5, 3.1.24

f(x) = 3x² + 5; find f(x + 3) - [f(x) + 3]

Answers

Answer 1

Given that [tex]f(x) = 3x^2 + 5[/tex], we have

[tex]f(x + 3) = 3 (x + 3)^2 + 5 \\\\= 3 (x^2 + 6x + 9) + 5 \\\\= 3x^2 + 18x + 32[/tex]

so that

[tex]f(x+3) - (f(x) + 3) = (3x^2 + 18x + 32) - (3x^2 + 8) \\\\= \boxed{18x + 24}[/tex]


Related Questions

41% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is​ (a) exactly​ three, (b) at least​ four, and​ (c) at most two. If​ convenient, use technology to find the probabilities.

Answers

The probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

41% of adults say cashews are their favorite kind of nut.

P = 41% = 0.41

Q = 1 - P = 1 - 0.41 = 0.59

n = 2

From the binomial distribution:

[tex]\rm P(X = r) = C(n, r) P^r(1-P)^{n-r}[/tex]

a) Exactly​ three

[tex]P(X=3) = C(12, 3) (0.41)^3(0.59)^9[/tex]

P(X = 3) = 0.131

b) At least​ four:

P(X≥4) = P(X=4)+ P(X=5)+ P(X=6)+..............+ P(X=13)

[tex]\rm P(X\geq 4)=C(12, 4) (0.41)^4(0.59)^9+C(12, 5) (0.41)^5(0.59)^8+...............+C(12, 3)(0.41)^3(0.59)^9[/tex]

P(X ≥ 4) = 0.795

c) At most two:

P(X≤2) =P(X=0)+ P(X=1)+ P(X=2)

[tex]\rm =C(12, 0) (0.41)^0(0.59)^12+C(12, 1) (0.41)^1(0.59)^1^1+C(12, 2)(0.41)^2(0.59)^1^0[/tex]

P(X ≤ 2) = 0.0733

Thus, the probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.

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\Triangle X Y Z is shown. Angle X Z Y is 63 degrees. The length of X Z is 2.7 and the length of X Y is 2.8.
Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction

Which is the approximate measure of angle Y? Use the law of sines to find the answer.

52°
59°
64°
67°

Answers

That would be the because if you chose it really wouldn’t make

Please help, will give the brainliest!


(J) 80 • 125

(K) (80+65) • 125

(L) (65 • 80) + (80 • 60)

M (65•80)+(80•60)

N (65•80)+ 1/2 (125 • 100)

Answers

Answer:

option N is the correct option, apply Formula of area of rectangle and triangle by splitting figure into 2 parts

In the following answer, why does 830 convert to 83000?

Answer:
Money borrowed from insurance company = $1000

Step-by-step explanation:

Let the money borrowed by her friend at 8% interest = x

Then the money borrowed by bank at 9% interest = 2x

Total money borrowed = $10,000

So, the money borrowed from insurance company = 10,000-(2x+x)

= 10,000-3x

Total interest for the first year = $830

We have the equation,

8%(x) + 9%(2x) +5% (10,000-3x) = 830

8x+18x+50,000-15x = 83,000

11x = 83000-50000

11x = 33,000

x = $3000

Then the money borrowed insurance company = 10,000-3x

= $1,000

Answers

Then the money borrowed insurance company is $1,000.

Money borrowed from insurance company = $1000

Let the money borrowed by her friend at 8% interest = x

Then the money borrowed by the bank at 9% interest = 2x

What is the total money?

Total money borrowed = $10,000

So, the money borrowed from the insurance company = 10,000-(2x+x)

= 10,000-3x

Total interest for the first year = $830

We have the equation,

8%(x) + 9%(2x) +5% (10,000-3x) = 830

8x+18x+50,000-15x = 83,000

11x = 83000-50000

11x = 33,000

x = $3000

Then the money borrowed insurance company = 10,000-3x

Then the money borrowed insurance company is $1,000.

