Classify each polynomial by its degree and number of terms

Final answer:

The horizontal asymptote of the function g(x) = e^x + 4 is the line y = 4.

Explanation:

The question asks about the asymptote of the function g(x) = e^x + 4. An asymptote is a line that a graph approaches but never touches. To find the horizontal asymptote of this function, observe that as x approaches positive or negative infinity, the term e^x either grows very large or approaches zero. Therefore, the term +4 determines the horizontal asymptote since it shifts the entire graph of e^x up by 4 units. Thus, the horizontal asymptote is the line y = 4, which means the function approaches this line but never reaches it for x tending toward positive or negative infinity.

The original side of square is [tex]10\;\rm{in[/tex].

Given: the dimensions of a square are altered so that [tex]8[/tex] inches is added to one side while [tex]3[/tex] inches is subtracted from the other. The area of the resulting recatangle is [tex]126\;\rm{in^2}[/tex].

As per question,

Let the side of square be [tex]x[/tex].

According to the question,

Length of new rectangle be [tex]x+8[/tex].

Breadth of new rectangle be [tex]x-3[/tex]

Area of rectangle [tex]=l\times b[/tex]

     [tex](x+8)(x-3)=126[/tex]

[tex]x^2+8x-3x-24=126\\[/tex]

      [tex]x^2+5x-150=0[/tex]

[tex]x^2+15x-10x-150=0\\x(x+15)-10(x+15)=0\\[/tex]

        [tex](x+15)(x-10)=0\\[/tex]

So, [tex]x=10\;\rm{in[/tex] and neglecting [tex]x=-15\;\rm{in[/tex] as distance can't be negative.

Hence, original side of square is [tex]10\;\rm{in[/tex].

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Answer:

It's A 3x

Step-by-step explanation:

I just did the test it's 3x hope this helped. :)

The area of a 2D form is the amount of space within its perimeter. The area of the given parallelogram is 812 in².

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The given figure is a parallelogram, and the area of the parallelogram is given by the formula,

Area of parallelogram = Base × Altitude

                                     = 29 in × 28 in

                                     = 812 in²

Hence, the area of the given parallelogram is 812 in².

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It can be written as [tex]\rm{log_32187 = 7}[/tex].

A log function is a way to find how much a number must be raised in order to get the desire number. [tex]a^c = b[/tex] can be  written as

[tex]\rm{log_{a}b= c}[/tex]

where a is the base to which the power is to be raised,

b is the desired number that we want when power is to be raised,

c is the power that must be raised to a to get b.

For example, let's assume we need to raise the power for 10 to make it 1000 in this case log will help us to know that the power must be raised by 3.

[tex]\rm{log_{10}1000 = 3}[/tex]

Given to us,

Exponential, [tex]3^7 = 2187[/tex]

Now, a = 3, b= 2187, and c = 7.

Therefore, it can be written as [tex]\rm{log_32187 = 7}[/tex].

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The correct option is A.

Vanessa can borrow approximately $6255.57, represented by option A: [tex]$\frac{(\$ 1405)\left((1+0.004)^{240}-1\right)}{(0.004)(1+0.004)^{240}}$[/tex].

To determine the value of the most money Vanessa can borrow with a monthly payment of $1405 for a 20-year house loan with an APR of 4.8%, compounded monthly, we can use the formula for the monthly payment of a mortgage:

[tex]\[P = \frac{M}{\frac{r}{12} \left(1 - \left(1 + \frac{r}{12}\right)^{-nt}\right)}\][/tex]

Where:

P = Principal amount (the amount she can borrow)

M = Monthly payment ($1405)

r = Monthly interest rate (APR divided by 12, or 0.048/12)

n = Number of times the interest is compounded per year (12 for monthly)

t = Number of years (20)

Now, let's plug in the values and solve for P:

[tex]\[P = \frac{1405}{\frac{0.004}{12} \left(1 - \left(1 + \frac{0.004}{12}\right)^{-12*20}\right)}\][/tex]

Let's calculate the exponent and simplify:

[tex]\[P = \frac{1405}{\frac{0.004}{12} \left(1 - \left(1 + \frac{0.004}{12}\right)^{-240}\right)}\][/tex]

Now, we can simplify the monthly interest rate:

[tex]\[P = \frac{1405}{\frac{0.004}{12} \left(1 - \left(1.000333333\right)^{-240}\right)}\][/tex]

[tex]\[P = \frac{1405}{0.333333 \left(1 - 0.328624967\right)}\][/tex]

Now, let's calculate the value inside the parentheses:

[tex]\[P = \frac{1405}{0.333333 \times 0.671375033}\][/tex]

[tex]\[P \approx \frac{1405}{0.22487499}\][/tex]

Now, calculate P:

P ≈ 6255.57

So, Vanessa can borrow approximately $6255.57.

