Mathematics College

Which is a ppssible number of distinct real roots for a cubic function select all that apply.
0
1
3
4

Answers

Answer 1

Try graphing y=x^3.  It crosses the x-axis at (0,0), and this point represents the one and only real root.



Every form of a cubic function has a graph that crosses the x-axis in 1 or 3 places. 

Thus, the correct answers to this particular problem are B and C.



Additionally, certain cubic function forms have graphs that cross the x-axis in one unique place, but which touch (but do not cross) the x-axis.  Here you have one unique real root plus one repeated (duplicated) real root, for a total of 3 roots.



Using these facts, decide which of the four given answers are correct.

Related Questions

A math teacher gave her class two tests. 27% of the class passed both tests and 51% of the class passed the first test. What percent of those who passed the first test also passed the second test?

Answers

Assume that there are 100 students in the class.

(Working with numbers is easier than working with percentages).

There are 27 students who passed both tests, and 51 who passed only the first test.
The 27 students who passed both tests are included in the 51 who passed the first test.

We are asked "What percent of those who passed the first test also passed the second test?"

so we are asked "what percent of 51 is 27?"

let      51 be 100%
then   27  is [tex] \frac{27*100}{51} [/tex]%=52.941%


Answer: 52.941%

The variable Z is directly proportional to X. When X is 5, Z has the value 55.

What is the value of Z when X = 12

Answers

z is directly proportional to x, that means :
z = k.x, with k is the coefficient of proportionality:
Let calculate k:
When x = 5, z = 55. Plug in:
 55 = k.5  → k=55/5 ; k =11
The value of z when  = 12 is : z= kx; z = 11(12) and z = 132

Direct variation is of the form y=kx, in this case:

z=kx, we are given the point (5,55) so we can solve for the constant of variation

55=5k  divide both sides by 5

11=k so our equation is:

z=11x, so when x=12

z=11(12)

z=132

Evaluate the integral. (use c for the constant of integration.) sin^2(πx) cos^5(πx) dx

Answers

Using the identity cos^2(A)=1-sin^2(A)
transform 
integral of sin^2(πx)cos^5(πx)dx
=integral of sin^2(πx)[1-sin^2(πx)]^2 cos(πx)dx
=integral of [sin^2(πx)-2sin^4(πx)+sin^6(πx)]cos(πx)dx
using the substitution u=sin(πx), du=πcos(πx)dx
=integral of [u^2-2u^4+u^6] (du/π)
=1/π[u^3/3-(2/5)u^5+u^7/7] + C
back substitute u=sin(πx)
=1/π[sin(πx)^3/3-(2/5)sin(πx)^5+sin(πx)^7/7]
or
=sin(πx)^3/3π-2sin(πx)^5/5π+sin(πx)^7/7π


Find the half-life of an element which decays by 3.411% each day. Hint: use y = ab^t.

Answers

a/2=a((100-3.411)/100)^t

a/2=a(0.96589)^t

0.5=0.96589^t 

ln(0.5)=t(ln(0.96589))

t=ln(0.5)/ln(0.96589)

t≈19.97 days (to nearest hundredth of a day)

This is about half life of elements with exponential decay.

Half life = 20 years

We are given a decay rate of 3.411% per day.

We are given;

y = ab^(t)

Where;

t is the half life

y = a/2 is the amount of substance remaining after decay

a is amount of substance initially

b = 100% - 3.411% = 96.589% = 0.96589

Thus;

a/2 = a(0.96589)^(t)

a will cancel out to give;

0.5 = 0.96589^(t)

ln (0.5) = t(ln 0.96589)

t = ln(0.5)/ln(0.96589)

t = 19.968 days

This is approximately 20 days.

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Hours worked: 40 Rate: $3.85 Wages: ?

Answers

Answer: $154.00

Step-by-step explanation:

I am assuming you are looking for how much the person made.

Multiply 40 hours times $3.85

$154.00

Which set of numbers does 8 2/3 belong to

Answers

real and rational numbers

Joe Popoff, a collection agent, collected 90% of a debt of $5,600.00 that had been overdue 90 days. This collection rate was 5% more than the average collection rate for that agenr. The agent charged 25% commission. What are the net proceeds?

Answers

You are given the debt collected by Joe Popoff with a 90% of a debt of $5,600.00 that had been overdue 90 days. This collection rate was 5% more than the average collection rate for that agent. The agent charged 25% commission. You are asked to find the net proceeds. 

Amount collected
= $5,600 * 0.90
= $5,040

Commision
= $5,040 * 0.25
= $1,260

Net Proceeds
= $5,040 - $1,260
= $3,780 

0.063 written as fraction or a mixed number

Answers

63/1000 as a fraction

Balcony and orchestra tickets were sold for a Friday night concert last week. The balcony and orchestra tickets sold for $35 and $45, respectively. If 90 tickets were sold, and the total revenue was $3550 for the night, find the number of balcony and orchestra tickets sold.

