Answer:
see explanation
Step-by-step explanation:
Given a parabola in standard form
f(x) = ax² + bx + c ( a ≠ 0 )
Then the discriminant Δ = b² - 4ac informs us about the nature of the zeros
• If b² - 4ac > 0 then 2 real and irrational zeros
• If b² - 4ac > 0 and a perfect square then 2 real and rational zeros
• If b² - 4ac = 0 then 2 real and equal zeros
• b² - 4ac < 0 then zeros are not real
Given
f(x) = 3(x - 4)² - 12 ← expand factor using FOIL
= 3(x² - 8x + 16) - 12 ← distribute parenthesis by 3
= 3x² - 24x + 48 - 12
= 3x² - 24x + 36 ← in standard form
with a = 3, b = - 24 , c = 36 , then
b² - 4ac
= (- 24)² - (4 × 3 × 36
= 576 - 432
= 144 ← a perfect square
Then 2 zeros are real and rational and produce 2 x- intercepts
Classify the following polynomials according to the number of terms. Combine any like terms first.
x^2 + 3x + 2x
x^2 + 5x = Binomial
x^3 + x + 3x^2 - x
x^3 + 3x^2 = Binomial
4x^3 + x + x^2 - 2x
4x^3 + x^2 - x = Trinomial
3x^4 + x - 3x^4 - x
0 = No Polynomial/Zero Polynomial
Hope this helps!
The first given polynomial is binomial.
The second given polynomial is binomial.
The third given polynomial is binomial.
The fourth given polynomial is monomial.
What is polynomial?Polynomials are algebraic expressions that consist of variables and coefficients.
What is monomial?A monomial is an algebraic expression that has only one term.
What is binomial?Binomial is an algebraic expression that contains two different terms connected by addition or subtraction.
What is trinomial give?A trinomial is an algebraic expression that has three non-zero terms.
According to the given question.
We have some polynomials.
If we take the polynomial:
[tex]x^{2} +3x+2x[/tex]
The above polynomial can be written as
[tex]x^{2} + 5x[/tex]
Since, the above polynomial has only two terms therefore it is a binomial.
[tex]x^{3} +x+3x^{2} -x = x^{3} +3x^{2}[/tex]
The above polynomial has only two terms. Hence, the given polynomial is binomial.
[tex]4x^{2} + x + x^{2} -2x\\=5x^{2} -x[/tex]
The given polynomial has only two terms therefore it is binomial.
[tex]3x^{4} + x - 3x^{4} -x\\= 0[/tex]
The given polynomial has only one term therefore it is monomial.
Find out more information about classification of polynomials here:
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Using only the values given in the table for the function f(x) = x^3 - 3x - 2 what is the interval of x-values over which the function is decreasing?
Answer:
3 = 3(x² - 1) We know, any Function f(x) decrease s in interval [a, b] when f'(x) < 0 ... -1 < x < 1. Hence, function f(x) = x³ - 3x - 2 , is decreased in (-1, 1).
For 4 days the temperatures in Alaska at 9:00 a.M. Were 12 degrees, -2 degrees, -6 degrees, and 8.4 degrees, respectively. What was the average temperature?
Answer:
3.1°
Step-by-step explanation:
Given the temperature values :
12 degrees, -2 degrees, -6 degrees, and 8.4 degrees
To obtain the average temperature, take the sum of the temperatures and divide by the number of days
Sum of temperature values : (12 + (-2) + (-6) + 8.4) = 12.4 degree
Sum of temperature / 4
= 12.4 / 4
Average temperature = 3.1 degrees
On a unit Circle, the terminal point of 0 is (sqrt3/2, 1/2) what is 0?
This is a point, so it has x- and y-coordinates. Both of these coordinates are positive, therefore the point must be in the first quadrant.
The pattern for the points on a unit circle is 3 - 2 - 1 starting at 0 and up to pi/2. The pattern for the radian denominators on a unit circle is 6 - 4 - 3 starting at 0 and up to pi/2.
(sqrt(3) / 2, 1/2) = pi / 6 radians
Hope this helps!
