Given the function f(x) = x^3 - x + 3, explain how to write the new function for a horizontal and vertical stretch or shrink, a reflection in the x and y axes and a translation left or right.

(25 POINTS) GIVE ABOUT A PAPER AMOUNT OF WORDS (can give me none sense but make it smart) :)

Answer:

AB = PQ

Step-by-step explanation:

ABC = PQR

The angles are equal and the segments are equal

for the angles

A = P

B = Q

C = R

For the segments

AB = PQ

BC = QR

AC = PR

Answer:

Line AB is approximately equal to Line PQ

Answer:

74 and 18

Step-by-step explanation:

Answer:

0.

Step-by-step explanation:

The slope of the line is defined as the change of elevation of the line (\(\frac{rise}{run}\)).

In this case, there is no change in the slope as the line continues across (0 , 2), meaning that the slope of the line is 0.

If the slope of the line is 1, then the line will have (rise 1/run 1), meaning that it will have a linear slope. (See attached image).

Vertical lines have infinite slope, and so can also be called undefined as it moves neither left or right, giving it no run.

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For each relation, we would determine whether or not it is a function as follows;

Relation 1 is: B. not a function

Relation 2 is: B. not a function.

Relation 3 is: B. not a function

Relation 4 is: A. a function.

In Mathematics, a function is generally used for uniquely mapping an independent value (domain or input variable) to a dependent value (range or output variable).

This ultimately implies that, an independent value (domain) represents the value on the x-coordinate of a cartesian coordinate while a dependent value (range) represents the value on the y-coordinate of a cartesian coordinate.

Based on relations 1, 2, and 3, we can logically deduce that they do not represent a function because their independent value (domain) has more than one dependent value (range).

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The factoring of the quadratic function as a product of two binomials is given as follows:

x² + 10x + 24 = (x + 6)(x + 4).

The quadratic function for this problem is given as follows:

x² + 10x + 24.

To factor the quadratic function as a product of the two binomials, we must obtain it's roots, that is, solve:

x² + 10x + 24 = 0.

The coefficients of the quadratic function are given as follows:

a = 1, b = 10, c = 24.

Hence the discriminant is of:

D = 10² - 4 x 1 x 24 = 4.

The first root of the quadratic function is given as follows:

x = (-10 - square root of (4))/2 = -6.

The second root of the quadratic function is given as follows:

x = (-10 + square root of (4))/2 = -4.

Hence, using the Factor Theorem, the binomial product is given as follows:

x² + 10x + 24 = (x + 6)(x + 4).

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One possible set of positive integers that satisfies the given condition is the set of powers of 2, i.e., {2, 4, 8, 16, 32, ...}.

To see why this set works, note that any two distinct powers of 2 have a different binary representation, differing in at least one bit. This means that their sum will have one more "1" bit in its binary representation than either of the two numbers being added.

Since any prime number greater than 2 is odd, it follows that the sum of any two distinct powers of 2 will have an even number of distinct prime factors, namely the powers of 2 that appear in its binary representation.

First, let's note that every positive integer can be uniquely expressed as a product of prime powers, e.g., 36 = 2^2 * 3^2. The prime factors of an integer are the primes that appear in its prime factorization, e.g., the prime factors of 36 are 2 and 3.

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Answer:

Answer:

94.6ft

step by step explanation :

sine(52) = x/120

multiply both sides by 120

120 sine(52°) = x

put it in a calculator

X=94.56129043

round to nearest tenth

X = 94.56ft

The domain of the composite functions:

a). (f + g)(-2) = 23

b). (f - g) (-2) = 1

c). f(x) - g(x) = x² - 5x - 13

A function is composite when the co- domain of the first mapping is the domain of the second mapping

Given the functions f(x) = x² - 4x and g(x) = x + 13, we shall evaluate the domains of the functions as follows:

a). (f + g)(-2) = (-2)² - 4(-2) + (-2) + 13

(f + g)(-2) = 4 + 8 - 2 + 13

(f + g)(-2) = 23

b). (f - g) (-2) = (-2)² - 4(-2) - (-2) - 13

(f - g)(-2) = 4 + 8 + 2 - 13

(f - g) (-2) = 1

c). f(x) - g(x) = x² - 4x - x - 13

f(x) - g(x) = x² - 5x - 13

Therefore, the domain of the composite functions:

a). (f + g)(-2) = 23

b). (f - g) (-2) = 1

c). f(x) - g(x) = x² - 5x - 13

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Answer: hope this help

Step-by-step explanation:

Answer:

Step-by-step explanation:

There is a special quadratic form called "the difference of squares" that has useful application in a number of situations. The form is ...

  a² -b² = (a -b)(a +b)

This means that expressions where 'a' or 'b' are imaginary numbers or radicals can be simplified by using a factor that results in those values being squared.

