Given the function f(x) = 3x2+2x+4, find f(−2). You must show at least 3 lines of work.

The rectangular form of Θ = 3π/4 will be; y + x = 0.

Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.

On converting the rectangluar to polar form of the complex number;

x = rcosθ and y = rsinθ

z = r(cosθ+isinθ)

r is the modulus of the complex number and θ is the argument

r =√x²+y² and θ = tan⁻¹y/x

Given the Θ = 3π/4

Therefore, θ = tan⁻¹y/x  = 3π/4

y/x  = tan (3π/4)

Now multiply both side by x

yx/x  = tan (3π/4) x

y =  tan (3π/4) x

Thus, y = -x

in rectangular form y + x = 0

Hence, the rectangular form of Θ = 3π/4 will be; y + x = 0.

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Answer:

Step-by-step explanation:

Define Variables:

Let p= the price of each peach

Let m=the price of each mango

One peach costs $p, so 5 peaches cost 5p. One mango costs $m, so 6 mangos cost 6m. The total cost 5p+6m equals $17.75:

5p+6m=17.75

Likewise, if 2 peaches and 3 mangos cost $8, then:

2p+3m=8

Write System of Equations:

5p+6m=17.75

2p+3m=8

System of equations that could be used to determine the price of each peach and the price of each mango is 5p + 6m = 17.75 and 2p + 3m = 8.

Let p= the price of each peach

Let m=the price of each mango

One peach costs $p, so 5 peaches cost 5p. One mango costs $m, so 6 mangoes cost 6m. The total cost 5p+6m equals $17.75:

5p+6m=17.75

Likewise, if 2 peaches and 3 mangoes cost $8, then:

2p+3m=8

System of Equations:

5p+6m=17.75

2p+3m=8

Therefore System of equations that could be used to determine the price of each peach and the price of each mango is 5p + 6m = 17.75 and 2p + 3m = 8.

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In the first function have vertical compression by 1/2, in second function have horizontal compresion by 1/4, in third compression have Vertical reflection and in fourth function have Horizontal reflection and horizontal compression by 1/2.

In the given question we have to find the transformations that map the function y = [tex]8^x[/tex] onto each function.

Since we have to find the transformation, so we know that in a transformation;

The transformation from the first equation to the second one can be found by finding a, h and k for each equation.

[tex]y=ab^{x-h}+k[/tex]

The horizontal is define by the value of h. The horizontal shift is defined as:

g(x)=f(x+h) - The graph is shifted to the left h units.

g(x)=f(x−h) - The graph is shifted to the right h units.

Horizontal Shift: None

The vertical shift define on the value of k. The vertical shift is defined as:

g(x)=f(x)+k - The graph is shifted up k units.

g(x)=f(x)−k - The graph is shifted down k units.

Vertical Shift: None

The value of a describes the vertical stretch or compression of the graph.

a>1 is a vertical stretch

0<a<1 is a vertical compression.

(a) The given first function is [tex](\frac{1}{2})8^{x}[/tex].

y = [tex]8^x[/tex]

Combine [tex]8^x[/tex] and 1/2.

y = [tex]8^x[/tex]/2

Assume that

y = [tex]8^x[/tex]  is f(x)=[tex]8^x[/tex] and y= [tex](\frac{1}{2})8^{x}[/tex] is g(x)= [tex](\frac{1}{2})8^{x}[/tex].

On comparing the equation [tex]y=ab^{x-h}+k[/tex]

The value of a, h, and k for f(x)=[tex]8^x[/tex].

a=1, h=0, k=0

The value of a, h and k for g(x)=[tex](\frac{1}{2})8^{x}[/tex].

a=1/2, h=0, k=0

Since the value of h and k so tnere is no horizontal and vertical shift.

SInce the value of a changes from 1 to 1/2 and 1/2 is greater that 0 but less than 1 so there is vertical compression by 1/2.

(b) The given second function is [tex]8^{4x}[/tex].

y= [tex]8^{4x}[/tex] is g(x)= [tex]8^{4x}[/tex].

On comparing the equation [tex]y=ab^{x-h}+k[/tex]

The value of a, h and k for g(x)=[tex]8^{4x}[/tex].

a=1/4, h=0, k=0

Parent Function: f(x)=8^x

So, Horizontal Shift: None, Vertical Shift: None, Reflection about the x-axis: None, Vertical Compression or Stretch: None, horizontal compresion by 1/4.

(c) The given third function is [tex]-8^{x}[/tex].

y= [tex]-8^{x}[/tex] is g(x)= [tex]-8^{x}[/tex].

The value of a, h and k for g(x)=[tex]-8^{x}[/tex].

a=-1, h=0, k=0

Parent Function: f(x)=8^x

So, Horizontal Shift: None, Vertical Shift: None, Reflection about the x-axis: Reflected, Vertical Compression or Stretch: None.

