(-x+700)), which simplifies to A = x(350-x). To find the maximum area, we can take the derivative of this equation with respect to x, set it equal to 0, and solve for x. Doing this, we find that x = 175, which means that y = 525 - x = 350. Therefore, the dimensions that would produce the maximum enclosed area are 350ft x 350ft.

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Answer: To calculate the prevalence of chronic pain in the United States in 2019, we need to divide the number of people reporting living with chronic pain by the total population and then multiply by 100 to express the result as a percentage. We can then also express the prevalence as a number of cases per 100,000 people.

Prevalence of chronic pain = (Number of people with chronic pain / Total population) x 100

Prevalence of chronic pain = (50,200,000 / 328,239,523) x 100

Prevalence of chronic pain = 15.29%

Therefore, the prevalence of chronic pain in the United States in 2019 was 15.29%. This can also be expressed as 15,290 cases per 100,000 people.

Step-by-step explanation:

The surface area of the cylindrical tube is approximately 240.21 square inches.

What formula do we use to find the surface area of a cylinder?

The surface area of a cylinder is the sum of the areas of all its surfaces, including the curved surface area and the area of its two circular bases. It is a measure of the total area that the cylinder covers.

To find the surface area of a cylinder, we use the formula

[tex]A = 2\pi rh + 2\pi r^2[/tex]

where r is the radius of the base, h is the height of the cylinder, and π is a constant equal to approximately 3.14.

Calculating the surface area of the cylindrical tube -

The base of the tube has a diameter of 3 inches, which means the radius is 1.5 inches. The length of the poster is given as 24 inches, so we will assume that the height of the cylindrical tube is also 24 inches.

Substituting the values we have into the formula, we get:

[tex]A = 2\pi (1.5)(24) + 2\pi (1.5)^2[/tex]

[tex]A = 2\pi (36) + 2\pi (2.25)[/tex]

[tex]A = 72\pi + 4.5\pi[/tex]

[tex]A = 76.5\pi[/tex]

Using the approximation of [tex]\pi = 3.14[/tex], we get:

[tex]A[/tex]≈[tex]240.21[/tex] square inches .

Therefore, the surface area of the cylindrical tube is approximately 240.21 square inches.

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1- This is a rotation matrix because the determinant is 1 and the transpose is equal to the inverse. 2- The line passing through the origin and the point (1, 1, 1) is the axis of rotation. 3- 120° is the angle of rotation.

1. To show that this is a rotation matrix, we need to check that the matrix satisfies the following properties:
- The determinant of the matrix is 1.
- The transpose of the matrix is equal to its inverse.
The matrix that transforms a vector (x1, x2, x3) into (x2, x3, x1) is:
| 0  1  0 |
| 0  0  1 |
| 1  0  0 |
The determinant of this matrix is:
det = 0×0×0 + 1×1×1 + 0×0×0 - 0×0×1 - 1×0×0 - 0×1×0 = 1
The transpose of this matrix is:
| 0  0  1 |
| 1  0  0 |
| 0  1  0 |
The inverse of this matrix is:
| 0  0  1 |
| 1  0  0 |
| 0  1  0 |
Since the determinant is 1 and the transpose is equal to the inverse, this is a rotation matrix.

2. To find the axis of rotation, we need to find the eigenvector of the matrix corresponding to the eigenvalue of 1. The characteristic equation of the matrix is:
| -λ  1  0 |
| 0  -λ  1 |
| 1  0  -λ | = 0
Expanding the determinant, we get:
-λ × (-λ × (-λ)) - 1 × 1 x 1 = 0
λ = 1
The eigenvector corresponding to the eigenvalue of 1 is:
| -1  1  0 | | x1 | = | 0 |
| 0  -1  1 | | x2 |   | 0 |
| 1  0  -1 | | x3 |   | 0 |
Solving this system of equations, we get:
x1 = x2 = x3
So the eigenvector is:
| 1 |
| 1 |
| 1 |
This means that the axis of rotation is the line passing through the origin and the point (1, 1, 1).