Answers

x = balcony and y = orchestra

x + y = 90....x = 90 - y
35x + 45y = 3550

35(90 - y) + 45y = 3550
3150 - 35y + 45y = 3550
-35y + 45y = 3550 - 3150
10y = 400
y = 400/10
y = 40 <== 40 orchestra tickets

x = 90 - y
x = 90 - 40
x = 50 <== 50 balcony tickets



if x>2, then x^2-x-6/x^2-4=

Answers

consider the expression [tex] \frac{x^{2} -x-6}{ x^{2} -4} [/tex]

To factorize the expression in the denominator we use difference of squares: [tex]x^{2} -4=x^{2} - 2^{2} =(x-2)(x+2)[/tex]

To factorize [tex]x^{2} -x-6[/tex] we use the following method:

[tex]x^{2} -x-6=(x-a)(x-b)[/tex]

where a, b are 2 numbers such that a+b= -1, the coefficient of x,

and a*b= -6, the constant.

such 2 numbers can be easily checked to be -3 and 2

(-3*2=6, -3+2=-1)

So [tex]x^{2} -x-6=(x-a)(x-b)=(x+3)(x-2)[/tex]

[tex] \frac{x^{2} -x-6}{ x^{2} -4}= \frac{(x+3)(x-2)}{(x-2)(x+2)}= \frac{x+3}{x+2} [/tex]


[tex]\frac{x+3}{x+2}= \frac{x+2+1}{x+2}= \frac{x+2}{x+2}+ \frac{1}{x+2}=1+ \frac{1}{x+2}[/tex]

for x>2

[tex]\frac{1}{x+2}\ \textless \ \frac{1}{2+2}= \frac{1}{4} [/tex]

thus

for x>2, 

[tex]1+ \frac{1}{x+2}\ \textless \ 1+ \frac{1}{4}= \frac{5}{4} [/tex]


Answer: 

for x>2

[tex]\frac{x^{2} -x-6}{ x^{2} -4} = \frac{x+3}{x+2} \ \textless \ \frac{5}{4} [/tex], (but the expression is never 0)

Which of the following fractions is an equivalent fraction in lowest terms to the fraction ? -276/-540

A. 23/45
B. -23/45
C. 69/135
D. -69/135

Answers

23/45 would be the most simplified form of 276/540
[tex]\bf \cfrac{-276}{-540}\quad \begin{cases} 276=2\cdot 2\cdot 3\cdot 23\\ 540={2\cdot 2\cdot 3}\cdot 3\cdot 3\cdot 5 \end{cases}\implies \cfrac{\underline{-2\cdot 2\cdot 3}\cdot 23}{\underline{-2\cdot 2\cdot 3}\cdot 3\cdot 3\cdot 5} \\\\\\ \cfrac{23}{3\cdot 3\cdot 5}\implies \cfrac{23}{45}[/tex]

Find the area of a regular hexagon with apothem 2√3 mm. Round to the nearest whole number.

Answers

Join the center of the hexagon with the 2 base angles.

An equilateral triangle, with side length x, is formed.

(remark: a regular hexagon is made up of 6 equilateral triangles with equal length)

The height [tex]2 \sqrt{3} [/tex] forms 2 congruent right triangles with :

hypotenuse= x, side_1=x/2, and side_2= [tex]2 \sqrt{3} [/tex].

From the pythagorean theorem we have:

[tex] x^{2} = ( \frac{x}{2} )^{2}+(2 \sqrt{3})^{2} [/tex]

[tex]x^{2} = \frac{ x^{2} }{4} +12[/tex]

[tex] \frac{3}{4} x^{2} =12[/tex]

[tex] x^{2} = \frac{12*4}{3}=4*4 [/tex]

thus, x=4.

The area of the triangle is 1/2 * 4 * [tex]2 \sqrt{3}[/tex]=6.93 (mm squared)

The area of the hexagon is 6* the area of the triangle = 42 (mm squared)


Answer: a. 42 (mm squared)

How are midsegments of trapezoids and triangles alike? How are they different?

Answers

similarity 1. 

Midsegments of a triangle and a trapezoid are alike, because their endpoints, are the midpoints of the sides they touch. 

similarity 2.
The length of the midsegment of a trapezoid is (large base+small base)/2

whereas, the length of a midsegment of a triangle is base/2. 

difference 1:

Midsegments of triangles and trapezoids are different, because we can draw 3 of them in triangles, but only one in trapezoids. 

(we can only join the midpoints of the nonparallel sides of a trapezoid to form its only midsegment.)



