(e) If f(x+3) = f(x) + f(5) then prove that: f(2)= 0 and f(5) = -f(-1)

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Answer:

I thinks is

A is the best answer

Answer:

g(x) = x² + 2

Step-by-step explanation:

If we want to shift a function down, we subtract the number we are asked to move outside the function's argument:

⇒ To shift f(x) b units down → f(x) - b

Similarly, in function notation, if we want to shift a function up, we add the number we are asked to move outside the function's argument:

⇒ To shift f(x) b units up → f(x) + b

Given function f(x) = x²

Shift 2 units up ⇒ x² + 2

Therefore, g(x) = x² + 2

Answer: g(4)=-17

Step-by-step explanation:

You just plug in 4 into x.

-3(4)-5
-12-5
=17

Answer:

g(4) = -17

Step-by-step explanation:

Hello!

Substitute 4 for x in the equation.

g(4) is -17.

The average rate of change of f(x) = x over the interval [4, 9] is 1.

To find the average rate of change of a function f(x) over an interval [a, b], you can use the formula:

Average Rate of Change = (f(b) - f(a)) / (b - a)

In this case, we have the function f(x) = x and the interval [4, 9]. Let's substitute the values into the formula:

Average Rate of Change = (f(9) - f(4)) / (9 - 4)

Calculating the values:

f(9) = 9

f(4) = 4

Average Rate of Change = (9 - 4) / (9 - 4)

= 5 / 5

= 1

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Answer:16

Step-by-step explanation:

Area of a rectangle = height × width

= 5b × 3a

= 15ab

To determine the maximum number of 2/0 AWG THW aluminum compact conductors permitted in a 2½-inch PVC conduit, Schedule 80, we need to consult the applicable electrical code or standards.

The number of conductors allowed in a conduit is typically governed by factors such as fill capacity and heat dissipation.

The specific requirements may vary depending on the jurisdiction and the electrical code being followed. It is recommended to consult the local electrical code or a qualified electrician to ensure compliance with the regulations in your area.

They will be able to provide the precise guidelines and restrictions for conductor fill capacity based on the conduit size, type, and the specific application.

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In the recent art project, the teacher purchased 94 pieces of red construction paper and 80 pieces of blue construction paper. To determine the exact ratio of red construction paper to blue construction paper, we divide the number of red construction paper pieces by the number of blue construction paper pieces.

The ratio of red construction paper to blue construction paper can be expressed as:94:80

However, we can simplify this ratio by dividing both numbers by their greatest common divisor. In this case, the greatest common divisor of 94 and 80 is 2.

Dividing 94 by 2 gives us 47, and dividing 80 by 2 gives us 40.

Therefore, the exact simplified ratio of red construction paper to blue construction paper is: 47:40

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3/8 in a decimal, divide the denominator by the numerator to get 3/8 as a decimal 3/8 is 0.375.

We divide the numerator by the denominator to convert a fraction to a decimal number. This results in a decimal value because, when dividing, we add the decimal place and then add the necessary number of zeros to finish the division.

3/8

3[1/2 x 1/2 x 1/2]

3[0.5 x 0.5 x 0.5]

3 x 0.125

0.375

To convert a fraction to a decimal, all you have to do is divide the numerator by the denominator. We position the number over its place value when converting a decimal to a fraction.

Just dividing the numerator by the denominator is all that is required to convert a fraction to a decimal.

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Answer:

2.5

Step-by-step explanation:

Option B is correct, in constructing a unique triangle we need to provide  all three sides or the measure of the hypotenuse and a side in a right triangle.

In order to construct a unique triangle, you need to provide either all three sides or the measure of the hypotenuse and a side in a right triangle.

These two conditions are sufficient to determine a unique triangle.

Providing two sides and the included angle is enough, but this is not true. Two sides and an included angle can form multiple different triangles, so it does not guarantee a unique triangle.

Providing two angles and the included side is enough, but this is also not true.

Two angles and the included side can form multiple different triangles, so it does not guarantee a unique triangle.

