Find the following for the function f(x)=3x^2+3x−3 (a) f(0) (b) f(3) (c) f(−3) (d) f(−x) (e) −f(x) (f) f(x+2) (g) f(3x) (h) f(x+h)

cosx = cos4x = cos5x.

19. Using the identity sin2x + cos2x = 1, we can rewrite the equation as:

sin2x/2 - sin2x/2 = cosx/sinx

Simplifying both sides: cosx/sinx = 0

Therefore, cosx = 0 and sinx = 0.


20. Using the identities secx = 1/cosx, tanx = sinx/cosx, and sec2x = 1 + tan2x, we can rewrite the equation as:

secx(secx tanx) - sec4x(secx tanx) = sec5x tanx

Simplifying: secx - sec4x = sec5x

Therefore, secx = sec4x = sec5x.

Simplifying further: 1/cosx = 1/cos4x = 1/cos5x

Therefore, cosx = cos4x = cos5x.

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The correct coordinates for N' after a 180° rotation about the origin are (-3, -4).

Ari's likely error was that they incorrectly flipped the signs of the coordinates independently.

It should be noted that to rotate a point 180° about the origin, we need to flip the sign of both coordinates of the point. Therefore, the correct coordinates for N' after a 180° rotation about the origin are (-3, -4), not (-4, 3) as Ari claimed.

Ari's likely error was that they incorrectly flipped the signs of the coordinates independently, rather than flipping both signs together. This mistake could have arisen from a misunderstanding of the geometric concept of rotation or a simple arithmetic error.

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The value of the length WY is 40√3 mm. Option J

The different types of trigonometric identities are;

From the information given, we have that;

Opposite side = WY

Angle of elevation, θ = 60 degrees

Adjacent side = 40mm

Now, let's use the tangent identity;

tan θ = WY/40

substitute the value

tan 60 = WY/40

cross multiply

WY = 40 × √3

Multiply the values

WY = 40√3 mm

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On simplifying ((7)/(8)+(1)/(2))/(2(1)/(4)) the correct answer is 2 3/4.

To solve the problem ((7)/(8)+(1)/(2))/(2(1)/(4)), we can follow these steps:

Step 1: Simplify the expression inside the parentheses in the numerator.
(7/8) + (1/2) = (7/8) + (4/8) = (11/8)

Step 2: Simplify the expression inside the parentheses in the denominator.
2(1/4) = (2/1)(1/4) = (2/4) = (1/2)

Step 3: Divide the simplified numerator by the simplified denominator.
(11/8) ÷ (1/2) = (11/8) × (2/1) = (22/8) = (11/4)

Step 4: Simplifying the final expression, if possible.
(11/4) = 2 3/4

Therefore, the correct answer is 2 3/4.

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The equation of a horizontal line that passes through (4,2) in slope intercept form is y = 2.

A horizontal line has a slope of 0, which means that the y-value remains constant while the x-value changes. In slope intercept form, the equation of a line is written as y = mx + b, where m is the slope and b is the y-intercept.

Since the slope of a horizontal line is 0, the equation of a horizontal line can be written as y = 0x + b, or simply y = b. The y-intercept is the value of y when x = 0, which is the same as the y-value of any point on the line.

In this case, the line passes through the point (4,2), so the y-value is 2. Therefore, the equation of the line in slope intercept form is y = 2.

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The new price of the notebooks is $2.40.

To find the original price and the new price of the notebooks, we can use a proportion model. Let's call the original price "x" and the new price "y".

The proportion model for this problem would be:

40/100 = 1.60/x

To solve for x, we can cross-multiply:

40x = 100(1.60)

And then divide both sides by 40:

x = 4

So the original price of the notebooks was $4.00. To find the new price, we can subtract the decrease in price from the original price:

y = x - 1.60

y = 4 - 1.60

y = 2.40

So the new price of the notebooks is $2.40.

40/100 = 1.60/4

0.4 = 0.4

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The paper is 147/8 square inches in size. If preferred, this can be condensed to a mixed number or decimal.

A three-dimensional object's surface area is the sum of its sides. It is a measurement of the object's visible surface area. Depending on the shape of the item, different surface area formulas apply. For instance, adding the surface areas of all six sides of a rectangular prism will yield its surface area. The calculation for a rectangular prism's surface area is: Flat area equals 2lw + 2lh + 2wh where the rectangular prism's dimensions are l for length, w for breadth, and h for height.

given

The length and breadth of the postcard must be multiplied to determine its area.

