Given a function described as the equation y = 4x - 4, what is y when x is 1, 2, and 3?​

Based on the definition of the functions, the value of x if f(x) = g(x) is 3

The equations of the functions are given as

f(x) = -2x + 4

g(x) = 2x - 8

It should be noted that the above equations are linear equations

From the question, we understand that the functions are equal

This means that, we have the following equation

f(x) = g(x)

Substitute the known values in the above equation

So, we have the following equation

-2x + 4 = 2x - 8

Collect the like terms in the above equation

So, we have

2x + 2x = 8 + 4

Evaluate the like terms in the above equation

So, we have

4x = 12

Divide both sides by 4

x = 3

Hence, the value of x such that the equations are equal is 3

See attachment for the graph of the functions

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The correct answer is d. dp/dt = 1/1200 P (500-P).

Rate of change is a major of house quickly one quantity change in relation to another it is parisu of the changing 122 the changing another quantity over specified time period it is commonly used mathematics physics economic and other discipline to make operate of vijay process is a caring rate of changing also known as velocity, derivative or slope.

This differential equation describes the rate of change of the number of people entering a movie theater. It states that the rate of change (dp/dt) is equal to the product of 1/1200 and the current number of people (p) in the theater, multiplied by the difference between the capacity of the theater (500) and the current number of people (p). This equation indicates that the rate of change of people entering the theater is proportional to the difference between the capacity and the current number of people.

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Answer:

889 hours.

Step-by-step explanation:

Divide $7,993 by $3, you get a decimal so you increase it to the next hour so you can have all the needed money.

Answer: Yes

Step-by-step explanation: by SAS

Answer:

Step-by-step explanation:

ASA postulate of congruence.

625 decreased to 125

a.

The absolute change = | final value - initil value |

= |125 - 625| = 500

The absolute change is 500

b.

The percentage change:

Answer:

\(A. \ x-4y=8\)

Step-by-step explanation:

1) if to re-write the given equations, then A. y= 1/4 x-2; B. y= -1/4x +2; C. y= -4x-2 and D. y=4x+2;

2) the answer A. y=1/4 x-2 is correct.

Answer:

\(n=(\frac{2.58(80)}{7})^2 =869.407 \approx 870\)

So the answer for this case would be n=870 rounded up to the nearest integer

Step-by-step explanation:

Information given

\(\sigma = 80\) represent the deviation

ME = 7 represent the margin of error

Solution

The margin of error is given by this formula:

\( ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\)    (a)

And on this case we have that ME =7 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

\(n=(\frac{z_{\alpha/2} \sigma}{ME})^2\)   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. The significance level would be \( \alpha=0.01\) and \(\alpha/2 =0.05\). The critical value would be \(z_{\alpha/2}=2.58\), replacing into formula (b) we got:

\(n=(\frac{2.58(80)}{7})^2 =869.407 \approx 870\)

So the answer for this case would be n=870 rounded up to the nearest integer

Answer:

  (a)  5 : 8 < 7 : 10

  (b) 9/6 = 36/24

Step-by-step explanation:

Perhaps simplest to explain is the use of a common denominator: 40.

  \(5 : 8 = (5\cdot5):(8\cdot5)=25:40\\\\7:10=(7\cdot4):(10\codt4)=28:40\\\\25:40 < 28:40\quad\leftrightarrow\quad\boxed{5:8 < 7:10}\)

__

Other ways you can do this comparison are ...

  Multiply by 8·10 = 80, the product of the denominators:

     5·10 = 50 < 7·8 = 56

  Convert the fractions to decimal:

     5/8 = 0.625 < 7/10 = 0.700

__

Remove a factor of 4 from the second fraction:

  \(\dfrac{9}{6}\text{ and }\dfrac{36}{24}\quad\leftrightarrow\quad\boxed{\dfrac{9}{6}=\dfrac{9\cdot4}{6\cdot4}}\)

Answer:

The last one: Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.

Step-by-step explanation:

To get to (-3 1/2, -2), you would have to go left 3 1/2 units, and down 2 units.

The circled portion in the confidence interval formula p ± z represents the Margin of Error, which plays a crucial role in interpreting the range of plausible values for the population parameter.

In the confidence interval formula p ± z, the circled portion represents the Margin of Error.

The Margin of Error is a critical component of a confidence interval and quantifies the level of uncertainty in the estimate.

It indicates the range within which the true population parameter is likely to fall based on the sample data.