Answer:
A. pi/6 radians
Step-by-step explanation:
The ratio of the lengths of the sides of a 30-60-90 triangle is
1/2 : sqrt(3/2) : 1
sin theta = opp/hyp
tan theta = 1/2 / 1
tan theta = 1/2
theta = pi/6 radians
Answer: A. pi/6 radians
hlp pleassssssssssssssssssssss
Answer:
Volume of a cube is s×s×s
hence 7 cube=343
343 is the answer. Hope this helps you. Good luck^_^
154.1 ÷ 0.5 as a mixed number
Answer:
308.2
Step-by-step explanation:
= 308.2
Rewrite the expression in the form x^n:
x^-10/3
---------
x^3
Answer:
x^ (-19/3)
Step-by-step explanation:
x ^ (-10/3) ÷ x^3
We know a^b ÷ a^c = a^(b-c)
x ^ (-10/3) ÷ x^3 = x^(-10/3 - 3) = x^(-10/3 - 9/3) = x^ (-19/3)
In how many ways can 10 people be divided into three groups of 2, 3, and 5 people respectively
Given:
Total number of people = 10
To find:
The number of ways in which 10 people can be divided into three groups of 2, 3, and 5 people respectively.
Solution:
We know that the number of ways to select r items form n times is:
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
The number of ways to select 2 people from 10 is [tex]^{10}C_2[/tex].
The number of remaining people is [tex]10-2=8[/tex].
The number of ways to select 3 people from 8 is [tex]^{8}C_3[/tex].
The number of remaining people is [tex]8-3=5[/tex].
The number of ways to select 5 people from 5 is [tex]^{5}C_5[/tex].
Now, the total number of ways is:
[tex]Total=^{10}C_2\cdot ^{8}C_3\cdot ^{5}C_5[/tex]
[tex]Total=\dfrac{10!}{2!(10-2)!}\cdot \dfrac{8!}{3!(8-3)!}\cdot \dfrac{5!}{5!(5-5)!}[/tex]
[tex]Total=\dfrac{10\times 9\times 8!}{2\times 1\times 8!}\cdot \dfrac{8\times 7\times 6\times 5!}{3\times 2\times 1\times 5!}\cdot 1[/tex]
[tex]Total=45\cdot 56\cdot 1[/tex]
[tex]Total=2520[/tex]
Therefore, the total number of ways is 2520 to divide 10 people into three groups of 2, 3, and 5 people respectively.
Help pls :(
Solve for x.
-4 + 3x = 20
Answer:
x = 8
Step-by-step explanation:
Given
- 4 + 3x = 20 ( add 4 to both sides )
3x = 24 ( divide both sides by 3 )
x = 8
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{-4 + 3x = 20}\\\rightarrow\large\textsf{3x - 4 = 20}\\\\\large\text{ADD 4 to BOTH SIDES}\\\large\textsf{3x - 4 + 4 = 20 + 4}\\\large\text{CANCEL out: \textsf{-4 + 4} because that gives you \textsf 0}\\\large\text{KEEP: \textsf{20 + 4}} \text{ because it gives you the \textsf{x-value}}}\\\\\large\textsf{20 + 4 = \bf 24}\\\\\large\text{DIVIDE 3 to BOTH SIDES}\\\\\mathsf{\dfrac{3x}{3}= \dfrac{24}{3}}\\\large\text{CANCEL out: }\mathsf{\dfrac{3}{3}}\large\text{ because that gives you \textsf 1}[/tex]
[tex]\large\text{KEEP: }\mathsf{\dfrac{24}{3}}\large\text{ because it helps gives you the result of the \textsf{x-value}}\\\\\mathsf{x = \dfrac{24}{3}}\\\\\large\textsf{x= 24}\div \large\textsf{3}}\\\large\textsf{x = \bf 8}\\\\\boxed{\boxed{\huge\text{Therefore, your answer is: \textsf{x = 8}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
cho tam giác ABC. gọi M,N lần lượt là trung điểm AB,AC trên tia đối của tia NM lấy điểm D sao cho N là trung điểm MD, chứng minh
a, CD song song AM
b, CD = MB
d, tam giác BMC= tam giác DCM
e, MN= 1/2 DC
Mình gửi bạn
Bạn xem câu cuối có sai đề không
make g the subject 4m+2g=p
Step-by-step explanation:
4m+2g=p
2g=p-4m
g=(p-4m)/2
Answer:
g = p/2 - 2m
Step-by-step explanation:
4m +2g = p
Subtract 4m from each side
4m -4m +2g = p-4m
2g = p -4m
Divide each side by 2
2g/2 = p/2 - 4m/2
g = p/2 - 2m
the sum of the ages of chukwu and Caroline is 45 years if the difference in their age is 3 years find the age of chukwu (chukwu is older than Caroline)
Step-by-step explanation:
let,the sum of the ages of chukwu & Caroline be X & Y.