The mixed integers must first be transformed into improper fractions:

5 1/4 = 21/4

3 1/2 = 7/2

We can now multiply:

Area is equal to length times breadth.

Area = (21/4) × (7/2)

Area = (21 × 7) / (4 x 2)

Area = 147/8

The paper is 147/8 square inches in size. If preferred, this can be condensed to a mixed number or decimal.

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The solution for each expression is given as follows:

To solve an expression for a variable, we isolate the desired variable applying the inverse operations.

The solution for x of the first expression is obtained as follows:

2x + 5y = 5

2x = 5y - 5

x = 5(y - 1)/2

x = 2.5(y - 1).

The solution for y of the second expression is obtained as follows:

3x - 2y = 9

2y = 3x - 9

2y = 3(x - 3)

y = 3/2(x - 3)

y = 1.5(x - 3).

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Answer:

). The rocket was launched from 73 feet above ground.

b). The rocket took [Vy / g] = 30 / 3 = 10s to reach its maximum height of [Vy^2 / (2 * g)] = 30^2 / 6 = 150 feet.

It then fell -(73 + 150) = -223 feet to the ground in a time of sqrt(2 * -223 / -3) = 12.192894s.

Total time of flight = (10 + 12.192894) = 22.192894s.

The rocket landed with a vertical velocity of -sqrt(2 * -223 * -3) = -36.578682ft/s.

Step-by-step explanation:

Answer:

Unfortunately, there is no equation provided in the question. However, I can provide a general formula for the height of a rocket launched from a certain height h0 with an initial velocity v0, under the influence of gravity:

h(t) = -1/2gt^2 + v0t + h0

where g is the acceleration due to gravity, which is approximately 32.2 feet per second squared.

Using this formula, we can calculate the height of the rocket 3 seconds after it is launched:

h(3) = -1/2(32.2)(3)^2 + 0 + 4

= -1/2(32.2)(9) + 4

= -145.35 + 4

= -141.35

To the nearest foot, the height of the rocket 3 seconds after it is launched is -141 feet. Note that the negative sign indicates that the rocket has fallen below its initial height of 4 feet due to the influence of gravity.

Answer: A circle

Step-by-step explanation: a circle

slope = -1/5

used slope forumula

The expression that is equivalent to m + m + m + m that is the product of a coefficient and a variable is 4m, where 4 is the coefficient and m is the variable.

What are algebraic expressions?

An algebraic expression is a mathematical phrase that contains one or more variables, numbers, and arithmetic operations (such as addition, subtraction, multiplication, and division). It can also include exponents, roots, and other mathematical symbols.

Algebraic expressions are used to represent mathematical relationships and to solve problems in various areas of mathematics, science, and engineering. Examples of algebraic expressions include 3x + 5, 2y - 7, and 4x² - 3xy + 2.

A. The expression that is equivalent to m + m + m + m that is the product of a coefficient and a variable is 4m, where 4 is the coefficient and m is the variable.

B. The expression that is equivalent to m + m + m + m that is the sum of two terms is 2m + 2m, where 2m is one term and the other term is also 2m.

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The values of x are 0.732 and -2.732.

Given function:f(x) = g(x)We need to determine the value of x.For, f(x) = g(x), we have the following equation:f(x) = x^2 + 2x + 1 = 2x + 3g(x) = 2x + 3To solve for x, we can substitute the value of g(x) in the first equation:x^2 + 2x + 1 = g(x)Substituting g(x) = 2x + 3 in the above equation:x^2 + 2x + 1 = 2x + 3x^2 + 2x - 2 = 0x^2 + 2x - 2 = 0Applying the quadratic formula, we get:$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$Where, a = 1, b = 2, and c = -2Substituting the values in the formula, we get:$$x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-2)}}{2(1)}$$$$x = \frac{-2 \pm \sqrt{12}}{2}$$$$x = -1 \pm \sqrt{3}$$Therefore, the value of x is x = -1 + √3 or x = -1 - √3.To round off the answer to 3 decimal places, we get:x = -1 + 1.732 = 0.732 or x = -1 - 1.732 = -2.732Hence, the values of x are 0.732 and -2.732.

