HELP ASAP

Part A: If (62)x = 1, what is the value of x? Explain your answer. (5 points)

Part B: If (60)x = 1, what are the possible values of x? Explain your answer. (5 points)

Multiply amount she saves per month by 5 months:

35 x 5 = $175

$175 is less than the price of the player so she won’t have enough to buy it.

197.99 - 175 = $22.99

She needs $22.99.more

Answer:

\(y = -2x + 10\)

Step-by-step explanation:

Slope: \(m = \frac{y_{2}-y_{1} }{x_{2}-x_{1}}\)

Slope-Intercept Form: \(y=mx+b\)

\(m=\frac{8-0}{1-5}\)

\(m = -2\)

\(y = -2x + b\)

\(0 = -2 (5)+b\)

\(0=(-10)+b\)

\(b = 10\)

\(y = -2x + 10\)

Answer:

Step-by-step explanation:

\(a_1=2\\a_2=9\\d=a_2-a_1=7\\\\a_n=a_1+d(n-1)\\\\a_{63}=2+7(63-1)=2+7(62)=2+434=436\)

The 63rd term of the given  arithmetic progression is 436.

An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant. A sequence -

a₁ , a₂, a₃ , a₄ ...... aₙ

will be an arithmetic progression if -

a₂ - a₁ = a₃ - a₂ = a₄ -  a₃ = d (constant) is called common difference of A.P. and a₁ = 'a' as the first term.

Given is the following sequence -

2, 9, 16, ..... nth term

First term [a] = 2

common difference [d] = 9 - 2 = 7

We can calculate the nth term of an A.P. using the formula -

a[n] = a + (n - 1)d

a[63] = a + (63 - 1) d

a[63] = 2 + 62 x 7

a[63] = 2 + 434

a[63] = 436

Therefore, the 63rd term of the given  arithmetic progression is 436.

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Answer:

Step-by-step explanation: The area of a circle can be found with the equation A=(pi)*r^2. Use the equation to find the answer:

A=(pi)*5.5^2 (or A=3.14*5.5^2)

A=94.99 or 95.03 in exact pi

Have a nice day! :)

Answer:

24.4 degrees

Step-by-step explanation:

This is a right triangle so you can use trig to solve. If you take the arctan of 5/11 you get 24.4(rounded to the nearest tenth)

Answer:

45 degrees

Step-by-step explanation:

90+45+45=180 degrees

:))

Answer:

\(m\angle A=45\textdegree\)

Step-by-step explanation:

All triangles have a sum of 180°. The problem shows us that two of the angles are 90° and 45°. Therefore, the last angle is 45°.

\(m\angle A+45+90=180\\m\angle A+135=180\\m\angle A=45\)

Answer:

Step-by-step explanation:

I thought of a 2 digit number. The digits of my number are different:  [XY]

Then I'm lost. Does "The unit digit of my number is the tens digit raised third power" mean that the X is raised to the third power?:

X^3

But then we need more information.  X could be 1, 2,3, or 4.  At 5 it becomes a three digit number.  All of the other option result in a two digit number with different digits, so all seem possible.  I don't know how to answer this without more information.

Answer:

2x+9

Step-by-step explanation:

(4x-15)-(2x-24)

4x - 2x - 15 - -24

4x - 2x - 15 + 24

2x - 15 + 24

2x + 9

2x+9

Answer:

(6, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

3x - 5y = 13

x + 4y = 10

Step 2: Rewrite Systems

x + 4y = 10

Step 3: Redefine Systems

3x - 5y = 13

x = 10 - 4y

Step 4: Solve for y

Substitution

Step 5: Solve for x

Answer:

(6,1)    x=6 and y=1        

Step-by-step explanation:

EASY we can use Elimination or Substitution process

We are going to solve by

Elimination process

Subtract each other

(3x-5y=13)

(x+4y=10)

3x-5y=13;x+4y=10

To solve this multiply (x-4y=10) by 3 to get rid of the x

3x-12y=30

now u can subtract both

3x-12y=30 minus

3x-5y=13

17y=17

Divide both sides by 17

y=1

Now we have y lets plug it in to find x

x+4(1)=10

x+4=10

subtract 4 from both sides

x=6

x=6 and y=1

To find all functions \(\(f\)\) such that \(\(f(bt)\)\) is a martingale, we can apply \(Itô's\) Lemma to \(\(f(bt)\).\)

The \(Itô's\) Lemma formula in one dimension is:

\(\[df(t) = f'(t)dt + f''(t)dW(t)\]\)

Where:

- \(\(f(t)\)\) represents the function we want to find.