The correct expression that represents the value of the most money she can borrow is:

A. [tex]$\frac{(\$ 1405)\left((1+0.004)^{240}-1\right)}{(0.004)(1+0.004)^{240}}$[/tex]

The complete question is here:

Vanessa can afford a [tex]$\$ 1405$[/tex]-per-month house loan payment. If she is being offered a 20-year house loan with an APR of [tex]$4.8 \%$[/tex], compounded monthly, which of these expressions represents the value of the most money she can borrow?

A. [tex]$\frac{(\$ 1405)\left((1+0.004)^{240}-1\right)}{(0.004)(1+0.004)^{240}}$[/tex]

B. [tex]$\frac{(\$ 1405)\left((1-0.048)^{240}-1\right.}{(0.048)(1+0.048)^{249}}$[/tex]

C. [tex]$\frac{(\$ 1405)\left((1-0.004)^{200}-1\right)}{(0.004)(1+0.004)^{240}}$[/tex]

D. [tex]$\frac{(51405)\left((1+0.048)^{200}-1\right)}{(0.048)(1+0.048)^{240}}$[/tex].

Using the formula for monthly loan payment, we find Vanessa can borrow up to $220,000 with a 20-year loan at 4.8% APR.

To find the maximum amount Vanessa can borrow, we can use the formula for the monthly payment of a loan:

[tex]\[ P = \frac{A \times r}{1 - (1 + r)^{-n}} \][/tex]

Where:

-  P  = monthly payment

-  A = loan amount (the value we want to find)

-  r  = monthly interest rate (APR divided by 12)

-  n  = total number of payments (number of years multiplied by 12)

Given:

- Monthly payment ( P) = $1405

- APR ( r ) = 4.8% = 0.048

- Loan term = 20 years

First, we calculate r :

[tex]\[ r = \frac{4.8}{100 \times 12} = 0.004 \][/tex]

Then, calculate n:

[tex]\[ n = 20 \times 12 = 240 \][/tex]

Now, plug the values into the formula and solve for A:

[tex]\[ 1405 = \frac{A \times 0.004}{1 - (1 + 0.004)^{-240}} \][/tex]

Solve for A:

[tex]\[ A = \frac{1405 \times (1 - (1 + 0.004)^{-240})}{0.004} \][/tex]

[tex]\[ A \approx \$220,000 \][/tex]

So, Vanessa can borrow a maximum of $220,000.

The question probable maybe:

Vanessa can afford a $1405-per-month house loan payment. If she is being offered a 20-year house loan with an APR of 4.8%, compounded monthly, What is the value of  the most money she can borrow?

Answer: 50 pages per Hour

Step-by-step explanation:

El cambio climático ha empeorado en los últimos años, la razón principal es la contaminación excesiva tanto del aire, del agua, del suelo y muchas otras cosas.

Todos debemos tomar conciencia del daño que estamos ocasionando con la contaminación excesiva. El cambio climático nos ha traído grandes problemas por no actuar con responsabilidad en el cuidado del medio ambiente. Si no tomamos conciencia de lo que estamos perjudicando, en un tiempo más adelante habrá consecuencias negativas peores de las que ya hay.

El cambio climático no se da de forma negativa por sí solo, somos nosotros los que estamos perjudicándolo con la contaminación.

deberiamos de Cuidar  la planeta para que no haya tanto exceso de contaminación y así evitar cambios drásticos en el clima

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Answer:

$33,000,000

Step-by-step explanation:

Recycled newspaper sells for $5.00 for 1 ton.

Let x ton be the amount recycled in 1991 by U.S.

so to represented this situation expression will be F(x) = 5 x

Now we replace x = 6.6 million tons

                              ≈ 6.6 × [tex]10^{6}[/tex] tons

Total money made by recycling 6.6 × [tex]10^{6}[/tex] tons

                                                 = 5 × 6,600,000

                                                 = $33,000,000

In 1991 U.S. made $33,000,000 from the sale of recycled newspapers.

