-5
-4
-3
-2
- 1
-3
-4
-5
The equation of the line in this graph is y=
2021 Edmentum. All rights reserved.

Answer:

1,600

Step-by-step explanation:

I did a bit of guessing becuase I don't know the exact way to reverse the formula, but here is what I did!

I guessed around 1,550 at first, but it was too low. I kept increasing the base number until I reached 1,600, and came to the conclusion by doing the equation;

1,600(0.6)=960

Then, since it increases each month by 60% of the previous month's value, you do

1,600+960=2,560

Answer:

what's

Step-by-step explanation:

the test

Answer:

what is this what does this mean

Step-by-step explanation:

The true statement is now presented: If \(c > 0\) and \(|u| > c\), then \(u > c\) or \(u < -c\).

Mathematically speaking, the absolute value is defined by following expression:

\(|a| = \left \{ {{a,\,a \ge 0} \atop {-a,\,a < 0}} \right.\) (1)

If \(c > 0\) and \(|u| > c\), then \(u > c\) or \(-u > c\). Hence, \(u > c\) or \(u < -c\).

Therefore, if \(c > 0\) and \(|u| > c\), then \(u > c\) or \(u < -c\). (By tricotomy)

We kindly invite to see this question on absolute values: https://brainly.com/question/4691050

Answer:

8/10

Step-by-step explanation:

id hope your have a great day

Answer:

80%

Step-by-step explanation:

80÷100=.8 which is 80%

answer

0

Step-by-step explanation:

you plug in the 2 into every xbox value

Answer:

f(x)= x²-2x

For finding f(x²), replace x with x²

f(x²)= (x²)²-2x²

= x⁴-2x²

Hope it helps :-)

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

Learn more about integrations here:

https://brainly.com/question/30217024

#SPJ1

Answer:

1/9 rise 1 run 9

Step-by-step explanation:

if you graph the y coordinate as 3 and find the x value, x value should be 0. Point (0,3) and (-9,2) and do rise over run

A linear equation for h as a function of time, t, in seconds since it was fired is; h(t) =  (18t + 28) ft

We are given that the Rate of increasing of height is 18 ft/s

We are told that at t = 5 seconds, the height is 118 feet,

This means that;

h(5) = 118 ft

We know that height of rocket is increasing 18 ft for every second passed, and it will also have an initial height.

Thus;

h(t) = 18t + h₀

where;

h₀ is the initial height

Plugging in the relevant values for a height of 5 seconds gives;

118 = (18 * 5) + h₀

h₀ = 118 -90

h₀ = 28 ft

Thus, the equation for the height is;

h(t) =  (18t + 28) ft at a time t seconds.

Read more about projectile equation at; https://brainly.com/question/16866199

#SPJ1

Answer:

800(1 + r)³ + 300(1 + r)² + 625(1 + r)

Step-by-step explanation:

At the beginning of the first year $800 is deposited.

At the end of the first year the amount of money in account = $800 × growth factor = 800(1 + r)

At the beginning of the second year, $300 is deposited, the money in account = 800(1 + r) + 300

At the end of the second year the amount of money in account is multiplied by growth factor. = [800(1 + r) + 300] × 1 + r = 800(1 + r)² + 300(1 + r)

At the beginning of the third year, $625 is deposited, the money in account = 800(1 + r)² + 300(1 + r) + 625

At the end of third year the money = [800(1 + r)² + 300(1 + r) + 625] × 1 + r = 800(1 + r)³ + 300(1 + r)² + 625(1 + r)

The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

To learn more on Sequence click:

https://brainly.com/question/21961097

#SPJ1

It is verified that the given vectors x₁ and x₂ are solutions of the given system. Using Wronskian it is shown that they are linearly independent. Then, \(W(t)=7e^{-3t}\). The general solution of the given system is written as \(x(t)=\left[\begin{array}{c}3c_1e^{2t}+c_2e^{-5t}\\2c_1e^{2t}+3c_2e^{-5t}\end{array}\right]\).

Wronskian analysis helps to determine whether a solution is linearly dependent or independent.

Given the system is \(x'=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x\).