3. To find the angle of rotation, we can use the formula:
cosθ = (trA - 1)/2
Where trA is the trace of the matrix A. The trace of the matrix is:
trA = 0 + 0 + 0 = 0
So the angle of rotation is:
cosθ = (0 - 1)/2 = -1/2
θ = 120°
Therefore, the angle of rotation is 120°.

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The expression that represents the total travel time is 16x − 8

To add polynomial expressions we need to add or subtract like terms and constant terms.

In the given problem to find the total travel time we need to add the time takes to travel to work and the time takes to travel from work to home.  

Here we have

The expression represents the time takes to travel to work = 5x − 7

The expression represents the time takes to travel from work = 11x – 1

The total travel time =  5x − 7 + 11x – 1  

=> 5x + 11x  − 7 – 1  

=> 16x − 8  

Therefore,

The expression that represents the total travel time is 16x − 8  

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The given polynomial is P(x) = x^3 + 5x^2 - 6x + 6. The given c is 3. To use the Remainder Theorem, we must divide P(x) by (x - c). The result of this division will be a quotient and a remainder. The remainder is the value of the polynomial when x = c, so in this case when x = 3, the remainder is 45.

This is because when x = 3, P(x) = 45. Therefore, according to the Remainder Theorem, the remainder when we divide P(x) by (x - 3) is 45. This means that when we divide P(x) by (x - 3), the remainder is 45. Thus, the Remainder Theorem can be used to determine the remainder when we divide a polynomial P(x) by (x - c), where c is some given constant.

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Answer: X':(2,2) Y':(4,4) Z":(6,0)

Answer:

1.4

Step-by-step explanation:

If 6/p =15/3.5

You can cross multiply the equation

6x3.5 =15P

21=15P

Divide both sides by 15

21/15 = P

1.4 =P

The amount that Beth borrowed at the annual interets of 30% is found to be  £4880.

We can use the relation to find the original borrowed which is,

original amount x (1 + interest rate)² = total amount to be paid

The interest in annual so the value of interest of the loan that Beth took is 30% and the amount to be paid is £8112. Let x be the borrowed amount,

Now, putting all the values in the relation above-mentioned,

Based on the given conditions, formulate:

x+(1+30%)² = 8112

x(1.3)² = 8112

Divide both sides of the equation by the coefficient of variable,

x = 8112/(1.30)²

Calculated value of x = 4800

The original amount that Beth borrowed is £4880.

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The equivalent equations are given as follows:

Equivalent equations are equations that have the same result when they are solved.

The first equation is solved as follows:

2 + x = 5

x = 5 - 2

x = 3.

The second equation is solved as follows:

x + 1 = 4

x = 4 - 1

x = 3.

Hence it is equivalent to the first, as both have the same result of x = 3.

The third equation is solved as follows:

9 + x = 6

x = 6 - 9

x = -3.

The fourth equation is solved as follows:

x - 4 = 7

x = 7 + 4

x = 11.

The fifth equation is solved as follows:

-5 + x = -2

x = -2 + 5

x = 3.

Which is equivalent to the first and to the second equation.

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The expression x^(2)((1)/(8)x^(3))(40x^(-12)) equals (5/8)/(x^(7)) where the coefficient c is 5/8 and the exponent e is -7.

The expression x^(2)((1)/(8)x^(3))(40x^(-12)) can be simplified by combining the coefficients and adding the exponents of the same base.

First, we'll combine the coefficients:

(1)(1/8)(40) = 5/8

Next, we'll add the exponents of the same base:

2 + 3 + (-12) = -7

So the simplified expression is:

(5/8)x^(-7)

Now we can see that the coefficient c is 5/8 and the exponent e is -7.