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solve for t to get t = 4

1. To find the derivative of f(x) = (3 – 2x^3)^3 we can apply the power rule, the chain rule, and the product rule. The power rule states that the derivative of f(x) = x^n is f'(x) = nx^n-1. The chain rule states that the derivative of f(x) = g(h(x)) is f'(x) = g'(h(x))*h'(x). The product rule states that the derivative of f(x) = uv is f'(x) = u'v + uv'. In this case, we can rewrite f(x) as f(x) = (h(x))^3 where h(x) = 3 - 2x^3. We then apply the chain rule to get f'(x) = 3(3 - 2x^3)^2(-6x^2). Similarly, we can find the derivative of f(t) = 100(6-t)/t+3. We can rewrite f(t) as f(t) = u(t)v(t) where u(t) = 100 and v(t) = (6-t)/t+3. Applying the product rule, we get f'(t) = 100(-1/(t+3)^2) + (6-t)(-1/(t+3)^2).

2. To find other information about a function, we can use the derivative we just found. For example, if we want to find the maximum or minimum values of a function, we can set the derivative equal to 0 and solve for the x or t values. In the case of f(x), we can set 3(3 - 2x^3)^2(-6x^2) = 0 and solve for x to get x = (sqrt(3/2))^(1/3). Similarly, for f(t) we can set 100(-1/(t+3)^2) + (6-t)(-1/(t+3)^2) = 0 and solve for t to get t = 4. We can also use derivatives to find the equation of a tangent line to a function at any given point. In this case, we would use the derivative we found in order to calculate the slope of the tangent line at any given point and then use point-slope form to find the equation of the line.

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Answer:

11

Step-by-step explanation:

The equation of the line that passes through the point (14,3) and is perpendicular to the given equation is y = x - 11.

To solve the equation 5(y+x)-6(x-y)=-8, we need to use the distributive property and combine like terms.

5(y+x)-6(x-y)=-8

Distribute the 5 and -6:

5y + 5x - 6x + 6y = -8

Combine like terms:

11y - x = -8

Now, we need to find the slope of the line that passes through the point (14,3) and is perpendicular to the given equation.

The slope of the given equation is -1, so the slope of the perpendicular line is the negative reciprocal, which is 1.

Using the point-slope form, we can write the equation of the perpendicular line:

y - 3 = 1(x - 14)

Distribute the 1:

y - 3 = x - 14

Add 3 to both sides:

y = x - 11

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Check the picture below.

400 children and 600 adults bought tickets to the circus.

Let's call the number of children who bought tickets "C" and the number of adults who bought tickets "A". We can set up two equations to represent the information given in the question:

C + A = 1000 (the total number of people who bought tickets)
15C + 40A = 30000 (the total gate revenue)

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for C in terms of A:

C = 1000 - A

Now we can substitute this equation into the second equation to solve for A:

15(1000 - A) + 40A = 30000
15000 - 15A + 40A = 30000
25A = 15000
A = 600

So 600 adults bought tickets. We can use the first equation to find the number of children who bought tickets:

C + 600 = 1000
C = 400

So 400 children bought tickets. Therefore, the answer is that 400 children and 600 adults bought tickets to the circus.

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The total cost of the dress including sales tax is 95.21.

The amount of discount that Isabella received on the dress is:

35% of 135.00 = 0.35 x 135.00 = 47.25

So, the price she paid for the dress after the discount is:

135.00 - 47.25 = 87.75

To find the total cost including sales tax, we need to add the sales tax to the price of the dress:

Sales tax = 8.5% of 87.75 = 0.085 x 87.75 = 7.46

Total cost = Price of dress after discount + Sales tax

= 87.75 + 7.46

= 95.21

Therefore, the total cost of the dress including sales tax is 95.21.

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About 22,500 people at the Super Bowl game will not be wearing team jerseys.

Here the entire population is proportional to the number of people who entered the main gate without wearing team jerseys.

Find the proportion of people not wearing team jerseys by dividing 150 by 500. Now multiply the resultant proportion by the actual population.

Here we have

150 out of the first 500 people who entered the main gate were not wearing team jerseys,

The proportion of people not wearing team jerseys  

=> p = 150/500 = 0.3

Given that the sample is representative of the entire population of 75,000 people attending the game,

The population that will not be wearing team jerseys can be calculated as follows

75,000 x 0.3 = 22,500

Therefore,

About 22,500 people at the Super Bowl game will not be wearing team jerseys.

