y=7x
2x+y=63
Solve this equation

Using the Factor Theorem, it is found that the linear factorization of the function is:

\(f(x) = \left(x + \frac{11}{3}\right)\left(x - \frac{7}{2}\right)(x - 1 - 3i)(x - 1 + 3i)\)

The Factor Theorem states that a polynomial function with roots has linear factorization given by:

\(f(x) = (x - x_1)(x - x_2) \cdots (x - x_n)\)  

Using a calculator, the roots of the function \(f(x) = 6x^4 - 11x^3 - 19x^2 + 164x - 770) are given by: \(x_1 = -\frac{11}{3}, x_2 = \frac{7}{2}, x_3 = 1 + 3i, x_4 = 1 - 3i\)

Hence, applying the Factor Theorem, considering the given roots, the linear factorization given by:

\(f(x) = a(x - x_1)(x - x_2)(x - x_3)(x - x_4)\)

\(f(x) = \left(x + \frac{11}{3}\right)\left(x - \frac{7}{2}\right)(x - 1 - 3i)(x - 1 + 3i)\)

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Answer:

Yes they do :)

(o´▽`o)ﾉ x

"Let x be any vector in \(C^n\), let q = \(x^T\)Ax, and let A be an n-by-n real matrix with the characteristic that \(A^T\) = A. By confirming that q = q, the equalities below demonstrate that q is a real number.

Let A be n x n real matrix with the property that. \(A^T = A\).

if Ax = λx.

(Ax) = λx

\(xA^T=\) λx

xA = λx( and therefore dλ are real, A =\(A^{T}\) = and dλ = λ).

x(A-λL) = 0

Therefore, A-λL is a real matrix.

Assume that A is a n by n matrix with a characteristic polynomial defined by det(λI−A). The number of times an eigenvalue of A appears as a root of that distinctive polynomial is known as its multiplicity.

and x (λI-A) = 0

Therefore, x(λL-A) is also real.

X1 is real.

Therefore, since is one of A's eigenvalues, there exists a nonzero vector X\(C^n\) such that AX=X

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The distance from the center of the Earth to the point where the net gravitational force is zero is one-ninth the distance from the Earth to the Moon.

Let's assume that the distance from the center of the Earth to this point is denoted as x.

Given:

Mass of the Moon (M\(_{moon}\)) = 1/81 × M\(_{earth}\)

Distance from Earth to Moon (d\(_{moon}\)) = distance on center

According to the principle of gravitational equilibrium, the gravitational force from the Earth and the gravitational force from the Moon acting on an object at that point must balance out. Mathematically, we can express this as:

F\(_{earth}\) = F\(_{moon}\)

The gravitational force between two objects can be calculated using Newton's law of universal gravitation:

F \(_{gravity}\)= G × (m₁ × m₂) / r²

Where:

G is the gravitational constant (approximately 6.67430 x 10⁻¹¹m²/kg/s²)

m₁ and m₂ are the masses of the two objects

r is the distance between the centers of the two objects

Considering the gravitational forces involved:

F\(_{gravity}\)\(_{earth}\) = G ₓ (M\(_{EARTH}\)  ₓ m\(_{OBJECT}\)) / (d\(_{earth}\))²

F\(_{gravity}\) \(_{moon}\) = G ₓ (M \(_{moon}\) ₓ m\(_{object}\)) / (d \(_{moon}\))²

Since we are looking for the point where the net gravitational force is zero, we set these two forces equal to each other:

G × (M\(_{earth}\) × m\(_{object}\)) / (d\(_{earth}\))²   =     G × (M \(_{moon}\) × m\(_{object}\)) / (d \(_{moon}\))²

Canceling out the common factors of G and m\(_object}\), and substituting the given values:

(M\(_{earth}\) × 1) / (d\(_{earth}\))² = (M \(_{moon}\) × 1) / (d \(_{moon}\))²

Rearranging the equation:

(d\(_{earth}\))²/ (M\(_{earth}\)) = (d \(_{moon}\))² / (M \(_{moon}\))

Taking the square root of both sides:

d\(_{earth}\) / √(M \(_{moon}\))) = d_moon / √(M \(_{moon}\))

Substituting the given values:

d\(_{earth}\) /√(M\(_{earth}\)) = d\(_{moon}\) / √(1/81 × M\(_{earth}\))

Simplifying further:

d\(_{earth}\)  / √(M\(_{earth}\)) =d\(_{moon}\)  / (1/9 × √(M\(_{earth}\)))

Multiplying both sides by √(M\(_{earth}\)):

d\(_{earth}\) = (1/9) × d\(_{moon}\)

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Answer:

7 x 8x

Step-by-step explanation:

Answer:

−16890

Step-by-step explanation:

Simplify the expression.

Answer:

  2

Step-by-step explanation:

You want to know the average rate of change on the interval -8 ≤ x ≤ -7 of the cubic function shown in the graph.

The average rate of change of a function f(x) on interval [a, b] is given by ...

  rate of change = (f(b) -f(a))/(b -a)

Here, we have ...

Using these values in the formula for rate of change, we get ...

  rate of change = (2 -0)/(-7 -(-8)) = 2/1 = 2

The average rate of change of f(x) on [-8, -7] is 2.

