Evaluate the function f(x)= x^2 + 2x + 8 at the given values of the independent variable and
simplify.



a. f(6)
b. f(x+4)
c. f(-x)

The system of equations has infinitely many solutions, which corresponds to option (OB).

We can use the graphing function on a calculator to find the solution to the system of equations:

\(3y - 12x = 18\\\\2y - 8x = 12\)

To do this, we can rearrange each equation to solve for y in terms of x:

\(3y = 12x + 18\\\\y =4x + 6\)

For the second equation.

\(2y = 8x + 12\\\\y = 4x + 6\)

We can see that the two equations have the same slope (4) and y-intercept (6). Therefore, the two equations represent the same line, and any point on that line will satisfy both equations.

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Answer:

2.5 km/h

Step-by-step explanation:

Here we have a distance problem where we are given the distance the time time:

Rate = ?

Time = 2hrs

Distance = 5km

The simplest way to do this is to rearrange the formula to suit our need and plug in the numbers:

\(R*T=D\\R*\frac{T}{T}=\frac{D}{T} \\R=\frac{D}{T}\)

Now, plug in the numbers and solve:

\(R=\frac{D}{T}\\R=\frac{5}{2} \\R=2.5\)

On solving the provided question, we can say that Probability(A and B) = P(A)P(B|A) and P(E or F) = P(E) + P(F) - P(E and F)

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

Probability(A and B) = P(A)P(B|A).

P(A and B) = P(B and A), this may also be written as P(A and B) = P(B)P(A|B).

Using the general multiplication rule, we have

P(E and F) = P(E)P(F|E)

.392 = P(E)(.7)

P(E) = .56

   P(E and F) = P(F)P(E|F)

.392 = P(F)(.56), so

P(F) = .7

P(E or F) = P(E) + P(F) - P(E and F)

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Answer: 47.5

Step-by-step explanation:

Given

2x-10+x+x=180

combine like term x      

       4x-10=180

addition property of equality (add 10 on both sides)

             4x=190

division property (divide 4 on both sides)

               x=47.5

Hope this helps!! :)

Please let me know if you have any question or need any further explanation

Answer:

your answer will be 47.5

Step-by-step explanation:

the set F of the factors of 6 :

F ={1, 2, 3, 6}

The measure of dispersion that measures how much the data differ from the mean is called the standard deviation.

Standard deviation is a statistical measure of dispersion as opposed to the measure of central tendency like mean, median and mode.

The standard deviation is a measure of how spread out data values are around the mean.

It is defined as the square root of the variance and represented with the Greek letter σ.

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The number of distinct color groupings is given as follows:

39,916,800.

The number of possible arrangements of n elements(order n elements) is given by the factorial of n, that is:

\(A_n = n!\)

For this problem, we have that there are 11 tubes of paint, hence the parameter n is given as follows:

n = 11.

Meaning that the number of distinct color groupings is given as follows:

n = 11! = 1139,916,800.

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Therefore, if 24 teaspoons of vegetable oil were used, we would need 16 teaspoons of vinegar to make the recipe correctly.

According to a salad recipe, each serving requires 6 teaspoons of vegetable oil and 9 teaspoons of vinegar. If 24 teaspoons of vegetable oil were used, we can determine the amount of vinegar needed for the recipe to be correct as follows:

First, we must determine the ratio of vinegar to oil in the recipe. To do this, we divide the amount of vinegar needed per serving (9 teaspoons) by the amount of oil needed per serving (6 teaspoons):

9 ÷ 6 = 1.5

This means that for every 1.5 teaspoons of oil used, we need 1 teaspoon of vinegar. Next, we use this ratio to determine the amount of vinegar needed when 24 teaspoons of oil are used:

1.5 ÷ 1 = 1.5

(teaspoons of oil per 1 teaspoon of vinegar)

24 ÷ 1.5 = 16

(teaspoons of vinegar needed)

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The probability of drawing the ace of spades is 1/52 for the first card and 1/51 for the second card. P(B|As) ≈ 0.1176.

The likelihood of drawing the trump card on the primary draw is for sure 1/52. Be that as it may, when the principal card is drawn, there are presently 51 cards remaining, and only one of them is the trump card. In this way, the likelihood of drawing the trump card on the subsequent draw, considering that the principal card isn't the trump card, is 1/51.

With regards to the issue, the occasion As is characterized as the trump card being picked, whether or not it is the first or second card. Since the issue determines that the two cards are drawn without substitution, there are two cases to consider: either the trump card is drawn first, with likelihood 1/52, or it is drawn second, considering that the principal card isn't the trump card, with likelihood (51/52)*(1/51) = 1/52. Accordingly, the likelihood of occasion Similar to the amount of these two probabilities, which is 1/52 + 1/52 = 1/26.