So the answer is:

The expression x^(2)((1)/(8)x^(3))(40x^(-12)) equals (5/8)/(x^(7)) where the coefficient c is 5/8 and the exponent e is -7.

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To prove that the functions f(x)= (2)/(3)x-8 and g(x)=(3)/(2)x+12 are inverses, we can use composition of functions. We can do this by setting f(g(x)) = x and g(f(x)) = x and showing that they are equivalent.

First, let's look at f(g(x)). We can substitute g(x) into the equation for f(x), so we have: f(g(x)) = (2)/(3)((3)/(2)x+12)-8. Simplifying, we have: f(g(x)) = (4x+48)/6 - 8. Distributing the 4 and rearranging, we have: f(g(x)) = x.

Now let's look at g(f(x)). We can substitute f(x) into the equation for g(x), so we have: g(f(x)) = (3)/(2)((2)/(3)x-8)+12. Simplifying, we have: g(f(x)) = (2x-32)/3 + 12. Distributing the 2 and rearranging, we have: g(f(x)) = x.

Therefore, we have shown that f(g(x)) = x and g(f(x)) = x, which means that f(x) and g(x) are inverses of each other.

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Expressions A, B, and F are equivalent to (a²-16(a+4)).

Equivalent is a term that means equal in value, measure, force, effect, or significance. It can be used to describe two or more things that are of the same value or having the same characteristics. For example, a 1:1 ratio is said to be equivalent because it has the same value on both sides. Equivalent can also mean having the same or similar effect, such as two different treatments for a disease that have the same outcome.

The expressions A, B, and F are equivalent to (a²-16(a+4)). Expression A is equal to a² - 16a - 64. This expression can be rewritten as a³ - 64, which is equal to A. Expression B is equal to (a - 4)³. This expression can be rewritten as a³ - 64, which is equal to A. Expression F is equal to [(a)²-(4^2)](a+4). This expression can be rewritten as (a² - 16)(a+4), which is equal to A. Therefore, expressions A, B, and F are equivalent to (a²-16(a+4)).

Expression C is equal to (a+4)³, which is not equivalent to (a²-16(a+4)). Expression D is equal to (a+4)²(a-4), which is not equivalent to (a²-16(a+4)). Expression E is equal to (a-4)²(a+4), which is not equivalent to (a²-16(a+4)). Expression G is equal to(a-4)(a+4)(a+4), which is not equivalent to (a²-16(a+4)). Therefore, expressions C, D, E, and G are not equivalent to (a²-16(a+4)).

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The length of AC would be 9.6 units.

What is the basic proportionality theorem?

The basic proportionality theorem (also known as the "Thales' theorem") is a fundamental theorem in geometry that states that if a line is drawn parallel to one side of a triangle, then it divides the other two sides proportionally. In other words, if a line intersects two sides of a triangle and is parallel to the third side, then the ratio of the lengths of the two segments formed on one of the sides is equal to the ratio of the lengths of the other two sides.

In the given figure, we can apply the basic proportionality theorem

AB/BD = AC/CE
8/10 = AC/12
4/5 = AC/12
AC = 48/5
AC = 9.6 units

Hence, the length of AC would be 9.6 units.

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A-1 = (A - 2I)-1(A2 + 2A + 4I)-1.

6. To show that T:R2→R2 defined by T([x y]) = [x y 0] is not a linear transformation, consider T(u+v) = T([u1 + v1, u2 + v2]) = [u1 + v1, u2 + v2, 0]. Since T(u+v) is not equal to T(u) + T(v), which is [u1, u2, 0] + [v1, v2, 0] = [u1 + v1, u2 + v2, 0], then T is not a linear transformation.

7. Assume A is a square matrix that satisfies A3 - 3A + 2I = 0. This equation can be written as (A - 2I)(A2 + 2A + 4I) = 0. Since A - 2I is non-zero and A2 + 2A + 4I is non-zero, then A - 2I and A2 + 2A + 4I are both invertible and therefore A is invertible. Since A is invertible, A-1 = (A - 2I)-1(A2 + 2A + 4I)-1.

