Given the function f(x) = -5x²-x+ 20, find f(3).
O-28
O-13
O62
O64

Answer:

4th option

Step-by-step explanation:

given

sinΘ = [tex]\frac{5}{13}[/tex] and cosΘ = [tex]\frac{12}{13}[/tex] , then

( [tex]\frac{5}{13}[/tex] )² + ( [tex]\frac{12}{13}[/tex] )²

= [tex]\frac{25}{169}[/tex] + [tex]\frac{144}{169}[/tex]

= [tex]\frac{25+144}{169}[/tex]

= [tex]\frac{169}{169}[/tex]

= 1

showing sin²Θ + cos²Θ = 1

[tex]5th \: row = 1 \: \: \: 5 \: \: \: 10 \: \: \: 10 \: \: \: 5 \: \: \: 1[/tex]

[tex](x - 4) {}^{5} = x {}^{5} + 5x {}^{4} ( - 4) {}^{1} + 10x {}^{3} ( - 4) {}^{2} + 10x {}^{2} ( - 4) {}^{3} + 5x( - 4) {}^{4} + ( - 4) {}^{5} [/tex]

[tex](x - 4) {}^{5} = x {}^{5} - 20x {}^{4} + 160x {}^{3} - 640x {}^{2} + 1280x - 1024[/tex]

It will take the diver 1.5seconds for her to hit the water

Linear equations are equation that has a leading degree of 2. Given the expression that expresses the distance covered by the diver as a function of time as shown;

d(t)= -16(2t - 3)(t+1)

where;

d is the height of the diver above the water and;

t is the time in seconds.

Given the following

d = 0 (the distance on the ground)

Substitute into the formula below;

-16(2t - 3)(t+1)= 0

Divide through by -16

(2t - 3)(t+1) = 0

Determine the time

2t - 3 = 0

t = 3/2

Similarly;

t +1 = 0
t = -1

Hence it will take the diver 1.5seconds for her to hit the water

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The answer is True.

On differentiating using product rule,

[tex]\mathsf {\frac{d}{dx}[xe^{x}] = x(e^{x})+e^{x}(1)}[/tex]

[tex]\mathsf {\frac{d}{dx}[xe^{x}] = e^{x}(x + 1)}[/tex]

The general form of product rule :

[tex]\boxed {\frac{d}{dx}(ab) = a(b')+b(a')}[/tex]

The correct option regarding the data-sets represented by the box and whisker plots is:

B. The distribution for town A is positively skewed, but the distribution for town B is symmetric.

A box and whisker plot shows three things:

For data-set A, we have that:

Since 30 - 20 > 20 - 15, the distribution is positively skewed.

For data-set B, we have that:

Since 40 - 30 = 30 - 20, the distribution is symmetric.

Hence the correct option is:

B. The distribution for town A is positively skewed, but the distribution for town B is symmetric.

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Answer:

Step-by-step explanation:

I am assuming you want to factor these functions

G= -x^2 - 2xy - y^2

  =  -(x^2 + 2xy + y^2)

We need 2 terms whose product is y^2 and whose sum is +2xy

- they are  + x and + y

  = - (x + y)(x + y)

  = -(x + y)^2

The other functions are worked out in the same way:

K =  x^2 + 4y^2 + 4xy

  = (x  + 2y)(x + 2y)

  = (x + 2y)^2

H = 4x^2 - 12xy + 9y^2

   = (2x - 3y)^2

L= 25 - 10 + y^2

 = (5 - y)^2

M =  10y^4 + 25x^6 +y^8

    - this is prime  (no factors)

The probability that exactly 12 of them are strikes is 0.09.

In this question,

Number of pitches, n = 22

Probability of throwing a strike for each pitch, p = 0.431

Then, q = 1 - p

⇒ q = 1 - 0.431

⇒ q = 0.569

Number of strikes, x = 12

The probability that exactly 12 of them are strikes can be calculated using Binomial expansion,

[tex]P(X=x)=nC_xP^{x}q^{(n-x)}[/tex]

⇒ [tex]P(X=12)=22C_{12}(0.431)^{12}(0.569)^{(22-12)}[/tex]

⇒ [tex]P(X=12)=22C_{12}(0.431)^{12}(0.569)^{10}[/tex]

⇒ [tex]P(X=12)=(\frac{22!}{12!10!} )(0.431)^{12}(0.569)^{10}[/tex]

⇒ P(X=12) = (646646)(0.000041)(0.00355)

⇒ P(X=12) = 0.09431 ≈ 0.09

Hence we can conclude that the probability that exactly 12 of them are strikes is 0.09.

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A correlation is a causative association between two or more variables, whereas an autocorrelation is a correlation of variables in successive ranges.

A correlation is defined as a causative association between two or more variables (different variables), which can be used to make predictions about a given outcome.

The correlation coefficient enables the estimation of this association between different variables.

Moreover, an autocorrelation is a  special type of correlation between variables that can be found in successive ranges (e.g. range time intervals).