For a rational expression with a complex number in the denominator, you can make the denominator be a real number by multiplying numerator and denominator by a factor that looks like the denominator, but with the opposite sign.

  \(\dfrac{-2i}{1+i}=\dfrac{-2i}{1+i}\cdot\dfrac{1-i}{1-i}=\dfrac{-2i(1-i)}{1^2-i^2}\\\\=\dfrac{-2i+2i^2}{1-(-1)}=\dfrac{-2i+2(-1)}{2}=\dfrac{-2-2i}{2}=\boxed{-1-i}\)

For the most part, the value "i" can be treated as though it were any variable. Like terms add and subtract the way they always do. Products are formed in the usual way. The only difference is that i² = -1, so any time you see that power of i, you can replace it with -1. Similarly, any time you see √(-1), you can replace it with i.

__

  (i+2)/(1+i) = (2+i)(1-i)/(1² -i²) = (2 -i -i²)/2 = (3 -i)/2

__

The quadratic formula can be used to solve these. It tells you the solution to ...

  ax² +bx +c = 0 is ...

  \(x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)

You have a = -3, b = 1, c = -3, so the solutions are ...

  \(x=\dfrac{-1\pm\sqrt{1^2-4(-3)(-3)}}{2(-3)}=\dfrac{1\pm\sqrt{1-36}}{6}=\boxed{\dfrac{1\pm i\sqrt{35}}{6}}\)

__

You have a = 2, b = -4, c = 7, so the solutions are ...

  \(x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(2)(7)}}{2(2)}=\dfrac{4\pm\sqrt{16-56}}{4}=\boxed{\dfrac{2\pm i\sqrt{10}}{2}}\)

_____

Additional comment

Sometimes answer checkers don't like parentheses. This means you might need to write out the sums.

  (3 -i)/2 = 3/2 -1/2i

  (2±i√10)/2 = 1+i√10/2, 1-i√10/2 . . . . the /2 is outside the radical

the temperature on the scale is given as follows,

at 10 pm the temperature will be - 1 F

at 8 am the temp is - 3 F as it is given 3 F less than zero

at 1 pm the temp is -3 + 14 = 11 F as it is given that it rose 14 F from -3 F .

at 10 pm the temp is 11 - 12 = -1 F as it is given that it dropped 12 F from 11 F.

Answer:

The two angles that are directly across the intersection point from each other are called vertical angles. Vertical angles are always congruent.

Step-by-step explanation:

brainliest???

Vertical angles are two angles that are opposite of each other when two intersect. These angles are congruent.

Vertical angles are angles opposite to each other where two lines cross.

When two lines intersect, they naturally form two pairs of vertical angles. Vertical angles share the same vertex or corner, and are opposite each other.

These pair of angles are congruent which means they have the same angle measure.

Hence, Vertical angles are two angles that are opposite of each other when two intersect. These angles are congruent.

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Answer:

0 hundreds

0 tens

7 ones

.

4 tenths

0 hundredths

8 thousandths

Standard form=7.408

Step-by-step explanation:

Lets first solve (7x1)+(4x1/10)+(8x1/1000)

7+0.4+0.008

Simplify:

7.408

The probability that a truck drives between 150 and 156 miles in a day is 0.0247. Using the standard normal distribution table, the required probability is calculated.

The formula for calculating the probability distribution for a random variable X, Z-score is calculated. I.e.,

Z = (X - μ)/σ

Where X - random variable; μ - mean; σ - standard deviation;

Then the probability is calculated by P(Z < x), using the values from the distribution table.

The given data has the mean μ = 120 and the standard deviation σ = 18

Z- score for X =150:

Z = (150 - 120)/18

   = 1.67

Z - score for X = 156:

Z = (156 - 120)/18

  = 2

So, the probability distribution over these scores is

P(150 < X < 156) = P(1.67 < Z < 2)

⇒ P(Z < 2) - P(Z < 1.67)

From the standard distribution table,

P(Z < 2) = 0.97725 and P(Z < 1.67) = 0.95254

On substituting,

P(150 < X < 156) = 0.97725 - 0.95254 = 0.02471

Rounding off to four decimal places,

P(150 < X < 156) = 0.0247

Thus, the required probability is 0.0247.

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Answer:

B(-3, -8)

Step-by-step explanation:

Answer:

all values greater than or equal to -11

Step-by-step explanation:

For a square root to be a real number, the value under the square root must be positive. Therefore, all values of x must ensure that the value under the square root remains positive.

Answer:

-------------------------------------------

The square root is  defined when the expression under the root is not negative.

