PLS HELP ANSWER THIS QUESTION ITS ALGEBRA 1

Considering the parent function f(x) = x², describe the transformations applied to graph the function f(x) = (x-3)^2-8

As a result of inflation, the worth of the house today is $619,149.51.

Inflation is the persistent rise in the general price levels. As a result of inflation, the value of the house would increase overtime.

The formula for calculating future value:

FV = P (1 + r)^n

Where:

FV = Future value

P = Present value

R = interest rate

N = number of years

$160,000x (1.07)^20 = $619,149.51

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Option D, All I, II, III, is false. The log of f(n) is O(log g(n)) is true.

What is logarithm ?

The logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

The statement(s) that is/are false is option D. All I, II, III.

I. log f(n) is O(log g(n)) - True

II. 2f(n) is O(2g(n)) - False

III. f(n)^2 is O(g(n)^2) - False

The big O notation describes the upper bound of the growth rate of a function, but it does not take into account the exact relationship between two functions. So, it is possible that the log of f(n) is O(log g(n)), but it does not necessarily mean that 2f(n) is O(2g(n)) or that f(n)^2 is O(g(n)^2).

Option D, All I, II, III, is false. The log of f(n) is O(log g(n)) is true.

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The answer is 11. We can approach this problem by using a systematic method. Since we are looking for two-digit values of x such that f(f(x)) = 3,

We can start by listing all the possible values of f(x) that would satisfy the condition.

If f(x) = 3, then x can take the following values:

12

21

30

If f(x) = 12, then x can take the following values:

39

48

57

66

75

84

93

If f(x) = 21, then x can take the following values:

129

138

147

156

237

246

345

If f(x) = 30, then x can only take the value:

399

Thus, there are a total of 11 two-digit values of x that satisfy the condition f(f(x)) = 3.

To see why this is the case, note that the maximum value of f(x) for any two-digit value of x is 18 (when x = 99). Since f(x) can never be greater than 18, we can conclude that there are only a finite number of possible values for f(f(x)). By systematically listing out all the possibilities as we did above, we can find that there are only 11 values of x that satisfy the condition f(f(x)) = 3.

Therefore, the answer is 11.

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Answer:

g(2) = 9

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

g(t) = 5 + 2t

g(2) is t = 2

Step 2: Evaluate

Answer:

∠EGC

Step-by-step explanation:

Just like for the other problem, you're looking for an angle that's opposite the one you're given and is the same size as the one you're given (meaning they're congruent). If you use you hands to cover the parts of the line AD, you can see how ∠FGB and ∠EGC are opposite of each other and are congruent..

Answer:

Step-by-step explanation:

Find your fractional portion and multiply by the area

=\(\frac{45}{360}\) * \(\pi\) r²      substitute r=10 and simplify

=\(\frac{45*10}{360}\) \(\pi\)         Reduce the fraction

=\(\frac{5\pi }{4}\)       D

Answer:

9/41

Step-by-step explanation:

Cosine represents adjacent / hypotenuse.

When A is the reference angle, AB is the adjacent side (9) and AC is the hypotenuse (41).

9/41 is already simplified.

they played 15 games

they were defeated during four games

they won 11 games

Answer:

89.8 feet

Step-by-step explanation:

In ΔBCD, the measure of ∠D=90°, the measure of ∠B=75°, and DB = 93 feet. Find the length of BC to the nearest tenth of a foot.

We would solve the above question using Sine rule

The formula is given as:

DB/sin D = BC/sin B

93/sin 90 = BC/sin 75

We cross multiply

sin 90 × BC = 93 × sin 75

BC = 93 × sin 75/sin 90

BC = 89.83 feet

Approximately BC = 89.8 feet

Answer:

x = -3, x = 2

Step-by-step explanation:

x² + 3 = -x + 9

x² + x - 6 = 0

(x+3)(x-2) = 0

Answer:

f(g(2)) = 50

Step-by-step explanation:

evaluate g(2) then substitute the result obtained into f(x)

g(2) = 3(2) - 2 = 6 - 2 = 4 , then

f(4) = 2(4 + 1)² = 2(5)² = 2(25) = 50

Answer:

f[g(2)] = 50

Step-by-step explanation:

Given functions:

\(f(x)=2(x+1)^2\)

\(g(x)=3x-2\)

We are asked to determine f[g(2)], which is known as a composite function. When solving composite functions, you always work inside out.

Step 1: Find the value of g(2) by substituting 2 for x in function g(x).

\(\implies g(2)=3(2)-2\)

\(\\\implies g(2)=6-2\Rightarrow g(2)=\boxed{4}\)

Step 2: Substitute the found value into the composite function.

\(\\\implies f[g(2)]= 2(4+1)^2\)

\(\implies f[g(2)] = 2(5)^2 \Rightarrow 2(25) \Rightarrow \boxed{50}\)

Hence, the value of the composite function f[g(2)] is 50.