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Fill in the blanks below.
Find the slope of the line passing through the points (8,5) and (8,-4).

Answers

Step-by-step explanation:

please mark me as brainlest

Figure ABCD is transformed to obtain figure A′B′C′D′:


DIAGRAM INCLUDED! 100 Points!

Part A: Write the sequence of transformations that changes figure ABCD to figure A′B′C′D′. Explain your answer and write the coordinates of the figure obtained after each transformation. (6 points)

Part B: Are the two figures congruent? Explain your answer. (4 points)

Answers

Answer:

Part A

Reflect over the y-axis:  (x, y) → (-x, y)
A (-4, 4) → (4, 4)
B (-2, 2) → (2, 2)
C (-2, -1) → (2, -1)
D (-4, 1) → (4, 1)
Shift 4 units down:  (x, y-4)
(4, 4-4) → A' (4, 0)
(2, 2-4) → B' (2, -2)
(2, -1-4) → C' (2, -5)
(4, 1-4) → D' (4, -3)

Part B

Two figures are congruent if they have the same shape and size.  (They are allowed to be rotated, reflected and translated, but not resized).

Therefore, ABCD and A'B'C'D' are congruent.  They are the same shape and size as they have only be reflected and translated.

Question 13 of 50
Choose two statements (the original conditional statement and its converse)
that could form the biconditional "The object weighs a ton if and only if the
scale reads 2000 pounds."
A. If the object weighs a ton, then the scale reads 2000 pounds.
B. If the scale does not read 2000 pounds, then the object does not
weigh 2000 pounds.
C. If the scale reads 2000 pounds, then the object weighs a ton.
D. The scale reads 2000 pounds if and only if the object weighs a
ton.


it can be more then one answer too

Answers

Conditional statements are ones that begin with a hypothesis and end with a conclusion. The correct option is A and C.

What are conditional Statements?

Conditional statements are ones that begin with a hypothesis and end with a conclusion. It is sometimes referred to as a "If-then" statement. If the hypothesis is correct but the conclusion is incorrect, the conditional statement is incorrect.

The two statements that among which one is original and the other one is its converse is If the object weighs a ton, then the scale reads 2000 pounds, and  If the scale reads 2000 pounds, then the object weighs a ton.

Hence, the correct option is A and C.

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A Cepheid star is a type of variable star, which means that its brightness is not constant.

The relationship between the brightness of a Cepheid star and its period, or length of its pulse, is given by

M = − 2.78 (log P) − 1.35,

where M is the absolute magnitude, or brightness, of the star, and P is the number of days required for the star to complete one cycle.

Use a calculator to solve each problem. Round your answers to the nearest hundredth.

What is the absolute magnitude of a star that has a period of 62 days?

Answers

A function assigns the values. The absolute magnitude of a star that has a period of 62 days is -6.3328.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The relationship between the brightness of a Cepheid star and its period, or length of its pulse, is given by

M = − 2.78 (log P) − 1.35,

Given the absolute magnitude of a star that has a period of 62 days is,

M = − 2.78 (log 62) − 1.35

M = -6.3328

Hence, the absolute magnitude of a star that has a period of 62 days is -6.3328.

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i give brainliest to first person who gets it correct

Answers

Answer:

(-4,-3)

Step-by-step explanation:

The point where those 2 equations intersect is (-4,-3)

The mean of 6 numbers is 17. Four of the numbers are 15, 17, 20, and 22. The remaining two numbers are each equal to x. Calculate the sum of the 06 numbers and the value of x.

Answers

Answer:

Sum of 6 no. = 102

X = 14

Let the unknown no. be X

mean= sum of all no. / no. of terms

17 = 15 + 17 + 20 + 22 + X+ X / 6

17 * 6 = 74 + 2X

102 - 74 = 2X

28 = 2X

28/2 = X

14= X

What is the square root of -1? Complex numbers

Answers

Answer:

The square root of -1 is i

Step-by-step explanation:
"i" is the imaginary unit and represents the value of sqrt -1

Two trains leave station 416 miles apart. One train is traveling 90 miles per hour while the other is traveling 70 miles per hour. How long will it take the two trains to meet

Answers

Answer:

2.6 hours

Step-by-step explanation:

Let t be the time that the trains meet.

