a(t) = (t - k)(t - 3)(t - 6)(t + 3) is a polynomial function of t, where k is a constant. Given that a(2) = 0, what is the absolute value of the product of the zeros of a?

Answers

Answer 1
If a(2) = 0, then k=2. The product of the zeros is
(2)*(3)*(6)*(-3) = -108

The absolute value of the product of zeros of a(t) is 108.
Answer 2
zeros:
t-k=0, t=k
t-3=0, t=3
t-6=0, t=6
t+3=0, t=-3
abs value of the product= abs value of (t*3*6*-3)=54t

Related Questions

Answer to question 3

Answers

If you repeat this polling process numerous times including computing the confidence interval, the true proportion of the population favoring the amendment will fall within the confidence interval 95% of the time.

Can there be a right triangle with side lenghts of 1,2,3

Answers

Nope, it doesn't follow the Pythagorean Theorem.

The admission fee at the county fair is $2 for children and $4 for adults. on a certain day, 2000 people enter the fair and $5000 is collected. using c as the variable to represent the number of children and a as the variable for adults, write a system of equations to determine how many children and how many adults attended. note down this system of equations so that you can use it for the next question.

Answers

a + c = 2000 . . . . . . 2000 people entered the fair
4a +2c = 5000 . . . . $5000 was collected in admission fees

_____
Solving by your favorite method reveals
.. a = 500
.. c = 1500

Triangle ABC has vertices at A(4, 7) , B(13, 7) , and C(9, 11) .

Triangle FGH has vertices at F(1, 1) , G(10, 1) , and H(6, 5) .

Which sequence of transformations shows that triangle ABC and triangle FGH are congruent?

Select each correct answer.




A Translate ​ triangle FGH ​ down 6 units, and then translate ​ triangle FGH ​ left 3 units. ​

B Translate ​ triangle FGH ​ up 6 units, and then translate ​ triangle FGH ​ right 3 units. ​

C Translate ​ triangle ABC ​ up 6 units, and then translate ​ triangle ABC ​ right 3 units.

D Translate ​ triangle ABC ​ down 6 units, and then translate ​ triangle ABC left 3 units.
The coordinates of the vertices of triangle XYZ are given in the table.

X Y Z
(0, −6) (−10, 4) (3, −1)


Triangle XYZ is reflected across the y-axis.

What are the vertices of triangle X′Y′Z′ ?



Enter your answers in the boxes.



X′ : (
, ​
​)

Y′ : (
, ​
​)

Z′ : (
, ​
​)



The coordinates of the vertices of triangle XYZ are given in the table.

X Y Z
(0, −6) (−10, 4) (3, −1)


Triangle XYZ is reflected across the y-axis.

What are the vertices of triangle X′Y′Z′ ?



Enter your answers in the boxes.



X′ : (
, ​
​)

Y′ : (
, ​
​)

Z′ : (
, ​
​) The coordinates of the vertices of triangle XYZ are given in the table.

X Y Z
(0, −6) (−10, 4) (3, −1)


Triangle XYZ is reflected across the y-axis.

What are the vertices of triangle X′Y′Z′ ?



Enter your answers in the boxes.



X′ : (
, ​
​)

Y′ : (
, ​
​)

Z′ : (
, ​
​)



































































Answers

1) F - A = (1, 1) -(4, 7) = (-3, -6). Triangle FGH has been translated left 3 and down 6, corresponding to selection D.

2) Reflecting (x, y) across the y-axis changes it to (-x, y).
.. X' = (0, -6) . . . . . the point maps to itself. It is on the line of reflection.
.. Y' = (10, 4)
.. Z' = (-3, -1)

HOW TO DO THIS? Find value of x

Answers

the value of x can be found using the tangent ratio.

tan 25 = x/5
5 (tan 25) = x
2.33 = x

Hope this helps :)
tan (25) = x / 5
x = 5 * tan (25)
x = 5 * .46631
x = 2.33155



Kareem wants to wallpaper the back wall of his bedroom. The wall is in the shape of a rectangle. Its length is
13 feet and its width is 12
feet. The wallpaper costs $8
for each square foot. How much will wallpaper cost for the wall?

Answers

The first step in solving this problem is to compute for the area of the rectangular wall. The formula in computing the area of a rectangle is:

A = LW

Substituting the given measurements in the problem to the formula:

A = 13 (12)

A = 156

Therefore, the area of the wall is 156 square feet. To compute the wallpaper cost of the wall, you have to multiply the cost per square foot to the total area.