Utilizing Bayes' recipe, we have:

P(B|As) = P(As|B) * P(B)/P(As)

We previously determined P(As) to be 1/26. To ascertain P(As|B), note that in the event that the two cards are aces, the trump card should be one of them, so P(As|B) = 1. At last, to compute P(B), note that there are (4 nCr 2) = 6 methods for picking two aces out of the four in the deck, and there are (52 nCr 2) = 1326 methods for picking two cards out of the deck without substitution, so P(B) = 6/1326 = 1/221.

Subbing these qualities into Bayes' recipe, we get:

P(B|As) = 1 * (1/221)/(1/26) = 26/221 ≈ 0.1176

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Answer:

Mode is 83

Median is 85

Step-by-step explanation:

To find the median: Arrange the data points from smallest to largest.

To find the mode: Place all numbers in a given set in order; this can be from lowest to highest or highest to lowest, and then count how many times each number appears in the set

Answer:

5 years

Step-by-step explanation:

Principal Amount to be paid=$4500

Interest rate = 2%

Number if Times compounded= number of years

Number of years = x

Among total= $5010

A= p(1+r/n)^(nt)

But n= t =x

A= p(1+r/x)^(x²)

5010=4500(1+0.02/x)^(x²)

5010/4500 = (1+0.02/x)^(x²)

1.11333=( 1+0.02/x)^(x²)

Using trial and error method the number of years maximum to give approximately $5010 is 5 years

Answer: C

Step-by-step explanation:

Point D is at -14 on the number line.

In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).

Since E is the midpoint of line segment CD, we can logically deduce the following relationship:

Line segment CD = Line segment C + Line segment D

Midpoint E = (point C + point D)/2

By substituting the given points into the equation above, we have the following:

-3 = (8 + D)/2

-6 = 8 + D

D = -6 - 8

D = -14

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Answer:

\((x-5-\sqrt{19})(x-5+\sqrt{19})\)

Step-by-step explanation:

1) In general, given \(ax^2+bx+c\), the factored form is:

\(a(x-\frac{-b+\sqrt{b^2-4ac} }{2a} )(x-\frac{-b-\sqrt{b^2-4ac} }{2a})\)

2) In this case, \(a=1\), \(b= -10\) and \(c=6\).

\((x-\frac{10+\sqrt{(-10)^2-4\times6} }{2} )(x-\frac{10-\sqrt{(-10)^2-4\times6} }{2} )\)

3) Simplify.

\((x-\frac{10+2\sqrt{19} }{2} )(x-\frac{10-2\sqrt{19} }{2} )\)

4) Factor out the common term \(2\).

\((x-\frac{2(5+\sqrt{19)} }{2} )(x-\frac{10-2\sqrt{19} }{2} )\)

5) Cancel \(2\).

\((x-(5+\sqrt{19} ))(x-\frac{10-2\sqrt{19} }{2} )\)

6) Remove parentheses.

\((x-5-\sqrt{19} )(x-\frac{10-2\sqrt{19} }{2} )\)

7) Factor out the common term \(2\).

\((x-5-\sqrt{19} )(x-\frac{2(5-\sqrt{19}) }{2} )\)

8) Cancel \(2\).

\((x-5-\sqrt{19})(x-(5-\sqrt{19}))\)

9) Remove parentheses.

\((x-5-\sqrt{19})(x-5+\sqrt{19})\)

Thanks,
Eddie Echevarria

Answer:

what question?...........

The simplified expression of x(3x + 5)-5(2x - 1) is 3x² - 5x + 5

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

x(3x + 5)-5(2x - 1)

Open the brackets

So, we have

3x² + 5x - 10x + 5

Evaluate the like terms

So, we have

3x² - 5x + 5

Hence, the simplified expression is 3x² - 5x + 5

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Answer:

17.3 cm

Step-by-step explanation:

20² = 10² + x²

400 = 100 + x²

300 = x²

x = 17.3 cm

Answer:

5/2 is the answer which is the last one

Step-by-step explanation:

The amplitude is 2. Amplitude means height from the x-axis to the crest/trough.

The period is 2pi. It is from crest to crest (next crest) or trough to trough (next trough).

Note that crest are the highest points of a wave, and that troughs are the lowest points of a wave. (we are talking about transverse waves, but this is more of a physics thing).

Function of graph:
By playing around in a graphing calculator, I got the equation to be

2 (cos (x + pi/2)).

the 2 changes the amplitude, and the + pi/2 shifts the graph by pi/2 to the left.

The required sine function is

y = 2 sin (3π/4 (x) + 3

For given function,

A sine function that has a midline of 3, an amplitude of 2 and a period of 3pi/4

A = 2

T = 3π/4

Since we know

The values of all trigonometric functions depending on the ratio of sides in a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.

