The vertex of g(x) = [tex]\rm 3x^2 - 12x + 7[/tex] is (2, -5), the correct option is C.
What is the vertex of the parabola?The vertex of a parabola is the highest or lowest point, also known as the maximum or minimum of a parabola.
The standard equation of the vertex of the parabola is;
[tex]\rm a(x - h)^2 + k[/tex]
Where h and k are the coordinates of the vertex of the parabola.
The given expression is;
[tex]\rm =3x^2 - 12x + 7\\\\= 3(x^2 - 4x) + 7\\\\ = 3[ (x - 2)^2 - 4)] + 7\\\\= 3(x - 2)^2 - 12 + 7\\\\= 3(x - 2)^2 - 5[/tex]
On comparing with the standard form of vertex of the parabola
h = 2 and k = -5
Hence, the vertex of g(x) = [tex]\rm 3x^2 - 12x + 7[/tex] is (2, -5).
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The graphic shows a sample 401k investment. a sample 401 (k) investment has an annual contribution of 5,000 dollars, employer match of 5 percent, employer contribution of 2500 dollars, and total contribution of 7500 dollars. based on the graphic, what advantage does this 401k have over other types of investments? it encourages employees to contribute by offering an employer bonus. it ensures that employees who contribute will retire with more money. it guarantees employees a return on their investment because of a company match. it incentivizes employees to contribute by offering an employer match.
The advantage 401k have over other types of investments is:it incentivizes employees to contribute by offering an employer match.
What is 401(k) Investment?401(k) investment can be defined as the process in which an employer enables an employee to save ahead of their retirement.
401(k) investment help to motivate or encourage employee to save for retirement by enabling the employer to as well contribute a certain amount toward the employee retirement .
It as well help to lower the tax amount paid on the amount contributed by an employee based on the fact that the contribution are often deducted before tax.
Therefore the advantage 401k have over other types of investments is:it incentivizes employees to contribute by offering an employer match.
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Answer:
D.) It incentivizes employees to contribute by offering an employer match.
Step-by-step explanation:
Michelle gets her hair done every 8 weeks and Zuri gets hers done every 5 weeks. If they both got their hair done today, in how many weeks would they both get their hair done again on the same day?
The number of weeks when both Michelle and Zuri would both have their hair done again on the same day is 6 weeks.
When would they both have their hair done?In order to determine when they would both have their hair done on the same day, the common multiple of 8 and 5 has to be determined.
A multiple of a number is the product of an integer and that number.
Multiple of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
Multiple of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
Common multiple = 40
Number of weeks = 40 / 7 = 5.71 = 6 weeks
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a square barn has sides that are 7 meters long. what is the perimeter
Answer:
28
Step-by-step explanation:
A square has 4 sides, and 7 times 4 is 28.
Answer:
28 Meters
Step-by-step explanation:
A square has 4 sides of equal length, and a perimeter is the distance around the shape, so if each side is 7 meters long, then that is 4 lines that are 7 meters long...
7 × 4 = 28
The perimeter is 28.
Brainliest please?
The table displays the scores of students on a recent exam. Find the mean of the
scores to the nearest 10th.
Score Number of Students
80
4
85
6
90
9
95
6
100
8
I believe the answer is 48.3
Step-by-step explanation:
sorry if I'm wrong
Tyler wonders what proportion of students at his school would dye their hair blue if their parents would let them. He surveyed a random sample of 10 students at his school, and 2 of them said they would. Kiran didn’t think Tyler’s estimate was very accurate, so he surveyed a random sample of 100 students, and 17 of them said they would.
Based on Tyler's sample, estimate what proportion of the students would dye their hair blue.______
Based on Kiran's sample, estimate what proportion of the students would dye their hair blue.______
Whose estimate is more accurate? Type Tyler or Kiran.______
Using the proportion concept, it is found that:
According to Tyler's sample, the estimate is of 0.2 = 20%.According to Kyran's sample, the estimate is of 0.17 = 17%.Due to the higher sample size, Kyran's estimate is more accurate.What is a proportion?A proportion is a fraction of a total amount, and larger sample sizes lead to more accurate predictions.
