Answer:
The common difference is -1/2
Step-by-step explanation:
we know that
In an Arithmetic Sequence the difference between one term and the next is a constant and is called the common difference
we have
a1=2/3
a2=1/6
a3=-1/3
a4=-5/6
so
a2-a1=1/6-2/3=-1/2
a3-a2=-1/3-1/6=-1/2
a4-a3=-5/6-(-1/3)=-5/6+1/3=-1/2
therefore
The common difference is -1/2
The EU has challenged the U.S."s position in the global economy. True or False
Answer:
False
Step-by-step explanation:
EU and the US are very good friends and they often trade with them.
Answer:
The answer to your question is True
Step-by-step explanation: Because The EU is largely viewed as a cornerstone of European stability and prosperity. For much of the last decade, however, many EU countries have faced considerable economic difficulties.
Hope this helps :)
And please mark my answer as the brainliest
On a graphing calculator, you can use the function normalcdf(lower bound, upper bound, μ, σ) to find the area under a normal curve for values of x between a specified lower bound and a specified upper bound. You can use −1E99 as the lower bound to represent negative infinity and 1E99 as the upper bound to represent positive infinity. Suppose that cans of lemonade mix have amounts of lemonade mix that are normally distributed with a mean of 350 grams and a standard deviation of 4 grams. What percent of cans have less than 362 grams of lemonade mix?
__% of cans have less than 362 grams of lemonade mix.
Answer:
99.87% of cans have less than 362 grams of lemonade mix
Step-by-step explanation:
Let the the random variable X denote the amounts of lemonade mix in cans of lemonade mix . The X is normally distributed with a mean of 350 and a standard deviation of 4. We are required to determine the percent of cans that have less than 362 grams of lemonade mix;
We first determine the probability that the amounts of lemonade mix in a can is less than 362 grams;
Pr(X<362)
We calculate the z-score by standardizing the random variable X;
Pr(X<362) = [tex]Pr(Z<\frac{362-350}{4})=Pr(Z<3)[/tex]
This probability is equivalent to the area to the left of 3 in a standard normal curve. From the standard normal tables;
Pr(Z<3) = 0.9987
Therefore, 99.87% of cans have less than 362 grams of lemonade mix
In a kitchen there are three containers that can hold different quantities of water, as shown in the figure below:
Three containers of the same shape but different sizes are shown, starting with the shortest and ending with the longest. The following quantities are written below the containers. x minus 10 liters below the first, x minus 5 liters below the second, and x liters below the third.
How many liters of water can the three containers hold in all?
x − 15
3x − 15
x3 + 50
3x3 − 15
Answer:
3x-15
Step-by-step explanation:
(x-10)+(x-5)+(x)=3x-15
3x - 15
Simply add the different container sizes together. The first container holds x - 10 liters, the second holds x - 5 liters, and the third holds x liters.
(x - 10) + (x - 5) + x
Because of the associative property of Addition, we can remove the parentheses.
x - 10 + x - 5 + x
Because of the communicative property of addition, we can reorder the terms so that the like terms are next to each other.
x + x + x - 10 - 5
Now, combine the x’s.
3x - 10 - 5
Finally, subtract -10 minus - 5.
3x - 15
Match each description with its symbolic representation.
1. P(A)
2. PAB)
3. P(AUB)
The probability that event A occurs
given the fact that event B occurs
The probability that either event A
or event B occurs
The probability that both events A
and B do not occur together, but either
may occur by itself
The probability that neither event A
or event B occurs
The probability that event A occurs
The probability that both event A
and event B occur
4. 1 - P(ANB)
5. 1- P(AUB)
6. P(AIB)
NEYT QUESTION
ASY OR WIP
TURN IT IN
Answer:
i) P(A) ; The probability that event A occurs
ii) P(AB) ; The probability that both event A and event B occur
iii) P(AUB) ; The probability that either event A or event B occurs
iv) 1 - P(ANB) ; The probability that both events A and B do not occur together, but either may occur by itself
v) 1- P(AUB) ; The probability that neither event A or event B occurs
vi) P(AIB) ; The probability that event A occurs given the fact that event B occurs
Step-by-step explanation:
i)
P(A) simply represents the probability that an event A will occur. This event could be passing an examination, having snow in summer, arriving to work on time and so forth.