Answer:

1

Step-by-step explanation:

One is the starting term

1, 2, 4, 8, 16, 32, 64, 128, 256,

Answer:

1023/4

Step-by-step explanation:

shown in the picture

For the given inverse functions we have:

a) f⁻¹(5) = 7

b) f(-2) = -3

Remember that if f(x) and g(x) are inverse functions, then:

\(f(x) = y\\then\\g(y) = x\)

a) Now we know that:

f(7) = 5

Then if f⁻¹(x) is the inverse, we have:

f⁻¹(5) = 7

b) Now we know that:

f⁻¹(-3) = -2

Again, using the rule for inverse functions, we will have:

f(-2) = -3

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Answer:

quarterly

Step-by-step explanation:

i just took the unit exam i got it right, its quarterly.

Answer:

Use photomath and look at each step! Sorry I would help but I’m bad at math.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1232 oz flour × (1 loaf)/(12 oz flour) = 102 loaves remainder 8 oz flour

To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

Answer:

The question is not complete

The value of Var(Y) is 1/18 for x and y have the joint probability density function f(x,y).

In probability proposition, a probability viscosity function, or viscosity of a nonstop arbitrary variable, is a function whose value at any given sample in the sample space can be interpreted as furnishing a relative liability that the value of the arbitrary variable would be equal to that sample.

We have the equation as,

f(x, y) = [2y/x²]

\(Since f(y) =\)   \(\int\limits^1_y {f(x, y)} \, dx\)

\(\int\limits^1_y {2y/x^2} \, dx = 2y\int\limits^1_y {x^-1} \, dx\\\\2y (1/y - 1)\)

= 2 - 2y

\(E(Y) =y\int\limits^1_0 {(2-2y)} \, dy = \frac{1}{3}\)

\(E(Y^2) =y^2\int\limits^1_0 {(2-2y)} \, dy = \frac{1}{6}\)

V(Y) = E(Y²) - E(Y)² = 1/6 - 1/9

V(Y) = 1/18

Therefore, Var(y) = 1/18.

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Complete question:

let x represent the amount of compensation that a doctor requests from a health insurer for heart surgery. let y represent the amount of compensation that the doctor actually receives from the health insurer. an actuary determines that x and y have the joint probability density function f(x,y)

f(x, y) = {2y/x²}

Calculate Var(Y)

The GCD of 5! and 7! is 2^3 * 3^1 * 5^1 = 120.

the greatest common divisor of 5! and 7! is 120.

To find the greatest common divisor (GCD) of 5! and 7!, we need to factorize both numbers and identify the common factors.

First, let's calculate the values of 5! and 7!:

5! = 5 * 4 * 3 * 2 * 1 = 120

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040

Now, let's factorize both numbers:

Factorizing 120:

120 = 2^3 * 3 * 5

Factorizing 5,040:

5,040 = 2^4 * 3^2 * 5 * 7

To find the GCD, we need to consider the common factors raised to the lowest power. In this case, the common factors are 2, 3, and 5. The lowest power for 2 is 3 (from 120), the lowest power for 3 is 1 (from 120), and the lowest power for 5 is 1 (from both numbers).

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Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.

The mean refers to the average value.

The average is the quotient of the total value divided by the number of items in the data set.

The number of boys in the class = 26

The number of girls in the class = 20

The total number of boys and girls in the class = 46

The mean number of counters that the boys have = 28

The total number of counters that the boys have = 728 (28 x 26)

The mean number of counters that the girls have =19

The total number of counters that the girls have = 380 (19 x 20)

The total number of counters that the class has = 1,108 (728 + 380)

The average or mean number of counters in the class = 24 (1,108 ÷ 46)

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Answer: 84 mph   60 mph

Step-by-step explanation:

Let her average speed to home was x mph

Hence, the average speed to her parents was (x+24) mph

Thus:

Jessie spent for the trip to her parents' house: 385/x hours

Jessie spent for the trip to home: 385/(x+24) hours

\(\displaystyle\\\frac{385}{x} +\frac{385}{x+24} =11\\\\385(x+24)+385(x)=11(x)(x+24)\\\\385x+9240+385x=11x^2+264x\\\\770x+9240=11x^2+264x\\\\770x+9240-770x=11x^2+264x-770x\\\\9240=11x^2-506x\\\\9240-9240=11x^2-506x-9240\\\\0=11x^2-506x-9240\\\\Divide\ both\ parts\ of\ the \ equation\ by\ 11:\\\\0=x^2-46x-840\)

\(\displaystyle.\\Thus,\\\\x^2-46x-840=0\\\\D=(-46)^2-4*1*(-840)\\\\D=2116+3360\\\\D=5476\\\\\sqrt{D} =\sqrt{5476} \\\\\sqrt{D}=74 \\\\x=\frac{466б74}{2*1} \\\\x=\frac{46-74}{2} \\\\=\frac{-28}{2} \\\\x=-14\notin(x > 0)\\\\x=\frac{46+74}{2}\\\\x=\frac{120}{2} \\\\x=60\ miles\ per\ hour\)

\(60+24=84\ miles\ her\ hour\)

Answer:

The middle! Please vote Brainliest!