Let's differentiate x₁ concerning t, and we get,

\(\begin{aligned}x_1'&=\left[\begin{array}{c}\frac{d}{dt}(3e^{2t})&\\\frac{d}{dt}(2e^{2t})&\end{array}\right] \\&=\left[\begin{array}{c}6e^{2t}&\\4e^{2t}&\end{array}\right] \end{aligned}\)

Now,

\(\begin{aligned}\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x_1&=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]\left[\begin{array}{c}3e^{2t}\\2e^{2t}\end{array}\right]\\&=\left[\begin{array}{c}12e^{2t}-6e^{2t}\\18e^{2t}-14e^{2t}\end{array}\right]\\&=\left[\begin{array}{c}6e^{2t}\\4e^{2t}\end{array}\right]\\&=x_1'\end{aligned}\)

From this, we can write,

\(x_1'=\left[\begin{array}{cc}4&-3\\6&-7\end{array}\right]x_1\)

Therefore, we conclude that x₁ is a solution to the given system.

Let's differentiate x₂ concerning t, and we get,

\(\begin{aligned}x_2'&=\left[\begin{array}{c}\frac{d}{dt}(e^{-5t})&\\\frac{d}{dt}(3e^{-5t})&\end{array}\right] \\&=\left[\begin{array}{c}-5e^{-5t}&\\-15e^{-5t}&\end{array}\right] \end{aligned}\)

Now,

\(\begin{aligned}\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x_2&=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]\left[\begin{array}{c}e^{-5t}\\3e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}4e^{-5t}-9e^{-5t}\\6e^{-5t}-21e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}-5e^{-5t}\\-15e^{-5t}\end{array}\right]\\&=x_2'\end{aligned}\)

From this, we can write,

\(x_2'=\left[\begin{array}{cc}4&-3\\6&-7\end{array}\right]x_2\)

Therefore, we conclude that x₂ is also a solution to the given system.

Now, find the Wronskian of x₁ and x₂, we get,

\(\begin{aligned}W(t)&=\text{det}[x_1\;x_2]\\&=\text{det}\left[\begin{array}{cc}3e^{2t}&e^{-5t}\\2e^{2t}&3e^{-5t}\end{array}\right] \\&=(3e^{2t}\times3e^{-5t})-(e^{-5t}\times2e^{2t})\\&=9e^{2t-5t}-2e^{2t-5t}\\&=9e^{-3t}-2e^{-3t}\\&=7e^{-3t}\\&\neq0\end{aligned}\)

From this, we can conclude that x₁ and x₂ are independent.

Finally, we write the general solution of the system as follows,

\(\begin{aligned}x(t)&=c_1x_1+c_2x_2\\&=c_1 \left[\begin{array}{c}3e^{2t}\\2e^{2t}\end{array}\right] +c_2\left[\begin{array}{c}e^{-5t}\\3e^{-5t}\end{array}\right] \\&=\left[\begin{array}{c}3c_1e^{2t}\\2c_1e^{2t}\end{array}\right] +\left[\begin{array}{c}c_2e^{-5t}\\3c_2e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}3c_1e^{2t}+c_2e^{-5t}\\2c_1e^{2t}+3c_2e^{-5t}\end{array}\right] \end{aligned}\)

The complete question is -

First, verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearly independent. Finally, write the general solution of the system.

\(x'=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x;\; x_1=\left[\begin{array}{ccc}3e^{2t}\\2e^{2t}\end{array}\right], \;x_2=\left[\begin{array}{cc}e^{-5t}\\3e^{-5t}\end{array}\right]\)

To know more about Wronskian:

https://brainly.com/question/14309076

#SPJ4

Answer:

D

The light reflected during the first quarter and third quarter moon phases appears equal because the sun, moon, and Earth are at right angles.

Answer:

Step-by-step explanation:

if the discriminate is 0, it means that both roots are the same. Not only that, but it also means that the roots are real. I would pick D, but realize that that is the expected answer and the answer could be B, depending on how the person writing the problem thinks about it.

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

The graph of g(x) is obtained by shifting up the graph of f(x) by 15 units.

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

The angle PMR in the quadrilateral is 32 degrees.

The angle PMR can be found as follows;

The line AP is an angle bisector of angle RPM. Therefore, the following relationships are formed.

