Find f(-2) for f(x) = 2 • 3^x

The least polynomial with degree 3 is equal to f(x) = x³ - (8 / 7) · x² + 4 · x - 32 / 7.

In this problem we need to determine the least polynomial such that its degree is 3 and - i 2 and 8 / 7 are roots of the resulting expression. By quadratic formula, the roots - i 2 is along with its conjugate i 2 to obtain a quadratic equation with real coefficients. The factor form of the cubic polynomial is:

f(x) = a · (x - r₁) · (x - r₂) · (x - r₃)

Where:

And we must determine the standard form of the polynomial by means of algebra properties. This form is shown below:

f(x) = a · x³ + b · x² + c · x + d

Where a, b, c, d are real coefficients.

First, write the polynomial in factor form: (a = 1)

f(x) = (x - 8 / 7) · (x + i 2) · (x - i 2)

f(x) = (x - 8 / 7) · (x² + 4)

f(x) = x³ - (8 / 7) · x² + 4 · x - 32 / 7

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The freight train is 88.88 feet long.

Speed = Distance/Time

Distance = Speed X Time

Time = Distance / Speed

As the trains travel in opposite direction then

Relative speed = (42 + 18) = 60 Km/ hr

                                            = 60 x 5/18 = 300/ 18

                                             = 100/9 m/s

So, length of the freight train = 100/9 x 8

                                               = 88.88 feet

Hence, The freight train is 88.88 feet long.

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Answer:

function 2

Step-by-step explanation:

function 1 has a slope of 8/7 which is equal to 0.75 and function 2 has a slope of 1 so function 2 is greater than function 1.

Answer: <

Step-by-step explanation:

One number is less than another number if their difference is less than zero.

Since x=2y-4 - 0.75 = -0.75 which is less than zero, x=2y-4 is less than 0.75

Therefore, x=2y-4 is 0.75 less/lower than 0.75

The incumbent is the current holder of an office or position, usually in relation to an election.

The variable of interest is:

X: Number of people that support the candidate.

You need to calculate the sample size to estimate the population proportion of supporters given a confidence level of 99% and a margin of error of 4%

The margin of error of the confidence level for the population proportion is

d = [tex]Z_{1} - \frac{\alpha }{2} * \sqrt{\frac{p^{|}(1 - p^{|} ) }{n} }[/tex]

=[tex]\frac{d}{Z_{1}-\alpha /2 } =\sqrt{\frac{p^{2}(1-p^{2} ) }{n} }[/tex]

sample proportion "p'" since there is no sample information, nor any previous information is known, you have to consider it as the "worse case scenario" and use the value of p'= 0.50

d= 0.04

She has to take a sample of 1045 people to estimate the population proportion of her supporters with a confidence level of 99% and a margin of error of 4%

=[tex]0.5*0.5*(\frac{2.586}{0.04} } )^{2} =1044.9=1045[/tex]

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Answer: (x-2)(x-10)

Step-by-step explanation:

1. Factor out 3x by diving everything by it, this makes the monomial 3x(x^2-12x+20)

2. From here, you do your basic factoring and reach that the answer is (x-2)(x-10)

lmk if you need more details for explanation

After the markup, the selling price of the item will be $39.

We know that a store owner decides to mark up all items by 30%, so basically we need to increase all the costs by 30%.

If the original cost is C, then the cost after the mark up will be:

P = C*(1 + 30%/100%)

P = C*(1 + 0.3)

P = C*(1.3)

In this case, we want to find the selling price P for an object whose original cost C is $30, then we can replace C in the equation above so we get:

P = $30*1.3 = $39

The selling price P  is $39.

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x=6

d=12

7x+12 or 7x+d

7(6) + 12 or (7x6) + 12 = 54

78-12 = 66

66/6 = 11

11x + 12 =78.

Answer:

x = 55

Step-by-step explanation:

[tex]\frac{x-5}{10}[/tex] = 5 ( multiply both sides by 10 to clear the fraction )

x - 5 = 10 × 5 = 50 ( add 5 to both sides )

x = 55

Slope of Parallel line is 3/4

Slope of Perpendicular line is -4/3

What is Slope of Line?

The slope of a line indicates its steepness. Slope is computed mathematically as "rise over run" (change in y divided by change in x).