$8 per square foot x 156 square feet = $1,248

Therefore, the wallpaper cost for the wall is $1,248

One day a store sold 29 sweatshirts. White ones cost​ $10.95 and yellow ones cost $ 13.50. In​ all, ​$353.25 worth of sweatshirts were sold. How many of each color were​ sold?

Answers

there would be 10 yellow shirts and 19 white shirts...hope its right...

Subtract the linear expression: (8x + 5) - (2x- 4)

Answers

Remove parenthesis: 8x+5-2x-4. Combine like terms: 8x-2x+5-4.
Solve: 6x+1 if I’m correct.

The single equivalent discount rate of 9/5/4 is .17008. True or False?

Answers

i think its true but i may be wrong

the answer is true. i just had it on a quiz.

Calculate.

0 = x² + 10x + 16

Enter your answers in the boxes.

Answers

x = -2 and x = -8. 

You can get this by factoring the polynomial and solving for x or by using the quadratic formula. 

An instructional video is 4.2 minutes long. How long is the video in seconds? How long is it in hours?

Answers

384 seconds, 0.106 hours
252 seconds, and the hours hang on just a sec! 

The Great Pyramids of Giza, Egypt are dedicated the following pharaohs EXCEPT ___________.
a. Khafre
b. Tutankhamen
c. Khufu
d. Menkaure,

Answers

The Great Pyramids of Giza are dedicated to Khafre, Khufu, and Menkaure. Tutankhamen did not have a pyramid dedicated to him and the tomb he was buried in was even smaller than was typical by that point in Egyptian history for someone of his social status.
Final answer:

The Great Pyramids of Giza in Egypt are dedicated to Khafre, Khufu, and Menkaure, but not Tutankhamen.

Explanation:

The Great Pyramids of Giza in Egypt are dedicated to three pharaohs - Khafre, Khufu, and Menkaure. The pharaoh that is not associated with one of the Great Pyramids is Tutankhamen. Tutankhamen, also known as King Tut, ruled during the 18th dynasty of the New Kingdom but was not part of the Fourth Dynasty that built the pyramids at Giza.

Wally buys nine books that coast $19.50 apiece. How much does Wally spend?

Answers

Hi there!

To solve this problem, we need to multiply the cost of each book by the amount of books Wally bought.

$19.50 × 9 = $175.50

So, the total amount payed was $175.50.

Hope this helps!
you have to multiply  19.50 x 9 = 175.5

What is the area of this figure?



Enter your answer in the box.


units²

Answers

Area of top triangle = 1/2(7)(2) = 7
Area of rectangle = 4 x 7 = 28
Area of bottom triangle = 1/2(7)(2) = 7

Area of figure = 7+ 28 + 7 = 42

answer
42 units²

Answer:

The answer to this is 42 units²

Step-by-step explanation:

solve the system by either elimination or substitution
3x-5y=21
2x+y=1
A.2,-3
B.2,3
C.-2,-1
D.-2,1
My guess is c

Answers

The correct answer is A: x=2 and y=-3. Either method would work, but for example, let's use elimination. If you multiply the second equation by 5, you get: 10x +5y = 5. When you add both equations, you can then cross out both y terms. You are left with one equation that reads: 13x=26. Solving for x gives you 2. You can substitute 2 in for x in either equation and you will receive -3 for your y value.

What number is 32% of 75?



Which of the following equations could be used to solve the problem?


n = 0.32(75)
0.32n = 75
n = 75 ÷ 0.32

This is just a reassurance question It's
n = 75 ÷ 0.32 Right?,

Answers

32% of 75 is 24


Explanation:

A percentage is a value out of 100

32% of 75

32/100*75/1


32/100*75/1   Cancel and Simplify.



8/1*3/1

Answer = 24


2: The following equation used to solved the problem is:

(A):  N = 0.32(75)


Hope this helps.

24 is 32% of 75. The answer can be found by setting up a proportion: n/75 is set equal to 32/100, where x represents 32% of 75. By using cross multiplying and solving for the variable "n" we can determine that n = 24. Therefore, the equation n = 0.32(75) could be used to determine the correct answer. The formula n = 75 ÷ 0.32 is incorrect.