Vertical reflection

(d) The given fourth function is [tex]8^{-2x}[/tex].

y= [tex]8^{-2x}[/tex] is g(x)= [tex]8^{-2x}[/tex].

The value of a, h and k for g(x)=[tex]8^{-2x}[/tex].

a=-1/2, h=0, k=0

Parent Function: f(x)=8^x

So, Horizontal Shift: None, Vertical Shift: None, Reflection about the x-axis: Reflected, Vertical Compression or Stretch: None.

Horizontal reflection and horizontal compression by 1/2.

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Total students who graduated this year from this university is 3000.

This is a normal distribution problem with

Mean , μ = $20,000

Standard deviation, σ = $8,000

If 189 of the recent graduates have salaries of at least $32240.

Then, We first find the percentage of LU graduates with salaries more than $32240.

Required probability = P(x ≥ 32240)

We first normalize or standardize $32,240, then as we know,

z = (x - μ)/σ

= (32240 - 20000)/8000 = 1.53

The required probability:

P(x ≥ 32240) = P(z ≥ 1.53)

We'll use data from the normal probability table for these probabilities

P(x ≥ 32240) = P(z ≥ 1.53) = 1 - P(z < 1.53)

= 1 - 0.93699

= 0.06301

= 6.301%

So, 6.301% of the graduates this year = 189

Total Number of graduates this year = (189/0.06301) = 2999.5 = 3000 graduates this year.

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As per the given graph, the correct statement is option (A) The median of the density curve is 3.

Median:

Basically, median refers the middle value in a set of data.

And it can be obtained by organize and order the data from smallest to largest. And to find the midpoint value, divide the number of observations by two. And then if there are an odd number of observations, round that number up, and the value in that position is the median.

Given,

Here we have the graph.

Now, we have to identify in with of the option is correct according to the given graph.

While we looking into the given graph,

We have identified that it form the triangle and as the middle point as 3.

So, based on this fact me have identified that the median density of the curve is 3.

Therefore, the option (A) The median of the density curve is 3.

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Step-by-step explanation:

in that setup they will both explode after traveling the same distance.

A is just going faster and has to launch therefore a little bit later.

so, we need to make an equation based on distance traveled and find in that process the number of seconds needed to travel that distance.

speed is distance/time, so we need to multiply speed by time to get distance.

x = seconds for B

x - 0.25 = seconds for A

A is launched after B but explodes at the same time.

so, A's trip is of shorter time than B's trip.

(x - 0.25)×360 = x×320

360x - 90 = 320x

40x - 90 = 0

40x = 90

4x = 9

x = 9/4 = 2.25 seconds

both fireworks will explode 2.25 seconds after B launches (and 2.25 - 0.25 = 2 seconds after A launches).

the explosion will be at

320×2.25 = 360×2 = 720 feet height.

Value of x is 1.411

Given Eq.

[tex]9^{x+2} = 2^{5x-4} \\\\[/tex]

Applying exponent rules

[tex](x+2)ln(9) = (5x-4)ln(2)\\[/tex]

Solving for x

[tex]x = \frac{4ln(6)}{5ln(2)-2ln(3)}[/tex]

[tex]x = \frac{1.791}{5(0.693)-2(1.098)}[/tex]

[tex]x = \frac{1.791}{3.465-2.196} \\[/tex]

[tex]x = \frac{1.791}{1.269}[/tex]

[tex]x = 1.411[/tex]

Value of x is 1.411

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The numbers below to put them in order from least to greatest will be 6.42, 6.453, 6.486, 6.497, 6.53, and 6.66.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that the numbers are,6.42,6.53,6.497,6.66,6.453,6.486.

Ascending order refers to a list of numbers that are arranged from least to greatest. The numbers are arranged in ascending order in this form. The first figure must be less than the second figure. It is referred to in descending order when the numbers are listed from greatest to least.

Thus, the numbers below to put them in order from least to greatest will be 6.42, 6.453, 6.486, 6.497, 6.53, and 6.66.

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A) Chi-square test can be used if one of the samples has a value of less than five is the correct option.

Chi-square distribution and Chi-square test for independence:

The assumptions for the chi-square test are:

Hence, options (b), (c), and (d) are the assumptions that are true for chi-square test. Therefore, the options (b), (c), and (d) are considered incorrect.

Hence, option (a), that is, “a Chi-square test can be used if one of the samples has a value of less than five” is the correct option.

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We can change the base formula by:

                           logₐ b = logₓ a /logₓ b

                                         OR

                           logₓ a, logₓ b = logₓ a

The change of base formula is used to change the base of a logarithm.  We know that "log" stands for a logarithm of base 10 and "ln" stands for a logarithm of base e. But there is no option to calculate the logarithm of a number with any other bases other than 10 and e.