ii)
P(AB) is simply the probability that both event A and event B do occur. This is usually given by the product of the individual probabilities. Event A could be rolling a 6 in one throw of a fair die while B could be the event that a fair coin lands heads in a single toss.
iii)
P(AUB) refers to the probability that either event A or event B occurs. This is read out as the probability of A union B. This is usually given by the sum of the individual probabilities.
iv)
1 - P(ANB) is the probability that both events A and B do not occur together, but either may occur by itself. P(ANB) is the probability that both events A and B occur together. This is read out as the probability of A intersection B. Therefore implying that 1 - P(ANB) is simply the probability that either event A or B occurs but A and B can not occur together.
v)
1- P(AUB) refers to the probability that neither event A or event B occurs. Earlier we defined P(AUB) as the probability that either event A or event B occurs. 1- P(AUB) simply the complement of P(AUB).
vi)
P(AIB) refers to the probability that event A occurs given the fact that event B occurs. This is a conditional probability event which evaluates the likelihood of an event A occurring given that an associated event B has already occurred
Jordan is making a beaded necklace two thirds of the beads she uses are red and 4/21 of the beads are blue she wants the rest to be white what fraction of the beads should be white
2/3 - Red
4/21 - Blue
Change the red fraction so both fractions will have the same denominator
2/3 change to 14/21
Add blue and red together
14/21 + 4/21 = 18/21
Then subtract it from the total to get the white beads
21/21 - 18/21 = 3/21
Simplify it to get 1/7
Ans : 1/7
Fraction of white beads used is 1/7.
What is fraction?A number expressed as a quotient, in which a numerator is divided by a denominator.
Given:
red beads used = 2/3 = /1
blue beads used = 4/21
Total beads other than white
=14/21 + 4/21
= 18/21
N/ow, fraction of the beads should be white
=1- 18/21
=21/21 - 18/21
=3/21
=1/7
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Given cos theta = √3/4 and sin theta < 0. What is the value of sin theta?
Answer:
[tex] \sqrt{ \frac{13}{16} } [/tex]
Step-by-step explanation:
[tex]cos \: theta = \frac{ \sqrt{3} }{4} \\ sin \: theta = \sqrt{1 - {cos}^{2} theta} \\ = \sqrt{1 - {( \frac{ \sqrt{3} }{4} ) }^{2}} \\ = \sqrt{1 - \frac{3}{16}} \\ = \sqrt{ \frac{13}{16} } [/tex]
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identity
• sin²x + cos²x = 1 ⇒ sin x = ± [tex]\sqrt{1-cos^2x}[/tex]
Since sinΘ < 0 , then
sinΘ = - [tex]\sqrt{1-(\frac{\sqrt{3} }{4})^2 }[/tex]
= - [tex]\sqrt{1-\frac{3}{16} }[/tex]
= - [tex]\sqrt{\frac{13}{16} }[/tex] = - [tex]\frac{\sqrt{13} }{4}[/tex]
Graph linear equation -3y=2x-7
Answer:
Find the attached
Step-by-step explanation:
We are given the following linear equation;
-3y = 2x - 7
In order to graph it, we need to determine at least 3 pairs of points that lie on the line;
we first solve for y by dividing both sides of the equation by -3;
y = (-2/3)x + 7/3
let x be 3;
y = (-2/3)*3 + 7/3
y = 1/3
(3, 1/3)
let x be 6;
y = (-2/3)*6 + 7/3
y = -5/3
(6, -5/3)
let x be 9;
y = (-2/3)*9 + 7/3
y = -11/3
(9, -11/3)
Using the three set of points we graph our linear function. Find the attached;
Find the discount rate
Retail Price: $27.99
Discount: $12
Sale Price: $15.99
(Please show your work)
we'd do the same as before on this one as well.
if we take 27.99 to be the 100%, what is 12 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 27.99&100\\ 12&x \end{array}\implies \cfrac{27.99}{12}=\cfrac{100}{x}\implies 27.99x=1200 \\\\\\ x=\cfrac{1200}{27.99}\implies x\approx 42.87[/tex]
The discount rate can be determined by dividing the discount by the retail price, then multiplying by 100 to get the percentage. In this instance, the discount rate calculates to be approximately 42.87%.