Final answer:

In both trapezoids and triangles, midsegments connect the midpoints of two sides. They are parallel to one side and their lengths are determined by the measurements of certain sides. The main difference lies in the number of midsegments each shape can have: a trapezoid can have only one, while a triangle can have three.

Explanation:

In both trapezoids and triangles, a midsegment is a line segment that connects the midpoints of two sides. The similarity between these midsegments lies in their properties. In both cases, the midsegments are parallel to one of the sides of the figure (the base for the trapezoids and the third side for the triangles) and their length is equivalent to the average of the two bases in a trapezoid and half the length of the base in a triangle.

However, the main difference between midsegments of trapezoids and triangles is the number of such segments each figure can have. A trapezoid has only one midsegment, that connects the midpoints of the non-parallel sides, while a triangle can have up to three midsegments, one for each side of the triangle.

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What are the solutions to the quadratic equation (5y + 6)2 = 24? y = and y = y = and y = y = and y = y = and y =

Answers

For this case we have the following quadratic expression:

[tex] (5y + 6) ^ 2 = 24
[/tex]

From here, we must clear the value of y.

For this, we follow the following steps:

1) We clear the square term:

[tex] (5y + 6) =+/-\sqrt{24} [/tex]

[tex] (5y + 6) =+/-2\sqrt{6} [/tex]

2) Pass the value of 6 by subtracting:

[tex] 5y =-6+/-2\sqrt{6} [/tex]

3) Pass the value of 5 to divide:

[tex] y =\frac{-6+/-2\sqrt{6} }{5} [/tex]

Answer:

The solutions to the quadratic equation are:

[tex] y =\frac{-6+2\sqrt{6} }{5} [/tex]

[tex] y =\frac{-6-2\sqrt{6} }{5} [/tex]

Consider a game in which player 1 moves first. the set of actions available to player 1 is a1={a,b,c}. after observing the choice of player 1, player 2 moves. the set of actions available to player 2 is a2={a,b,c,d}. at how many information sets does player 2 move?

Answers

since player 1 moves first, At the Time player-2 Only has 3 information sets to move at which means from player 1 's A ( player-2 can play a,b,c,d) , player-1's B ( player-2 can play a,b,c,d)and player-1's C ( player-2 can play a,b,c,d).

Felicia invested money at an interest rate of 4%. After six months, she had earned $90.00 interest. How much money did Felicia invest?

Answers

The formula is
I=prt
I interest earned 90
P amount invested?
R interest rate 0.04
T time 6/12
Solve the formula for p
P=I÷rt
P=90÷(0.04×(6÷12))
P=4,500 ....answer

Answer:

the answer is 4500 i got it right

Step-by-step explanation:

The excluded values of a rational expression are 2 and 5. Which of the following could be this expression?

Answers

A value will be excluded from a rational expression if it causes the denominator to be zero as dividing by zero is undefined.

An example that would work for your specific question is:

[tex] y = \frac{(x - 3)(x-1)}{(x-2)(x-5)} [/tex]

If you plug in either 2 or 5 into this equation the denominator will be zero causing the expression to undefined there, so the values 2 and 5 are excluded from the domain of the expression.

Answer: d on eng

Step-by-step explanation:

a=one half bh solve for b

Answers


A = [1/2] bh

1) Multiply both sides by 2 =>

2A = 2 * [1/2] bh

2A = [2/2]bh

2A = bh

2) Divide both sides by h =>

2A/h = bh / h

=> 2A/h = b

Answer: b = 2A/h

Teachers of two history classes bought tickets to go on a field trip to a local museum. Mr. Lowe paid $115 for 4 adult tickets and 20 student tickets. Mrs. Tucker paid $135.25 for 5 adult tickets and 23 student tickets. Fill in the missing information in the system of equations for the situation. 4a + As = 115 5a + 23s = B

Answers

4a + 20s = 115
5a + 23s = 135.25

Answer with Step-by-step explanation:

Let a represents the cost of one adult ticket

and s represents the cost of one student ticket

Mr. Lowe paid $115 for 4 adult tickets and 20 student tickets.

i.e. 4a+20s=115

Mrs. Tucker paid $135.25 for 5 adult tickets and 23 student tickets.

i.e. 5a+23s=135.25

We get system of equations:

4a+20s=115

5a+23s=135.25

On comparing the above system with

4a + As = 115

5a + 23s = B

We get

A=20

and B=135.25

What are the coordinates of a point on the unit circle if the angle formed by the positive x-axis and the radius is 60?

Answers

Arc length equal to the radius of a circle

solve these equations fast.

(6 + 3i)(6 − 3i) =


(4 − 5i)(4 + 5i) =


(−3 + 8i)(−3 − 8i) =

Answers

(6 + 3i)(6 − 3i) = 45
(4 − 5i)(4 + 5i) = 41
(−3 + 8i)(−3 − 8i) = 73

Answer:

The correct answers are 45,41,73

Step-by-step explanation:

6840 round to nearest hundredth

Answers

6800 is 6840 rounded to the nearest hundredth.