Quadrilateral ABCD is inscribed in circle O.

What is ​ m∠B ​ ?



Enter your answer in the box.

Answers

The measure of angle B is 125 degrees in the given quadrilateral inscribed in circle O.

In a quadrilateral inscribed in a circle, opposite angles are supplementary.

Therefore, we can set up the equation:

∠A + ∠C = 180 degrees

Substituting the given values:

(2x-7) + (x+4) = 180

Combining like terms:

3x - 3 = 180

Adding 3 to both sides:

3x = 183

Dividing both sides by 3:

x = 61

Now we can find ∠B:

∠B = 2x + 3

∠B = 2(61) + 3

∠B = 122 + 3

∠B = 125

Therefore, m∠B is equal to 125 degrees.

To know more about quadrilateral, refer here:

https://brainly.com/question/32841982

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List the angles of triangle DEF in order from smallest to largest measure if DE = 7, EF = 9, and DF = 3.


∠D, ∠E, ∠F


∠E, ∠F, ∠D


∠F, ∠E, ∠D


∠D, ∠F, ∠E

Answers

The angles in order from smallest to largest would be ∠E, ∠F, ∠D.

∠D is opposite side EF.  ∠E is opposite side DF.  ∠F is opposite side DE.  The sides that are the smallest correspond with the smallest angles, and the sides that are the largest correspond with the largest angles.
Answer: The order from smallest to largest is <E, <F, <D

First, you should draw a picture of triangle DEF and label all of the sides. Then, you will have an idea of what the triangle looks like and the relative size of the angles.

You can also look at the side opposite of the angle. The larger the opposite side, the larger the angle.

Can someone give me the answer to the question?

Answers

(7 cm)*(7 cm) = (10 cm)*(x)
x = 49 cm^2/(10 cm)
x = 4.9 cm

IF YOU HELP ME ILL WILL GIVE YOU BRAINLIST AND 50 PONITS HELP ME PLZZZZZ



Which statement or statements are TRUE?

I. The data distribution is skewed
II. The interquartile range is 6
III. The median is 10
A) I only
B) II only
C) I and II only
D) II and III only

Answers

I think the answer is A because the data is skewed to the right 
The median (middle) isn't 10, it's 8 
The interquartile range (IQR) is 7 not 6 because you have to subtract the first and third quartile 13 - 6 = 7 not 6

Hope this helps! ;)

I think the answer is A

10 POINTS + BRAINLIEST ANSWER!!

Given the right triangle PQR below, which of the following is equal to y/x?

A. cos P

B. cos Q

C. tan P

D. tan Q

Answers

C. tanP =QR/QP=y/x
p/s : follow me and I will help you more about maths

The value of tan P = y /x , Option C is the right answer.

What is a Right Angled Triangle ?

A triangle in which one of the sides is 90 degree is called a Right angled Triangle.

A right angled Triangle is given in the question

The sides of the triangle is x and y

The trigonometric ratios are given and it has to be determined that x/ y represents which one of the given option.

The value of tan x =  Perpendicular / Base

y/ x =  Perpendicular / Base for angle P

Therefore , The value of tan P = y /x , Option C is the right answer.

To know more about Right angled Triangle

https://brainly.com/question/3770177

#SPJ2

HELP PLEASE!!?!
5. The half-life of a certain radioactive material is 78 hours. An initial amount of the material has a mass of 790 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 18 hours. Round your answer to the nearest thousandth.,

Answers

The half life is 78 hours and the amount after 78 hours is 395 kg hence time constant is 395 = 790 * e^(p*78) By taking 790 common and natural log on both side ln (395 / 790) = (p*78) -0.6931 = 78*p -0.0088 = p (or -0.88%) Material left after 18 hours is A(18) = 790 * e^(-0.0088*18) A = 673.301 kg

https://brainly.com/question/1800343#:~:text=5.%20D)%20y%3D790(1/2)%5E1/78x%3B%20673.233%20kg

Please show work! Thank you

Answers

Answers:
Factored Form is (x+4)(x+2)
Expanded Form is x^2+6x+8

----------------------------------------------------------
----------------------------------------------------------

Explanation:

The factored form is simply a matter of reading off the values from the given image. There isn't much work to show here.
Along the left side we have x and 4 so x+4 is one of the factors. Along the bottom we have x and 2, so x+2 is another factor
The two factors are (x+4) and (x+2) so that's why the factored form is (x+4)(x+2)

-------------------------------

Let's expand out the factored form

The overall rectangle is broken up into four parts. I'll label the four smaller rectangles as...