The Margin of Error is calculated by multiplying the critical value (z) by the standard deviation of the sampling distribution.

The critical value is determined based on the desired level of confidence, often denoted as (1 - α), where α is the significance level or the probability of making a Type I error.

The Margin of Error accounts for the variability in the sample and provides a measure of the precision of the estimate.

It reflects the trade-off between the desired level of confidence and the width of the interval.

A larger Margin of Error indicates a wider confidence interval, implying less precision and more uncertainty in the estimate.

Conversely, a smaller Margin of Error leads to a narrower confidence interval, indicating higher precision and greater certainty in the estimate.

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Total number of rabbits produced in 9 years will be 45.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a rabbit can produce 5 new rabbits per year

Total number of rabbits produced in 9 years will be -

n = 5y = 5 x 9 = 45 new rabbits

Therefore, total number of rabbits produced in 9 years will be 45.

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Answer:

slope = 1/3, equation is y = 1/3x - 2

Step-by-step explanation:

slope formula = change in y / change in x

= (0 - (-2)) / (6 - 0) = 2 / 6 = 1/3

Since we know the slope and the y-intercept we can write the equation in slope-intercept form which will be y = 1/3x - 2.

Answer:

y=1/3x -2

Step-by-step explanation:

points (0, -2) and (6, 0)

Slope- intercept form:

y=mx+b

y=1/3x+b

y=1/3x -2

Let's see how the while loop functions for n = 2345. Inside the loop, the reversed number is calculated using the formula reverse = reverse * 10 + remainder. n. n != 0.

Given,

arr: [7, 234, 58100]

Expected Output:

7 + 432+ 18500 = 18939

Input:

arr: [0, 100, 220]

Expected Output:

0 + 100 + 220 = 320

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Answer:

3.46 gallons

Step-by-step explanation:

write your ratio: x gallons/800in^3 = 1 gallon/231in^3

cross multiply: 1*800 = 231*x

simplify: 800 = 231x

divide both sides by 231: 3.4632034632 = x

round+flip: x = 3.46 gallons

Answer:

Halo!!! i wrote my answer below your epic btw

Step-by-step explanation:

you first have to break up the surface of the shape into smaller shapes so that they are easier to work with. you then calculate all of the shapes and add them together. this can be used in the real world to find the area of houses when you need to find how much space an area of the house has.

PS:If u didnt learn to find surface area this way insert anything you want into the beggining sorry i dont know what youve been learning

We can use the logarithmic identity log_a(b) + log_a(c) = log_a(bc) to simplify the left side of the equation:

log_2(x) + log_4(x+1) = log_2(x) + log_2((x+1)^(1/2))

Using the rule log_a(b^c) = c*log_a(b), we can simplify further:

log_2(x) + log_2((x+1)^(1/2)) = log_2(x(x+1)^(1/2))

Now we can rewrite the equation as:

log_2(x(x+1)^(1/2)) = 3

Using the rule log_a(b^c) = c*log_a(b), we can rewrite this as:

x(x+1)^(1/2) = 2^3

Squaring both sides, we get:

x^2 + x - 8 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 1, and c = -8. Plugging in these values, we get:

x = (-1 ± sqrt(1^2 - 4(1)(-8))) / 2(1)

x = (-1 ± sqrt(33)) / 2

x ≈ -2.54 or x ≈ 3.54

However, we must check our solutions to make sure they are valid. Plugging in x = -2.54 to the original equation results in an invalid logarithm, so this solution is extraneous. Plugging in x = 3.54 yields:

log_2(3.54) + log_4(4.54) = 3

0.847 + 0.847 = 3

So x = 3.54 is the valid solution to the equation.

Answer:

778ft

Step-by-step explanation:

Answer: 25

Step-by-step explanation:

Answer: 225

Step-by-step explanation:

Create a ratio part/whole for radians = part/whole for degrees

\(\frac{\frac{5\pi }{4} }{2\pi } = \frac{x}{360}\)      Keep change flip because you are dividing fractions for left side

\(\frac{5\pi }{4} (\frac{1}{2\pi }\)) = \(\frac{x}{360}\)

\(\frac{5}{8} (\frac{360}{1} ) =x\)

x = 225

Answer:

20%

Step-by-step explanation:

Think about it. 100 divided by 25 is four so just multiply 5 times 4 and you got 20. giving you the probability of 20%. Your Welcome! And I'm not a genius it's just simple math.

The information from the histogram are as follow,

Students exercised for 4 or more hours are 14.

Students exercised for 9 or fewer hours are 13.

