Answer:
The polynomial is:
[tex]p(x) = x^3 + 2x^2 - 3x + 20[/tex]
Step-by-step explanation:
A third degree polynomial can be written in function of it's zeros [tex]x_1, x_2, x_3[/tex] the following way:
[tex]p(x) = a(x - x_1)(x - x_2)(x - x_3)[/tex]
In which a is the leading coefficient.
Integer coefficient that have zeros: 1+2i, 1-2i, -4
Leading coefficient: 1
So
[tex]p(x) = 1(x - (1+2i))(x - (1-2i))(x - (-4))[/tex]
[tex]p(x) = (x - 1 -2i)(x - 1 + 2i)(x + 4)[/tex]
[tex]p(x) = ((x-1)^2 - (2i)^2)(x + 4)[/tex]
[tex]p(x) = (x^2 - 2x + 1 - 4i^2)(x + 4)[/tex]
Since [tex]i^2 = -1[/tex]
[tex]p(x) = (x^2 - 2x + 1 + 4)(x + 4)[/tex]
[tex]p(x) = (x^2 - 2x + 5)(x + 4)[/tex]
[tex]p(x) = x^3 + 4x^2 - 2x^2 - 8x + 5x + 20[/tex]
[tex]p(x) = x^3 + 2x^2 - 3x + 20[/tex]
Pythagorean’s theorem
Step-by-step explanation:
Given
Hypotenuse (h) = 7
base (b) = 4
perpendicular (p) =?
Using Pythagoras theorem we get,
p = √h² - b²
= √7² - 4²
= √33
= 5.74
Hope it will help :)❤
p = a
a = 5.74 or u can write
a = √33
Answer:
5.74
Step-by-step explanation:
a=?
b=4
c=7
a^2=c^2-b^2
=7^2-4^2
=49-16
=33
a=√33
a=5.74
Which table matches the rule “subtract 4 from the input number"?
Input 8 9 10 13
Output 12 13 14 17
А
Input 12 13 14 17
Output 8 9 10 13
B
Input 8 9 10 13
Output 14 15 16 17
Input 12 15 16 19
Output 8 9 10 13
Answer:
B
Step-by-step explanation:
You just subtract it by 4. 12-4=8 etc.
A shirt is originally priced at $24.50 a shirt goes on sale for 30% off the original price how much money to the nearest cent does the shirt cost including 7% tax on the sale price
Answer:
7.86 is the answer
Step-by-step explanation:
30% of 24.50 is 7.35.
7.35+ 7% is 7.86
7.86 to the nearest cent is 7.86
12. Quadrilateral ABCD is located at A(-4,-2), B(0, -2), C(1, 2), and D(-3,2). What is
the most specific classification of ABCD?
PLEASE HELP ???
Answer:parallelogram
Step-by-step explanation:
20 POINTS AND BRAINLIEST FOR CORRECT!!!!
3 1/3 OF 10
Answer:
33.333333333
Step-by-step explanation:
simply turn 3 1/3 into an improper fraction by multiplying the denominator by the coefficient and adding the numerator to get 10/3, which simplifies to 3.3333 and multiply it by 10 and you get 33.3333.
I really need help please
Answer:
-16y-6
=2(-8y-3)
2x (-8y)= -16y
2x(-3) = -6
Answer:
1) -8y
2) -3
Hope this helps!
3
45 X
Pleaseee help meeee
Answer:
135..........................
Answer: 45*3= 135
135 is the answer for 45*3.
PLEASE HELP !! Select all the correct answers.
Janine needs to calculate the value of log12 81
Which expressions could she input into her calculator to find this value?
Answer: In 81/ In 12 AND log 81/log 12
Step-by-step explanation: PLATO ANSWER I got 100%
To solve the problem we must know about the change of base rule for Logarithm.
What is the change of base rule for Logarithm?The change of base rule for Logarithm helps us to change the base of any logarithmic expression to any other logarithmic expression.
[tex]log_ab = \dfrac{log_x b}{log_x a}[/tex]
where x is any base.
The expression can be expressed as [tex]\dfrac{log\ 81}{log\ 12}[/tex].