[tex]90t = 416 - 70t[/tex]

[tex]160t = 416[/tex]

[tex]t = 2.6[/tex]

Addison and Kelsey are running on a path modeled by x2 + y2 – 14x – 16y – 287 = 0, where the distance is in meters. What is the maximum distance between the runners at any given time?

20 meters
32 meters
40 meters
140 meters

Answers

Answer:

40 meters

Step-by-step explanation:

The maximum distance between the runners at any given time 40 meters. Therefore, option C is the correct answer.

Given that, Addison and Kelsey are running on a path modeled by x² + y² - 14x - 16y - 287 = 0.

What is a circle equation?

The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.

The standard equation of a circle with center at (x1,y1) and radius r is (x-x1)²+(y-y1)²=r²

Here, the circular path is modeled by x² + y² - 14x - 16y - 287 = 0

We complete the squares to place it in the standard format, thus:

x² - 14x + 49 + y² - 16y +64 = 287+49+64

⇒ (x-7)² + (y-8)² = 400

⇒ (x-7)² + (y-8)² = 20²

So, r² = 20²

⇒ r = 20 meters

Maximum distance = d = 2r

= 40 meters

The maximum distance between the runners at any given time 40 meters. Therefore, option C is the correct answer.

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1
2
3
at
4
927
5
6
Which graph represents g(x)?
7
8
The graph of f(x) = x² is translated to form g(x) = (x - 5)² + 1. What does the graph look like?
6
10

Answers

Do you have a picture

in the game of​ roulette, a player can place a ​$ 7 bet on the number 28 and have a 1/38 probability of winning. if the metal ball lands on ​28, the player gets to keep the ​$7 paid to play the game and the player is awarded ​$245. ​ otherwise, the player is awarded nothing and the casino takes the​ player's ​$7. what is the expected value of the game to the​ player? if you played the game 1000​ times, how much would you expect to​ lose?

Answers

Answer: The player expects to lose 184.21 dollars.

=========================================================

Explanation:

X = net winnings in dollars

Ignore the "28" because it's really not that relevant here. All we care about is the probability 1/38 which is the probability of winning money. The probability of losing money is 1 - (1/38) = 37/38. Put another way: there's 1 way to win, and 37 ways to lose.

If the player wins, then they walk away with 7+245 = 252 dollars

If the player loses, then their "winnings" is -7

So either X = 252 or X = -7 are the only two options.

Let's form a table showing those options with their corresponding probabilities.

[tex]\begin{array}{|c|c|} \cline{1-2}X & P(X)\\\cline{1-2}252 & 1/38\\\cline{1-2}-7 & 37/38\\\cline{1-2}\end{array}[/tex]

Now multiply each X value and P(X) value across the rows.

252*(1/38) = 6.631579

-7*(37/38) = -6.815789

These values are approximate.

[tex]\begin{array}{|c|c|c|} \cline{1-3}X & P(X) & X*P(X)\\\cline{1-3}252 & 1/38 & 6.631579\\\cline{1-3}-7 & 37/38 & -6.815789\\\cline{1-3}\end{array}[/tex]

Add up the results of the third column

6.631579 + (-6.815789) = -0.18421

This represents the net winnings for any average spin of the wheel. The player unfortunately expects to lose, on average, about $0.18421 or 18.421 cents per spin.

Do this 1000 times and the player should expect to lose about

1000*(0.18421) = 184.21 dollars

Keep in mind that due to the random nature of roulette wheel, the player may get lucky or their luck may be worse than what is described. The idea is that over the long run, the average should be somewhat close to losing 184.21 dollars.