Answer: first event 12/35 times second event 10/34  

12/119

The rate of increase of the bacteria population is found by calculating the population increase (final amount - initial amount), dividing by the initial amount, and multiplying by 100 to get the percentage. The calculated value is 66.66%, which doesn't match with any of the provided options.

The subject of this question is bacterial population growth, which falls under the mathematics category, specifically in the section known as growth rates. To find the rate of increase of the bacteria population, first, we have to find the increase in the population amount, which is the final amount (250 bacteria) minus the initial amount (150 bacteria). This gives us an increase of 100 bacteria.

Next, divide this increase (100) by the initial amount (150 bacteria) and multiply by 100 to convert it to a percentage. This gives the formula (250-150)/150*100 = 66.66%. But among the provided choices, we don't have this exact value, which implies that there might be a miscommunication or typographical error in the question.

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To begin, we need to find the slope of the equation x = 2y + 3. The easiest way to find the slope is to put this equation into slope-intercept form, y=mx+b, where the variable m represents the slope. To do this, we must get the variable y alone on the left side of the equation. First, we subtract 2y from both sides.

x = 2y + 3

-2y + x = 3

Next, we subtract x from both sides.

-2y = -x + 3

Finally, we divide both sides by -2 (there cannot be a coefficient on the variable y in this form).

y = 1/2x + 3

Therefore, the slope of this equation is 1/2. However, we are looking for the slope of a line that is perpendicular to this one. This means that it creates four 90 degree angles where the lines cross, and it has the opposite reciprocal slope.

The opposite reciprocal of 1/2 is -2 (you take the opposite in this case by changing the value from positive to negative, and take the reciprocal by switching the numerator and the denominator).

Thus, your answer is -2.

Hope this helps!

The slope of a line perpendicular to the line represented by the equation x = 2y + 3 is -2.

The equation given is x = 2y + 3. To find the slope of a line perpendicular to this line, we need to determine the slope of the given line. The given equation is not in slope-intercept form, which is y = mx + b, where m represents the slope. So, we can rewrite the equation in slope-intercept form by rearranging it as 2y = x - 3 and then dividing both sides by 2, giving us y = (1/2)x - (3/2).

The slope of the line represented by this equation is 1/2. To find the slope of a line perpendicular to this line, we take the negative reciprocal of the slope of the given line. The negative reciprocal of 1/2 is -2. So, the slope of a line perpendicular to the line represented by the equation x = 2y + 3 is -2.

A line with a slope of -2 will have a steepness that is twice as steep as the line represented by the equation x = 2y + 3.

Answer:

Amount covered by insurance = 130000

Step-by-step explanation:

Cost of Andy's home = 260000

Percentage covered by insurance = 50%

Amount covered by insurance = 50% of Cost of Andy's home

                                                   = 50% of 260000

                                                   = 0.50 * 260000         [50% written as a decimal is 0.50]

                                                   = 130000

Answer:

175 students.

102 students go to movies at least twice a week and 73 students either go 1 times or not going to the movies.

So

Students go 0-1 times per week = 73/175 = 0.4172 = 41.71%

Answer: last option

Answer:

The last one. Which is choice D.

Answer:

the dimensions of rectangle are length = 15 m and width = 6 m

Step-by-step explanation:

Given;  The width  of a rectangle is [tex]\frac{2}{5}[/tex] its length i.e, [tex]w=\frac{2}{5}l[/tex]

and perimeter of rectangle is 42 meters.

Perimeter(P)of a rectangle in meters is given by:

[tex]P = 2(l+w)[/tex] ;  where [tex]l[/tex] is the length of the rectangle and w is the width of the rectangle.

then, substitute the value of P =42 m and [tex]w=\frac{2}{5}l[/tex] in above formula we get;

[tex]42 = 2(l+\frac{2}{5}l) =2 \cdot (\frac{7}{5}l)[/tex]

divide both side by 2 we get;

[tex]21=\frac{7}{5}l[/tex]

On Simplify:

[tex]l = \frac{21 \cdot 5}{7} =3 \cdot 5 =15[/tex] m

Now, substitute the value of [tex]l = 15[/tex] m  in [tex]w=\frac{2}{5}l[/tex] to solve for w;

[tex]w= \frac{2}{5} \cdot 15 =2 \cdot 3 =6[/tex] m

Therefore, the dimensions length = 15 m and width = 6 m