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The 9th term of the geometric sequence 3, -15, 75, ... is 1171875.

The given sequence is 3, -15, 75, ... We can see that each term is obtained by multiplying the previous term by -5. Therefore, the common ratio is -5.

We can use the formula for the nth term of a geometric sequence to find the 9th term. The formula is given by:

aₙ = a₁ x rⁿ⁻¹

where,

aₙ = nth term of the sequence

a₁ = first term of the sequence

r = common ratio of the sequence

n = index of the term we want to find

Using the given sequence, we have:

a₁ = 3 (first term)

r = -5 (common ratio)

To find the 9th term, we substitute n=9 into the formula:

a₉ = a₁ x r⁹⁻¹

a₉ = 3 x (-5)⁸

a₉ = 3 x 390625

a₉ = 1171875

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Given,

f(x) = -2x + 4

g(x) = -6x - 7

To find,

The value of f(x) - g(x)

Solution,

The value of f(x) - g(x) is 4x + 11.

We can simply solve the given mathematical problem by the following process.

We know that,

f(x) = -2x + 4

g(x) = -6x - 7

Now,

f(x) - g(x) = (-2x+4) - (-6x-7)

             = -2x - 4 + 6x + 7

             = 4x + 11

Thus, the value of f(x) - g(x) is 4x+11.

Step-by-step explanation:

in the part a take the f(x) as the normal equation but in the place of x put the equation of g , its as g is now x .

in part b its the exact same only that instead of the x in equation of g(x) the gave you a number to plug into the x

The mathematical model for constant of proportionality is given:

1. y = k/x2
2. h = k/s1/2
3. F = kr2/g
4. R = k(T - Te)
5. F = k(m1*m2) / r2

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2x^2 + 7x + 3 factors into (2x + 1)(x + 3).

What is factoring?

The factoring approach can be used if the quadratic polynomial can be divided into two linear factors:

Look for two numbers that add up to b and multiply to c.

With these numbers, rewrite the quadratic polynomial as the sum of two terms.

Choose the term that has the most in common with each group of terms.

Remove the common binomial factor between the two groups.

Take the quadratic polynomial 2x2 + 7x + 3, for instance. We must choose two values that sum up to seven and multiply by three in order to factor this polynomial. These are the numbers 3 and 1. The quadratic can then be rewritten as follows:

2x² + 3x + 4x + 3

Then, for each collection of terms, we factor out the term with the highest common factor:

x(2x + 3) + 1(4x + 3)

Lastly, we remove the common binomial factor between the two groups:

(2x + 1)(x + 3)

As a result, 2x2 + 7x + 3 equals (2x + 1)(x + 3).

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The exact value of Sin^-1 (cos π) can be found without using a calculator by using the properties of the unit circle and the trigonometric functions.

First, we need to find the value of cos π. On the unit circle, the point (1,0) corresponds to an angle of 0 radians or 0°. The point (-1,0) corresponds to an angle of π radians or 180°. Therefore, cos π = -1.

Next, we need to find the inverse sine of -1. The inverse sine function, Sin^-1, is the inverse of the sine function. This means that Sin^-1(sin x) = x. Therefore, we need to find an angle x such that sin x = -1.

On the unit circle, the point (0,-1) corresponds to an angle of 3π/2 radians or 270°. Therefore, sin 3π/2 = -1. This means that Sin^-1(-1) = 3π/2.

Therefore, the exact value of Sin^-1 (cos π) is 3π/2.

Answer: 3π/2.

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Answer:

2

Step-by-step explanation:

Elevation = 0 - 1050 × Time or Elevation = -1050t, where Elevation is in feet and Time is in hours, is the expression that describes the connection between the submarine's elevation and time.