Another way to think of it could be to have 1000 players doing the same game (rather than have 1 person play the same game 1000 times). Some players may get lucky, while others may not get so lucky. But their collective average should be losing that $184.21

Find the equation of a line containing the points (−2,−4) and (1,−3).

Answers

Using the points, we can make a system of equations:
-4 = m(-2) + b
-3 = m(1) + b —> -3 = m + b —> -3 - m = b


Substitute (-3 - m) for b:
-4 = m(-2) + (-3 - m)
-4 = -2m -3 - m
-1 = -3m
1/3 = m


Plug in the solved m value to solve for b:
-4 = (1/3)(-2) + b
-4 = -2/3 + b
-3 1/3 = b

Write your final equation:
y = 1/3x - 10/3

Based on the circle graph,how many pounds of milk and eggs does the average American consume each year?PLEASE EXPLAIN IMAGE IS PROVIDED
E.300
F.368
G.460
H.552

Answers

About 492 pounds of milk and egg were consumed each year

Pie charts and percentages

Given the following parameters from the chart

Total consumption = 1640 pounds per person

The percentage of milk and egg = 100 -(38 + 10 + 10 +8 + 4)

The percentage of milk and egg = 30%

Determine the amount consumed each year

Amount of milk and egg consumed = 30% of 1640

Amount of milk and egg consumed = 492 pounds

Hence about 492 pounds of milk and egg were consumed each year

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The pH can be calculated using the equation pH = –log(H+), where H+ is the hydronium ion concentration. Find the hydronium ion concentration of a particular soda if the pH level is 2.3.​

Answers

Answer:

Step-by-step explanationp :

ph =lo 4

The earnings for a cashier at the local grocery store varies directly with how many hours she works. If the cashier is paid $524 for a 40 hour work week, how many hours would it take for him to make 720.50? Enter the number only.

Answers

Using proportions, it is found that it would take 55 hours for him to make $720.50.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

He is paid $524 for a 40 hour work week, hence per hour he earns?

r = 524/40 = $13.1.

The amount of hours he would need to make $720.50 is given by:

h = 720.50/13.1 = 55.

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Which of the following best describes the expression below when i = √-1?
3+4i
A. Complex number
B. Real number
C. Irrational number
D. Rational number

Answers

The answer is A. Complex number

On a unit circle, Ø = 60°. Identify the terminal point and Tan Ø

Answers

The terminal points when the value of r is 1 will be 0.5 and 0.86 and the value of tan 60 will be 1.732.

What is angle measurement?

An angle measure is the measurement of the angle created by two rays or arms at a shared vertex in geometry. A protractor is used to measure angles in degrees (°).

Given;

Ø = 60°

Let's assume the value of r = 1 units

The terminal points are;

x= rcosΘ

x=1 × cos 60°

x=0.5

y=rsinΘ

y=rsin60°

y = 0.86

The terminal points when the value of r is 1 will be 0.5 and 0.86.

The value of the tan for the given value of the angle;

Tan 60° = 1.732

Hence, the terminal points when the value of r is 1 will be 0.5 and 0.86 and the value of tan 60 will be 1.732.

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At 50 minutes how far is the winning runner use ur equations

Answers

Answer:

3.5 km

Step-by-step explanation:

On a coordinate plane, a dashed solid line has an equation of y less-than five-thirds x + 1. It has a positive slope and goes through (negative 3, negative 4) and (0, 1). Everything to the right of the line is shaded.
Which linear inequality will not have a shared solution set with the graphed linear inequality?

y < Five-thirdsx – 2
y < Negative five-thirdsx + 1
y > Five-thirdsx + 2
y > Negative five-thirdsx + 2

Answers

The inequality is represented by y < 5/3(x+1)

Use the information about the straight line and find the equation of the line.