The change of base formula solves this issue of changing base from e to 10, and from base 10 to e. Also, it is used in solving several logarithms problems.

Base Formula: -

The change of base formula is used to write a logarithm of a number with a given base as the ratio of two logarithms each with the same base that is different from the base of the original logarithm. This is a property of logarithms. You can see the change of base formula here.

Change of base formula

                            logₐ b = logₓ a /logₓ b

                                         OR

                            logₓ a, logₓ b = logₓ a

Change of Base Formula

Change of base formula can be represented as follows. Here the base of the given logarithm is also changed to a logarithm with a new base. The basic logarithm with a base is transformed to two logarithms with a new and same base. The change of base formula is:

                          logₐ  b = [logₐ x] / [logₐ y]

In this formula,

Change of Base Formula Derivation

Change of base formula derivation can be understood from the following steps. Let us assume that

log ₐ b = p, logₙ a = q, and logₙ b = r.

By converting each of these into exponential form, we get,

a = [tex]b^{p}[/tex], a = [tex]x^{q}[/tex], and b = [tex]n^{r}[/tex]

From the first two equations,

[tex]x^{q}[/tex] = [tex]n^{r}[/tex]

Substituting b =  [tex]n^{r}[/tex] (which is from third equation) here,

([tex]n^{r}[/tex])[tex]^{p}[/tex] = [tex]x^{q}[/tex]

[tex]n^{r}[/tex])[tex]^{p}[/tex] = [tex]x^{q}[/tex](Using a property of exponents)

p r = q

p = q / r

Substituting the values, we get,

logₐ  b = [logₐ x] / [logₐ y]
For Example:

Evaluate the value of log₆₄ 8 using the change of base formula.

Solution:

We will apply the change of base formula (by changing the base to 10). Note that log₁₀ is same as log.

log₆₄ 8 = [log 8] / [log 64]

            = [log 8] / [log 82]

            = [log 8] / [2 log 8]              [∵ log am = m log a]

            = 1 / 2

Answer: log₆₄ 8 = 1 / 2

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to get the slope of any straight line, we simply need two points off of it, so let's use those two in the picture below.

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-1)}}} \implies \cfrac{-8}{1 +1} \implies \cfrac{ -8 }{ 2 } \implies - 4[/tex]

Answer:

No, Eduardo made a mistake from Step 1 to Step 2. Eduardo should have subtracted 4 from 6 instead of evaluating the exponent. The order of operations says to perform all operations inside parentheses first.

Answer:

B

Step-by-step explanation:

We can notice that based on the given pattern, the average rate of change from [tex]x=n[/tex] to [tex]x=n+1[/tex], where [tex]n \in \mathbb{Z}[/tex], is [tex]-2n-1[/tex].

So, the average rate of change from [tex]x=8[/tex] to [tex]x=9[/tex] is [tex]-2(8)-1=-17[/tex].

The rate of change for the interval from x = 8 to x = 9 is -17.

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.

The relationship defining how one quantity changes in relation to the change in another quantity is given by the rate of change formula.

We know the standard form of quadratic function

y = a (x - b)² + c with vertex (b, c)

Since the vertex is (0, -1) then b= 0, c= -1.

Then, the quadratic equation is:

y= ax² - 1 passes through (1, 2), (2, -5),.....

So, the rate of change in interval (8, 9) is

= y(9)- y(8)/ (9-8)

= -9² -1 - 8² - 1/ 1

= -17.

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Check the picture below.

The order of in which the operation in the expression 9 + 3·2² - 1·4, indicates;

3. (a) The value of the expression, 9 + 3·2² - 1·4 is 17

(b) The left and right side of the grouping symbol (the left side) should be placed between the number 3 and 2 and then (the right side should be placed between 1 and 4, so that we get;

9 + 3 × (2² - 1) × 4 = 45

The order of operations is a rule or guide, that states the sequence in which the operations in an expression are to be performed.

3. The specified expression is; 9 + 3·2² - 1·4

(a) The value of the expression 9 + 3·2² - 1·4 can be found using the order of operation of PEMDAS, which stands for; operations from left to right, items in Parenthesis, then Exponents, followed by Multiplication, and Division first then Addition and Subtraction of the terms from left to right as follows;

Therefore;

9 + 3·2² - 1·4 = 9 + 3 × 4 - 1 × 4 = 9 + 12 - 4 = 17

(b) A grouping symbol is the parenthesis.