now,
X+y=45
X-y=3
(+) (+) (-)
__________
2x=42
or,X=42/2
or,X=21
putting the value of X,
X+y=45
or, 21+y=45
or,y=45-21
or,y=24
therefore,X=21
y=24
pls help me i really need it!
Answer:
A
Step-by-step explanation:
Which of the following shapes is the cross-section for a cone?
O A. Pentagon
O B. Square
O C. Triangle
O D. Circle
Answer:
The choose (D)
D. Circle
I hope I helped you^_^
The required cross-section for a cone is a circle. Option D is correct.
What is a conic section?A conic section is a geometric shape that is obtained by intersecting a cone with a plane. Conic sections include circles, ellipses, parabolas, and hyperbolas.
The type of conic section that is formed depends on the angle of the plane relative to the axis of the cone, as well as the distance of the plane from the vertex of the cone.
Here,
The cross-section of a cone is a circle.
A cross-section is a shape that you get when you slice a 3D object with a plane. If you slice a cone parallel to its base, you get a circle as the cross-section.
Therefore, the correct answer is option D.
Learn more about the conic section here;
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The sum of three numbers is 78. The second number is 10 more than the first, and the third number is two times the second number.
1. Write an equation that will help you determine the 3 numbers.
2. Solve the equation showing all your steps.
3. Tell what the 3 numbers are.
Step-by-step explanation:
a+b+c=78
b=10+a
c=2b
then, we back the first
a+10+a+2b=78
2a+2b=78- 10
2a+2(10+a)=68
2a+2a=48
4a=48
a=12
b=22
c=44
which one is the 25th island of Greece?
1. amorgos
2. sus island
3. the hair of dog
Answer:
obviously sus island
Step-by-step explanation:
What is the measure of m?
Answer:
12
Step-by-step explanation:
bc it is
find the missing length
Answer:
it is an rigjt angle triangle you shoult pythogores therom if you will know it it will be easy to you to understand this question
In figure above, if l1 | | l2 then value of x is:
a) 40°
b) 50°
c) 80°
d) 100°
Answer:
its letter c so 80
Step-by-step explanation:
I hope this help
xpower4 minus 16 bracket b minus c whole power 4
Answer
6372 - power 4
Step-by-step explanation:
help me fast plzzzzzz
Answer:
has been saving is the correct answer I believe
Answer:
"has been saving" is the right answer.
State the equation, in slope-intercept form, of each of the following graphs of linear relations.
Explain how the equation was determined.
Answer: y=80/5x+80
Step-by-step explanation:
At one point graph goes from (0,400) to (25,800). So the y intercept is 400 because that’s where the line was at x=0. 0 to 25 is 25. 400 to 800 is 400. So the equation would be y=400/25x+400. But you can divide all of it by 5 to get y=80/5x+80.
I NEED HELP ASAP
i will award brainlyest
or however you spell it
Answer:
f(x) + 2 is it I am not sure but do not lie
Answer:
I think it's D or C, but am leaning towards D. Don't take my word for it though.
Step-by-step explanation:
f(x-2)
(Do not use my answer though as I am not completely sure since the parent function f(x) might be looking for a certain location where the plus-minus 2 is.)