Given to us
[tex]log_{12}81[/tex]Change of base rule[tex]log_{12}81\\[/tex]
use the change of base rule, [tex]log_ab = \dfrac{log\ b}{log\ a}[/tex],
[tex]log_{12}81=\dfrac{log\ 81}{log\ 12}[/tex]
Hence, the expression can be expressed as [tex]\dfrac{log\ 81}{log\ 12}[/tex].
Learn more about Logarithm:
https://brainly.com/question/7302008
Builder’s Warehouse has a clearance on overstocked merchandise. A picnic table that usually sells for $167 is on sale for $149. What is the markdown?
167-149= The answer is 18
HELPPP I NEED HELP DUE VERY SOONNN
Answer:
x . 1 . 3 . 5 . 7 . 9
y . 6 . 18 . 30 . 42 . 54
Step-by-step explanation:
X-values are the odd numbers
Y-values are the corresponding x-values multiplied by 6
What is the area of the figure below?
43 in
3 in
48 in 2
5 in.
68 in 2
1
88 in 2
5 in
3 in
3 in
7 in,
Answer:
68in
Step-by-step explanation:
I ready test
Answer: 68
Step-by-step explanation:
‘Multiply all of them and boom
I need help Im helping my lil sis but im to lazy to help her out so can someone answer?
Shelly ate 7/10 of the gummy worms and Max ate 11/100
Answer: ok it is 81/100.
Step-by-step explanation:Just add them together which gives you 81/100 .chnage 7/100 to 70/100 then combine 11/100 which equals 81/100.
:)
multiply (-18)(-13) its for usatestprep
Answer:
Step-by-step explanation:
Here you go mate
Step 1
(-18)(-13) Equation/Question
Step 2
(-18)(-13) Multiply
234
Answer
234
A cow can be milked in 5 minutes, but it must be milked twice a day. If 6 cows can be milked at a time, how many cows can be milked in 10 minutes?
answer: 12
explanation:
you can milk 6 in five minutes so you multiple 6 by to because 10 is 5 two times
If the equation of a line is 4x + 4y = 1 and equation of a second line is x + y = -8 which of the following is true
Answer:
Step-by-step explanation:
Two lines are perpendicular. The equation of the first line is y = 4x + 1. Which of the following cannot be the equation of the second line? A. y = -1/4x -2 B. x - 4y = -2 C. x + 4y = 2 D. 8y = -2x - 5
what is the complement of rolling a 3 on a die
Answer:
Part of a train timetable is shown.
Aberystwyth
Shrewsbury
Birmingham
08 30
10 17
12 30
14 19
13 55
16 05
17 20
a)
Bob catches the 12 30 train from Aberystwyth. He arrives in Shrewsbury 8 minutes late. What time does he arrive in Shrewsbury?
b) How long is Bob's journey from Aberystwyth to Shrewsbury? Give your answer in minutes.
minutes
11 30
15 30
Judy catches the 12 30 train from Aberystwyth.
She arrives in Shrewsbury on time.
She attends a job interview.
She gets back to Shrewsbury station 1 hour and 50 minutes later. Is she back in time to catch the 16 05 train to Birmingham?
You must show your working.
Mrs. Smith has a total of 25 kids in her class. There are 3 more boys than there are girls. Write a system of equations to model this. Use b to represents the boys and g to represent the girls.
Answer:
b + g = 25
b = g + 3
Step-by-step explanation:
Let b = number of boys.
Let g = number of girls.
"Mrs. Smith has a total of 25 kids in her class."
b + g = 25
"There are 3 more boys than there are girls."
b = g + 3
The system of equations is:
b + g = 25
b = g + 3
HELP ASAP-The girls’ soccer team won 80% of its games this season. They won 12 games. -The boys’ soccer team won 70% of its games this season. They won 14 games. How many games did each soccer team play this season?
Answer:
12 and 14
Step-by-step explanation:
15 - 20% = 12
20 - 30% = 14
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When is it appropriate to use the paired t test (involving the mean of the differences)? A. When two independent samples are compared. B. When two dependent samples are compared. C. When four samples are compared at once. D. When any two samples are compared.
