A company developed the following linear model to help budget annual expenses over time. In this model, x represents the number of years after 2009, and y represents the expense budget (in dollars). Interpret the y-intercept. y = 189,785 + 37,896x

A. The company's expense budget for 2009 was $189,785.

B. The company's expense budget for 2008 was $37,896.

C. The company's expense budget for 2009 was $37,896.

D. The company's expense budget for 2008 was $189,785.

Answer: decreases by 3%

Step-by-step explanation:

Answer:  The vertex form of the given function is [tex]y=5\left(x+\dfrac{3}{2}\right)^2-\dfrac{53}{4}[/tex] and its axis of symmetry is [tex]x=-\dfrac{3}{2}.[/tex]

Step-by-step explanation:  The given quadratic function is

[tex]y=5x^2+15x-2~~~~~~~~~~~~~~(i)[/tex]

We are to rewrite the above function in vertex form and to determine its axis of symmetry.

We have from equation (i),

[tex]y=5x^2+15x-2\\\\\Rightarrow y=5(x^2+3x)-2\\\\\Rightarrow y=5\left(x^2+2\times x\times \dfrac{3}{2}+\dfrac{9}{4}\right)-\dfrac{45}{4}-2\\\\\Rightarrow y=5\left(x+\dfrac{3}{2}\right)^2-\dfrac{45+8}{4}\\\\\Rightarrow y=5\left(x+\dfrac{3}{2}\right)^2-\dfrac{53}{4}.[/tex]

So, the given function is a parabola with vertex at the point [tex]\left(-\dfrac{3}{2},-\dfrac{53}{4}\right).[/tex]

Therefore, the axis of symmetry is given by

[tex]x=-\dfrac{3}{2}.[/tex]

Thus, the vertex form of the given function is [tex]y=5\left(x+\dfrac{3}{2}\right)^2-\dfrac{53}{4}[/tex] and its axis of symmetry is [tex]x=-\dfrac{3}{2}.[/tex]

To convert the quadratic function y = 5x² + 15x - 2 into vertex form, completing the square yields y = 5(x + 1.5)² - 13.25, with an axis of symmetry at x = -1.5.

To rewrite the quadratic function y = 5x² + 15x - 2 in vertex form and find the axis of symmetry, follow these steps:

Complete the square

Start with the given quadratic function:

y = 5x² + 15x - 2

To complete the square, first factor out the coefficient of x² (which is 5):

y = 5(x² + 3x) - 2

Now, focus on the expression inside the parentheses, x² + 3x.

To complete the square, need to add and subtract a constant term that will make it a perfect square trinomial.

add (3/2)² = 2.25 and subtract the same value inside the parentheses:

y = 5(x² + 3x + 2.25 - 2.25) - 2

Simplify the expression inside the parentheses

Now, simplify the expression inside the parentheses:

x² + 3x + 2.25 = (x + 1.5)²

So, the equation becomes:

y = 5[(x + 1.5)² - 2.25] - 2

Distribute the 5 and simplify further

y = 5(x + 1.5)² - 5(2.25) - 2

Rewrite in vertex form

y = 5(x + 1.5)² - 11.25 - 2

y = 5(x + 1.5)² - 13.25

Now, the quadratic function is in vertex form:

y = 5(x + 1.5)² - 13.25

Find the axis of symmetry

The axis of symmetry of a parabolic equation in the form y = a(x - h)² + k is given by x = h.

The axis of symmetry is x = -1.5 (opposite sign of the value inside the parentheses).

Therefore, the axis of symmetry for the quadratic function y = 5x² + 15x - 2 is x = -1.5.

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Final answer:

The trigonometric identity (tan(x) + tan(y)) / (1 - tan(x)tan(y)) = (sin(x)cos(y) + cos(x)sin(y)) / (cos(x)cos(y) - sin(x)sin(y)) can be verified by using the angle addition formulas for sine and cosine, and by applying the tangent sum formula. Both sides reduce to tan(x + y), confirming the identity.

Explanation:

The given trigonometric identity to verify is:
(tan(x) + tan(y)) / (1 - tan(x)tan(y)) = (sin(x)cos(y) + cos(x)sin(y)) / (cos(x)cos(y) - sin(x)sin(y)).

Trigonometric identities are equations involving trigonometric functions that are true for all values of the occurring variables where both sides of the equation are defined.

Let's verify the given identity step by step. First, rewrite the right-hand side using the angle addition formulas for sine and cosine:

So, the right-hand side can be written as sin(x + y) / cos(x + y). This is equivalent to tan(x + y).

Now, let's examine the left-hand side and apply the tangent sum formula:

As we can see, the left-hand side is exactly the tangent sum formula; therefore it also simplifies to tan(x + y).

Since tan(x + y) is a common form for both sides of the identity, we can conclude that the identity is verified:

(tan(x) + tan(y)) / (1 - tan(x)tan(y)) = sin(x + y) / cos(x + y)

Answer:

49 odd numbers are there between 101 and 199.

Step-by-step explanation:

Given  : 101 and 199.

To find : How many odd integers are there between 101 and 199.

Solution : We have given  101 and 199.

Total number(N) between 101 and 199

N = 199 - 101 = 98

N = 98 .

We can see 98 is even number so, there are half numbers are odd and half numbers are even .

Odd number = [tex]\frac{N}{2}[/tex].

Odd number =  [tex]\frac{98}{2}[/tex].

Odd number = 49.

Therefore, 49 odd numbers are there between 101 and 199.

Answer:

g(x) increase at a faster rate.

Step-by-step explanation:

Given : Two functions  [tex]f(x)=x^2[/tex] or [tex]g(x)=2^x[/tex]

To find : Which function increase at a faster rate on 0 to infinity

Solution :

We put some value of x in the functions and note down the observation.

            x               →  0      1      2       3       4        5        6         7      

[tex]f(x)=x^2[/tex]  →  0      1       4      9      16       25       36      49

[tex]g(x)=2^x[/tex] →   1      2      4       8      16        32      64      128

Comparing the values of f(x) and g(x), we can see that that g(x) increases at a faster rate on 0 to infinity.

Reason - The exponential function, g(x), has a constant multiplicative rate of change and will increase at a faster rate than the quadratic function f(x).  

Answer:

The Degree of a Polynomial is the largest of the degrees of the individual terms. Add the degrees of the variables of each term to decide what is the Degree of the Polynomial. Degree of term 1 is 2 (1+1= 2), Degree of term 2 is 6 (2+4 = 6), Degree of term 3 is 7 (5+2 = 7) 7 is the Degree of the Polynomial.

Answer:

The answer is option C.

Step-by-step explanation:

Here, according to the given question, margin of error means that the number of people who rated the vacation as 'delightful' ranges between 81% (83-2) and 85% (83+2) of the population at a 95% confidence interval. The range is formed as 81% to 85% as its given that the margin of error is ±2% .

Therefore, only option C is having both the ranges, 81% and 85%. So, option C is the correct answer.

C.It can be concluded, with 95% confidence, that between 81% and 85% of all employees will rate the vacation policy as "delightful."

Answer:

10:35

Step-by-step explanation:

Just add 9.55 and 40 mins:

9.55+40=10:35a.m

In order to know what is the reasonable amount of tile for Mandana to order, you have to divide the choices with the area of the floor and deduct with 1 and multiply by 100. You have to assess if the answer you will get will fall between 15% and 20% which is the goal of Mandana.

a.       131/116.9 = (1.1206 – 1) x 100 = 12.06%, this does not fall between 15% and 20%

b.      138/116.9 = (1.1805 – 1) x 100 = 18.05%, this fall between 15% and 20%

c.       133/116.9 = (1.1377 – 1) x 100 = 13.77%, this does not fall between 15% and 20%

d.      141/116.9 = (1.2062 – 1) x 100 = 20.62%, this does not fall between 15% and 20%

Therefore, the reasonable amount of tile for Madana to order that is between 15% and 20% extra of the materials is 138 square feet.

The log base 3 of 27 is equal to 3.

To solve log base 3 of 27 by hand, we need to determine the exponent to which the base 3 must be raised to obtain 27.

In this case, 3 raised to the power of what exponent equals 27?

By observing that [tex]3^3[/tex] equals 27, we can conclude that:

log base 3 of 27 = 3.

Therefore, the solution to log base 3 of 27 is 3.

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To create a scatter plot for the given data, label the axes with 'Stretch distance (cm)' and 'Weight (Newtons)', plot the points, and observe the correlation. A positive trend is expected as weight increases with stretch distance.

To create a scatter plot with the given data of stretch distance versus weight, you would typically use graphing software or graph paper. Here's a step-by-step explanation on how to plot the data:

After plotting all the points, your scatter plot might show a positive correlation between stretch distance and weight, indicating that weight increases as the stretch distance increases.

Final answer:

Ursula, swimming at 60 meters per minute, and given Andre a 1-minute head start who swims at 48 meters per minute, will catch up to Andre 4 minutes after she starts.

Explanation:

Ursula and Andre competed against each other in a swimming race. Ursula swam at a rate of 60 meters per minute and Andre swam at a rate of 48 meters per minute. Ursula gave Andre a 1-minute head start. To determine who wins the race, we need to calculate the time it takes for Ursula to catch up to Andre, given the head start.

Let's denote the time it takes for Ursula to catch up to Andre as t (in minutes). Since Andre has a 1-minute head start, he would have swum 48 meters before Ursula starts. Therefore, the distance Andre swims in t+1 minutes is 48(t+1). Ursula's swimming distance in t minutes is 60t.

To find out when Ursula catches up to Andre, we set these distances equal to each other:

Thus, Ursula will catch up to Andre 4 minutes after she starts swimming, which is 5 minutes after Andre starts.