Which of the following graphs represents the function f(x) = −2x3 − x2 + 3x + 1?

graph with 3 real zeros, down on left, up on right
graph with 3 real zeros, up on left, down on right
graph with 2 real zeros, down on left, down on right
graph with 2 real zeros, up on left, up on right

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).

to anyone who may be a lil' sus, the previous answer is correct.

Answer:

Step-by-step explanation:

5x+ 4y greater than or equal to 650,000

500,000

y greater than or equal to 200,00

Answer is : 5x+4y greater than or equal to 650,000

X less than or equal to 500,000

Y is less than or equal to 200,000

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)

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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.

Answer:

[tex]\text{The roots of }3x^2+5x-8=0\text{ are }x=1,\frac{-8}{3}[/tex]

Step-by-step explanation:

[tex]\text{Part A: Given a quadratic equation }3x^2-15x+20=0[/tex]  

[tex]\text{Comparing above equation with }ax^2+bx+c=0[/tex]  

a=3, b=-15, c=20

Discriminant can be calculated as

[tex]D=b^2-4ac[/tex]

[tex]D=(-15)^2-4(3)(20)=225-240=-15<[/tex]

The roots are imaginary

The solution is

[tex]x=\frac{-b\pm\sqrt{D}}{2a}[/tex]

[tex]x=\frac{-(-15)\pm \sqrt{-15}}{2(3)}=\frac{15\pm\sqrt{15}i}{6}[/tex]

The roots are not real i.e these are imaginary    

[tex]\text{Part B: Given a quadratic equation }3x^2+5x-8=0[/tex]  

[tex]\text{Comparing above equation with }ax^2+bx+c=0[/tex]  

a=3, b=5, c=-8

Discriminant can be calculated as

[tex]D=b^2-4ac[/tex]

[tex]D=(5)^2-4(3)(-8)=25+96=121>0[/tex]

The roots are real

By quadratic formula method

The solution is

[tex]x=\frac{-b\pm\sqrt{D}}{2a}[/tex]

[tex]x=\frac{-5)\pm \sqrt{121}}{2(3)}=\frac{-5\pm 11}{6}[/tex]

[tex]x=1,\frac{-8}{3}[/tex]

which are required roots.

I choose this method because I can get the solutions directly by substituting the values in formula, and I don't have to guess the possible solutions.

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 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.

perimeter of a square = is side times 4

so divide 544 by 4

544/4 = 136

the property is 136 feet wide

Answer:

Isabel’s competition,who sells books and no other products, charges a shipping fee of $1.99 per book plus a fixed fee of $3 for each order. Let x be the number of books purchased and f(x) be the price of shipping one order of books. Write a function that expresses f(x) and explain the value of f(x) for x = 0. (5 points)

The price of the shipping ( f(x)) is equal to the cost of the fixed fee per order (3) plus the product of the number of books ordered (x) and the cost of the fee per book (1.99).

f(x)= 1.99x +3

for f(0) = 1.99(0)+3

f(0) =3

For F(0) there is a order of 0 books.  The price is only for the shippping.

Step-by-step explanation:thats it buddy

A function that expresses f(x) is f(x) = 1.99x + 3. Graph is continuous.

A continuous function is a function that does not have discontinuities that means any unexpected changes in value. A function is continuous if we can ensure arbitrarily small changes by restricting enough minor changes in its input.

For this case we have the following data:

A shipping fee of $ 1.99 is charged for each book sold.

There is a fixed fee of 3 dollars per order.

We must express the total cost by a function of the form .

If x represents the number of books sold, we have an expression of the form:

f(x) = 1.99x + 3

That is, according to the number of books sold, represented by x, a different value will be obtained for the total cost given by function f (x). For example:

If 3 books are sold, we have:

f(x) = 1.99x + 3

f(0) = 1.99(0) + 3

f(0) = 3

Thus, the value of f(x) for x = 0 is f(0) = 3.

The graph is continuous. Continuous is something that can and must be able to be broken down into fractions and decimals. Discrete means something that cannot be broken down into fractions or decimals.

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a fraction should be number of balls over time per second

 so it should be 16/4 which is 4 balls per second

Answer: fraction 16 over 4

Step-by-step explanation:

The given graph shows the number of paintballs a machine launches, y, in x seconds.

We know that the rate of change of a line is given by :-

[tex]k=\frac{y_2-y_1}{x_2-x_1}[/tex]

The ordered pairs on the line in graph are (4, 16) and (8, 32) and (12, 48) and (16, 64).

Thus, the rate per second at which the machine launches the balls is given by :-

[tex]k=\frac{32-16}{8-4}=\frac{16}{4}

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

From Plato: Φ =7π/7 or π.

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.

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