- \(\(df(t)\)\) represents the differential of the function.

- \(\(f'(t)\)\) represents the first derivative of \(\(f\)\) with respect to \(\(t\).\)

- \(\(dt\)\) represents an infinitesimal change in time.

- \(\(f''(t)\)\) represents the second derivative of \(\(f\)\) with respect to \(\(t\).\)

- \(\(dW(t)\)\) represents the differential of the Wiener process (a standard Brownian motion).

Now, let's apply \(Itô's\) Lemma to \(\(f(bt)\):\)

\(\[df(bt) = f'(bt)dbt + f''(bt)dW(bt)\]\)

Where:

- \(\(b\)\) represents a constant.

- \(\(db(t)\)\) represents an infinitesimal change in \(\(b\).\)

To make \(\(f(bt)\)\) a martingale, we require that the drift term in the differential equation is zero. Therefore, we have:

\(\[f'(bt)dbt = 0\]\)

This implies that \(\(f'(bt) = 0\)\) for all \(\(t\)\). Thus, \(\(f(bt)\)\) must be a constant function. Let's denote this constant as \(\(C\).\) Therefore, we have:

\(\[f(bt) = C\]\)

So, all functions \(\(f(bt)\)\) that satisfy the condition of being a martingale are constant functions of the form \(\(f(bt) = C\).\)

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Answer:

Part A: If Beatrice inputs −8 into the function, she must get an output of 8.

Part B: (−4,8) , (4,−8) , (8,−4)

Step-by-step explanation:

Part A:

We know that a function is a relation that maps elements from one set (The domain, the set of the inputs) into elements from another set (the range, the set of the outputs)

Such that each input can be mapped into only one output.

Then if we know that our function maps the input -8 into the output 8.

Always that we use this function with the input -8. we will have the same output, 8.

Then we can conclude that the correct option to the first part is:

"If Beatrice inputs −8 into the function, she must get an output of 8. "

Part B:

Remember, -8 is mapped into 8, then the point (−8,4) (this says "-8 is mapped into 4) can never be on the graph of the function.

But the points:

(−4,8) , (4,−8) , (8,−4)

Could be on the graph of the function.

Answer:

correct A:-8,8

B: -4,8

Step-by-step explanation:

Answer:

Sharon's brother is 4

Step-by-step explanation:

half of 24 is 12 and 4 is 3 times youger then 12

Answer:

heptagon; rectangles; heptagonal prism

Step-by-step explanation:

Since the base is a heptagon (hepta- is seven sides), that gets rid of both the pentagon answers. Since the sides are all rectangles, that gets rid of the Heptagon and Triangles answer. :)

To write 31/25 as a decimal, we can divide 31 by 25 using long division or a calculator and we get 1.24

A decimal is a way of expressing a number as a fraction of one.

Rounding off is a mathematical process that involves replacing a number with an approximate value that is easier to work with. When you round off a number, you choose the nearest whole number, ten, hundred, etc., depending on the place value you are rounding to.

For example, if you are asked to round the number 3.6 to the nearest whole number, you would round it off to 4, because 4 is the nearest whole number to 3.6.

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Answer:

a

Step-by-step explanation:

10u + t is the expressions shows the value of the reversal of digits in a two digit number, t = the tens digit and u = the ones digit. This can be obtained by multiplying 10 with the tens digit and adding unit digit.