Answer:
B. Two dependent samples are compared
Step-by-step explanation:
We use it when we are comparing Two dependent samples. The paired t-test can be likened to the repeated measures ANOVA test. Both of these two test are useful when comparing how a static group does in different test conditions.
But the difference between these two are:
We use the paired t-test if the explanatory variable has two levels.
While the Repeated measures ANOVA is used when the explanatory variable has greater than two levels.
I will mark you brainliest
Answer:
[tex](15s)^6[/tex] is the same as [tex]15^6[/tex] × [tex]s^6[/tex]
The above statement can be proven by a rule related to exponents that states: [tex](ab)^c = a^c[/tex] × [tex]b^c[/tex][tex]3s^4[/tex] × [tex]5s^2[/tex] = [tex]15s^6[/tex]
(Work for the equation above ---> You would multiply the 3 and 5 together (3 x 5 = 15) and then multiply the s terms together [tex]s^4[/tex] x [tex]s^2[/tex] , and this can be done using the exponent rule --> [tex]a^b[/tex] x [tex]a^c[/tex] = [tex]a^{b+c}[/tex]. This means that [tex]s^4[/tex] x [tex]s^2 = s^{4+2} = s^6[/tex]) This results in [tex]15s^6[/tex][tex]15s^6 \neq 15^6[/tex] x [tex]s^6[/tex]
Hope this helps in any way!! :D
Locate and classify all the critical points of the function. (If an answer does not exist, enter DNE.)
f(x, y) = 2x² + 3y² + 4
Answer:
Step-by-step explanation:
f(x,y)=2x2+3y2−4x−1 ⇒ ∇f =⟨4x−4,6y⟩=⟨0,0⟩ ⇒ x=1, y = 0. Thus (1,0) is the only critical point of f, and it lies in the region x2+y2<16.Ontheboundary,g(x,y)=x2+y2=16 ⇒ λ∇g=⟨2λx,2λy⟩,so6y=2λy ⇒ eithery=0orλ=3. Ify=0,then x=±4;ifλ=3,then4x−4=2λx ⇒ x=−2andy=±2√3. Now f(1,0) = −3, f(4,0) = 15, f(−4,0) = 47, and f−2,±2√3 = 51. Thus the maximum value of f(x,y) on the disk x2+y2 ≤ 16 is f−2,±2√3 = 51, and the minimum value is f (1, 0) = −3.
6 in
4 in
4 in.
What is the surface area of the right square pyramid?
Answer:
48in
Step-by-step explanation:
6 x 4 x 4
96
divide it by 2
48
Answer:
48
Step-by-step explanation:
grhgbfjsbrvgjxbwifbcozbwicovbsnw
Given the figure below, which of the following points name a line segment, a line, or a ray?
point B and point C
point A and point C
point D and point A
point E and point A
Answer:
Point a and point c
i dont know anything else
Answer:
a and c
Step-by-step explanation:
plz give me brainliest
The price paid for a $4.50 pen after a 60% discount is applied
Answer:
1.80
Step-by-step explanation:
trust me 100% sure
If point C is the circumcenter, find each missing value(picture attached)
Answer:
is this a test > : (
Step-by-step explanation:
Answer:
f
Step-by-step explanation:
Find two ratios equivalent to the ratio in Exercise 1.
Answer:
12:26, 24:52 :D
Mrs. Smith bought 4 dozen doughnuts and paid a total of $13.92. What was the cost of 1 doughout
. A. $0.29
B. $3.48
C. $0.35
D. $1.16
Answer:
A $0.29
Step-by-step explanation:
4 dozen donuts is 48 donuts. (A dozen is 12 so 4 times 12 is 48). $13.92 divided by 48 is $0.29.
HELP NOW PLZ U GET POINTS!!!
Answer:
3
is the answer
Answer:
3
Step-by-step explanation:
What is the y-intercept
of this line?
please help asap
Answer: 9 because of the (0,9)
Step-by-step explanation:
Do not round your answer. Type in just the number. 0.48 is what % of 1 .6
Answer:
0.00768
Step-by-step explanation:
Answer:
30%
Step-by-step explanation:
1.6÷100=0.016
1% - 0.016
0.48÷0.016=30