Solution:

General Form of Line: y = mx + c

here, m is the slope

4y = 3x + 6

y = 3/4x + 3/2

Parallel Line have the same Slope = 3/4

Perpendicular Line:

Product of Slope = -1

Slope of Perpendicualr Line = -4/3

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Answer:

11.6 years

Step-by-step explanation:

Given

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

we can solve for [tex]t[/tex]

[tex]t=\frac{ln(\frac{A}{P} )}{n*ln(1+\frac{r}{n}) }[/tex]

We are given

[tex]A=1800\\P=900\\r=0.06\\n=12[/tex]

We can evaluate [tex]t[/tex].

[tex]t=\frac{ln(\frac{1800}{2} )}{12*ln(1+\frac{0.06}{12}) }[/tex]

[tex]t=11.6[/tex]

Answer:

Step-by-step explanation:

to put into an equation:

8c=6.00

c=6.00/8

c=$0.75

The cost of one apple is $0.75

Answer:

i think it would be a; When the price of housing increases, more homeowners want to sell their house.

Answer: no

Step-by-step explanation:

Recipe calls for a 3:4 ratio of raisins to peanuts

If his intention was to make a 1.5x recipe, he should have used 6 cups peanuts and 4-1/2 cups raisins (not 5!) to make the recipe in the correct ratio.

Answer:

C

Step-by-step explanation:

Linear Function- points on a graph that make up a straight line negative or positive.

Only Values of (C) makes a perfect line.

The standard form equation for the line through the points (3,-4) and (6,-2) is  -2/3 x + y = 4.

What is the equation of the line passing through the two-point?

To find the equation for the line through two points we can use the formula:

y - y1 = m(x - x1)

where (x1, y1) is one of the points, and m is the slope of the line. The slope of the line is equal to the change in y over the change in x, which can be calculated as:

m = (y2 - y1) / (x2 - x1)

where (x2, y2) is the other point.

Substituting the given points and the formula for the slope into the formula for the equation of the line, we get:

y - (-4) = ((-2) - (-4)) / (6 - 3) (x - 3)

This simplifies to:

y + 4 = -2/3 (x - 3)

To write the equation in standard form, we can distribute the -2/3 and then rearrange the terms:

-2/3 x + y = 4

Hence, the standard form equation for the line through the points (3,-4) and (6,-2) is  -2/3 x + y = 4

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A rectangle is one of the types of four sided figures generally refers to as quadrilaterals. The required proof is as stated below:

Rectangles, Parallelograms, square, trapezium, kite and rhombus are a family of quadrilaterals, since they all have four straight sides. Each of these figures have individual properties that can be used to differentiate one from the other.

Some peculiar properties that can be used to identify a rectangle are:

Therefore to prove that IJKL is a rectangle;

<1  ≅  <2 (Given)

IL ≅ JK (opposite sides are equal)

IJ  ≅  LK (opposite sides are equal)

IK  ≅ JL (diagonals have equal length)

M is the midpoint of IK and JL respectively.

<JIK  ≅ <IKL (alternate angles property)

<IJL  ≅  <KLJ (alternate angles property)

IL ⊥ IJ

IJ ⊥ JK

JK ⊥ LK

LK ⊥ LI

Therefore, the given figure is a rectangle.

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The value of expression  13 1/3 divided by 2/3 would be; 20

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.

We need to find the expression of 13 1/3 divided by 2/3

Therefore,

40/3 divided by 2/3

40/3 x 3/2

20

Therefore, The value of expression  13 1/3 divided by 2/3 would be; 20

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The ending Raw Materials Inventory balance for March is 31,800.

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots.

Main Body:

We use the Inventory identity to solve for ending inventory

Beginning Inventory + Purchase = ending Inventory + used

20,800 +159,000 = ending inventory + used materials

used materials:

135,600 direct

12,400 indirect

148,000 total materials used

20,800 + 159,000 = Ending Inventory + 148,000

20,800 + 159,000 - 148,000 = Ending Inventory

Ending Inventory = 31,800

Hence the ending Raw Materials Inventory balance for March is 31,800.

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True. An ordinary regression (or ANOVA) model that treats the response Y as normally distributed is a special case of a GLM, with a normal random component and identity link function.

A flexible framework for modeling the relationship between a response variable Y and one or more predictor variables X is called a generalized linear model (GLM).

A GLM model allows for the use of non-identity link functions as well as for the response variable to have a distribution other than the normal distribution.