Given that, in a two digit number,

t = the tens digit

u = the ones digit

The expression for the digit will be ,

10×t + u = 10t + u

The value of its reversal,

u = the tens digit

t = the ones digit

10×u + t = 10u + t is the required expression

For example,

37 = 10×3 + 7 = 30 + 7 and its reverse 73 = 10×7 + 3 = 70 + 3

Hence 10u + t is the expressions shows the value of the reversal of digits in a two digit number, t = the tens digit and u = the ones digit.

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Hannah's debt-to-equity ratio when her liabilities was $30,000 (excluding her mortgage of $100,000 ) and her net worth is $45,000 is 0.75.

Debt-to-equity ratio is a financial ratio that measures the proportion of total liabilities to shareholders' equity. To calculate the debt-to-equity ratio for Hannah, we need to first calculate her total liabilities and shareholders' equity.

We are given that Hannah has liabilities of $30,000 excluding her mortgage of $100,000. Therefore, her total liabilities are $30,000 + $100,000 = $130,000.

We are also given that her net worth is $45,000. The net worth is calculated by subtracting the total liabilities from the total assets. Therefore, the shareholders' equity is $45,000 + $130,000 = $175,000.

Now we can calculate the debt-to-equity ratio by dividing the total liabilities by the shareholders' equity.

Debt-to-equity ratio = Total liabilities / Shareholders' equity = $130,000 / $175,000 = 0.74 (rounded to two decimal places)

Therefore, Hannah's debt-to-equity ratio is 0.74, which is closest to option 0.75.

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a)  f'(x) = 2x.

b)The inverse function is \(f^{(-1)\)(x) = sqrt(x - 5).

c) The compound function f'(\(f^{(-1)\)(x)) = 1 / (2 * sqrt(x - 5)).

To find its derivative, inverse function, and the compound function using the provided informatio:

(a) The derivative of the function, f'(x):

can be found by differentiating f(x) with respect to x. The derivative of \(x^2\) is 2x, and the derivative of 5 is 0. Therefore, f'(x) = 2x.
(b) To find the inverse function, f^(-1)(x):

we need to swap x and y in the original function and then solve for y. In this case, the function becomes \(x = y^2 + 5\). Subtract 5 from both sides, and then take the square root:
y = sqrt(x - 5)
So, the inverse function is \(f^{(-1)\)(x) = sqrt(x - 5).
(c) To find the compound function f'(\(f^{(-1)\)(x)):

we first plug in\(f^(-1)\)(x) into f'(x):
f'(f^(-1)(x)) = 2 * sqrt(x - 5)
Now, find the derivative of the inverse function with respect to x:
d/dx [sqrt(x - 5)] = 1 / (2 * sqrt(x - 5))
Therefore, the compound function f'(f^(-1)(x)) = 1 / (2 * sqrt(x - 5)).

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Answer:

True

Step-by-step explanation:

Where the above conditions are given,  the correct option is: Plan 1 is a better deal for more than 5 cards purchased.

To determine   which pricing plan is a better deal,we need to compare the total cost for a certain number of game cards purchased.

Let's calculate the   total cost for different numbers  of game cards.

For Plan 1  -

- Admission fee  - $5 (fixed)

- Cost per game card  - $1

For Plan 2  -

- Admission fee  - $2.50 (fixed)

- Cost per game card  - $1.50

Now, let's compare the total cost for different numbers of game cards  -

1. If you purchase 1 game card  -

  - Plan 1  - $5 (admission fee) + $1 (cost per game card) = $6

  - Plan 2  - $2.50 (admission fee) + $1.50 (cost per game card) = $4

2. If you purchase 5 game cards  -

  - Plan 1  - $5 (admission fee) + $5 (cost for 5 game cards) = $10

  - Plan 2  - $2.50 (admission fee) + $7.50 (cost for 5 game cards) = $10

3. If you purchase 8 game cards  -

  - Plan 1  - $5 (admission fee) + $8 (cost for 8 game cards) = $13

  - Plan 2  - $2.50 (admission fee) + $12 (cost for 8 game cards) = $14.50

Based on these calculations, we can conclude that  -

- Plan 1 is a better deal for more than 5 cards purchased.