Given coordinates (-3,-4) and (0,1), we can find the slope

Slope,  

Change in y = y2 – y1 = 1-(-4) = 5

Change in x = x2 – x1 = 0-(-3) = 3

Therefore, Slope (m) = Change in y / Change in x = 5/3

Equation of line using m = 5/3 and points (0,1) and (x, y) in form of y = mx + c

Y – 1/ X – 0 =5/3

3(Y-1) = 5(X)

3Y -3 = 5X

3Y = 5X + 3

Y = 5X + 3/3

Y = 5/3(X + 1)

To find the inequality take a point in the shaded region and check it in the above equation.

Given Options

a. y < Five-thirds x – 2

b. y < Negative five-thirds x + 1

c. y > Five-thirds x + 2

d. y > Negative five-thirds x + 2

 Let’s take points (-3,-4) for verification

  Option a: y < 5/3 (x-2)

                     -4 < 5/3(-3-2)

                      --4 < -3.33

-4 is less than -3.33

Thus option a is in the shaded region

 Option b: y < -5/3 (x+1)

                     -4 < -5/3(-3+1)

                      --4 < 3.33

-4 is less than 3.33

Thus option a is in the shaded region

 Option c: y > 5/3 (x+2)

                     -4 > 5/3(-3+2)

                      --4 > -1.67

-4 is NOT GREATER than -1.67

Thus option c is NOT in the shaded region

Option d: y > -5/3 (x+2)

                     -4 > - 5/3(-3+2)

                      --4 > 1.67

-4 is NOT GREATER than 1.67

Thus option d is NOT in the shaded region

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Answer:

y > Five-thirdsx + 2

Step-by-step explanation:

If AABC= ADEF, which congruences are true by CPCTC? Check all that
apply.

Answers

∠A ≅ ∠D , BC≅ EF , AC ≅   DF  , option B , C , F are the correct answer.

What is CPCTC ?

CPCTC stands for corresponding parts of congruent triangles are congruent .

This means when two triangles are congruent then the corresponding sides are also congruent.

In the given triangles , Δ ABC ≅ ΔDEF

∠A ≅ ∠D

BC≅ EF

AC ≅   DF

Therefore option B , C , F are the correct options

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Please help asap! 30 points
Given that f(x)=11, g(x)=x^2-6x+3, and h(x)= -x+4, find the function (g •h)(x).

Answers

Answer:

[tex](g \cdot h)(x)=x^2-2x+23[/tex]

Step-by-step explanation:

For composite functions, it's important to understand what the functions mean:

[tex](g\cdot h)(x)[/tex]  which is read as "g of h, of x" means [tex]g ( \text{ }h(x) \text{ })[/tex] which is read as "g of, h of x" (with slight pauses at the comma).  This means that x goes into the h function, and the output of the h function goes into the g function.

Putting "x" into the h function

[tex]h(x)=-x+4[/tex]

Since it is just "x" going into the h function, the function as written is the output when x is the input.

Putting the h function output, into the g function

[tex]g(x)=x^2-6x+3[/tex]

[tex]g(h(x))=(h(x))^2-6(h(x))+3[/tex]

Substitute

[tex]g(h(x))=(-x+4)^2+-6(-x+4)+3[/tex]

Squaring means the something multiplied by itself

[tex]g(h(x))=(-x+4)*(-x+4)+-6(-x+4)+3[/tex]

Use distributive property; (some people know binomial distribution as "FOIL" -- First, Outer, Inner, Last):

[tex]g(h(x))=[(-x)(-x)+4(-x)+4(-x)+4*4)]+[6x+4]+3[/tex]

Simplify the binomial terms:

[tex]g(h(x))=[x^2-8x+16]+[6x+4]+3[/tex]

Group like terms:

[tex]g(h(x))=x^2-2x+23[/tex]

Remember that [tex](g\cdot h)(x)[/tex]  means [tex]g ( \text{ }h(x) \text{ })[/tex]

[tex](g \cdot h)(x)=x^2-2x+23[/tex]

So, [tex](g \cdot h)(x)=x^2-2x+23[/tex]

Simplify the following expression. (2x − 1)(3x + 2) Simplify the following expression . ( 2x − 1 ) ( 3x + 2 )​

Answers

FOIL: 6x^2+4x-3x-2
=6x^2+x-2

Which expression is equivalent?