Rectangle A in the upper left corner (this rectangle is x by x)
Rectangle B in the upper right corner (this rectangle is 2 by x)
Rectangle C in the lower left corner (this rectangle is x by 4)
Rectangle D in the lower right corner (this rectangle is 2 by 4)

The idea is that adding the areas of rectangles A through D leads us to the overall area for this largest rectangle.

Area of Rectangle A = (length)*(width) = x*x = x^2
Area of Rectangle B = (length)*(width) = 2*x = 2x
Area of Rectangle C = (length)*(width) = x*4 = 4x
Area of Rectangle D = (length)*(width) = 2*4 = 8

Notice we have the like terms 2x and 4x (areas of rectangle C and D respectively). They combine to 2x+4x = 6x

So after adding all the individual areas and combining like terms, we arrive at the fully expanded form of x^2+6x+8

21/80 as a percentage

Answers

21/80 = 0.2625

To get a percentage from a decimal, move the decimal point to the right 2 place values

0.2625 becomes 26.25%

26.25% is your answer

hope this helps

Please help I don’t understand it

Answers

c= number of crickets
g= number of grasshoppers= twice number of crickets= 2c
T= total number of both= 561

If you add the number of crickets and the number if grasshoppers, you'll get a total of 561.

c + g= T
c + g= 561

Now we also know that grasshoppers are 2c (twice the crickets). Substitute 2c for g in the equation to solve for c.

c + g= 561
c + 2c= 561
combine like terms
3c= 561
divide both sides by 3
c= 187 crickets

Substitute number of crickets back in equation to find g.

c + g= 561
187 + g= 561
subtract 187 from both sides
g= 374 grasshoppers

CHECK:
Since grasshoppers are twice the number of crickets, then multiplying the number of crickets by two should equal the number of grasshoppers.
187 * 2= 374
374= 374

ANSWER: 187 crickets and 374 grasshoppers

Hope this helps! :)

What is the trigonometric ratio for cosD ?

Enter your answer, as a simplified fraction.

Answers

we know that cosine(cos) is the = adj/hyp
in our case
cos D=21/75=7/25

What is the value of x

Answers

well i atleast know its not 10 lol
Hello,

Answer A x=5 since

x/(x+5)=(x-2)/(x+1)==>x²+x=x²-2x+6x-10==>2x=10==>x=5

I don't understand how to do this one, any help??


Is it a.?

Answers

C, because the equation of the table is y=80x. The equation for the graph is y=45x. When x is 11, you have 880 and 495. The difference is 385.
c because you multiply than divide. find the slope for both

The 9 officers of the Student Council are going on a trip to an amusement park. Each student must pay an entrance fee plus $5 for meals. The total cost of the trip is $225. Solve the equation 9(e + 5) = 225 to find the cost e of the entrance fee for each student. Question options: A) $25 B)$14 C) $45 D) $20

Answers

D) $20 because if you plug it in to the equation it equals $225

Answer:

The Answer to this question is $20

Step-by-step explanation:

9 x 5 = $45

225 - 45 =180

180/9 =20

The function y = 41 ? 0.95x models the difference (in minutes) between men's and women's finishing times for the boston marathon. the number of years since women first officially ran the race in 1972 is represented by x.

a. does the exponential function represent growth or decay?

b. estimate the difference between finishing times in 1990.

c. predict the difference between finishing times in 2005.

Answers

We are given a function:
[tex]y=41* 0.95^{x} [/tex]

a. Does the exponential function represent growth or decay?
To find out if this is growth or decay we need to observe number that is connected with x. If number is less than 1 we have decay and if it is greaer than 1 we have growth.
In our case we have number 0.95 which is less than 1 so we have decay.

b. Estimate the difference between finishing times in 1990.
x represents the number of years since 1972.
[tex]x=1990-1972=18[/tex]
Now we insert this number into equation to get solution.
[tex]y=41* 0.95^{18} = 16.29[/tex]

c. Predict the difference between finishing times in 2005.
[tex]x=2005-1972=33[/tex]
[tex]y=41* 0.95^{33} = 7.55[/tex]
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