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The debt consolidation loan will cost Sheng an additional $1,997.69 in interest charges compared to his credit cards.

From question, we are to calculate how much more in interest the debt consolidation loan will cost Sheng

To calculate the interest charges for Sheng's credit cards, we need to use the following formula:

Interest Charges = Balance x APR x Number of Days in Billing Cycle / 365

Using this formula, we can calculate the interest charges for each of Sheng's credit cards:

For Credit Card A:

Interest Charges = $2,500 x 0.19 x 30 / 365 = $4.94

For Credit Card B:

Interest Charges = $3,000 x 0.22 x 30 / 365 = $6.01

So, the total interest charges for Sheng's credit cards are:

Total Interest Charges = $4.94 + $6.01 = $10.95

Now, let's calculate the total cost of the debt consolidation loan:

Total Cost = Total Monthly Payments x Number of Payments - Loan Amount

Total Monthly Payments = $179.37

Number of Payments = 6 x 12 = 72

Loan Amount = ?

To find the loan amount, we need to solve for it using the interest rate and the total interest charges:

Loan Amount = Total Interest Charges / (APR x Number of Payments / 12)

Loan Amount = $3,414.39 / (0.107 x 72 / 12) = $25,000

So, the total cost of the debt consolidation loan is:

Total Cost = $179.37 x 72 - $25,000 = $2,008.64

Therefore, the additional interest charges for the debt consolidation loan compared to Sheng's credit cards are:

Additional Interest Charges = Total Cost - Total Interest Charges

Additional Interest Charges = $2,008.64 - $10.95 = $1,997.69

Hence, the debt consolidation loan will cost him an additional $1,997.69 in interest charges

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The result of the (3-3x^(3)-7x^(2))-(-2x^(2)-3x+7)  polynomial  is -3x^(3) - 5x^(2) + 3x - 4.

A polynomial is a mathematical expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

To find the result of the given polynomials, we need to combine like terms. Like terms are terms that have the same variable and the same exponent.

Step 1: Distribute the negative sign to the second polynomial:
(3 - 3x^(3) - 7x^(2)) - (-2x^(2) - 3x + 7) = (3 - 3x^(3) - 7x^(2)) + (2x^(2) + 3x - 7)

Step 2: Combine like terms:
3 - 3x^(3) - 7x^(2) + 2x^(2) + 3x - 7 = -3x^(3) - 5x^(2) + 3x - 4

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not completely sure

3x25=75

answer 75

i think so bye

The standard deviation of Y is 0.49.

Let's assume that D=20 (the last two digits of your student ID). Therefore, there are 20 defective motherboards in a package of 100 motherboards.

The Probability Mass Function (PMF) of Y is given by:
P(Y=0) = (80/100)*(79/99)

=> 0.64
P(Y=1) = (20/100)*(80/99) + (80/100)*(20/99)

=> 0.32
P(Y=2) = (20/100)*(19/99)

=> 0.04

The Cumulative Distribution Function (CDF) of Y is given by:
P(Y<=0) = P(Y=0)

=> 0.64
P(Y<=1) = P(Y=0) + P(Y=1)

=> 0.64 + 0.32

=> 0.96
P(Y<=2) = P(Y=0) + P(Y=1) + P(Y=2)

=> 0.64 + 0.32 + 0.04

=> 1

The mean of Y is given by:
E(Y) = 0*P(Y=0) + 1*P(Y=1) + 2*P(Y=2)

=> 0 x 0.64 + 1 x 0.32 + 2 x 0.04

= 0.4

The standard deviation of Y is given by:
Var(Y) = SD(Y)

=> [tex]\sqrt{(Var(Y))[/tex]

=>[tex]\sqrt{(0.24)[/tex]

=> 0.49

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Answer:If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations. the intersection points (-3,3) Since the system is infinite it means there is 1 line on the graph-

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

becuas eyou divide it all togtheir and then subtract 42 from 83 and you ga the anwer

the height of the cylinder is 12/π inches. This is an exact value, but if you want an approximate decimal value, you can use a calculator and substitute 3.14 or 22/7 for π. For example, if we use π ≈ 3.14, we get:

h ≈ 12/3.14

h ≈ 3.822 inches (rounded to three decimal places)

Answer:

Step-by-step explana2 4

457

6.46