- Plan 2 is a better deal for more than 8 cards purchased.

Therefore, the correct option is  - Plan 1 is a better deal for more than 5 cards purchased.

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Given:

Secret number is more than 11 units away from 50.

To find:

The absolute- value inequality that gives the possible values of Mai's number.

Solution:

Let the secret number be x.

Secret number is more than 11 units away from 50. It may be less than 50 or more than 50.

Case 1: If x<50, then \(50-x>11\)

Case 2: If x>50, then \(x-50>11\)

It means the absolute difference between secret number and 50 is greater than 11.

\(|x-50|>11\)

Therefore, the required inequality is \(|x-50|>11\).

Answer:

Step-by-step explanation:

Plot 213, −56, and −312 on the number line.

Improved concentration is a result of educated efforts, leading to the discovery of inspiring words that satisfy the ache for growth and progress.

Concentration plays a crucial role in enhancing productivity and achieving success. When one's ability to concentrate improves, it becomes easier to focus on tasks at hand and delve deeper into the subject matter.

This improvement is not a mere coincidence but a result of deliberate and educated efforts. By employing various techniques such as time management, minimizing distractions, and practicing mindfulness, individuals can train their minds to concentrate better.

During the process of developing concentration skills, one may come across a variety of words that inspire and motivate. These words act as catalysts, triggering a desire for growth and progress. When exposed to meaningful and impactful words, individuals can feel a sense of inspiration that propels them forward.

These words have the power to ignite passion, instill determination, and awaken creativity. The discovery of such words acts as a driving force, reminding individuals of their goals and aspirations, and helping them stay focused on their journey of self-improvement.

As concentration improves and inspiring words are discovered, individuals experience a satisfying sense of accomplishment. The ache for personal and professional growth finds solace in the progress made through educated efforts.

With improved concentration, individuals can delve deeper into their studies, work on complex projects, or pursue their passions with unwavering dedication. This satisfaction stems from the knowledge that their hard work and commitment have paid off, resulting in tangible advancements and personal development.

In conclusion, the path to improved concentration begins with educated efforts and leads to the discovery of inspiring words. These words serve as sources of motivation, fueling the desire for progress and growth.

As individuals concentrate better, they experience a satisfying sense of accomplishment, knowing that their efforts have yielded positive outcomes. By continuously honing their concentration skills and seeking inspiration through words, individuals can unlock their full potential and achieve their goals.

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a) The statement is true for Euclidean geometry only because this is one of the fundamental postulates in Euclidean geometry. A line can intersect with another line at one point and create a right angle or a perpendicular. In other geometries, this is not true, for example, hyperbolic geometry.

b) The statement is false for hyperbolic geometry and true for Euclidean geometry because the fifth postulate, also known as the parallel postulate, is unique for Euclidean geometry. It says that for any line and point, there is exactly one line parallel to the original line passing through the point.

c) The statement is true for Euclidean geometry only because it is one of the fundamental postulates in Euclidean geometry.

d) The statement is true for Euclidean geometry only because it is one of the fundamental postulates in Euclidean geometry.

e) The statement is true for both Euclidean and hyperbolic geometry because perpendiculars can be drawn to parallel lines in both geometries.

f) The statement is false for Euclidean geometry and true for hyperbolic geometry because in Euclidean geometry, a perpendicular can always be constructed to two parallel lines, but in hyperbolic geometry, it is not possible to construct a perpendicular to two parallel lines.

g) The statement is false for Euclidean geometry and true for hyperbolic geometry because the sum of the interior angles of a triangle in hyperbolic geometry is less than 180 degrees, whereas the sum of the interior angles of a triangle in Euclidean geometry is 180 degrees.

h) The statement is true for both Euclidean and hyperbolic geometry because a triangle in hyperbolic geometry can have a sum of angles less than 180 degrees, whereas a triangle in Euclidean geometry has a sum of angles of exactly 180 degrees.