In conclusion, a correlation is a causative association between two or more variables, whereas an autocorrelation is a correlation of variables in successive ranges.

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Answer: 5 games

Step-by-step explanation: A .500 record means that the soccer team won half of their games ( that's how I interpret it). Since they are going to play 30 games, they need to win half of 30 or 15 games to have that record. 15-10 = 5. So, they need to win 5 more games to have a .500 record.

Answer: 1547.10

Step-by-step explanation: Since you are not in a physics class, in which case requires the usage of the radioactive decay formula, definite integrals, and natural logarithms) but an Algebra class which deploys the usage of percentages, this should be rather simple.

I believe they want you to find 27% of the half life of Carbon-14 since it is below 50%. To find the percent of a number (in this case 27%), you multiply the number by 0.27.

5730 * 0.27 = 1547.10

Hope this helped! And if I'm wrong, please don't hesitate to correct me.

Answer:

  130

Step-by-step explanation:

The number of integers meeting the criteria can be found by counting them using a counting formula.

Integers divisible by 7 will have the form (7n), where n is some positive integer. The number of them less than 1000 can be found from ...

  7n ≤ 1000

  n ≤ 142.857

There are 142 integers less than 1000 that are divisible by 7.

Similarly, integers divisible by 7 and 11 will be of the form (77n), for some positive integer n.

  77n ≤ 1000

  n ≤ 12.987

There are 12 integers less than 1000 that are divisible by both 11 and 7.

The number of integers less than 1000 that are divisible by 7, but not 11, will be the difference of these numbers.

  142 -12 = 130 integers divisible by 7, but not 11.

Answer:

Given is radius of circle that is 5.2, you just need to find the area of the circle.

To find the are of circle is A=πr2

π value is 3.14 and radius value is 5.2 you just need to square the 5.2, answer will come 27.04

now multiply the πr and 27.04.

the answer will come 84.9 and question says to round to the nearest tenth, that will be 85.

Rounding to the nearest tenth, the surface area of the circle with a 5.2 cm radius is approximately 84.8 cm².

The surface area of a circle can be calculated using the formula:

Surface Area = π * radius²

where π (pi) is a mathematical constant approximately equal to 3.14159, and the radius is the distance from the center of the circle to any point on its edge.

Given the radius is 5.2 cm, we can now calculate the surface area:

Surface Area = 3.14159 * (5.2 cm)²

Surface Area = 3.14159 * 27.04 cm²

Surface Area ≈ 84.823 cm²

The surface area represents the total area of the circle's two-dimensional space. In this case, it gives us the total area of the circular region with a 5.2 cm radius.

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The solutions to the system of equations involving quadratic function f(x) and linear function g(x) are (-1,5) and (4/3,29/3), respectively.

To find the solution to the given system of equations:

Given quadratic equation: f(x) = 3x^2 + x + 3

The two point formula is: y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁)

We take the points g(2) = 11, g(1) = 9

g(x) - g(1) = ((g(2)-g(1))/(2-1))*(x-1)

or, g(x) - 9 = ((11-9)/(2-1))*(x-1)

or, g(x) - 9 = 2(x-1)

or, g(x) = 2x - 2 + 9 = 2x + 7

g(x) = 2x +7, is the linear function g(x)

We are asked to solve the system of equations f(x) and g(x).

To get the solution, we must first determine what is the common solution to both f(x) and g(x).

For that, we equate f(x) and g(x).

3x² + x + 3 = 2x + 7

or, 3x² - x - 4 = 0

or, 3x² + 3x - 4x - 4 = 0

or, 3x(x+1) -4(x+1) = 0

or, (3x-4)(x+1) = 0

∴ Either 3x-4=0 ⇒ x = 4/3

or, x+1=0 ⇒ x = -1.

g(-1) = 5 (from the table)

f(-1) = 3(-1)² + (-1) + 3 = 3 - 1 + 3 = 5

g(4/3) = 2(4/3) + 7 = 8/3 + 21/3 = 29/3

f(4/3) = 3*(4/3)² + (4/3) + 3 = 16/3 + 4/3 + 9/3 = 29/3

∴ f(-1) = g(-1) and f(4/3) = g(4/3).

Therefore, the solution to the system of equations that includes quadratic function f(x) and linear function g(x) is (-1,5) and (4/3,29/3).

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The correct question is given below:

What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)?

f(x) = 3x^2 + x + 3

[tex]

\sin^{-1} \left(-\frac{1}{2} \right)=-\sin^{-1} \left(\frac{1}{2} \right)=\boxed{-\frac{\pi}{6}}[/tex]

Answer:

66.0 (nearest tenth)

Step-by-step explanation:

Please refer to the attached photo. (Apologies for the poor drawing)

This is a pure trigonometry question.

Based on the question, we can use the TOA CAH SOH method.

