3. (03.04 HC)Given a polynomial function f(x), describe the effects on the y-intercept, regions where the graph is increasing and decreasing, and thebehavior when the following changes are made. Make sure to account for even and odd functions.• When f(x) becomes f(x) - 3• When f(x) becomes -2. f(x)(10 points)

Question 11

The slope is 7/2 (so the line is increasing), and the y-intercept is 3.

Question 12

The slope is -8/3 (so the line is decreasing), and the y-intercept is -5.

A)

b)

If r = -6,  s = -2, v = 10 and w = 3, then the response of the expression vs(r-s) ÷ 2 + rw is option (D) 22

The expression is

vs(r-s) ÷ 2 + rw

The values are

r = -6

s = -2

v = 10

w = 3

Substitute the values in the given expression

= 10×-2 (-6-(-2)) ÷ 2 + -6×3

First we have to do the arithmetic operation in brackets

= 10 × -2 (-4) ÷ 2 + -6×3

Next we have to do the multiplications

= 80 ÷ 2 -18

Do the division

= 40-18

= 22

Hence, if r = -6,  s = -2, v = 10 and w = 3, then the response of the expression vs(r-s) ÷ 2 + rw is option (D) 22

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Santiago needs to invest  50467.3 dollars for the value of the account to reach $81,000 in 16 years at a rate of 3.3%.

Simple interest is often a predetermined percentage of the principle amount borrowed or lent paid or received over a specific time period.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

Given Santiago is going to invest in an account paying an interest rate of 3.3% compounded annually for the value of the account to reach $81,000 in 16 years.

We know the formula of compound interest which is A = P(1 + r/100)ⁿ,

where A = Amount, P = Principle, n = Time in years and r = rate percentage.

∴ 81000 = P( 1 + 3.3/100)¹⁶.

81000 = P( 1 + 0.03)¹⁶.

81000 = P( 1.03)¹⁶.

81000 = P×1.605.

P = 81000/1.605

P = 50467.3 dollars.

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We can see here, from the first term to the second term, we minus 2. From the second term to the third term, we minus 2.

So, we're constantly reducing by an amount, therefore making this sequence an arithmetic sequence.

The common difference, said above, is -2 (since if the terms are getting smaller the common difference is a negative number.)

The change left when Susan buys lotion for $2.33 and gives the bill is $8.

Susan buys lotion for $2.33. She gives the clerk a $10 bill, three dimes, and three pennies. The total amount will be:

= $10 + (3 × 0.1) + (3 × 0.01)

= $10.33

The change left will be:

= Total amount - Cost of lotion

= $10.33 = $2.33

= $8

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The  expression that can be considered as been equivalent to 3/4-2/5 is 15/20-8/20.

The  equivalent expression be gotten by finding the values of the given answer one after the other, from the given option, we can see that the value of the difference in the given expression is 0.35, then the value option A is also 0.35 which implies that the option A as well as the given expression have the same value.

It should be noted that the option A can as well be simplified as still get the vale of the given option.

Therefore, option A is correct.

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Equation

Steps

1. Group the variables and constants on each side of the equality

2. Operate the variables and operate the constants.

3. Divide both parts by 4 to clear y

The answer would be y = 5/4

Answer:

11 degrees

Step-by-step explanation:

Answer: 28 degrees

Step-by-step explanation: Set the two equations equal to each other, and solve. X equals 4 and then you plug that into 7x. 7x4 is 28.

Step-by-step explanation:

when an object gains height, Kinetic energy in the object is converted to gpe. gpe = mgh

when an object loses height and falls down, the object is accelerated by gravity (free fall) therefore, gains velocity which means the gpe is converted to kinetic energy.

kinetic energy = 1/2 × m × v²

this is applicable only when the mass is constant.

hope it helps. :)

Answer: 4/1

Step-by-step explanation: You go on the y-axis up to 6 then you count up until you get to 10 then you go over 1 so the equation would be 4/1

△ABC is congruent to △CDA (△ABC ≅ △CDA) under (A) SAS condition.

So, to prove that △ABC ≅ △CDA as follows:

So, △ABC ≅ △CDA under SAS condition.