My reasoning is that I went to a graphing calculator and the first two choices are incorrect where it is something like f(x) + 2 or - 2.
The graph is lower than the parent function meaning it probably involves a negative or positive since the graph is much steeper.
CAN SOMEONE HELP ME PLEASE
A taxi fare is $3 and then $0.40 for every kilometre. A taxi fare is $9 . How far has the taxi travelled?
Answer:
y = 3 + 0.40x
Step-by-step explanation:
Fixed cost of taxi fare = $3
Additional cost = $0.40
Let
y = Total cost
x = number of kilometers
The equation:
Total cost = Fixed cost of taxi fare + (Additional cost * number of kilometers)
y = 3 + 0.40x
=
-1
Use the distributive property with factoring to find the equivalent expression.
33x + 22y = 11 X + y
Answer:
22x + 21y = 0
Step-by-step explanation:
33x + 22y = 11x + y
Subtract y from both sides.
33x + 21y = 11x
Subtract 11x from both sides.
22x + 21y = 0
Find the missing length.
Answer:
hello,
Step-by-step explanation:
12²=(x-16)*16
9=x-16
x=25
Relation metric in a right triangle
SEE QUESTION IN IMAGE
Answer:
42Required probability:
P(≤4) = (18 + 14 + 20 + 16)/(18 + 14 + 20 + 16 + 15 + 17) = 68/100 = 0.6843Required probability:
P(>3) = (20 + 16 + 15 + 17) / (18 + 14 + 20 + 16 + 15 + 17) = 68/100 = 0.6844At least 2 students pass:
P(2 or 3) = (3/5)² + (3/5)³ = 9/25 + 27/125 = 72/125 = 0.57645Number of x's:
x/108 = 4/27x = 108*4/27x = 16Find the missing length indicated
Answer:
x = 240
Step-by-step explanation:
Using the Altitude- on- Hypotenuse theorem
(leg of large triangle)² = ( part of hypotenuse below it) × (whole hypotenuse)
x² = 144 × 400 = 57600 ( take the square root of both sides )
x = [tex]\sqrt{57600}[/tex] = 240
x = 240
Using Pythagoras' theorem on the 3 triangles of sides (as shown in the graphic - the 2 smaller inner triangles and the large main triangle) it can be shown that the height is the square root of the product of both segments of the baseline.
let's call the 2 segments p and q.
p+q = 400
p = 144
q = 400 - 144 = 256
so, as said before, height = sqrt(p×q) = sqrt(144×256) = 192
now the main Pythagoras with the smallest triangle to get x
x² = 192² + 144² = 36864 + 20736 = 57600
x = 240
now, FYI, why is that formula true ?
as we said, we called the segments of the long baseline p and q.
then we can the sides of the main triangle x and y.
and the height is simply h.
so, then we have for the main rectangular triangle
(p+q)² = x² + y²
and for the 2 smaller triangles
x² = p² + h²
y² = q² + h²
=>
p² +2pq + q² = p² + h² + q² + h²
2pq = 2h²
h² = pq
h = sqrt(pq)
and there you have it. just as simple as that.
Bob is hired by Company A and is given an annual salary of $35 000 with a 10% raise
after 1 year. Sam is hired by Company B and is paid $3842.42 per month with a 5% raise
after 1 year. Determine the difference of salary after 1 year.
Step-by-step explanation:
Bob's salary : $35000 per year plus 10% after one year
100% = 35000
1% = 100%/100 = 35000/100 = $350
10% = 10×1% = 10×350 = $3500
so in total, his salary will be $35000+$3500 = $38500 after one year.
Sam's salary : $3842.42 per month plus 5% after one year.
100% = $3842.42 per month. but to make it comparable to Bob's salary, we need to calculate the annual salary.
so, 100% 12×3842.42 = $46109.04
1% = 100%/100 = 46109.04/100 = $461.09
5% = 5×1% = 5×461.09 = $2305.45
so, in total, his salary will be $46109.04+$2305.45 = $