The location of the parenthesis in the specified expression so that the value is 45 can be found as follows;

Placing the grouping symbol between 3 and 2 and the right parenthesis between 1 and 4, we get;

9 + 3·2² - 1·4 = 9 + 3·(2² - 1)·4 = 9 + 3 × (2² - 1) × 4

9 + 3 × (2² - 1) × 4 = 9 + 3 × (3) × 4 = 9 + 36 = 45

The location to place the grouping symbol so that the value of the expression is 45 is between 3 and 2 and between 1 and 4.

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Answer:

C

Step-by-step explanation:

The actual attendance at the baseball game is 7168 fans

A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics. The abbreviations "pct," "pct," and occasionally "pc" are also used to represent percentage in addition to the symbol "%". A% has neither a recognized unit of measurement nor any dimensions. Take this as an example: There will be 50 men in the class if there are 100 students total and there are 50 men in the class. There are 250 male students overall, or 250 out of 500.

Given,

The actual attendance at the game=5600 fans

Also given that, the threat of a storm caused many to stay home, and his prediction wound up being 28% higher than the actual attendance.

Then,

28% of 5600

=5600×(28/100)

=1568

Total=5600+1568

Total=7168

Therefore, the actual attendance at the baseball game is 7168 fans.

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Answer:

4,375 fans

Step-by-step explanation:

percent error= amount of error/correct amount

1.28x=5600

1.28x/1.28= 5000/1.28

x=4375

Answer:

I think you are right.Because im sure

Applying the triangle midsegment theorem:

a. x = 17; y = 2

b. Length of DF = 20 units.

The triangle midsegment theorem states that the midsegment of a triangle is always parallel to the third side, and has a length that is half the length of the third side of the triangle.

GH is said to be the midsegment of triangle DEF, therefore:

a. GH = 1/2(EF) [triangle midsegment theorem]

Substitute

x - 3 = 1/2(28)

2(x - 3) = 28

2x - 6 = 28

2x = 28 + 6

2x = 34

2x/2 = 34/2

x = 17

HF = x - 7

Plug in the value of x

HF = 17 - 7

HF = 10

HF = DH = 10

y + 8 = DH

y + 8 = 10

y = 10 - 8

y = 2

b. Length of DF = HF + DH

Length of DF = 10 + 10 = 20 units.

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The given polynomial is a binomial and the degree is 2.

In a given expression if we have to know the degree of the polynomial we must look at the HIGHEST degree of the polynomial. This along with the table given below will help us identify the degree of the polynomial.

Degree 0 Constant Polynomial

Degree 1          Linear Polynomial

Degree 2 Quadratic Polynomial

Degree 3 Cubic Polynomial

Degree 4 Quartic Polynomial

The above mentions the various degrees of the polynomial , you may refer to it for future references .

The given expression is [tex]15x^2[/tex]

since the degree of the given polynomial is 2

the given is a binomial polynomial .

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Answer:

-24

Step-by-step explanation:

-3[-4(3-10)-12]/-2(-1)

-3[-4(-7)-12]/2

-3[28-12]/2

-3[16]/2

-48/2

-24

Hopes this helps

Answer:

? ≈ 5.01

Step-by-step explanation:

using the sine ratio in the right triangle

sin24.3° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2.06}{?}[/tex] ( multiply both sides by ? )

? × sin24.3° = 2.06 ( divide both sides by 24.3° )

? = [tex]\frac{2.06}{sin24.3}[/tex] ≈ 5.01 ( to 3 significant figures )

Answer: 24

Step-by-step explanation:

You can use proportions to calculate this:

[tex]\frac{6}{2} =\frac{x}{8} \\\\2x=6*8\\\\2x=48\\\\x=\frac{48}{2} =24[/tex]

The system of equations is x + y = 11 and 2x + 3y = 29 and variables are x and y.

Let us assume the number of two point shots be x and the number of three point shots be y. Forming the equation now -

x + y = 11 : Equation 1

2x + 3y = 29 : Equation 2

Rewriting the equation 1 as per x.

x = 11 - y : Equation 3

Keep the value of x form equation 3 in equation 2

2(11 - y) + 3y = 29

Performing multiplication on Left Hand Side of the equation

22 - 2y + 3y = 29

y = 29 - 22

y = 7

Keep the value of y in equation 3.

x = 11 - 7

x = 4

So, the two point shots are 4 and three points shots are 7. The variables are x and y and system of equations are equation 1 and equation 2.

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Answer:

For example, a population with a 2% annual growth would have a doubling time of 35 years.Mar 24, 2015

Step-by-step explanation:

Answer:

y = x + 6

Step-by-step explanation:

y = mx + c

2 = -4m + c

-2 = -8m + c

2 + 4m = c

-2 = -8m + 2 + 4m

-2 - 2 = -4m

-4 = -4m

-4/-4 = m

m = 1

2 + 4(1) = c

c = 6

y = x + 6