It is shown as:

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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Answer:

70%

Step-by-step explanation:

35/50 = 0.7

Answer:

35 is 70% of 50.This means that a $50 item with a $35 discount is receiving a 70% discount.

Given:

Sandra Wallace walks at 5 miles per hour

Michael Sanders walks at 3 miles per hour

when Sandra has walked 20 miles

So, the number of hours = 20/5 = 4 hours

Michael starts to walk in a certain direction 2 hours before Sandra

So, the number of waking hours of Michael = 4 + 2 = 6 hours

So, the number of miles that Michael walked = 6 * 3 = 18 miles

So, the difference between them = 20 - 18 = 2 miles

So, the answer will be

Michael will be 2 miles behind Sandra

The midpoint of segment YZ is (-a, -2b).

Given the coordinates of the rhombus WXYZ:

W(0, 4b)

X(2a, 0)

Y(0, -4b)

Z(-2a, 0)

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Substituting the coordinates of Y and Z:

Midpoint of YZ = ((0 + (-2a)) / 2, (-4b + 0) / 2)

= (-a, -2b)

Therefore, the midpoint of segment YZ is (-a, -2b).

To demonstrate that the segments joining the midpoints of the rhombus are perpendicular, we need to prove that the slopes of these segments are negative reciprocals of each other.

Let's consider the segments joining the midpoints:

Segment joining the midpoints of WX and YZ:

Midpoint of WX: ((0 + 2a) / 2, (4b + 0) / 2) = (a, 2b)

Midpoint of YZ: (-a, -2b)

Slope of WX = (2b - 4b) / (a - 0) = -2b / a

Slope of YZ = (-2b - (-4b)) / (-a - 0) = 2b / a

The slopes of WX and YZ are negative reciprocals of each other, indicating that these segments are perpendicular.

We have shown that the segments joining the midpoints of a rhombus are perpendicular to each other and have equal lengths. Therefore, these segments form a rectangle.

Additionally, the midpoint of segment YZ is (-a, -2b).

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Answer:

  30 inches

Step-by-step explanation:

Assuming the banner you want is similar to the sketch you made, the length of the banner is 10 times the letter height.

For 3-inch letters, the banner length will be 30 inches.

Answer:

30 ft

Step-by-step explanation:

**According to the image of the banner, the banner should be 3 foot high (not 3 inches)**

Create a ratio of letter height to length of phrase for the sketch and the banner.  Let x be the length of the banner.

NB There is no need to convert the measurements between inches and feet, since the letter height and length of phrase is measured in the same way for each banner.

Ratio:                      letter height : length of phrase

Sketch (in inches):                   2 : 20

Banner (in feet):                       3 : x

Equate the ratios and solve for x:

\(\sf \implies 2 : 20 = 3 : x\)

\(\sf \implies \dfrac{2}{20}=\dfrac{3}{x}\)

\(\sf \implies 2x=3 \cdot 20\)

\(\sf \implies 2x=60\)

\(\sf \implies x=\dfrac{60}{2}\)

\(\sf \implies x=30\)

Therefore the length of paper your should buy to make the banner is 30ft.

The algebraic expression of raise t to the 10th power then add the result to 3 is t¹⁰ + 3

An algebraic expression is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, multiplication, exponent, etc.

Given: raise t to the 10th power then add the result to 3

Note: t is the variable here

Let's write algebraic expression now:

raise t to the 10th power => t¹⁰

then add the result to 3 => t¹⁰ + 3

Therefore, the algebraic expression is t¹⁰ + 3

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Answer:

the amount that has already left the container, i believe

Step-by-step explanation:

Answer:

Ans: 1/-2 , -1/3 , 3/10 , 3/4

Step-by-step explanation:

The LCM of 2, 3, 4 and 10 is 60.

Let's make denominator equal,

→ 3/4 , -1/3 , 1/-2 , 3/10

→ 3×15/4×15 , -1×20/3×20 , -1×30/2×30 , 3×6/10×6

→ 45/60 , -20/60 , -30/60 , 18/60

Now we can order in ascending,

→ -30/60 , -20/60 , 18/60 , 45/60

→ 1/-2 , -1/3 , 3/10 , 3/4 {final answer}

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

The proposition with logical connectives for the following statements will be : A) r⋀~q  B) p⋀q⋀r  C) r⇒p  D) p⋀~q⋀r  E) (p⋀q)⇒r  F) r⇔(p⋁q).

We know that in proposition, when 2 propositions are connected using "and" then ⋀ is used, similarly for "or" ⋁ is used and for negation "~"  is used. When a statement implies some other statement then "⇒" is used and when 2 propositions are co dependent on each other then Biconditional connective  "⇔" is used.  Now :

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Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426