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The percentage of races with a finishing time between 64.5 and 65.5 seconds is given as follows:

68%.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

The measures in this problem are within one standard deviation of the mean, as:

Hence the percentage is of 68%.

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a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

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Answer:

If the video game that Ethan bought usually costs $39.99, and it was on sale for 20% off, then the discount on the game would be $39.99 x 20/100 = $8.00. To determine the final price of the game after the discount, we can subtract the discount from the original price of the game, which gives us:

Final price = $39.99 - $8.00 = $31.99

Therefore, Ethan paid $31.99 for the video game that was on sale. This can be rounded to the nearest cent to give us a final answer of:

Final price = $31.99 ≈ $32.00.

Therefore, Ethan paid $32.00 for the video game that was on sale.

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

The area A of a trapezoid is the height h times the average of the parallel bases a and b.  

A = (1/2)(a + b)h

Solving for a,

2A = (a+b)h

2A/h = a+b

a = 2A/h - b

We have A=59.64, b=4, h=8.4

a = 2(59.64)/8.4 - 4

a = 10.2 yards

Answer: 10.2

To test the hypothesis that two additional years of work experience have the same effect on the annual salary as being affiliated with a private university, we can use a statistical test called multiple regression analysis.

The null hypothesis (H0) in this case would state that the coefficients for both work experience and affiliation with a private university are equal to zero, indicating that neither variable has a significant effect on the annual salary. In other words, the null hypothesis assumes that the additional years of work experience and affiliation with a private university have no impact on salary.

Null hypothesis (H0): The coefficients for work experience and affiliation with a private university in the multiple regression model are both equal to zero.

Alternative hypothesis (H1): The coefficients for work experience and affiliation with a private university in the multiple regression model are not equal to zero.

To test this hypothesis, we would collect data on individuals' annual salaries, their years of work experience, and their university affiliation (private or not). We would then perform a multiple regression analysis, which allows us to examine the relationship between the dependent variable (annual salary) and the independent variables (work experience and university affiliation).

The results of the multiple regression analysis would provide estimates of the coefficients for work experience and university affiliation, along with their associated p-values. If the p-values for both variables are statistically significant (typically with a significance level of 0.05 or lower), we can reject the null hypothesis and conclude that there is evidence that two additional years of work experience and affiliation with a private university have different effects on annual salary. If the p-values are not statistically significant, we would fail to reject the null hypothesis and conclude that there is not enough evidence to support a difference in the effects of work experience and university affiliation on annual salary.

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\(Given second order ODE is;d²y/dx²-6dy/dx+9y=sin2x\)By using D-Operator method we find the complementary \(function(CF) of ODE;CF=d²/dx²-6d/dx+9\)

\(We assume a solution of particular(SOP) of the given ODE as; Yp=Asin2x+Bcos2x\)

\(We find the first and second derivative of Yp; Y1=2Acos2x-2Bsin2xY2=-4Asin2x-4Bcos2x\)

Now we substitute these values in \(ODE;d²y/dx²-6(dy/dx)+9y=sin2x(d²Yp/dx²)-6(dYp/dx)+9Yp=sin2x=>d²Yp/dx²-6(dYp/dx)+9Yp=(2cos2x-2Bsin2x)-6(-2Asin2x-2Bcos2x)+9(Asin2x+Bcos2x)=2cos2x-4Asin2x=2(sin²x-cos²x)-4Asin2x=2sin²x-6cos²x\)

Now we equate the coefficient of Yp in ODE to the coefficient of Yp in RHS;9A=2A => A=0

Similarly, the coefficient of cos2x in LHS and RHS must be equal;-6B=-4B => B=0

Therefore, SOP of given ODE is;Yp=0

\(The general solution(GS) of the given ODE is;Y=CF+Yp=>d²y/dx²-6dy/dx+9y=0\)

The characteristic equation of CF;d²/dx²-6d/dx+9=0=>(D-3)²=0=>D=3(doubly repeated roots)

\(Therefore,CF=C1e³x+C2xe³x\)

\(The general solution of the given ODE is;Y=CF+Yp=C1e³x+C2xe³x\)

\(The solution is thus given by the relation;$$\boxed{y=e^{3x}(c_1+c_2x)}$$\)

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In order to calculate the percentage relation you proceed as follow:

(35.46/ 49.25)*100 = 72

Then, the percentage is 72%.