Explanation:To find the discount rate, you must first understand that it is the difference between the retail price and the sale price, divided by the retail price, and then multiplied by 100 to turn it into a percentage.
In this case, let's use the numbers from the problem. The retail price is $27.99 and the discount is $12, leaving a sale price of $15.99. We already know the discount is $12, so to find the rate we divide $12 (the discount) by $27.99 (the original price), and then multiply by 100.
Doing the calculation, ($12/$27.99) * 100 = approx. 42.87%. So the discount rate is approximately 42.87%.
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Write the coordinate pairs of 3 points that can be connected to construct a line that is 5 1/2 units to the right of and parrallel to the y-axis.
Answer:
(5 1/2, 1), ( 5 1/2, 2) and (5 1/2, 3).
Step-by-step explanation:
The x coordinates will all be 5 1/2 so we could have 3 points with coordinates:
(5 1/2, 1), ( 5 1/2, 2) and (5 1/2, 3).
using a hose, katelyn is spraying water into the air and initial velocities of 48 feet per second. the function h(t)=-16t^2+48t+4 represents the path of the water from the hose. what is the maximum height of the water?
36 feet
40 feet
44 feet
48 feet
Check the picture below.
so then, the highest point will be at the y-coordinate of its vertex.
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+48}t\stackrel{\stackrel{c}{\downarrow }}{+4} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\bf \left( \qquad ,~~4-\cfrac{48^2}{4(-16)} \right)\implies \left( \qquad ,~~4+\cfrac{2304}{64} \right)\implies (\qquad ,~4+36) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (\qquad ,~~\stackrel{\stackrel{\textit{how high}}{\textit{it went}}}{40})~\hfill[/tex]
find the midpoint of the segment with the given end points D(5,1) and E(13,11)
Answer:
The midpoint is (9,6)
Step-by-step explanation:
The midpoint is just the average of the two end points.
x: (5 + 13)/2 = 18/2 = 9
y: (1 + 11)/2 = 12/2 = 6
The midpoint is (9,6)
What are the outcomes in a or b?
Answer:
its c
Step-by-step explanation:
Answer b:
Step-by-step explanation:
1,35,36,37,37,38 mean median mode
Answer:
The answers are already in order, so it makes this more simple to solve. To find the mean of all those numbers, you must add all the numbers up, then divide by the numbers that is given. In which this problem, it gives 6 numbers.
So, 1+35+36+37+37+38= 184. Then, divide it 184/6= 30.6. The mode is the number that occurs the most in that set of numbers. In this case, it would be 37. The median is basically the number in the middle when the set of numbers is ordered from least to greatest. 1,35,36,37,37,38 (here's a hint: cross it off on each side) If there is no obvious middle number, in this case because we have an even set of numbers, we can calculate the median by taking the mean of the 2 middlemost terms and: 36, 37.
36+37= 73
After that, divide by 2.
73/2= 36.5
Answer:
Mean=30[tex]\frac{2}{3}[/tex] Median= 36.5 Mode= 37
Step-by-step explanation:
Mean= You add up all of the numbers and then divide by 6.
Median= You go in from the right and the left till you are in the middle (for an even number of data points you add the two data points together and then divide by 2).
Mode= It is the most common number.
Please help right away
Answer:
D) 5985
Step-by-step explanation:
Total area: 150×100 = 15000
Area for stars: 6×6 = 36
Total area - area for stars = area for fans
15000-36= 14964
14964ft² for fans, each takes up 2.5 ft²
14964 ÷2.5 = 5985.6 fans
Since we can't have 0.6 of a person, we round down to 5985 fans
Answer:
5,985 fans
Step-by-step explanation:
First you will need to get the floor area of the store
The dimensions are:
150' by 100'
This is 150 ft by 100 ft
Area would be:
Side x side (Assuming that the floor area is a quadrilateral)
150 ft x 100 ft = 15000 ft²
Next we solve for the area of the stars only:
6' by 6'
Side x side
6 ft x 6 ft = 36 ft²
So here we subtract the stars only area from the total floor area:
15,000 ft² - 36 ft² = 14,964 ft²
This is the floor area that the fans can occupy.