If we consider an ordinary regression model or an analysis of variance (ANOVA) model that assumes a normal distribution of response variable Y, this can be considered a special case of a GLM, with the normal distribution as the random component and the identity link function.

Here,  the variance of the response is assumed to be constant, and the mean of the response variable is assumed to be a linear function of the predictor variables.

Let

Y ~ N(μ,σ²)

μ = β₀ +β₁X₁ + β₂X₂ + ... + βₙXₙ

In this case, a normal distribution, with mean μ and variance σ² id followed by response variable Y.

here we can see that the mean μ is a linear function of the predictor variables X₁, X₂, ..., Xₙ, with coefficients β₀, β₁, β₂, ...,βₙ.

The identity link function, that is, that μ is equal to the predicted value of Y is used.

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The estimate of the average height of all the trees having a trunk diameter of 7 inches is y = 18.1 feet. This is obtained by using the LSRL equation. Option A is the correct value.

The LSRL equation is defined as the Least squares regression line. This is the line that minimizes the variance. So, it is the best line of fit for a set of data points.

The equation is in the form of Y = a + bX

Here a is the intercept and b is the slope.

It is given that,

X is given as the diameter of a tree trunk in inches

Y is given as the tree height in feet

The given data points are:

X: 4, 2, 8, 6, 10, 6

Y: 8, 4, 18, 22, 30, 8

For these data points, the least squares regression line is given by the equation Y = - 3.6 + 3.1X

So, the estimate of the average height of all trees having a trunk diameter of 7 inches is

Y = - 3.6 + 3.1X ⇒ Y = -3.6 + 3.1 × 7

⇒ Y = -3.6 + 21.7

∴ Y = 18.1 feet

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Answer:

Step-by-step explanation:

Find the equation of lines m, n and p

                    The equation of line:      

                       [tex]\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]

Line m: (-3,2)  (3,6)

x₁=-3   x₂=3   y₁=2   y₂=6

[tex]\displaystyle\\\frac{x-(-3)}{3-(-3)} =\frac{y-2}{6-2} \\\\\frac{x+3}{3+3} =\frac{y-2}{4} \\\\\frac{x+3}{6}=\frac{y-2}{4}[/tex]

Multiply both parts of the equation by 4:

[tex]\displaystyle\\\frac{x+3}{6}(4)=y-2\\\\\frac{2}{3} (x+3)=y-2\\\\\frac{2}{3}x+2=y-2\\\\\frac{2}{3}x+2+2=y-2+2\\\\\frac{2}{3}x+4=y\\\\Thus,\ y=\frac{2}{3} x+4\\\\Hence,\ m_m=\frac{2}{3}[/tex]

Line n: (-5,-5)  (5,1)

x₁=-5   x₂=5   y₁=-5   y₂=1

[tex]\displaystyle\\\frac{x-(-5)}{5-(-5)}=\frac{y-(-5)}{1-(-5)} \\\\\frac{x+5}{5+5}=\frac{y+5}{1+5} \\\\\frac{x+6}{10}=\frac{y+5}{6}[/tex]

Multiply both parts of the equation by 6:

[tex]\displaystyle\\\frac{3}{5}( x+5)=y+5\\\\\frac{3}{5} x+3 =y+5\\\\\frac{3}{5} x+3-5=y+5-5\\\\\frac{3}{5} x-2=y\\\\Thus,\ y=\frac{3}{5}x-2\\\\Hence,\ m_n=\frac{3}{5}[/tex]

Line p: (3,-4)  (-3,6)

x₁=3   x₂=-3   y₁=-4   y₂=6

[tex]\displaystyle\\\frac{x-3}{-3-3} =\frac{y-6}{6-(-4)} \\\\\frac{x-3}{-6} =\frac{y-6}{6+4} \\\\\frac{x-3}{-6}=\frac{y-6}{10} \\[/tex]

Multiply both parts of the equation by 10:

[tex]\displaystyle\\-\frac{5}{3} x+5=y-6\\\\-\frac{5}{3} x+5+6=y-6+6\\\\-\frac{5}{3} x+11=y\\Thus,\ y=-\frac{5}{3}x+11 \\\\Hence,\ m_p=-\frac{5}{3}[/tex]

[tex]Question# 5: \ m_m\neq m_n\ \ \ \ m\ isn't\ parallel \ to\ n\\\\Question# 6:\ m\ isn't \ congruent \ to\ p\\\\Question#7 :\ n\ isn't \ congruent \ to\ p[/tex]

[tex]n \bot p[/tex]

Answer:

5) No the lines are not parallel because in order for this to be true, the slopes have to be equal. Line m has a slope of 2/3 and line n has a slope of 3/5. Both slopes are not equal so it is not parallel

6) No, m is not congruent to p

7) No, n is not congruent to p

(Is there any chance that you meant to say perpendicular instead of "congruent"?)