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The expected number of times that they will end up flipping the coin \(\boxed{N}$.\)

Let P be the probability that Alpha goes bankrupt before either player reaches 2N dollars. We can calculate this probability using a recursive approach. Let p_i be the probability that Alpha goes bankrupt given that Alpha has i dollars and Beta has 2N-i dollars. Then we have:

\($p_i = \frac{1}{2}p_{i-1} + \frac{1}{2}p_{i+1}$\)

The first term represents the probability that Alpha loses the next flip and ends up with i-1 dollars, while the second term represents the probability that Alpha wins the next flip and ends up with i+1 dollars. The boundary conditions are\(p_0 = 1\) (Alpha is already bankrupt) and \($p_{2N} = 0$\) (Alpha has reached 2N dollars). We can solve this system of equations to find:

\($p_i = \frac{i}{2N}$\)

This result can be verified by induction.

Now, let\($E_i$\)be the expected number of flips required to reach the endpoint of the game (either bankruptcy or 2N dollars) starting from the state where Alpha has i dollars and Beta has \($2N-i$\)dollars. Then we have:

\($E_i = 1 + \frac{1}{2}E_{i-1} + \frac{1}{2}E_{i+1}$\)

The first term represents the flip that is about to be made, while the second and third terms represent the expected number of flips required to reach the endpoint starting from the new state after the next flip. The boundary conditions are \($E_0 = E_{2N} = 0$\)(we have already reached an endpoint). We can solve this system of equations to find:

\($E_i = 2N\left(1 - \frac{i}{2N}\right)^2$\)

Therefore, the expected number of flips required to reach the endpoint of the game starting from the initial state where both players have N dollars is:

\($E = E_N = 2N\left(1 - \frac{1}{2}\right)^2 = \boxed{N}$\)

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Answer:

so if the number was 3 red marbles and 5 blue marbles the ratio would be 3:5

Step-by-step explanation:

Answer:

300 g

Step-by-step explanation:

weight of a can of biscuits= (23- 0.5)/15= 1.5 kg

weight of 8 cans= 1.5 * 8= 12 kg

mass of the empty box Q= 12.3- 12= 0.3 kg= 300 g

Answer:

300 g or 0.3 kg

Step-by-step explanation:

23 kg - 500g = 22.5 kg

each can of biscuits weighs 22.5 ÷ 15 = 1.5 kg

if the box Q weighs 12.3kg when there's 8 box of biscuits then

8 × 1.5 = 12 kg is the weight of biscuits and the remaining 300 g is box Q's weight

Answer:

6 to the north

Step-by-step explanation:

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∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements from the given information

Two angles are given.

∠g = (2x-90)°

∠h = (180-2x)°

We have to find the statement which is true about the angles g and h.

If both angles are greater than zero.

Complementary angles add up to 90 degrees

i.e., ∠g and ∠h are complementary if ∠g + ∠h = 90°.

Substituting the given values:

∠g + ∠h

= (2x-90)° + (180-2x)° = 90°

Thus, ∠g and ∠h are complementary angles.

and both the angles are less than 90 degrees so we can tell that angles ∠g and ∠h  are acute.

So the statement ∠g and ∠h are acute angles is also true

Hence, ∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements

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Answer:

[1] Addition property of equality

[2] Division property of equality

Step-by-step explanation:

Given the equation, \( 4x - 6 = 34 \), the following are steps and justification for each step taken:

\( 4x - 6 = 34 \) => Given equation

Add 6 to both sides

\( 4x - 6 + 6 = 34 + 6 \) => addition property of equality [1]

\( 4x = 40 \) => simplify

Divide both sides by 4

\( \frac{4x}{4} = \frac{40}{4} \) => Division property of equality [2]

\( x = 10 \) => simplify

The justification for the steps taken are:

[1] Addition property of equality

[2] Division property of equality

Answer:

1/2

Step-by-step explanation:

The answer  is that a 400-troy-ounce gold ingot weighs approximately 12.4 kilograms or 27.34 pounds. This weight is equivalent to 3,110 grams or 3.11 kilograms. In summary, a 400-troy-ounce gold ingot weighs around 12.4 kilograms or 27.34 pounds and is equivalent to 3,110 grams or 3.11 kilograms.

The 400-troy-ounce gold ingot weighs, as the name suggests, 400 troy ounces. To provide some context, one troy ounce is equivalent to 31.1035 grams. Therefore, to determine the weight of the gold ingot in grams, you can perform the following calculation: 400 troy ounces x 31.1035 grams/troy ounce = 12,441.4 grams. In summary, the 400-troy-ounce gold ingot weighs 12,441.4 grams.