It is only necessary to calculte the quotient between the lower number and the higher one, and the result of the quotient is multiplied bu 100.

Answer:

y = tan x

Step-by-step explanation:

y = tan x has a period of pi, not 2pi.

The total amount is given by 2080 pesos.

At discounts of 14% , the discount amount will be

So amount due due to 14%

So the amount due due to 14% discount is

Now at 6% discount we have

And abount due will be

Answer:

which are the chocies???

Answer:

I don't know what the choices are but maybe y=25x+5

Step-by-step explanation:

Parallel lines have equal slope so

Lets check

Now

Lines are parallel

Answer:

The two lines are parallel

Step-by-step explanation:

If two lines are parallel, they have the same slope.

If two lines are perpendicular, the slopes will be negative reciprocals (the product of the slopes will be -1).

Given slopes:

\(\sf m_1=\dfrac{3}{4}\)

\(\sf m_2=\dfrac{12}{16}\)

Reduce m₂ to its simplest form by dividing the numerator and denominator by the largest common factor:

\(\sf m_2=\dfrac{12 \div 4}{16\div 4}=\dfrac{3}{4}\)

Therefore,

\(\sf as \quad \dfrac{3}{4}=\dfrac{3}{4} \implies m_1=m_2 \quad\)

As the given slopes are the same, the two lines are parallel.

Answer:

true for all x  or AllRealNumbers

Step-by-step explanation:

So the final expression is: (change in y/y) = n (change in a/a).

We can start by taking the natural logarithm of both sides of the equation:

ln(y) = ln(aⁿ)

Using the rule that ln(aⁿ) = n ln(a), we can simplify this to:

ln(y) = n ln(a)

Next, we can take the derivative of both sides with respect to a:

d/d(a) ln(y) = d/d(a) (n ln(a))

Using the chain rule, we can simplify the right-hand side to:

d/d(a) ln(y) = n (1/a)

Now, we can multiply both sides by a/y:

a/y * d/d(a) y = n(a/y) * (1/a)

Simplifying, we get:

dy/y = n da/a

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In its simplest radical form, the area of the right triangle is 8sqrt(3) square feet.

How is area determined?

The length of the other leg of the right triangle can be determined using the Pythagorean theorem:

\(a^2 + b^2 = c^2\)

where the hypotenuse is c and the triangle's legs are a and b.

We are aware that the hypotenuse c is 8 feet long and that leg an is 4 feet long. Let's work out the answer for the opposite leg's length, b:

\(b^2 = c^2 - a^2\sb^2 = 8^2 - 4^2\sb^2 = 64 - 16\sb\)

\(sqrt(48) = 4sqrt(3) foot where 2 = 48 b\)

Given that we know the lengths of both legs, we can use the following formula to get the triangle's area:

\((1/2) * Base * Height = Area\)

We may use the 4 ft leg as the base and the 4sqrt(3) ft leg as the height since one leg is 4 ft and the other is 4sqrt(3) ft:

Area: (1/2) * 4 feet * 4 square feet (3)

= 8sqrt(3) square feet

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Answer:

The maximum revenue is $25,000

Step-by-step explanation:

The model equation is;

R = -2.5p^2 + 500p

To find the maximum value, we differentiate this and set result = 0

The first differential of this model equation is -5p + 500

we set this to zero to get the maximum price

5p = 500

p= 500/5

p = 100

Now to get the maximum revenue, we simply substitute the value of the maximum price

That would be -2.5(100)^2 + 500(100)

= -2.5(10,000) + 50,000

= 25,000 + 50,000

= 25,000