Therefore, △ABC is congruent to △CDA (△ABC ≅ △CDA) under (A) SAS condition.

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In linear equation, $5.26  is her hourly wage .

What is linear equation in math?

Serita worked 6 h and earned $31.50.

1 hour of wage of serita = $31.50/6

                                       = $5.26

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Answer:

The limit from the left does not equal the limit from the right.

Answer:

3.5n + 29.99 × 15

Step-by-step explanation:

Since it is an expression there are no equals, and since we do not know how many colors there are in the design we leave the variable.

The area of the triangle is 18 cm.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

In Triangle ABC,

AB= 6cm

AC= 8cm

BC= 12cm.

Angle ACB= 26.4

The area of a triangle is given as:

Area = 1/2 x base x height

From the figure below,

Base = BC = 12

D is the midpoint of BC.

BC = BD + DC

DC = 12/2 = 6

Height = Tan 26.4

Tan 26.4 = AD / DC = AD / 6

0.50 = AD / 6

AD = 0.50 x 6

AD = 3

Now,

Area of the triangle ABC:

= 1/2 x base x height

= 1/2 x 12 x 3

= 18 cm

Thus,

The area of the triangle is 18 cm.

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Answer:

Number above 42 : 14

Number beside 2 : 1

Number above 0: 12

Step-by-step explanation:

Answer: x=0   x=2   x=-1

Step-by-step explanation:

[tex]x^3-x^2-2x=0\\\\x(x^2-x-2)=0\\\\x(x^2-2x+x-2)=0\\\\x((x-2)+(x-2))=0\\\\x(x-2)(x+1)=0\\\\x=0\\\\x-2=0\\\\x-2+2=0+2\\\\x=2\\\\x+1=0\\\\x+1-1=0-1\\\\x=-1[/tex]

Answer:

Factored form: x(x-2)(x+1)=0

Solutions: x=0, x=2, x=-1

Step-by-step explanation:

[tex]x^{3} -x^{2} -2x=0\\[/tex]

[tex]x(x^{2} -x-2)=0\\\left \{ {{x=0} \atop {x^{2}-x-2 =0}} \right. \\\left \{ {{x=0} \atop (x-2)(x+1)=0}} \right. \\x=0,x=2,x=-1[/tex]

A table that shows a function that is increasing only over the interval (–2, 1), and nowhere else:

A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 2, negative 4, negative 1, 1, 4, 3.

In this question, we have been given some table that shows functions.

A 2-column table consists of six rows. The first column is labeled x (input values). The second column is labeled f(x) (output values)

We need to find a function which is increasing only over the interval (–2, 1), and nowhere else.

We can observe that for a second table, the first column x with entries negative 3, negative 2, negative 1, 0, 1, 2 and the second column with entries negative 2, negative 4, negative 1, 1, 4, 3 function f(x) is increasing only over the interval (–2, 1), and nowhere else.

Therefore, a table that shows a function that is increasing only over the interval (–2, 1), and nowhere else:

A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 2, negative 4, negative 1, 1, 4, 3.

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In one revolution, cycle travels 18.84 feet.

A problem can be resolved using the unitary method by first calculating the worth of a single unit, and then multiplying that amount to find the required value. A single or unique unit is referred to as unitary. Determining values in relation to a single unit is the goal of this strategy. For instance, we can use the unitary technique to determine how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel. With the unitary method, you first determine the value of a single unit before determining the value of the necessary quantity of units.

Radius = 3 feet

If r is the radius of the wheel (including the tire), then the circumference of the wheel = 2πr

= 2 x 22/7 x 3 feet

= 18.84 feet

In one revolution, cycle travels 18.84 feet.

