2х - Зу= 2
х= бу - 5
X=
Y=

Answer:

Company B is cheaper by $180.

Step-by-step explanation:

just do 1,200 square feet x 0.15 = 180

Answer:

b as in big cat

Step-by-step explanation:

Answer:

Domain: \(-5\leq x\leq 4\)

Range: \(-5\leq y\leq 5\\\)

Function: yes

Step-by-step explanation:

Domain is all possible x values. In this function, domain would be: \(-5\leq x\leq 4\)

Range is all possible y values. In this function, range would be: \(-5\leq y\leq 5\)

This is a function because it passes the vertical line test.

Answer:

20π [in].

Step-by-step explanation:

1. formula is:

C=π*2r;

2. the circumference according to the formula is:

C=π*10*2=20π.

By definition of absolute value, you have

\(f(x) = |x+1| = \begin{cases}x+1&\text{if }x+1\ge0 \\ -(x+1)&\text{if }x+1<0\end{cases}\)

or more simply,

\(f(x) = \begin{cases}x+1&\text{if }x\ge-1\\-x-1&\text{if }x<-1\end{cases}\)

On their own, each piece is differentiable over their respective domains, except at the point where they split off.

For x > -1, we have

(x + 1)' = 1

while for x < -1,

(-x - 1)' = -1

More concisely,

\(f'(x) = \begin{cases}1&\text{if }x>-1\\-1&\text{if }x<-1\end{cases}\)

Note the strict inequalities in the definition of f '(x).

In order for f(x) to be differentiable at x = -1, the derivative f '(x) must be continuous at x = -1. But this is not the case, because the limits from either side of x = -1 for the derivative do not match:

\(\displaystyle \lim_{x\to-1^-}f'(x) = \lim_{x\to-1}(-1) = -1\)

\(\displaystyle \lim_{x\to-1^+}f'(x) = \lim_{x\to-1}1 = 1\)

All this to say that f(x) is differentiable everywhere on its domain, except at the point x = -1.

Answer:

2.167 (rounded to the nearest hundredths).

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, divide 2 from both sides of the equation:

(2(3x - 4))/2 = (5)/2

3x - 4 = 2.5

Next, isolate the variable, x. Add 4 to both sides of the equation:

3x - 4 (+4) = 2.5 (+4)

3x = 2.5 + 4

3x = 6.5

Then, divide 3 from both sides of the equation:

(3x)/3 = (6.5)/3

x = 6.5/3 = 2.167 (rounded).

~

Answer:

We have this equation

2*(3x-4) = 5

We can start solving the parentheses

2*(3x- 4) = 5

6x - 8 = 5

We can add 8 to both sides

6x - 8 + 8 = 5 + 8

6x = 13

And divide by 6

6x/6 = 13/6

x = 13/6

Answer:

sure

Step-by-step explanation:

but you gotta post the question...

The rent for The new monthly lease amount is $858.

To find out the new monthly lease amount, we need to take into account that there is one month free, which we need to apply to all the months of the lease period.

A one-year lease is for 12 months.

The total rent amount for 12 months = Regular rent for 12 months - One-month free rent= $936 × 12 - $936 = $11232 - $936= $10296

The free rent is distributed equally across the 12 months:$936 ÷ 12 = $78

The new monthly rent amount is the total rent amount for 12 months divided by the number of months:

Total rent amount for 12 months = $10296

New monthly lease amount = Total rent amount for 12 months ÷ 12

New monthly lease amount = $10296 ÷ 12

New monthly lease amount = $858

Therefore, the new monthly lease amount is $858.

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Answer:

-63

Step-by-step explanation:

The probability that next year there will be no snowfall in that town on January 1 is,

P (no snowfall) = 0.770

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

Based on a weather record, the probability of snowfall in a certain town in New York on January 1 is 0.230.

Now, WE get;

the probability that next year there will be no snowfall in that town on January 1 is,

P (no snowfall) = 1 - P (snowfall)

P (no snowfall) = 1 - 0.230

P (no snowfall) = 0.770

Thus, The probability that next year there will be no snowfall in that town on January 1 is,

P (no snowfall) = 0.770

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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.

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The solution is,  the domain is: x ∈ (-∞, ∞).

Here, we have,

When we have two functions, f(x) and g(x), the composite function:

(f°g)(x)

is just the first function evaluated in the second one, or:

f( g(x))

And the domain of a function is the set of inputs that we can use as the variable x, we usually start by thinking that the domain is the set of all real numbers, unless there is a given value of x that causes problems, like a zero in the denominator, for example:

f(x) = 1/(x + 1)

where for x = -1 we have a zero in the denominator, then the domain is the set of all real numbers except x = -1.

Now, we have:

f(x) = x^2

g(x) = x + 9

then:

(f ∘ g)(x) = (x + 9)^2

And there is no value of x that causes problems here, so the domain is the set of all real numbers, that, in interval notation, is written as:

x ∈ (-∞, ∞)

(g ∘ f)(x)

this is g(f(x)) = (x^2) + 9 = x^2 + 9

And again, here we do not have any problem with a given value of x, so the domain is again the set of all real numbers:

x ∈ (-∞, ∞)

(f ∘ f)(x) = f(f(x)) = (f(x))^2 = (x^2)^2 = x^4

And for the domain, again, there is no value of x that causes a given problem, then the domain is the same as in the previous cases:

x ∈ (-∞, ∞)

(g ∘ g)(x) = g( g(x) ) = (g(x) + 9) = (x + 9) +9 = x + 18

And again, there are no values of x that cause a problem here,

so the domain is:

x ∈ (-∞, ∞)

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complete question:

Consider the following functions. f(x) = x2, g(x) = x + 9 Find (f ∘ g)(x). Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.) Find (g ∘ f)(x). Find the domain of (g ∘ f)(x). (Enter your answer using interval notation.) Find (f ∘ f)(x). Find the domain of (f ∘ f)(x). (Enter your answer using interval notation.) Find (g ∘ g)(x). Find the domain of (g ∘ g)(x). (Enter your answer using interval notat

Answer:

D. 2r2 + 23r > 645

Step-by-step explanation:

The equation "2r^2 + 23r > 645" represents the situation because it states that the number of spaces in the parking lot, represented by the left-hand side of the equation (2r^2 + 23r), is greater than the maximum number of spaces that the parking lot can hold (645). This is consistent with the information given in the problem, which states that the parking lot has been expanded and can now hold more spaces.

The other equations given (A, B, C) do not accurately represent the situation because they do not take into account the expansion of the parking lot and the addition of new rows and spaces.

Answer:

12..........'.............

Answer:

Yeah the Answer is 12

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

The number of nights that are needed to cover 4 chapters of the science book by Anthony is 8.

A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.

Anthony reads 1/2 chapter of his science book each night.

He has 4 chapters left to read.

\(\begin{aligned} \rm \dfrac{1}{2} \ chapeter &\rightarrow 1 \rm \ night\\\\1 \ \rm chapter &\rightarrow 2 \ \rm nights\\\\4 \ \rm chapters &\rightarrow 8 \ \rm nights \end{aligned}\)

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The missing value for the quadratic function is given as follows:

y = -3.

As a function of it's roots x* and x**, the quadratic function is defined as follows:

y = a(x - x*)(x - x**)

In which a is the leading coefficient.

The roots of the function are the values of x when y = 0, hence:

x* = -4, x** = -2.

Thus:

y = a(x + 4)(x + 2)

y = a(x² + 6x + 8).

When x = 0, y = -8, hence the leading coefficient a of the function is given as follows:

8a = -8

a = -1.

Hence:

y = -x² - 6x - 8;

The missing value is the value of y when x = -1, hence:

y = -(-1)² - 6(-1) - 8

y = -3.