Mean of the data = 7.3.

median of the data = 6.33.

The histogram provides information about the distribution of hours students spent exercising in a week.

The number of students who exercised 4 hours or more,

= adding up the counts in the first and second bins.

= 9 + 5

= 14 students

The number of students who exercised 9 hours or fewer,

= adding up the counts in the first and second bins

= 9 + 4

= 13 students

The mean hours of exercise is not provided by the histogram

use the formula,

Mean = Σ\(x_{i} y_{i}\) / N

where

\(x_{i}\) is the midpoint of the ith bin

\(y_{i}\) is the frequency of the ith bin

N is the total sample size

Mean = [(2)(4)  + (7)(9) + (12)(5)] / 18

          = 7.3

The median hours of exercise is not provided by the histogram.

Median = L + ( (n/2 – F) / f ) × w

where

L=The lower limit of the median group

n = The total number of observations

F = The cumulative frequency up to the median group

f =The frequency of the median group

w = The width of the median group

median = 5 + ( ( 14/2 - 4 ) /9 × 4

             = 6.33

Therefore, from the histogram the number of students exercised for ,

4 hours or more are 14.

9 hours or fewer are 13.

mean = 7.3

Median = 6.33

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The volume of the solid formed by rotating the region inside the first quadrant enclosed by y=x⁴ and y=125x is 138438\(\pi\).

Let,

f(x) = 125x

g(x) = x⁴

Intersection points will be,

x⁴ = 125x

x = 0 , 3.3437

Volume V = \(\pi\)\(\int\limits^{3.34}_0{(125x)^{2} - x^8 } \, dx\)

=\(\pi\)\(\int\limits^{3.34}_0 {15625x^2-x^8} \, dx\)

=\(\pi\)[15625x³/3 - x⁹/9]₀³

=\(\pi\)[140625 - 2187]

= 138438\(\pi\)

The volume of the solid formed by rotating the region inside the first quadrant enclosed by two curves can be found using the method of cylindrical shells. This method involves cutting the solid into thin cylindrical shells and finding the volume of each shell. The sum of the volumes of the shells is equal to the volume of the solid.

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Answer:

It's written as

\(89.7 \times {10}^{9} \)

Or

\(8.97 \times {10}^{10} \)

Hope this helps you

Answer:

8.97 * 10 ^10

Step-by-step explanation:

We want one nonzero digit to the left of the decimal

8.97

We moved the decimal 10 places to the left

The exponent is positive 10 since we moved 10 places to the left

8.97 * 10 ^10

The formula for y in terms of x and c is given as follows:

\(y = \frac{c^5}{\sqrt{x}}\)

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other. This means that if one quantity is multiplied by a certain factor, the other quantity will also be multiplied by the same factor.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

An inverse proportional relationship is modeled as follows:

y = k/x.

In this problem, we have that y is inverse proportional to the square root of x, hence the equation is given as follows:

\(y = \frac{k}{\sqrt{x}}\)

When x = c², y = c^4, hence the constant k is obtained as follows:

\(c^4 = \frac{k}{\sqrt{c^2}}\)

k/c = c^4

k = c^5.

Hence the equation is:

\(y = \frac{c^5}{\sqrt{x}}\)

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There can be multiple outputs (monthly charges) for a given input (number of credit cards), violating the definition of a function. hence, Situation 3 does not represent a function.

Situation 3: the total amount of money charged monthly on credit cards to the number of credit cards owned does not represent a function.

In a function, each input (or x-value) should have a unique output (or y-value). However, in this situation, the total amount of money charged monthly on credit cards depends on the number of credit cards owned. It is possible to have different credit card numbers but still have the same total amount of money charged monthly.

For example, two people could own different numbers of credit cards but have the same monthly charges.

As a result, the definition of a function can be violated by having many outputs (monthly charges) for a single input (number of credit cards).

Because of this, case 3 does not represent a function.

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Abhasra ran 21 kilometers last week. By forming an equation, the required value is evaluated.

To write an equation from a words,

It is given that, Daniel ran 5 kilometers less than Abhasra last week.

And Daniel runs 16 kilometers that week.

From this, consider the number of kilometers by Abhasra as 'x'.

So, the number of kilometers by Daniel = x - 5

But we have x - 5 = 16

Thus, the required equation is x - 5 = 16.

By solving this we get the required number as

x - 5 = 16 ⇒ x = 16 + 5 = 21

Therefore, Abhasra ran 21 kilometers.

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