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Answer:

Step-by-step explanation:

According to quadratic formula:

y = - b  ±  √ b²- 4ac / 2a

y = - (-5) ± √ -5²- 4(2x-12) / 2(2)

y = 5 ± √ 25 - 4(-24) / 4

y = 5 ± √ 25 - (-96) / 4

y = 5 ± √ 121 / 4

y = 5 ± √ (11)² / 4

y = 5 ± 11 / 4

Now either,

y = 5 + 11 / 4

y = 4

Or,

y = 5 - 11 / 4

y = -3/2 = -1.5

Number of people = 6

(0+ 24 + 18 + 30 + 0 + 15)/ 6 = 87/6

. = 14 + 3/6

Then answer IS

Average number of cheeseburgers= 14

Given that a polynomial function [tex]f(x)[/tex] has,

And we need to find [tex]f(x)[/tex]

as we know that if a polynomial has zeroes as [tex]\alpha[/tex] , [tex]\beta[/tex] and [tex]\gamma[/tex] , then the cubic polynomial is given by,

[tex]\longrightarrow f(x)=k (x-\alpha)(x-\beta)(x-\gamma)\\ [/tex]

where ,

Now substitute the given zeroes, as ;

[tex]\longrightarrow f(x)=2[ (x-2)(x-\sqrt3)(x+\sqrt3)]\\ [/tex]

[tex]\longrightarrow f(x)= 2[(x-2)\{ x^2-(\sqrt3)^2\}][/tex]

[tex]\\\longrightarrow f(x)= 2[ (x-2)(x^2-3)]\\ [/tex]

[tex]\longrightarrow f(x)=2[ x(x^2-3)-2(x^2-3)]\\ [/tex]

[tex]\longrightarrow f(x)= 2[ x^3-3x -2x^2+6]\\ [/tex]

[tex]\longrightarrow \underline{\underline{ f(x)= 2x^3-4x^2-6x+12}}[/tex]

and we are done!

Answer:

[tex]f(x)=2x^3-4x^2-6x+12[/tex]

Step-by-step explanation:

Given characteristics of the polynomial:

As the polynomial has 3 roots, it is a cubic polynomial.

[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a cubic polynomial}\\\\$y=a(x-r_1)(x-r_2)(x-r_3)$\\\\where:\\ \phantom{ww}$\bullet$ $r_n$ are the roots. \\ \phantom{ww}$\bullet$ $a$ is the leading constant.\\\end{minipage}}[/tex]

Substitute the given leading coefficient and roots into the formula:

[tex]f(x)=2(x-2)(x-\sqrt{3})(x+\sqrt{3})[/tex]

Expand to standard form:

[tex]\implies f(x)=2(x-2)(x+\sqrt{3}x-\sqrt{3}x-3)[/tex]

[tex]\implies f(x)=(2x-4)(x^2-3)[/tex]

[tex]\implies f(x)=2x^3-6x-4x^2+12[/tex]

[tex]\implies f(x)=2x^3-4x^2-6x+12[/tex]

The shaded sections of the trapezoid are triangles.

We know how to find the area of triangles

A = 1/2 bh

Lets start with the left triangle

The bases is 1.1 inches and the height is 3.8 inches

A left triangle is

A = 1/2 ( 1.1) * 3.8 = 2.09

The right triangle has the same dimensions

A right triangle is

A = 1/2 ( 1.1) * 3.8 = 2.09

Add the two triangles together

2.09+2.09 = 4.18 in^2

The area of the shaded region is 4.18 in^2

Explanation:

The balance after t years can be calculated using the following equation:

Where P is the principal amount and r is the rate of interest per year.

So, replacing P by $300, r by 3.5%, and t by 5, we get:

So, the balance after 5 years is $356,3059

Answer: $356.3059

The minimum number of balls that must be chosen randomly from the box to ensure that we get 9 balls of the same color is 39.

Given that a box contains 6 red, 8 green, 10 blue, 12 yellow, and 15 white balls.

As the question says that the minimum number of balls chosen must ensure that we get 9 balls of the same color, so we must consider the balls of those colors which are more than 9 in number.

Here, 10 blue, 12 yellow, and 15 white balls are considered as they are more than 9.

By applying the Pigeon principle,

we can get.,

9 blue + 9 yellow + 9 white – 3 + 1 = 25

As we are picking randomly so we can get all the red and green balls before the above 25 balls.

Therefore we add the balls 6 red + 8 green + 25 = 39

Hence, the minimum number of balls that must be chosen randomly from the box to ensure that we get 9 balls of the same color is 39.

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Answer:

see below

Step-by-step explanation:

23 out of the 40 have cc or pecans

23/40