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Answer:

x = -5/2    x=1      x = -1

Step-by-step explanation:

p(x) = 2x^3 + 5x^2 – 2x – 5

Use factor by grouping

p(x) = 2x^3 + 5x^2       – 2x – 5

Factor x^2 from the first group and -1 from the second group

    x^2(2x +5) -1( 2x+5)

Then factor out 2x+5

p(x) = (2x+5) (x^2-1)

Factor x^2 -1 as the difference of squares

p(x) = (2x+5)(x-1)(x+1)

Set to zero to find the x intercepts

0 = (2x+5)(x-1)(x+1)

Using the zero product property

2x+5 =0    x-1 =0   x+1 =0

2x = -5        x=1       x=-1

x = -5/2    x=1      x = -1

Answer:

The zeroes are (-1,0), (1, 0) and (-5/2, 0)

Step-by-step explanation:

We can find the zeroes by factoring:

2x^3 + 5x^2 - 2x - 5 = 0  

x^2(2x + 5) - 1(2x + 5) = 0

(x^2 - 1)(2x + 5) = 0

(x - 1)(x + 1)(2x + 5) = 0

So x = -1, 1, -5/2.

Answer: B.

Step-by-step explanation:

Answer:

The answer is B: Reflection over the y-axis followed by a translation to the left by 2 units

Step-by-step explanation:

I had this on a test one time and I got 100%

Answer:

a.12.6   b.8.0

Step-by-step explanation:

First term (a1) = -7

Second term (a2) = -2

Common difference: a2 - a1 = -2-(-7) = 5

Hence, Fifth term = a1 + 4d = -7 + 4(5) = 13

Answer:

a. f(t) = h = 10·t/(π·r²)

b. The dependent and independent variables are ;

Dependent = The height of the water in the cup over time, h

Independent = The time of measurement of the water height in the cup

c. The domain is 0 < t < 10

d. The 5 in f(5), represents 5 seconds

e. Susan was trying to find out what the height of the water in the cup will be after 5 seconds

f. The numbers mean that at 7 seconds the water in the cup is 70 units high

Step-by-step explanation:

a. The rate at which water is added to the cup in the question = 10 mL per second

The volume of water in the cup is V = π × r² × h

dV/dt = 10

dV = 10 × dt

V = ∫10 × dt = 10·t

The height of the water in the cup, h = V/(π × r²) = 10·t/(π·r²)

Therefore, we have the function that models the height of the water in the cup over time given as follows;

f(t) = h = 10·t/(π·r²)

b. The dependent and independent variables are given as follows;

Dependent variable = The height of the water in the cup over time, h

Independent variable = The time of measurement of the water height in the cup

c. The domain is 0 < t < 10

Given that the cup has a capacity of 100 mL, we have;

The maximum volume the up can hold = 100 mL

The time it will take to fill the 100 mL cup given that the rate of at which she is pouring water into the cup at 10 mL per second = 100 mL/(10 mL/s) = 10 s

Therefore, a reasonable domain for the independent variable, t is 0 < t < 10

d. We have that the function f(t) = h = 10·t/(π·r²)

Therefore, the 5 in f(5), represents the time in seconds at which the function was being evaluated, which is 5 seconds

e. Given that Susan wrote f(5), Susan was trying to find the height of the water in the cup after 5 seconds

f. Given that Susan wrote f(7) = 70, we have that at 7 seconds the height of the water in the cup is 70 units, where one unit is 1/(π·r²)

Which gives;

f(7) = h = 10 × 7/(π·r²)  70/(π·r²)

f(7) = 70/(π·r²)

if we flip a coin, we would expect the probability of its landing heads to be the same as its landing tails is referred to as the law of large numbers.

The law of large numbers is a probability and statistics, which defines that as a sample size grows, its mean gets closer to the average of the whole population.

This is due to the sample being more representative of the population as the sample becomes larger.

This is the theorem that describes the result of performing the same experiment a large number of times because the average of the results obtained from a large number of trials is close enough to the expected value.

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