Step-by-step explanation:

For two lines to be parallel the slopes have to be equal

See attached to see the rise over run

line m: 2/3

line n: 3/5

The slopes are not equal so the lines are not parallel.

Answer:

x=6

Step-by-step explanation:

6x-16=20

Add 16 to both sides

6x-16=20

    +16. +16

6x=36

Divide 6 to both sides

6x=36

/6. /6

x=6

Hopes this helps please mark brainliest

Answer:

x = 6

Step-by-step explanation:

Given equation,

→ 6x - 16 = 20

Now the value of x will be,

→ 6x - 16 = 20

→ 6x = 20 + 16

→ 6x = 36

→ x = 36/6

→ [ x = 6 ]

Hence, the value of x is 6.

Answer: 6

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.  

Input the numbers that you are given.

|(2)(7)|−(−4) / 3    (Input the numbers)

=|14|−(−4) / 3       (Multiply your numbers, then you get 14.

=14−(−4) / 3     (find the absolute value (always will be positive) )

=18/3           (Change the fraction into a whole number)

=6

Answer:

$5000

Step-by-step explanation:

Let x represent the amount invested at 6% interest. Then 7000-x is the amount invested at 7% interest

6% interest = 6/100 = 0.06 in decimal

7% interest = 7/100 = 0.07

Interest earned from depositing x dollars at 6% = 0.06x

Interest earned from depositing 7000-x at 7% = 0.07(7000-x)

Total interest earned would be
0.06x + 0.07(7000-x)

Since this must be at least $440 we get the equation interest as

0.06x + 0.07(7000-x) = 440

Simplifying
0.06x + 0.07 x 7000 - 0.07x = 440

0.06x + 490 -0.07x = 440

-0.01x = 440 - 490

-0.01x = -50

Multiply both sides by -1

==> 0.01x = 50

==> x = 50/0.01 = 5000

So max amount that can be invested at 6% interest = $5000

Answer:

y = -2x + 5

Step-by-step explanation:

To find the slope use rise over run

To find the y-intercept see where the line intersects in the y-axis line

In 2000, the population of the state was 23.1 million and the population of the state reach 28.3 million in 2013

From the question, we have the following parameters that can be used in our computation:

A=23.1 е⁰⁰¹⁵²⁺

Also from the question, we have

The variable t represents the number of years after 2000.

This means that

t = Current year - 2000

Substitute the known values in the above equation, so, we have the following representation

t = 2000 - 2000

Evaluate

t = 0

So, we have

A=23.1 е⁰⁰¹⁵² ˣ ⁰

Evaluate the above equation

A = 23.1

Here, we have

A = 28.3

Substitute the known values in the above equation, so, we have the following representation

23.1 е⁰⁰¹⁵²⁺ = 28.3

Divide both sides by 23.1

е⁰⁰¹⁵²⁺ = 1.22510822511

Take the natural logarithm of both sides

0.0152t = 0.203

So, we have

t = 0.203/0.0152

Evaluate

t = 13

So, the year is

Year = 2000 + 13

Year = 2013

This means that the population of the state reach 28.3 million in 2013

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The required probability of winning is given as 0.32.

Given that,
Playing a game that involves tossing a single die. If roll one, you win $100. If you roll a 2, you win $50. roll anything else, you lose $25.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

here,
total number of sample spaces = 6
total of favorable outcome = 2
Probability fo the winning = 2 / 6 = 0.3333 or 0.32

Thus, the required probability of winning is given as 0.32.

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Answer:

x = 64

Step-by-step explanation:

63.         28

----    =    ----

144.         x

Now cross multiply:

144(28) = 63(x)

4,032 = 63x

x = 64

May I have a brainliest? Thank you!

Answer:

Step-by-step explanation:

23-15=8 (pour savoir combien elle a dépenser en tout)

8 diviser par 2= 4 (pour savoir le prix d'un stylo)

chaque stylo vaut 4 $