In this case, the midline is 3

⇒ D = 3

Using the generalized equation of sine function,

y = A sin (B (x + C)) + D

y = 2 sin (3π/4 (x + 0) + 3

y = 2 sin (3π/4 (x) + 3

Therefore, the required sine function is

y = 2 sin (3π/4 (x) + 3

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Answer:

When in space it is a meteorite. When it is entering the atmosphere, it is a meteor. When it hits the earth it;s classified as a meteoroid.

Hope this helps.

Step-by-step explanation:

Answer:

Meteorite s

Step-by-step explanation:

took the test

You can do brainiest if you want but you don't have too

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If Fran and Jill made a new years resolution to ride bikes.  it will take 3 weeks for Fran and Jill to have ridden the same number of miles..

Let's assume that it takes "x" number of weeks for Fran and Jill to ride the same number of miles.

In the first week, Fran rides 40 miles, and Jill rides 70 miles.

In the "x"th week, Fran will have ridden a total of 40 + 55x miles.

In the "x"th week, Jill will have ridden a total of 70 + 45x miles.

For Fran and Jill to ride the same number of miles in "x" weeks, we need to solve the following equation:

40 + 55x = 70 + 45x

Simplifying this equation, we get:

10x = 30

x = 3

Therefore, it will take 3 weeks for Fran and Jill to have ridden the same number of miles.

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We are given the radius of the scoop and asked to find the volume of ice cream in one scoop. By using the formula for the volume of a sphere and substituting the given radius, we can calculate the volume. The final answer is approximately 33.49 cubic inches.

a) The problem asks for the volume of ice cream in one scoop.

b) The given fact is that the radius of the scoop is 2 inches.

c) The formula to be used is the volume of a sphere, which is given by V = (4/3)πr³, where V is the volume and r is the radius.

d) Number Sentence:

  - Given: Radius (r) = 2 inches

  - Formula: V = (4/3)πr³

  - Substituting the value: V = (4/3)π(2)³

  - Simplifying: V = (4/3)π(8)

  - Evaluating: V = (4/3)(3.14)(8)

  - Multiplying: V = 33.49333333 (approx.)

e) Final answer: The volume of ice cream in one scoop is approximately 33.49 cubic inches.

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The arithmetic sequence's fifth term is therefore 84.

An arithmetic sequence's nth term is determined by a = a + (n - 1)d. So, enter the values a = 2 and d = 3 into the formula to determine the nth term.

The formula to determine the nth term of an arithmetic series is a = a1 + (n - 1)d if a1 is the first term and d is the common difference.

In the mathematical sequence, 84 is the fifth term.

The process for calculating value

An arithmetic sequence's nth term can be calculated using the following formula:

Tn = a + (n -1)d

Where;

First term is a.

N words are present.

d is the typical difference

We must substitute nas 5's value in order to find the fifth term.

T5 = 4 + (5-1) 20

T5 = 4 + 4(20) (20)

the bracket be expanded

T5 = 4 + 80

T5 = 84

The arithmetic sequence's fifth term is therefore 84.

The complete question is,

4 is the initial term and 20 is the constant difference in an arithmetic series. Discover the sequence's sixth phrase.

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Since then, it has spread to other rivers, colonized them, clogged the water intake pipes, and competed with local species for food. Zebra mussels are the method for removing a lot of plankton from the water column.

Here, we have,

The Caspian Sea in Asia is where zebra mussels, or Driessen polymorph, are found naturally.

They arrived in the Great Lakes region in the late 1980s via ballast water from a transatlantic ship.

The Great Lakes, Mississippi, Tennessee, Hudson, and Ohio river basins were all overrun by these mussels within ten years.

The lake's brilliant blue hue is a result of Tahoe's clean air and water.

There is more to this phenomenon than just the fact that Lake Tahoe's surface reflects the sky, which contributes to its blue color.

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complete question:

As you respond to Part A, Part B, and Part C, follow the directions below.

​

​Address all of the instructions in each prompt.

​Use evidence from the information provided and your own knowledge of science to support your responses.

Part A

​

Describe one way scientists near Lake Tahoe can detect if the lake has been impacted by zebra mussels.

Answer:

Step-by-step explanation:

Radioactive dating becouse they look how long the fossils were there

The equation of the line containing the paints A and B is y = -1/3x + 4

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

The graph

Where, we have

(6, 2) and (0, 4)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 4

Using the other points, we have

6m + 4 = 2

So, we have

6m = -2

Evaluate

m = -1/3

So, we have

y = -1/3x + 4

As an equation, we have

y = -1/3x + 4

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Answer:

Answer:

x = 12

Step-by-step explanation:

m∠S + m∠T = 180

8x + 7x = 180

15x = 180

x = 12

does this help?