Which expression is equivalent to 3(8 + 7)? 24 + 7 24 + 21 11 + 10 11 + 7

Answers

Multiply 3&8 and 3&7, this expands it to 24 + 21.
3(8 + 7) = 3(8) + 3(7)...distributive property
= 24 + 21 

answer is
24 + 21 

A radio telescope has a parabolic surface, as shown below.
If the telescope is 1 m deep and 12 m wide, how far is the focus from the vertex? (5 points)

Answers

check the picture below.

so.. "p" is the distance from the vertex to either, the focus point or the directrix.

thus the focus is "p" units from the vertex.

now, if we set the parabola at the origin, like in the picture, and then use another point on the parabola, let's say we'll use (6,1), then

[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} (y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\ \boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}})} \\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \begin{cases} h=0\\ k=0 \end{cases}\implies (x-0)^2=4p(y-0)\implies x^2=4py \\\\\\ \begin{cases} x=6\\ y=1 \end{cases}\implies (6)^2=4p(1)\implies \cfrac{6^2}{4}=p\implies \cfrac{36}{4}=p\implies 9=p[/tex]
Final answer:

For a parabolic dish, the focus is at a depth equal to one-fourth of the square of the width of the dish's aperture. Given the width as 12m, the focus of the radio telescope is 36m from the vertex.

Explanation:

For a parabolic dish like a radio telescope, the focus (or focal point) is located at the depth equal to one-fourth of the square of the width (i.e., one-fourth of the square of the diameter) of the dish's aperture.

Given the width (diameter) of the dish is 12 meters, we square it to get 144. Quarter of this value is 36 m. So, the focus is 36 m from the vertex of the parabola represented by the dish's surface.

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Without using a trigonometric ratio, find the distance from the ship to the buoy, B. Round the distance to the nearest tenth of a mile.

Answers

Without using the trigonometry ratio, we can find the distance between the ship and the buoy by:

the distance between City and Lemont SUBTRACT the vertical distance between City and the point parallel to the Ship

The distance between the City and Lemont can be worked out using the Sin rule 
[tex] \frac{57.8}{sin(36)}= \frac{City-Lemont}{sin(92)} [/tex]
[tex]City-Lemont= \frac{57.9sin(92)}{sin(36)} = 98.27.....[/tex]≈98.3

The vertical distance between the City and the point parallel to the ship can be worked out using the Pythagoras theorem
[tex] \sqrt{57.8^{2}- 44.6^{2} } =36.765... [/tex]≈36.8

The distance between the ship and the Buoy is given:
[tex]98.3-36.8=61.5 [/tex] miles

solve x2-8+41=0 for x

Answers

No real solutions or i square root 33

I'm taking x2 is x^2 or x squared

i stands for imaginary number
[tex]Problem: x^2-8+41= 0 \\ x^2+ 33 = ? \\ = 0 - 33 = (-33) \\ The Value Of 'x' is -33 \\ x= \sqrt{-33} [/tex] [tex]There \\ are \\ NO \\ Solution \\ in \\ this \\ equation! [/tex] [tex]Good Luck! [/tex]

What is next number after 2 7 8 3 12 9

Answers

2+5=77+1=88-5=33+9=1212-3=9Can someone help me and tell me why i can not figure this out?

Simplify this and show your work :

Answers

-2(x-3) = 5x+1

-2x +6 = 5x+1

subtract 5 x from each side

-7x+6 = 1

subtract 6 from each side

-7x = -5

divide both sides by -7

x = -5/-7 = 5/7

x = 5/7


On Saturday, a local hamburger shop sold a combined total of 273 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?

Answers

Final answer:

To determine the number of hamburgers sold on Saturday, we used the given total of 273 burgers and the relationship that cheeseburgers were twice as numerous as hamburgers. By setting up an equation and solving for the number of hamburgers, we found that 91 hamburgers were sold.

Explanation:

The question asks us to determine how many hamburgers were sold on Saturday given that the total number of hamburgers and cheeseburgers sold was 273, and the number of cheeseburgers was two times the number of hamburgers. Let's denote the number of hamburgers as H and the number of cheeseburgers as C. The problem states that C = 2H. The total number of burgers sold was H + C = 273. Substituting C with 2H, we get H + 2H = 273.

Solving for H, we combine like terms to get 3H = 273, and then we divide both sides by 3 to find H = 273 / 3. Therefore, H = 91. So, 91 hamburgers were sold on Saturday.

The three vertices drawn on a complex plane at represented by 0+0i, 4+0i, and 0+3i. What is the length of the hypotenuse

Answers

check the picture below

you can pretty much get the values for "a" and "b" from the grid.
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