Seconds, mins max, minutes, days, periods, months, and years are the fundamental elements of time. To determine the time of day, we use secs, minutes, as well as hours; to determine the date, we use times, months, and years. The lesser measures of time are seconds, minutes, and hours, while the larger ones are days, months, and years.

Assuming that the submarine is descending at a constant rate, we can use the equation:

Elevation = Initial Elevation - Rate × Time

where Initial Elevation is the starting elevation (in this case, the surface), Rate is the rate of descent, Time is the time elapsed, and Elevation is the current elevation.

In this case, the Initial Elevation is 0 feet (the surface), the Rate is -1050 feet per hour (since the submarine is descending at a rate of 1050 feet per hour), and Time is the elapsed time in hours.

Therefore, the equation that represents the relationship between the submarine's elevation and time is:

Elevation = 0 - 1050 × Time

or

Elevation = -1050t

where Elevation is in feet and Time is in hours.

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Answer: 37.68 feet

Step-by-step explanation:

Circumference = 2 x π x r

Plug in values:

C = 2 x 3.14 x 6

C = 12 x 3.14

C = 37.68

The circumference is 37.68 feet

Hope this helps!

The answer of the question based on the probability  that The spinner shows has 4 equal sized sections. Jackson spins the spinner 32 times the answer is 8 times.

A event is any outcome or the set of outcomes of experiment or random process.

An event can be as like as a single outcome or as complex as a combination of the outcomes. For example, flipping a coin and getting heads is an event, as is rolling a die and getting a 6.

The spinner has 4 equal sized sections, then each section has a probability of 1/4 or 25% of being landed on when the spinner is spun.

If Jackson spins the spinner 32 times, we can find the expected number of times each section will be landed on by multiplying the probability of landing on each section by the total number of spins:

Expected number of times to land on each section = (Probability of landing on section) x (Total number of spins)

Expected number of times to land on each section = (1/4) x (32)

Expected number of times to land on each section = 8

Therefore, we can expect each section to be landed on approximately 8 times out of the 32 spins.

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Answer: you can see herhere

Step-by-step explanation:

try times like x=1 and find the answer true

The combination that is produced contains 57.5% corn.. It is calculated by taking the weighted average of the corn content in the two bags, accounting for their respective weights.

(50% x 20 lbs) + (65% x 30 lbs)

= 1750 lbs + 1950 lbs

= 3700 lbs

3700 lbs/50 lbs

= 57.5%

The concentration of corn in the resulting mixture is 57.5%. This is calculated by taking the weighted average of the corn content in the two bags. The first bag, containing 20 pounds of calf starter mix, contains 50% corn. The second bag, containing 30 pounds, contains 65% corn. To calculate the concentration of corn in the mixture, the percentage of corn in each bag is multiplied by its respective weight, and the sums of these two products are then divided by the sum of the two weights. In this case, (50% x 20 lbs) + (65% x 30 lbs) = 1750 lbs + 1950 lbs = 3700 lbs. The resulting concentration of corn in the mixture is 3700 lbs/50 lbs = 57.5%.

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The equation of the line passing through (2/7,7/3) and having idenfinite slope is x = 2/7.

A straight line is a geometric figure that extends infinitely in both directions.

The point slope formula is:

y - y₁ = m(x - x₁)

Where m is the slope of the line, and (x₁, y₁) is a point on the line.

In this case, the slope of the line is undefined, which means that the line is a vertical line. Therefore, the equation of the line is x = 2/7, and there is no slope-intercept form of the equation.

So, the answer is: The equation of the line is x = 2/7.

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Answer:

y = 3.3x + 34.9

Step-by-step explanation:

the slope-intercept form is y = mx + b.

y = total pounds of cans accumulated

m (slope) = pounds of cans collected each week (3.3)

x = # of weeks after sally starts collecting

b (y-intercept) = initial pounds of cans collected (34.9)

so:

y = (pounds per week)(# of weeks) + initial weight

y = 3.3x + 34.9