Next since the fire marshal said 1 person must occupy an area no less than 2.5ft², we divide the floor area for fans by the requirement.
14,964 ft² = 5,985.6 fans
2.5ft²
Since we cannot have a decimal for people, we need to round it down. If it goes beyond 5,985.6 that means we do not meet the minimum requirement of 2.5 ft² per person. So we need to round it down, to the nearest whole number, the answer would be:
5,985 fans.
What are the solutions of the equation x4 + 6x2 + 5 = 0? Use u substitution to solve.
x = i and x = 5
x=t i and x = = 15
x=+ -1 and x = 1 -5
X= + -1 and x = 1 - 5
Answer:
x = i and x = i[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Given
[tex]x^{4}[/tex] + 6x² + 5 = 0
Using the substitution u = x², then
u² + 6u + 5 = 0 ← in standard form
(u + 1)(u + 5) = 0 ← in factored form
Equate each factor to zero and solve for u
u + 1 = 0 ⇒ u = - 1
u + 5 = 0 ⇒ u = - 5
Convert solutions back into terms of x
x² = - 1 ⇒ x = [tex]\sqrt{-1}[/tex] = i
x² = - 5 ⇒ x = [tex]\sqrt{-5}[/tex] = i[tex]\sqrt{5}[/tex]
Given y=x2 + 9x + 20 find the zeroes.
Answer:
x=-5 x=-4
Step-by-step explanation:
y=x^2 + 9x + 20
We need to factor the equation
What 2 numbers multiply to 20 and add to 9
4*5 = 20
4+5 =9
y=(x+5) (x+4)
To find the zero's we set the equation equal to zero
0= (x+5) (x+4)
Using the zero product property
x+5 = 0 x+4=0
x=-5 x=-4
How can we use theorems about the angles formed by transversals to help ensure that lines are parallel in the design and construction of real-world structures?
Answer:
We can use this knowledge in planning of cities
Step-by-step explanation:
The transversal is a line that intersects two or more parallel lines.Angles with similar characteristics are formed when this occurs.
In city planning, streets can be designed to resemble parallel lines with roads that do not meet.However, other roads can be constructed to allow people on the other street to cross to neighboring streets.Such roads allowing this access can be viewed as transversal.
The areas where street roads meet the transversal roads have similar angle characteristics thus could be used for CCTV cameras for surveillance and traffic lights positioning.
Carmen has 54 golf balls. He wants to put the same number of balls into each of
9 buckets. What multiplication sentence can Carmen use to find how many balls
to put in each bucket?
Answer:
Step-by-step explanation:
So, carmen has 54 golf balls. He wants to put the same number of balls into each of 9 buckets.So, 54 divided by 9 is 6
the answer is 6
Answer:
9*6=54
Step-by-step explanation:
54÷9=6. You must reverse the equation to make it multiplication. There will be 6 balls in each bucket.
6x(x − 4) − 16x2 − (9x − 1)?
A.
-10x2 − 33x + 1
B.
10x2 − 33x + 1
C.
-10x − 33x + 1
D.
-10x2 + 33x + 1
Answer:
[tex]\large\boxed{A.\ -10x^2-33x+1}[/tex]
Step-by-step explanation:
[tex]6x(x-4)-16x^2-(9x-1)\qquad\text{use the distributive property}\\\\=(6x)(x)+(6x)(-4)-16x^2-9x-(-1)\\\\=6x^2-24x-16x^2-9x+1\qquad\text{combine like terms}\\\\=(6x^2-16x^2)+(-24x-9x)+1\\\\=-10x^2-33x+1[/tex]
The expression simplifies to -10x^2 - 33x +1, following the distribution and combination of like terms.
The given question asks to simplify the expression 6x(x − 4) − 16x2 − (9x − 1). To solve, we follow these steps:
Distribute the 6x across the (x-4) to get 6x2 - 24x.Combine like terms: 6x2 - 24x - 16x2 - 9x + 1.Simplify the expression to -10x2 - 33x + 1.Therefore, the correct option is A. -10x2 − 33x + 1.