Step-by-step explanation:

Answer:

The middle choice

Step-by-step explanation:

The bars go the same amount foward

Answer:

To determine the possible degree(s) of a function from the graph alone, you need to examine the behavior of the graph at the extremes (far left and far right) and consider the number of turning points or changes in direction. Here's a step-by-step approach:

Look at the far left side of the graph: Determine the behavior of the graph as it approaches negative infinity. Does the graph approach a specific value, such as a horizontal line (asymptote) or the x-axis? If the graph approaches a horizontal line, it suggests a polynomial function of even degree. If the graph approaches the x-axis, it indicates a polynomial function of odd degree or possibly a function with a root of multiplicity greater than one.

Look at the far right side of the graph: Determine the behavior of the graph as it approaches positive infinity. Similar to step 1, observe if the graph approaches a specific value or a horizontal line. The behavior at the far right side should be consistent with the behavior at the far left side. This can help you identify if the function is even or odd degree.

Examine the number of turning points or changes in direction: Count the number of times the graph changes direction. These points are where the slope of the graph changes from positive to negative or vice versa. The number of turning points can provide an indication of the degree of the polynomial. For example, if there are two turning points, it suggests a polynomial function of degree 3.

Remember that this method provides potential degrees, but it may not definitively determine the exact degree of the function. Additional information or analysis might be required for a more accurate determination.

The smallest positive debt that can be paid off using sticker trading is $7$ dollars.

To find the smallest positive debt that can be paid off using sticker trading, we need to consider the values of the stickers (in dollars) and find the smallest positive amount that can be reached through a combination of these values.

Given that a Harry Potter sticker is worth $49 and a Twilight sticker is worth $35, we can approach this problem using the concept of the greatest common divisor (GCD) of these two values.

The GCD of $49$ and $35$ is $7$. This means that any multiple of the GCD can be represented using these sticker values.

In other words, any positive multiple of $7$ dollars can be paid off using sticker trading.

Therefore, the smallest positive debt that can be paid off using sticker trading is $7$ dollars.

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For Questions 10-13:

10. The equation that relates the time required to the number of people can be written as:

T = k/P

where

T = time required,

P = number of people, and

k = constant of variation.

Using the given information that it takes 25 hours for 2 people to hand out fliers, use this to find the value of k.

Plugging these values into the equation:

25 = k/2

To solve for k, multiply both sides of the equation by 2:

50 = k

11. Now complete the table:

People Time

2 25

4 12.5

6 8.3

8 6.3

10 5

(rounding to the nearest tenth of an hour)

12. To find out how long it takes for 10 people to hand out the fliers, we can substitute P=10 into the equation:

T = 50/10

T = 5 hours

13. Yes, the result makes sense with what we know about inverse variation. In inverse variation, as the number of people increases, the time required decreases. This is evident in the table, where as the number of people increases from 2 to 10, the time required decreases from 25 hours to 5 hours. This inverse relationship is consistent with the concept of inverse variation.

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Answer: 26129.6

Step-by-step explanation:

6721 x 381 = 2560701

14 + 84 = 98

2560701  / 98 = 26129.6

1- (2,7) x values are not repeated

2-(3,4) bc the x none of the x values are the same, so it makes a function

3-(7,1) the same ^^

Therefore, the school spent $28.36 on a pass and lunch for each student.

The term "cost" typically refers to the amount of resources, usually money, time, or effort, that is required to produce or obtain something. It is the expense incurred in order to achieve a particular goal or outcome.

cost can be further classified into different types, such as fixed costs (expenses that do not change regardless of the level of production), variable costs (expenses that change depending on the level of production), and opportunity costs (the cost of the next best alternative that is forgone when choosing a particular course of action).

First, we need to find the total number of people who need passes for the zoo.

30 students + 2 teachers = 32 people in total

The cost of the passes for 32 people is $634.24, so the cost per person is:

$634.24 ÷ 32 = $19.82 per person

Next, we need to find the cost of lunch per student. We know that the school spent $256.20 on lunch for just the students, so:

$256.20 ÷ 30 students = $8.54 per student

Finally, we can add the cost of the pass and the cost of lunch together to find the total cost per student:

$19.82 (pass) + $8.54 (lunch) = $28.36

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The correct radical form of b^1/5 is 5^√b.

Square root and nth roots are represented by the symbol "radical," which. a square root is a component of a radical expression, which is an expression.

A number's or an algebraic expression's simplest radical form is referred to as this. When a number or algebraic expression contains no elements that are perfect nth powers under the radical, it is said to have an nth root and is said to be in its simplest radical form.

When a number or algebraic expression contains no elements that are perfect nth powers under the radical, it is said to have an nth root and is said to be in its simplest radical form.

Explanation:

Convert to radical form using the formula

a^x/n=n^√a^x

5^√b.

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Answer:

no por que 1/3 es menor que 4

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

One pound (lb) is equal to 16 (oz). So, if you are trying to find how many ounces are in one pound, you have to divide the number of pounds by the 16,   the amount of ounces in one pound.