Answers

Answer:

Last one/D 9^9/5/5^9/10

Step-by-step explanation:

1. What is pi?

2. And why is it important?

Answers

Answer:

pi [π] is the ratio of a circle's circumference to its diameter, and it is constant [meaning it is always the case] for all circles.

{this is a long number, 3.141592653589793238... is not even the full length, but 3.14 [or 3.14159] is typically used for estimation}

The significance of pi is typically centered in math--it can be used to find values that we don't know of circles. There are other areas of math that have been related back to the value of pi--which is incredible, and genuinely relevant.

We can find pi in the shape of rivers, physics--including waves--DNA

[+ anywhere there is a circle]

hope this helps!! :)

Answer:

ratio of circle's circumference to diameter

it is constant

At a soccer game, a vendor sold a combined total of 220 sodas and hot dogs. The number of sodas sold was 46 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.

Answers

Answer:

133 sodas

87 hot dogs

I've completed the work in the photo, just trying to reach the letter count lol


Solve the compound inequality .
2w-2<-8 and 4w+3<11

Write the solution in interval notation. If there is no solution, enter 0

Answers

Answer: [tex](-\infty, -3)[/tex]

Step-by-step explanation:

[tex]2w-2 < -8\\\\2w < -6\\\\w < -3[/tex]

[tex]4w+3 < 11\\\\4w < 8\\\\w < 2[/tex]

So, the solution is [tex](-\infty, -3)[/tex]

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Which is an abiotic factor that can be found in a rain forest ecosystem? A paramedic maintains a time card for hours she works on the rescue squad. How many hours did she work per week ? what is the domain of the function f(x)=x-9/x+8? Write your answer in interval notation. Which example is most likely a modernist work of literature? a. a short story about the everyday fears of a normal person b. an epic poem about battles between kings and gods c. a lyric poem about the beauty of america's natural forests d. a novel about the dangers of scientific advancement A firm that sells e-books - books in digital form downloadable from the Internet - sells all e-books relating to do-it-yourself topics (home plumbing, gardening, and so on) at the same price. At present, the company can earn a maximum annual profit of $ when it sells copies within a year's time. The firm incurs a -cent expense each time a consumer downloads a copy, but the company must spend $ per year developing new editions of the e-books. The company has determined that it would earn zero economic profits if price were equal to average total cost, and in this case it could sell copies. Under marginal cost pricing, it could sell copies.Part 2In the short run, to the nearest cent, what is the profit-maximizing price of e-books relating to do-it-yourself topics? $enter your response here.Part 3At the profit-maximizing quantity, to the nearest cent, what is the average total cost of producing e-books? $enter your response here. Please help!!Construct the circle that circumscribes image DEF. The delegates who came to Philadelphia for the Constitutional Convention had the sameimmediate priorities on what should be considered in the discussions.Select one:O TrueO False Find the values of a and b 3 * 2 = a + b if Who/Whatdecides the3 basiceconomicquestions? If everything in a store is 20% off, and the discounted price of an item is $18.00, what isthe regular price? I need help with this assignment! learning activity handout: cell respiration summary The American Industrial Revolution was quite different from England's version. What made the one in the U.S. sodifferent?Far more brand new inventions were made in America compared to England.New innovations and improvements were discovered for older inventions.O For the first time, the United States was able to do things without foreign help.ONew water-powered technology advanced business. solve for y in 1/8^2-3y=2^y-2 What is the equation of the line that passes through (-3, 4) and (3, -2)?y = - x - 1y = x + 7y = x - 1y = - x + 1 Pls answer this asap the flashlight flickered then died, plunging wills into A structural member that has a straight longitudinal axis and constant cross section is best described as _______. Find the value of x Add the following two numbers in scientific notation. thanks to you all for you help