Question 7
Which shape is a rectangle?
A rectangle is a 4-sided flat shape with straight lines where all interior angles are rights angles (90°)
A shape that has two long sides &’ two short sides .
a roller coaster has a height of 325 feet before it's first hill, and the bottom of the hill is thirty feet off the ground. what is the height of the drop?
Subtract the 30 feet from the overall height:
325 - 30 = 295
The height of the drop is 295 feet.
Answer:
295 hope this helps!!
Step-by-step explanation:
Can someone please just give me a formula for solving this? Thank you.
When baking a cake, you have a choice of the following pans: a round cake pan that is 2 inches deep and has a 7 inch diameter.
a 6 inch x9 inch rectangular cake pan that is 2 inches deep.
A. which of these pans has the larger value? Justify your answer
Since you're looking for the volume of each...
Circle: you want to find the area (πr^2) times height
Rectangle: l×w×h
If the coordinates of point A are (8 , 0) and the coordinates of point B are (3 , 7), the y-intercept of is
Answer:
As a fraction: [tex]y=\frac{56}{5}[/tex]
As a decimal: [tex]y=11.2[/tex]
As an ordered pair: [tex](0,\frac{56}{5} )[/tex] or [tex](0,11.2)[/tex]
Step-by-step explanation:
First we are using the slope formula to find the equation of our line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where
[tex]m[/tex] is the slope of the line
[tex](x_1,y_1)[/tex] are the coordinates of the first point
[tex](x_2,y_2)[/tex] are the coordinates of the second point
our first point is (8, 0) and our second point is (3, 7), so [tex]x_1=8[/tex], [tex]y_1=0[/tex], [tex]x_2=3[/tex], and [tex]y_2=7[/tex].
Replacing values:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{7-0}{3-8}[/tex]
[tex]m=\frac{7}{-5}[/tex]
[tex]m=-\frac{7}{5}[/tex]
Now, to complete the equation of our line (and find its y-intercept), we are using the point slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
Where
[tex]m[/tex] is the slope
[tex](x_1,y_1)[/tex] are the coordinates of the first point
Replacing values:
[tex]y-0=-\frac{7}{5} (x-8)[/tex]
[tex]y=-\frac{7}{5} x+\frac{56}{5}[/tex]
Now, in a line of the form [tex]y=mx+b[/tex], [tex]b[/tex] is the way intercept. We can infer form our line that [tex]b=\frac{56}{5}[/tex], so the y-intercept of the line joining the points (8, 0) and (3, 7) is [tex]\frac{56}{5}[/tex].
during football practice a football player kicks a football. the height h in feet of the ball t seconds after it is kickedcan be modeled by thr function h=-4(4t-11). how long is the football in the air?
The football, kicked by a football player during a practice, is in the air for approximately 3.79 seconds based on the model h = -4(4t - 11)^2.
Explanation:The question asks for the duration that the football is in the air. This problem involves solving a quadratic function to determine the time when the height of the ball is zero, i.e., when it hits the ground again. The mentioned equation and given information form a quadratic equation.
The equation h = -4(4t - 11)^2 models the height of the football at any given time. The football is on the ground when h = 0. If we substitute h = 0, the equation becomes -4(4t - 11)² = 0. Using the quadratic formula, we find two solutions t = 0.54 s and t = 3.79 s.
As we are looking for the total time that the football is in the air, we are interested in when it falls back to the ground which corresponds to the larger solution. Therefore, the football is in the air for approximately 3.79 seconds.
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The football is in the air for 2.75 seconds.
Explanation:The given function h = -4(4t-11) models the height h of the ball t seconds after it is kicked. To find how long the football is in the air, we need to find the time when the ball reaches the ground. This occurs when the height h is equal to 0. So, we can set the equation -4(4t-11) = 0 and solve for t.
-4(4t-11) = 0
4t-11 = 0
4t = 11
t = 11/4
Hence, the football is in the air for 11/4 seconds or 2.75 seconds.
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Cara os making potato salad for a cook out. One serving of potato salad has 1 1/2 cups of cooked potatoes and 1/4 cup of mayonnaise. How many cups of potatoes would be needed if cara uses 3 1/4 cups of mayonnaise?