∠RPM ≅ ∠WPM

Hence,

∠RPM ≅ ∠WPM = 58 degrees

Therefore,

∠WPM = 58 degrees

∠PWM = 90 degrees

Let's find ∠PMR as follows

∠PMR = 180 - 90 - 58

∠PMR = 90 - 58

∠PMR  = 32 degrees

learn more on angles here:https://brainly.com/question/25779160

#SPJ1

Answer: 13.1

Explanation:

The data set we have is:

To calculate the mean, we need to add all the quantities and divide by the number of elements in the data set:

The number of elements in the data set is: 8 elements

And the sum of all the data is:

So, we substitute this into the Mean formula, and get the following result:

Rounding to the nearest tenth (1 decimal place):

Answer: 13.1

Answer:

  (c)  8 jars

Step-by-step explanation:

You want to know the number of 1.25 quart jars that can be filled from a 2.5 gallon container.

The number of jars can be found from ...

  (2.5 gal) × (4 qt/gal) × (1 jar)/(1.25 qt) = (2.5·4/1.25) jars = 8 jars

Lorraine can fill 8 jars from the 2.5 gallon pot.

<95141404393>

x²+6x+y²-10y+9=0

Answer:

Solution given:

(x-3)^2+(y-5)^2=25

Using formula (a-b)²=a²-2ab+b²

x²-2*x*3+3²+y²-2*y*5+5²=25

x²+6x+9+y²-10y+25=25

x²+6x+y²-10y+9=25-25

x²+6x+y²-10y+9=0 is a general form.

Answer:

I'm not that good at this but I'll try.

The difference between 25 and 40 is 15

The difference between 80 and 5 is 75

So, 15/75 = 0.20 or 20%

Sorry, that all I can come up with

Step-by-step explanation:

Answer:

The max is 85F

The min is 75F

Step-by-step explanation:

For the max 80+5=85F

For the min 80-5=75F

The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

= (x + 2) (x + 3) (x - 1)

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

To learn more about factorise here,

https://brainly.com/question/10718512

https://brainly.com/question/24734894

Answer

37

Step by Step explanation

replace x with -7

which gives

-(-7)^2-10(-7)+16

= 37

Mathematicians have used probability to determine how likely certain events are to occur. The possible values of  X will be 10, 0, -5 with following probabilities:

P(X = 10 ) = 0.23

P(X = 0 ) = 0.48

P(X = -5) = 0.29

Probability is the ability to happen. . From 0 to 1 is used to express the value. Whenever we are unsure of how an event will turn out, we can talk about the probabilities of various outcomes, or how likely they are. The study of probability-based events is often known as statistics. The amount of favorable outcomes and the overall number of outcomes thus affect how likely an event is to occur. The probability is typically expressed as a ratio between the number of positive outcomes and all of the outcomes in the sample space.

Given:

The probability distribution of X can be represented as:

X      P(X=x)

-5      0.29

0       0.48

10      0.23

The outcomes is attached as table below.

To learn more about probability, visit:

https://brainly.com/question/28045837

#SPJ1

The complete question is:

The table below to model the scenario is attached below:

Answer:

-5

Step-by-step explanation:

-3x + 7 < 11

-3(-5) + 7 < 11

Multiplying two negatives together, makes a positive number.

15 + 7 < 11

22 < 11

22 less than 11 is false, therefore -5 is the correct answer.

The correct answer is 4

Here's the Solution:

Transpose 7 to the right side

Now subtract 11 and 7

HOPE THIS HELPS. GOODLUCK:)

The probability of selecting an apple and a banana from the basket is 7/76.

To calculate the probability of selecting an apple and a banana from the basket of fruits, we need to determine the total number of possible outcomes and the number of favorable outcomes.

The total number of fruits in the basket is 5 bananas + 8 mangoes + 7 apples = 20 fruits.

When selecting the first fruit, there are 20 options. Let's say we select an apple. After removing one apple from the basket, there are 19 fruits left.

When selecting the second fruit, there are 19 options. This time, we want to select a banana. Since there are 5 bananas left in the basket, there are 5 favorable outcomes.

To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes = (Number of apples) * (Number of bananas) / (Total number of fruits) * (Total number of fruits - 1) = 7/20 * 5/19  = 35/380 = 7/76

For more such questions on probability

https://brainly.com/question/25870256

#SPJ8

Answer:

Slope 1; Y-intercept -1

Step-by-step explanation:

The equation is written in the form of y=mx=b (slope-intercept) where m is the slope and b the y-intercept, then find the terms.

Answer:

50.24

Step-by-step explanation:

8 x 3.14 x 2 = 50.24

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

For more such questions on vertex

https://brainly.com/question/25651698

#SPJ8