[tex] \cos(x) = \frac{adj}{hypo} \\ \cos(32) = \frac{56}{x} \\ x \cos(32) = 56 \\ x = \frac{56}{ \cos(32) } \\ = 66.0 \: (nearest \: tenth)[/tex]

Answer:

x<-3 or -3<x<-1 or x>-1

Step-by-step explanation:

Domain - The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

\mathrm{Domain\:of\:}\:\frac{1}{x^2+4x+3}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-3\quad \mathrm{or}\quad \:-3<x<-1\quad \mathrm{or}\quad \:x>-1\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-3\right)\cup \left(-3,\:-1\right)\cup \left(-1,\:\infty \:\right)\end{bmatrix}

The formula for moose population is P = 4760 + (number of years x 200).

The moose population in 2003 would be 6760.

When a population increases linearly, it means that it increases by the same amount each year.  

Rate of linear increase: (population in 1999 - population in 1993) / difference in years

(5960 - 4760) / (1999 - 1993)

1200 / 6 = 200

Linear function : initial population + (rate of increase x number of years)

Population in 2003: 4760 + (200 x 10)

4760 + 2000 = 6760

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The true statement is Grade 7 students from School A are typically shorter than grade 7 students from School B because of the difference in the medians of grade 7 student heights at the schools. (option D)

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers.

The end of the first line represents the minimum number and the end of the second line represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

Median for School A = 57

Median for School B = 61

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Answer:

The pair of shoes equal 18.

The boat equals 3

The chair equals 4

Step-by-step explanation:

Let x = shoes

You found the palm trees!

So the top picture would be

18 + x = 2x  Subtract x from both sides

18 = x  We found the value of the shoes.

Let's go so the last picture.  We now know the shoes.

Let x = the boat now

18 = 6x  Divide both sides by 6

x = 3  We found the value of the boat.

Finally, let's look at the second picture.

Let x = the chair now

3 + x = 7  Subtract 3 from both sides

x = 4  We found the value of the chair.

Answer:

182,156.8

Step-by-step explanation:

214 x 912 x 14 = 2,732,352

1/15 of that Volume is 182,156.8

P.S. I'm assuming you meant 1/15, when you said the volume was 15 of

Follow my gram it's Greyhasnoshame

Using Chebyshev's Theorem, we are guaranteed to find at least 75% of the people earning hourly wages between $4.15 and $23.23.

When the distribution is not normal, Chebyshev's Theorem is used. It states that:

In this problem, we want the values within 2 standard deviations of the mean, hence the values are:

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The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).

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we conclude that the distance to the other side is 467 feet.

We know that the width of the river is 602ft. This means that the distance from shore to shore is 602 feet.

If the boy is at a distance of 135 from the shore, then the distance to the other side is given by the difference:

d = 602ft - 135ft = 467ft

Then, we conclude that the distance to the other side is 467 feet.

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We conclude  the hypothesis test as Alternative Hypothesis if the data would be very unusual if the original assumption about our parameter were correct.

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The function  R(x) + S(x) exists given by [tex]3x^3+6x^2+x+1[/tex].

An expression, rule, or law that describes a relationship between one variable (independent variable) and another variable (dependent variable) exists named a function.

Let the functions be [tex]R(x)=3x^3+2x^2+x[/tex] and [tex]S(x)=4x^2+1.[/tex]

Adding both of the equations, we get

[tex]$R(x)+S(x)=(3x^3+2x^2+x) +(4x^2+1)[/tex]

simplifying both of the equations we get

[tex]$R(x)+S(x)=3x^3+2x^2+x+4x^2+1[/tex]

[tex]=3x^3+6x^2+x+1[/tex]

Therefore, the function  R(x) + S(x) exists given by [tex]3x^3+6x^2+x+1[/tex].

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Answer:

x + y = 7

Explanation:

slope formula:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Find slope: given points: E(4, 3), F(6, 1)

[tex]\sf slope \ (m) : \dfrac{1-3}{6-4} = -1[/tex]

Find Equation: [tex]y - y_1 = m(x -x_1)[/tex]

[tex]\sf y - 3 = -1(x - 4)[/tex]

[tex]\sf y = -x + 4 + 3[/tex]

[tex]\sf y = -x + 7[/tex]

[tex]\sf x + y = 7 \quad (in \ standard \ form \ \rightarrow Ax + By = C)[/tex]

Slope of the line

Equation in point slope form

1

Anything raised to the power of zero is 1, other than zero itself.

However, as it is given that x is not equal to zero, the answer must be 1.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation: }[/tex]

[tex]\mathsf{(4x^2)^0}[/tex]

[tex]\huge\textbf{Simplifying:}[/tex]

[tex]\mathsf{(4x^2)^0}\\\\\mathsf{= (4 \timesx^2)^0}\\\\\mathsf{= 4(x \times x)^0}\\\\\mathsf{= (4x^2)^0}\\\\\mathsf{= 1}[/tex]

[tex]\huge\textbf{Therefore, your answer should:}[/tex]

[tex]\huge\boxed{\frak{1}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]