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The steps peter could use in solving the quadratic equation is by applying the quadratic formula; x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

8x² + 16x + 3 = 0

using Quadratic formula

The following steps are involved

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

\(x = \frac{ -16 \pm \sqrt{16^2 - 4(8)(3)}}{ 2(8) }\)

\(x = \frac{ -16 \pm \sqrt{256 - 96}}{ 16 }\)

\(x = \frac{ -16 \pm \sqrt{160}}{ 16 }\)

\(x = \frac{ -16 \pm 4\sqrt{10}\, }{ 16 }\)

\(x = \frac{ -16 }{ 16 } \pm \frac{4\sqrt{10}\, }{ 16 }\)

\(x = -1 \pm \frac{ \sqrt{10}\, }{ 4 }\)

\(x = -1 \pm \frac{ \sqrt{5}\, }{ 2 }\)

\(x = -0.209431\)

or

\(x = -1.79057\)

Therefore, the steps peter could follow will give the result

\(x = -1 \pm \frac{ \sqrt{5}\, }{ 2 }\)

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Answer:

Part A:  \(\displaystyle f(x) = \frac{19}{2}x^2 + 15x + C\)

Part B:  \(\displaystyle f(x) = \frac{19}{2}x^2 + 15x - 5\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Functions

Calculus

Differentiation

Differential Equations

Integration

Integration Rule [Reverse Power Rule]:                                                               \(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)

Integration Property [Multiplied Constant]:                                                         \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Integration Property [Addition/Subtraction]:                                                       \(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle f'(x) = 19x + 15\)

Step 2: Find Antiderivative

Step 3: Find Particular Solution

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differential Equations

Answer:

3.38

Step-by-step explanation:

first do the multiplication

2×0.81

= 1.62

then the subtraction

5- 1.62= 3.38

The correct sentences in the passage are option A, option B, and option E.

Let's check all the options, then we have

Any two squares are either similar or congruent. The statement is true.

If two lines are parallel, they never intersect. The statement is true.

If all the angles of a polygon are congruent, then it is a square. The statement is false because a regular polygon has an equal angle but it may be a pentagon, hexagon, etc.

The intersection of two lines always forms 4 congruent angles. The statement is false because opposite angles are the same. But if adjacent angles become the same, then the statement will be true.

A line can be drawn through any two distinct points. The statement is true.

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Answer:

The answer is C

Step-by-step explanation:

If you plot them carefully.

a) 38 minutes are taken to have the same amount of water.

b) Both pools have an amount of 1701 liters when 38 minutes have passed.

a) Physically speaking, the capacity (\(Q\)) of each pool, in liters, is equal to the product of flow rate (\(Q\)), in liters per minute, and time (\(Q\)), in minutes. Hence, we derive the following functions for each pool:

\(Q_1=660+17.25\times t\) (1)

\(Q_2=44.75\times t\) (2)

The time needed to find both pools with the same amount of water is found by the following expression:

\(Q_1=Q_2\) (3)

By (1) and (2) in (3):

\(660+17.25\times t=44.75\times t\)

\(17.25\times t=660\)

\(t=38 \ \text{min}\)

38 minutes are taken to have the same amount of water.  

b) By (2) and knowing that \(t=38 \ \text{min}\), then we have the corresponding amount:

\(Q_2=44.75\times(38)\)

\(Q_2=1701 \ \text{L}\)

Both pools have an amount of 1701 liters when 38 minutes have passed.

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The value of y is 48

y= kx

let's solve for k which is the constant

y= 8 , x= 4

k= 8/4

k= 2

Next is to calculate the value of y when x is 24

y = 2 × 24

y= 48

Hence the value of y is 48

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Answer:

4

Step-by-step explanation:

(10-x)/x=3/2

so 2*(10-x)=3x

20-2x=3x

+2x        +2x

20=5x

x=20/5

x=4

verify

(10-4)/4=3/2

6/4=3/2

TRUE