2. The value of a Plasma TV bought new for $3,700 decreases 25% each year. Identify the function for the value of the television. Does the function represent growth, or decay?
V(t) = 3700(1.25)t; growth
V(t) = 3700(0.75)t; decay
V(t) = 3700(1.25)t; decay
V(t) = 3700(0.75)t; growth

Answer:

286°28'44

Step-by-step explanation:

Answer: The answer is (d) Find the slopes and show that their product is -1.

Step-by-step explanation:  Given in the question and shown in the attached figure that the vertices of the quadrilateral PQRS are P(0, 0), Q(a + c, 0), R(2a + c, b), and S(a, b). We are asked to use geometry to show that the diagonals PR and QS are perpendicular to each other.

We know that the two lines are perpendicular if the product of their slopes is --1.

So, first we will find the slopes of PR and QS, multiply them, and check the value.If the value is -1, then the diagonals are perpendicular to each other.

That is, if 'm' and 'p' are the slopes of the diagonals PR and QS, and if m × p = -1, then the two diagonals are perpendicular.

Thus, the correct answer is (d).

20 2/7 = 142/7 -20/35

find common denominator ( in this case it is 35)

35/7 =5 , multiply 142*5=710, 7*5 =35

142/7 = 710/35

710/35 - 20/35  = 710-20 = 690

690/35 now simplify that fraction

690/35 = 19.714

19*35 = 665

690-665=25

19 25/35

25/35 can reduce to 5/7

answer = 19 5/7

The value of the [tex]\rm ^6p_2[/tex] is 30.

The value of  P(6,2).

According to the question

The value of the [tex]\rm ^6p_2[/tex] is determined by using permutation.

The probability of selecting an ordered set of 'r' objects from a group of 'n' number of objects.

The order of objects matters in the case of permutation.

The formula to find [tex]\rm ^np_r[/tex] is given by:

[tex]\rm ^np_r = \dfrac{n!}{(n-r)!}[/tex]

Substitute n = 6 and r = 2 in the formula;

[tex]\rm ^np_r = \dfrac{n!}{(n-r)!}\\ \\ \rm ^6p_2 = \dfrac{6!}{(6-2)!}\\ \\ \rm ^6p_2= \dfrac{6 \times 5\times 4 \times 3\times2 \times 1}{4!}\\ \\ ^6p_2= \dfrac{6 \times 5\times 4 \times 3\times2 \times 1}{4\times 3 \times2 \times 1}\\ \\ ^6p_2= 6 \times 5}\\ \\ ^6p_2= 30[/tex]

Hence, The value of the [tex]\rm ^6p_2[/tex] is 30.

To know more about Permutation click the link given below.

https://brainly.com/question/10148445

The arc length is 4√26, which is confirmed by the distance formula for a line segment yielding approximately 20.396 units.

To find the length of the curve y = 5x − 4 over the interval −1 ≤ x ≤ 3, we can use the arc length formula for a function y = f(x). The formula for the arc length L is given as:

L = ∫ab√(1 + (dy/dx)2) dx, where dy/dx is the derivative of y with respect to x.

1. Calculate the derivative dy/dx:

y = 5x − 4, so dy/dx = 5.

2. Substitute the derivative into the arc length formula:

L = ∫-13√(1 + 5²) dx = ∫-13√26 dx.

3. Integrate the function:

L = √26 ∫-13 dx = √26 [x]-13 = √26 (3 − (-1)) = 4√26 ≈ 20.396.

To verify this using the distance formula (since the curve is a straight line), we take the points (−1,−9) and (3,11) from the given curve:

4. Apply the distance formula:

Distance = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) = (-1, -9) and (x2, y2) = (3, 11).

Therefore,

Distance = √((3 - (-1))² + (11 - (-9))²) = √((4)² + (20)²) = √(16 + 400) = √416 = 4√26 ≈ 20.396.

Thus, the arc length calculated using the formula and the distance formula are consistent.

The arc length is 4√26, which is confirmed by the distance formula for a line segment yielding approximately 20.396 units.

The sum of the first and third even integers is 136. By setting up an equation and solving for x, where x is the first integer, we determine that the consecutive even integers are 66, 68, and 70.

The problem asks us to find three consecutive even integers where the sum of the first and third integer is 136. Let's denote the first integer as x, the second integer as x + 2, and the third integer as x + 4 (since consecutive even numbers have a difference of 2). To solve for the values, we set up the equation x + (x + 4) = 136. Simplifying, we get 2x + 4 = 136. Subtracting 4 from both sides gives us 2x = 132. Dividing both sides by 2, we find out that x = 66. So, the first integer is 66, the second integer is 66 + 2 = 68, and the third integer is 66 + 4 = 70.