Answer:
19.5
Step-by-step explanation:
just look at the equation like this
1 1/2 - 1/4
???? - 3 1/4
divide 3 1/4 by 1/4 and multiply the result by 1 1/2
or just treat it as a ratio
1.5/x=.25/3.25
A triangle has an area of 64 yd and a base of 8 what is the height of the triangle?
[tex]\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} A=64\\ b=8 \end{cases}\implies 64=\cfrac{1}{2}(8)h\implies 64=4h \\\\\\ \cfrac{64}{4}=h\implies 16=h[/tex]
Can y’all answer the question for me please thank you
Answer: 544 ft²
Step-by-step explanation: 17*32=544 and ft*ft=ft² so it is 544 ft²
Which is an equivalent equation solved fort?
The equation f = v + at represents the final velocity of an
object, f, with an initial velocity, V, and an acceleration rate,
a, over time, t
o t=
t=alf-v)
t = v(f-a)
Answer:
t = (f - v)/a
Step-by-step explanation:
We have been given that;
The equation f = v + at represents the final velocity of an object, f, with an initial velocity, v, and an acceleration rate, a, over time, t.
The question requires us to solve for t;
The first step is to subtract v on both sides of the equation,
f - v = v + at - v
f - v = at
The next step is to divide both sides by a,
(f - v)/a = t
which is our required equation solved for t.
These figures are similar. The perimeter and area of one are given. The perimeter of the other is also given.
Find its area and round to the nearest tenth.
Please Help Me!!
Answer:
26.04cm^2
Step-by-step explanation:
28 divided by 20 is 1.4. 1.4 times the area will give you the area of the other figure. 1.4 x 18.6 = 26.04
use scale faction to solve and you get
36.5cm^2!
the function f(x)= 3x squared+12x+11 can be written in vertex form as A. f(x)=(3x+6) squared-25 B. f(x)=3(x+6) squared-25 C. f(x)= 3(x+2) squared-1 D. f(x)= 3(x+2) squared+7) explain and show your work and what is vertex form
Answer:
[tex]\boxed{\text{C. }{f(x) =3(x + 2)^{2} - 1}}[/tex]
Step-by-step explanation:
The vertex form of a quadratic function
ƒ(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.
You convert ƒ(x) = 3x² + 12x + 11 to the vertex form by completing the square.
Step 1. Move the constant term to the other side of the equation
y - 11 =3x² + 12x
Step 2. Factor out the leading coefficient
y - 11 =3(x² + 4x)
Step 3. Complete the square on the right-hand side
Take half the coefficient of x, square it, and add it to each side of the equation.
4/2 = 2; 2² = 4
y – 11 + 12 =3(x² + 4x + 4)
Note that when you completed the square by adding 4 inside the parentheses, you were adding 3×4 to the right-hand side, so you had to add 12 to the left-hand side.
Step 4. Simplify and write the right-hand side as a perfect square
y + 1 = 3(x + 2)²
Step 5. Isolate the y term
Subtract 1 from each side
y = 3(x + 2)² -1
[tex]\text{The vertex form of the equation is }\boxed{\mathbf{f(x) =3(x + 2)^{2} - 1}}[/tex]
If you compare this equation with the general vertex form and with the graph, you will find that h = -2 and k = -1, so the vertex is at (-2, -1).
The quadratic equation f(x) = 3x^2 + 12x + 11 can be rewritten in vertex form as C. f(x) = 3(x + 2)^2 - 1 after completing the square.
Explanation:The function f(x) = 3x2 + 12x + 11 can be rewritten in vertex form, which is y = a(x - h)2 + k, where (h, k) represents the vertex of the parabola. To convert the given quadratic to vertex form, we need to complete the square:
Group the x-terms together: f(x) = 3(x2 + 4x) + 11Complete the square: f(x) = 3(x2 + 4x + 4 - 4) + 11 = 3((x + 2)2 - 4) + 11Simplify: f(x) = 3(x + 2)2 - 12 + 11 = 3(x + 2)2 - 1So, the correct vertex form of the equation is C. f(x) = 3(x + 2)2 - 1.