The weight of a 400-troy-ounce gold ingot can be calculated as follows: One troy ounce is equal to approximately 31.1 grams. The troy ounce is commonly used as a unit of weight for precious metals like gold. To find the weight of a 400-troy-ounce gold ingot, we multiply 400 by the weight of one troy ounce: 400 troy ounces * 31.1 grams per troy ounce = 12,440 grams. Since there are 1,000 grams in a kilogram, we can convert the weight from grams to kilograms:

12,440 grams / 1,000 grams per kilogram = 12.44 kilograms.

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Answer: A and C

Step-by-step explanation:

Abs. val is distance from 0, and 100 and -100 are both the same distance from 0, so x=100 and x=-100.

Answer:

x = (-1)/2

Step-by-step explanation:

Solve for x:

2 x + 1 = 0

Subtract 1 from both sides:

2 x + (1 - 1) = -1

1 - 1 = 0:

2 x = -1

Divide both sides of 2 x = -1 by 2:

(2 x)/2 = (-1)/2

2/2 = 1:

Answer:  x = (-1)/2

Answer:

6. 12cm

7. 11.2 cm

8. 92 degrees

9. 53 degrees

10. 37.5 cm

11. $ 693.12

Step-by-step explanation:

For questions 6-9 the triangle is congurent which means both their angles will be equal.

For the sides you can see that the second triangle is 1.5 times smaller than the first one as taking one of the sides 21/14= 1.5

So for Q. 6 we can multiply side PQ by 1.5.

For Q.7 divide CA by 1.5.

For Q. 10 we can do cross multiplication:

5/4 = x/30

= 150= 4x

= 37.5=x

For Q 11 we can see the size of the paper is 1.9 times bigger than the original one (38/20)

So the shorter side is 30.4 cm.

Then we have to find the area of the paper to multiply the two dimensions and we get 1155.2 square inches.

Then to figure out the money we multiply again and we get $693.12.

Answer:

For a general quadratic equation like:

y = a*x^2 + b*x + c

a is the leading coefficient.

And we define the vertex of this as (h, k)

Where h is:

h = -b/(2*a)

and k is the y-value given when we use x = h.

Now, in this case we have:

f(x) = 5*x^2

We can see that the leading coefficient is 5, then a = 5.

To find the value of h we use:

h = -b/(2*a)

there is no lineal term, thus b = 0, then:

h = -0/(2*5) = -0/10 = 0

and k is given by

f(h) = f(0) = 5*0^2 = 0

then k = 0.

Concluding:

a = 5

h = 0

k = 0

The experimental probability for the numbers are:

P(3) = 1/12 (in fraction)

P(3) = 0.08 (in decimal)

P(3) ≈ 8% (in percentage)

P(6) = 3/12  

P(6) = 0.25

P(6) = 25%

P(less than 4) = 6/12

P(less than 4) = 0.5

P(less than 4) = 50%

Probability is the likelihood of a desired event happening.

Experimental probability is a probability that relies mainly on a series of experiments.

Blake rolled a die 12 times and 3 appears once (Given in the table). The experimental probability for 3 will be:

P(3) = 1/12 (in fraction)

P(3) = 0.08 (in decimal)

P(3) ≈ 8% (in percentage)

Blake rolled a die 12 times and 6 appears 3 times (Given in the table). The experimental probability for 6 will be:

P(6) = 3/12  

P(6) = 0.25

P(6) = 25%

The numbers less than are 1, 2 and 3. Six of the twelve outcome in the table are less than 4.

P(less than 4) = 6/12

P(less than 4) = 0.5

P(less than 4) = 50%

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The probability of getting a sum greater than 10 is 1/12.

From the question, we have

total outcomes = 6 ×6 = 36

Number of events of sum greater than 10: {5, 6}, {6, 5}, {6, 6} = 3

Probability = 3/36

=1/12

The probability of getting a sum greater than 10 is 1/12.

Probability:

Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

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Answer:

20.

Step-by-step explanation:

20+(1/5)20=24

The given integral ∫(2√(2^47x^23))/(√(4x^2-x+1)) dx can be evaluated by using the table of integrals. The specific integral does not appear in the table, indicating that it may not have a standard antiderivative representation.

The given integral involves a combination of power functions and a square root in the numerator and denominator. In order to evaluate it, we would typically refer to the table of integrals to find a matching entry. However, after consulting the table, we do not find an exact match for the given expression.

This suggests that the integral may not have a standard antiderivative representation in terms of elementary functions. In such cases, numerical methods or approximation techniques may be employed to estimate the value of the integral. These methods include numerical integration techniques like Simpson's rule or the trapezoidal rule.

In conclusion, due to the lack of a direct match in the table of integrals, the given integral ∫(2√(2^47x^23))/(√(4x^2-x+1)) dx may not have a simple algebraic solution in terms of elementary functions. Further analysis using numerical methods would be required to obtain an approximate value for the integral.

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Answer:

Option A is correct

Step-by-step explanation:

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