Therefore, the three consecutive even integers are 66, 68, and 70.

The easiest way to answer this is to try all choices, plug in values for the 1st term and 2nd term then check if the answer matches with 5 and 2. (n = 1 and n = 2)

We know that n starts with 1 because that is our 1st term, we do not have 0th term, therefore that leaves us with 2 choices.

Choice 1: an = 5 − 2(n − 1); all integers where n ≥ 1

n = 1

a1 = 5 – 2 (1 – 1) = 5 – 2 (0)

a1 = 5

n = 2

a2 = 5 – 2 (2 – 1) = 5 – 2 (1)

a2 = 3   (FALSE!)

Choice 2: an = 5 − 3(n − 1); all integers where n ≥ 1

n = 1

a1 = 5 – 3 (1 – 1) = 5 – 3 (0)

a1 = 5

n = 2

a2 = 5 – 3 (2 – 1) = 5 – 3 (1)

a2 = 2   (TRUE)

Therefore the correct answer is:

an = 5 − 3(n − 1); all integers where n ≥ 1

Answer:

A is INCORRECT

Step-by-step explanation:

Just finished the FLVS test

Given:

f(0) = 2

So first of all, we let x = 2012, y = 0: 

Then, F(2012) = 2012 + f(0)

Since f(0) = 2, then f(2012) = 2012 + 2 = 2014.

To add, the process that relates an input to an output is called a function.

There are always three main parts of a function, namely:

Input

The Relationship

The Output

The classic way of writing a function is "f(x) = ... ".

What goes into the function is put inside parentheses () after the name of the function: So, f(x) shows us the function is called "f", and "x" goes in.

What a function does with the input can be usually seen as:

f(x) = x2 reveals to us that function "f" takes "x" and squares it.

Option (c) represents an inconsistent system of equations, as the constant terms are not proportional, while the coefficients of x are. This system (y=4x-3, y=4x+3) has no solutions.

In mathematics, specifically in algebra, an inconsistent system is a system of equations that has no solutions. To check which system is inconsistent from the options you've given, we need to compare the coefficients of each equation within a system. An inconsistent system will have proportional coefficients of x and y between the two equations, but the constant terms will not be proportional.

Looking at each option:

Option (a): y=x+4 and y=2x+4
Option (b): y=x and y=−x
Option (c): y=4x−3 and y=4x+3
Option (d): y=2x−3 and 2y=4x−6

From here, we can see that option (c): y=4x-3, y=4x+3 is inconsistent. In this system, the coefficients of x are proportional (4), but the constant terms (-3 and +3) are not proportional.

https://brainly.com/question/35587704

#SPJ12

perimeter of a square = is side times 4

so divide 544 by 4

544/4 = 136

the property is 136 feet wide

The average rate of change can be found using a discrete graph by calculating the slope between two points on the graph. This provides insight into how the dependent variable changes as the independent variable varies.

The average rate of change can be found using a discrete graph by calculating the difference in the y-values of two points and dividing it by the difference in the x-values of those same points. This will give you the slope of the line connecting the two points, which represents the average rate of change between those two points. For example, if you have two points (x1, y1) and (x2, y2), the average rate of change can be calculated as:

(y2 - y1) / (x2 - x1)

By finding the average rate of change at different intervals on the graph, you can analyze how the dependent variable changes in relation to the independent variable.

The coordinate point of the other endpoint, G is (-1, 3)

The given parameters;

the midpoint = M(-2, 5)

one end point = H(-3,7)

To find:

Let the coordinate point of the other endpoint = G(x, y)

The coordinate point of the other endpoint, G will be calculated using midpoint formula.

[tex]M(-2, 5) =( \frac{x + (-3)}{2} , \frac{y + 7}{2} )\\\\-2 = \frac{x - 3}{2} \ \ \ and \ \ 5 = \frac{y+ 7}{2} \\\\x-3 = 2(-2)\\\\x - 3 = -4\\\\x = -4 + 3\\\\x = -1\\\\y+ 7 = 2(5)\\\\y + 7 = 10\\\\y = 10 -7\\\\y = 3\\\\G= (-1, 3)[/tex]

Thus, the coordinate point of the other endpoint, G is (-1, 3)

Learn more here: https://brainly.com/question/10812174

From Plato: Φ =7π/7 or π.

Answer:3s+2,000

Step-by-step explanation: