Mathematics College

Which of the following is a polynomial function in standard form with zeros at 0, 2, and 4?

Answers

Answer 1

x(x - 2)(x - 4)
x(x² - 6x + 8)
x³ - 6x² + 8x

Answer 2

Answer:

polynomial x³ -6x² +8x .

Step-by-step explanation:

Given : polynomial function in standard form with zeros at 0, 2, and 4.

To find : Which of the following is a polynomial function.

Solution : we have given that

zeros at 0, 2, and 4.

x = 0 .

x = 2

x = 4

(x -0)(x -2) (x -4).

x (x-2)(x-4).

x( x² -4x -2x +8).

x (x² -6x +8).

x³ -6x² +8x .

Therefore, polynomial x³ -6x² +8x .

Related Questions

If male and female college students work an average of 15 hours per week during the school year and the standard deviation is 5.4 for male students and 2.3 for female students, what may we conclude?

Answers

The variance of hours males spend working is almost two times as large as females. 60% of those females are more likely to work between 12.7 to 17.3 hours while 60% of the males work between 9.6 to 20.3 hours based on one standard deviation.

Answer: the male sample is more spread than the female sample

Step-by-step explanation:

The mean is the same for both genres, but the standard deviation form males is bigger than the one for females.

This means that the data of the male students is more spread than the female data (so there are more male students that study more hours, but there also are more male students that study less hours).

So the general conclusion is that the male sample is more spread than the female sample

To stay healthy, Kevin’s doctor says he should try to consume at most 2000 inequality to show the amount of calories Kevin should consume

Answers

x greater than or equal to sign 2000

[tex]c \leqslant 2000[/tex]
c stands for calories kevin should consume

Camelle manages her soccer team. She needs to order 4 practice jerseys for each player. There are y players. How many total practice jerseys does she need to order?

Answers

T= total # of jerseys to order
y= # of players

T= 4*y
Total equals 4 times # of players

T= 4y

Hope this helps! :)

Answer:

The required number of total practice jerseys does she need to order is '4y'.

Step-by-step explanation:

Given : Camelle manages her soccer team. She needs to order 4 practice jerseys for each player. There are y players.

To find : How many total practice jerseys does she need to order?

Solution :

Let the total practice jerseys does she need to order be 'x'.

According to question,

She needs to order 4 practice jerseys for each player.

Number of players are y.

So, Total jerseys she needs is

[tex]x=4\times y[/tex]

[tex]x=4y[/tex]

Therefore, The required number of total practice jerseys does she need to order is '4y'.

Find the equation of the plane with the given description. contains the lines r1(t) = 2, 1, 0 + t, 2t, 4t and r2(t) = 2, 1, 0 + 4t, t, 15t .

Answers

The intersection point of the two lines is (2,1,0).
The respective direction vectors are
L1: <1,2,4>
L2: <4,1,15>
Since the normal vector of the required plane is perpendicular to both direction vectors, the normal vector of the plane is obtained by the cross product of L1 and L2.
i j k
1 2 4
4 1 15
=<30-4, 16-15, 1-8>
=<26, 1, -7>

We know that the plane must pass through (2,1,0), the equation of the plane is

26(x-2)+1(y-1)-7(z-0)=0
simplifying,
26x+y-7z=52+1+0=53
or
26x+y-7z=53

Check:
Put points on L1 in the plane
26(t+2)+(2t+1)-7(4t+0)=53 ok
For L2,
26(4t+2)+(t+1)-7(15t+0)=53 ok

The equation of the plane containing the two given lines is found by calculating the normal vector through the cross product of direction vectors and then using the normal vector with a point from the lines to form the plane's equation, which is 26x + y - 7z = 53.

To find the equation of a plane that contains two given lines, we must first find two direction vectors that represent the lines. In this case, we are given the lines r1(t) = (2, 1, 0) + t(1, 2, 4) and r2(t) = (2, 1, 0) + t(4, 1, 15). The direction vectors for these lines are (1, 2, 4) and (4, 1, 15), respectively. To find the normal vector to the plane, we take the cross product of these two direction vectors.

Let's calculate the cross product:
(1, 2, 4) * (4, 1, 15) = (2*15 - 4*1, 4*4 - 15*1, 1*1 - 2*4) = (26, 1, -7).

The normal vector to the plane is (26, 1, -7), which also represents the coefficients of the variables in the plane's equation. Since both lines pass through the point (2, 1, 0), we can use this point and the normal vector to find the plane's equation.

The general form of the plane's equation is 'Ax + By + Cz + D = 0', where (A, B, C) is the normal vector to the plane. Plugging in the point (2, 1, 0) and the normal vector (26, 1, -7), we get:

26*(x - 2) + 1*(y - 1) - 7*(z - 0) = 0
26x - 52 + y - 1 - 7z = 0
26x + y - 7z = 53

And this is the Equation to the required plane containing the two given lines.

Find the area and the circumference of a circle with radius 2m. use the value 3.14, and do not round your answers. be sure to include the correct units in your answers.

Answers

The area of a circle is given by:
[tex]A_c = \pi r^2[/tex]
Plug and chug:
[tex]A_c = \pi (2)^2 = 12.56m^2[/tex]

Circumference is given by (d = 2r):
[tex]C_c = \pi d[/tex]
Plug and chug:
[tex]C_c = \pi (4) = 12.56m[/tex]

Those are your answers!

Final answer:

The area of a circle with a radius of 2m is 12.56 m² and the circumference is 12.56 m when using 3.14 for π, with both answers having two significant figures due to the radius given with two significant figures.

Explanation:

The area (A) and the circumference of a circle with radius 2m can be found using the formulas A = πr² and C = 2πr. Using 3.14 as the value for π, the calculations would be A = (3.14)(2m)² = 12.56 m² for the area, and C = 2(3.14)(2m) = 12.56 m for the circumference. It is important to note that when performing calculations, the result should have the same number of significant figures as the quantity with the fewest significant figures used in the calculation.

Your friend asks you to make picture frames and will give you 5 5 nickels for the first frame. You agree to help if she multiplies your payment by 5 5 for each frame completed. After 2 2 frames, you will receive 25 25 nickels, and after 3 3 frames, you will receive 125 125 nickels. What is the number of nickels for tenth frame?

Answers

Final answer:

To find the number of nickels for the tenth frame, we calculate 5 imes 5^9, which equals 9,765,625 nickels. This is a geometric sequence where the common ratio is 5, and the first term for the first frame is 5 nickels.

Explanation:

The question asks about the payment received for making picture frames where the payment is multiplied by 5 for each subsequent frame. To find out the number of nickels for the tenth frame, we can use the concept of geometric sequences, where each term is found by multiplying the previous term by a common ratio. The common ratio in this case is 5.

For the first frame, you get 5 nickels. For the second frame, 5 multiplied by 5 is 25 nickels. To find the payment for the tenth frame, we multiply the payment of the first frame by the common ratio to the power of the frame number minus one: 5 imes 5^(10-1) = 5 imes 5^9.

Calculating 5 to the power of 9 gives us 1,953,125. Multiplying this by 5 gives us 9,765,625 nickels for the tenth frame.

What is the equivalent factored form of 12x4 – 42x3 – 90x2? 6x(x – 5)(2x + 3) 6x2(x – 5)(2x + 3) 6x(x + 5)(2x – 3) 6x2(x + 5)(2x – 3)

Answers

B. Factor out x^2 first. 12*x^4-42*x^3-90*x^2=(x^2)*(12*x^2-42*x-90). See that 6 is a common divisor of 12, 42, 90, so factor out 6: (6x^2)*(2*x^2-7*x-15).Then factor (2x^2-7x-15) as (2x+3)*(x-5). So the original expression=(6x^2)(2x+3)*(x-5)

The equivalent factored form of 12x4 - 42x3 - 90x2 is 6x(x - 5)(2x + 3).

The equivalent factored form of 12x4 - 42x3 - 90x2 is 6x(x - 5)(2x + 3).

We can factor out the greatest common factor, which is 6x. That leaves us with 2x3 - 7x2 - 15x.

Then we can factor by grouping, which involves grouping terms that have a common factor. By factoring out an x from the first two terms, we get x(2x2 - 7x - 15). By factoring out a -5 from the last two terms, we get -5(2x2 - 7x - 15). This gives us the final factored form of 6x(x - 5)(2x + 3).

Learn more about Factoring here:

https://brainly.com/question/34290719

#SPJ6

Which of the following is a rational number? square root 97 square root 98, square root 99, square root 100

A.)square root 97
B.)square root 98
C.)square root 99
D.)square root 100

Answers

Its D since the square root of 100 is 10

Answer:

Step-by-step explanation:

the sum of two numbers is -12 one number is 3 less than twice the other what is the bigger number

Answers

STEP 1:
x= one number
2x-3= other number

x + (2x-3)= -12
combine like terms

3x - 3= -12
add 3 to both sides

3x= -9
divide both sides by 3

x= -3 one number

STEP 2:
substitute x= -3 to find other number
2x-3= 2(-3)-3= -6-3= -9 other number

CHECK:
-3 -9= -12
-12= -12

ANSWER: One #= -3, Other #= -9

Hope this helps! :)

Find the 29th term of the following sequence. 21, 15, 9, 3, . . .

Answers

BEST ANSWER IS -153......

Answer:

The correct answer would be -147

Step-by-step explanation:

What are the coordinates of the vertex of the table? Is it a minimum or a maximum?
X Y
0 1
-1 -2
-2 -3

Answers

For this case, we must first graph the function to observe the behavior of the same.
We see that the vertex of the function is located at the point:
(x, y) = (- 2, -3)
The point is a minimum.
Answer:
(x, y) = (- 2, -3)
It is a minimum.
See attached image.

Given the information below, match the following items.

Given statement: If two angles add to 180°, then they are supplementary.

1.converse
2.inverse
3. contrapositive

If two angles are supplementary, then they add to 180°

If two angles do not add to 180°, then they are not supplementary. 3.contrapositive

If two angles are not supplementary, then they do not add to 180°.

Answers

Let this be the guide in dealing with conditional statement.

Statement = if p, then q
Converse = if q, then p
Inverse = if NOT p, then NOT q
Contrapositive = if NOT q, then NOT P.

Statement:
If two angles add to 180°, then they are supplementary.

Converse:
If two angles are supplementary, then they add to 180°

Inverse:
If two angles do not add to 180°, then they are not supplementary.

Contrapositive:
If two angles are not supplementary, then they do not add to 180°

Answer:

Converse- If two angles are supplementary, then they add to 180°

Inverse- If two angles do not add to 180°, then they are not supplementary.

Contrapositive- If two angles are not supplementary, then they do not add to 180°

Step-by-step explanation:

A line and a plane are considered parallel if they have no points in common. True or False?

Answers

True Bc they both have two lines that are point in the same direction

What are the zeros of the polynomial function f(x) = x3 – 4x2 – 12x

Answers

fx=x3−4x2−12x.‌fx/x‌=‌x3−4x2−12x/x‌

f=x2−4x−12

x³ - 4x² - 12x
x(x² - 4x - 12)
x(x - 6)(x + 2)
x = 0
x = 6
x = -2
The zeros are 0, 6, and -2

Write 9.79 x 10^5 in standard notation

Answers

the number 9.79*10^5 in standard notation is 9.79*100000=979,000

What is the diameter of a circle that has an area of 452.16 mm 2? 144 mm 12 mm 24 mm 6 mm

Answers

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2\quad \begin{cases} r=radius\\ -----\\ A=452.16 \end{cases}\implies 452.16=\pi r^2 \\\\\\ \cfrac{452.16}{\pi }=r^2\implies \sqrt{\cfrac{452.16}{\pi }}=r\implies 11.99695787\approx r[/tex]

now, that's the radius of the circle, recall that the diameter is twice the radius.

Answer:

the diameter is 24

Step-by-step explanation:

Solve each equation f over 28=24

Answers

I need a letter sorry I could not help

A bus travels 36 miles in 45 minutes enter the number of miles the bus travels in 60 minutes at this rate

Answers

Write a proportion
36/45=x/60
Cross multiply
45x=36*60
45x=2160
x=48 miles

48 miles.
36 divided by 45 is .8, that is for one minute. So .8 miles times 60 minutes is 48 miles.

If 8 identical blackboards are to be divided among 4 schools, how many divisions are possible? how many if each school must receive at least 1 black- board?

Answers

We usually distribute smartboards instead of blackboards these days!

We have a stars and bars problem.

We represent the blackboards by n=8 stars, and divide into k=4 schools (A,B, C & D) using three bars. Two consecutive bars or a bar at the end means that school has no blackboards.

For example,
*|***|*|***
Means there are two schools with 1 blackboard, and two other ones with three blackboards. Another example:
|*||*******
will mean there are two schools (A &C) with no boards, and B will have one, while school D will have 7.

So the problem reduces to counting the number of ways we can put the three identical bars.

If there is no minimum number of boards for each school, then we can place the k=4 bars at n+1=8+1=9 locations each.
Using combination notation, there are
C(n+1, k-1)=C(8+1,4-1)=C(9,3)=9!/(3!(9-3)!)=84 ways of distributing 8 blackboards to 4 schools.

On the other hand, if there is a minimum of one board for each school, then each school will get one, leaving 4 to be distributed as above, in
C(4+1,4-1)=C(5,3)=5!/(3!(5-3)!)=10 ways.

Of the members of a student choir, 60% are boys. If there are 21 boys in the choir, how many members does the choir have in total?

Answers

Suppose there are x number of members in all.

Now we are given that 60% of these are boys.

So number of members who are boys = 0.6x

We are also given that there are 21 boys in the choir.

So making an equation ,

[tex] 0.6x =21 [/tex]

dividing both sides by 0.6,

x= 35

So there are total 35 members in the choir.

Jeremy goes to the store where he buys 18 bananas. After two days, he notices that there are only 10 bananas that are left. Which equation below would Jeremy use to find the percent of bananas that he has left?

A. 10/18 = 100/x
B. 18/10 = x/100
C. 5/9 = x/100
D. 10/18 = x/55.5

Answers

Total number of Bananas = 18
Number of Bananas that are left = 10

Percentage of Bananas that are left = x

Mathematically, x can be expressed as:

[tex]x= \frac{10}{18} * 100 \\ \\ \frac{x}{100}= \frac{10}{18} \\ \\ \frac{x}{100}= \frac{5}{9} [/tex]

Thus the correct percentage of number of bananas that are left is expressed by option c.

Find an equation for the nth term of the arithmetic sequence.

9, 11, 13, 15, ...

Answer Choices
A) an = 9 + 2(n - 1)
B) an = 9 + 2(n + 1)
C) an = 9 + 2
D) an = 9 + 2(n)

Answers

The first term is 9. The common difference is 11 -9 = 13 -11 = 2. The general term has the formula
an = a1 + d(n-1)

Substituting the values above, you have ...
A) an = 9 + 2(n - 1)

What is the area of this triangle? A= bh 2 12/13/5 is what it shows and here are the answers [A] 17 m2, [B] 30 m2, [C] 60 m2, [D] 60 m2, [E] 120 m2,

Answers

Assuming "A= bh 2 12/13/5 "
means
given Area=A=bh/2, and
the triangle has sides 5, 12 and 13.
(see diagram attached).

Since (5,12,13) for a Pythagoras triplet, it is a right triangle.
(13^2=12^2+5^2 => 169=144+25)
The two legs are 5 and 12, respectively b & h.
So the area of the triangle is bh/2=5*12/2=30
If the measures are in metres, then the area is 30 m^2.

I will give you brainliest.

simplify the ratio 120 cm / 1 m.

A 1 / 1

B 2/1

C 5 / 6

D 6 / 5

Answers

The answer is D 6/5
Because 1m = 100cm
When divided gives 6/5 or 1.2

There is 100 cm in 1m so 120cm/ 1m is the same as 120 cm/ 100 cm which you could then simplify by dividing by 20 and get 6/5 so the answer is D

Jorge is standing at a horizontal distance of 25 feet away from a building. his eye level is 5.5 feet above the ground and looking up he notices a window washer on the side of the building at an angle of elevation of 65, how high is the window washer above the ground

Answers

Find x using SOHCAHTOA
tan65 =x/25
x=25tan65
x=53.613ft
Answer is (5.5+53.613)ft
=59.113ft

Ming used the calculations shown to find out how much he would spend on 6 pounds of ground beef if 10 pounds of ground beef cost $25.00. What was Ming’s error?

10 pounds
_________
$25.00

=10 pounds/ 25
__________
$25. 00/25

=0.4
____
1

Unit Price=$0.40
$0.40 x 6 =$2.40

What was Ming’s error?
A. He determined pounds per dollar by dividing 10 by 25 but wrote the unit rate as a dollar value.
B. He divided the numerator and the denominator of the fraction by 25.
C. He made a mistake when finding the quotient of 10 pounds and 25 dollars.
D. He made a mistake when finding the product of $0.40 and 6.

Answers

For this case we have that Ming made the following division:
(10/25) = 0.4
The result of the division is correct numerically.
However, the units of the result are incorrect.
The correct units for this case are given by:
0.4 pound / $
Answer:
A. He determined pounds per dollar by dividing 10 by 25 but wrote the unit rate as a dollar value.

Answer:

The answer would be A. He determined pounds per dollar by dividing 10 by 25 but wrote the unit rate as a dollar value.

Brian’s school locker has a three-digit combination lock that can be set using the numbers 5 to 9 (including 5 and 9), without repeating a number. The probability that the locker code begins with a prime number is %. The probability that the locker code is an odd number is %.

Answers

The possible digits are: 5, 6, 7, 8 and 9. Let's mark the case when the locker code begins with a prime number as A and the case when the locker code is an odd number as B. We have 5 different digits in total, 2 of which are prime (5 and 7).

First propability:
[tex]P_A=\frac{2}{5}=40\%[/tex]

By knowing that digits don't repeat we can say that code is an odd number in case it ends with 5, 7 or 9 (three of five digits).

Second probability:
[tex]P_B=\frac{3}{5}=60\%[/tex]

Select the situation in which one quantity is changing at a constant rate in relation to the other quantity.
a. Barry spends $9 on lunch daily.
b. The market value of a new computer decreases by 6% every year.
c. Nathan's investments increase in value by 13.5% each month.
d. The number of ants in a colony doubles every 8 weeks.

Answers

Choice A is the only one that is changing at a constant rate. The reason is that for all three other choices the new rate is based on a different amount after the percent has been applied or the doubling of the ants has been applied. The price per day for the lunch Is constant because whatever the number of days is the amount would always stay the same for each of those days.

Answer:

A. Barry spends $9 on lunch daily.

Step-by-step explanation:

We are required,

To find the situation in which one constant is changing at a constant rate in relation to the other quantity.

So, according to the options, we have,

A. Barry spends $9 on lunch daily.

Let x= number of days and as the cost of lunch each day is $9

Then, the total cost of the lunch y, is [tex]y=9x[/tex]

Thus, this situation changes the variable with constant rate.

B. The market value of a new computer decreases by 6% every year.

Let, a= fixed initial value of the computer and x= number of years.

Since, the rate of decrease in value = 6% = 0.06

Then, the market value of the computer per year, y, is given by,

[tex]y=a(1-0.06)^x\\\\y=a(0.94)^x[/tex]

Thus, this situation changes the variable exponentially.

C. Nathan's investments increase in value by 13.5% each month.

Let, a= fixed initial investment and x= number of months.

Since, the rate of increase = 13.5% = 0.135

Then, the investment per month, y, is given by,

[tex]y=a(1+0.135)^x\\\\y=a(1.135)^x[/tex]

Thus, this situation changes the variable exponentially.

D. The number of ants in a colony doubles every 8 weeks.

Let, x= number of weeks where 'x' belongs to the se {1,8,16,24,...}.

Since, the number of ants is doubling every 8 weeks.

So, the number of ants in the colony, y, is [tex]y=2^x[/tex]

Thus, this situation changes the variable exponentially.

Hence, the situation that changes the variables with a constant rate is A.

Can anyone please help me I will give you 13 points and make your answer the brainliest.Please help.

Answers

The true statements are ...

2. All squares are rectangles.

3. Not all parallelograms are rectangles.

_____

The attached diagram shows the relationships between various quadrilataral types. The line connecting a lower box to a higher box means "all of the lower box is a higher box." For example, all square are rectangles, and all rectangles are parallelograms.

However, it is typical for a higher box to have several different lower boxes. That is "a higher box may be any of the list of lower boxes or none of them" For example, a parallelogram may be a rhombus or a rectangle or neither.

If 12 is replaced with 3 in the following set, what will happen to the value of the range?

28, 45, 12, 34, 36, 45, 19, 20

It will increase.
It will decrease.
It will stay the same.

Answers

Since the range of a set of numbers is based entirely on the smallest number and the largest number (the largest number minus the smallest), and since 12 is the smallest number, the value of the range will decrease.

Your correct answer is A: it will increase.

Hope this helps. :)

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