In Tyler's sample, 2 out of 10 students would dye their hair blue, hence:
p = 2/10 = 0.2.
In Kiran's sample, 17 out of 100 would, hence:
p = 17/100 = 0.17.
Due to the higher sample size, as 100 > 20, Kyran's estimate is more accurate.
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There are twenty-three apples and seventeen oranges in a fruit basket. How many
more apples are there than oranges?
Answer:
6 apples
Step-by-step explanation:
23 apples - 17 oranges
23 - 17
= 6
6 apples more than oranges
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Answer: 1 in = 3.6 ft
Step-by-step explanation:
The small car is a model of the large car. The small car is 5 inches long while the large car is 18 feet long.
We currently have a ratio of: [tex]\frac{18 ft}{5 in}[/tex]
We need to get either the 18 or the 5 to one single unit.
18 ft : 5 in
Divide both sides by 5 to isolate 1 inch.
[tex]\frac{18}{5}[/tex] ft : [tex]\frac{5}{5}[/tex] in
Simplify.
3.6 ft : 1 in
We found that the ratio of the scale model is 1 inch of the model is equal to 3.6 ft of the real car.
Therefore, 3.6 ft = 1 in, which is equivalent to 1 in = 3.6ft
38. On a recent shopping trip, you see a sale advertising 3 pairs of socks and 2 pairs of shoes for $60. Write an equation using x to represent the cost of socks and to represent the cost of shots.
2x + 3y = 60
3x + 2y =60
20x + 30 =60
30x 20y=60
Deepak randomly chooses two marbles from the bag, one at a time, and replaces the marble after each choice. what is the probability he will choose one green marble and then one red marble? express the probabilities in fraction form. p(green) = p(red) = p(green and red) =
Probability of an event measures its chance of occurrence. P(Green in first draw) = 5/14, P(Red in second draw) = 2/14. P(Green in first and red in second draw) = 5/98
How to calculate the probability of an event?Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
What is chain rule in probability?For two events A and B, by chain rule, we have:
[tex]P(A \cap B) = P(B)P(A|B) = P(A)P(B|A)[/tex]
where P(A|B) is probability of occurrence of A given that B already occurred.
How to find if two events are independent?Suppose that two events are denoted by A and B.
They are said to be independent event if and only if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
It is because
[tex]P(A|B) = P(A)\\P(B|A) = P(B)[/tex]
and therefore, using chain rule and above facts gives:
[tex]P(A \cap B) = P(A)P(B)[/tex]
The question is missing some informations, which are:
Total marbles in the bag = 14Total red marbles = 5Total green marbles = 2rest of the 7 marbles are of some other colors.The result of first draw and the second draw are independent of each other as Deepak replaces the marble after first draw, therefore, making no changes in the count of balls of each color in the considered bag, which decides the probability needed.
Now, let we take:
A = probability that Deepak picks green ball in first draw
B = probability that Deepak picks red ball in the second draw
Then, we get:
[tex]P(A) =\dfrac{5}{14}\\\\P(B) = \dfrac{2}{14}\\\\P(A \cap B) = P(A)P(B) = \dfrac{5 \times 2}{14^2} = \dfrac{5}{98}[/tex]
(there are 14 ways to select a ball, but 5 favorable ball for event A to occur, and 2 favorable balls for event B to occur,therefore the aforesaid probabilities.)
Thus, for this case, we get:
P(Green in first draw) = 5/14, P(Red in second draw) = 2/14. P(Green in first and red in second draw) = 5/98Learn more about probability here:
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pat needs 14 sticks of pepperoni to make 28 pizzas.How many sticks of pepperoni are needed to make 36 pizzas
Answer:
18 sticks of pepperoni
Step-by-step explanation:
In order to solve this problem, we have to find out how many pepperoni sticks are needed for just 1 pizza. If it takes 14 sticks to make 28 pizzas, that means it takes only half a stick to make a single pizza.
Now that we have this information, we can multiply 1/2 by 36 to find out how many sticks of pepperoni are needed to make 36 pizzas.
[tex]\frac{1}{2} * 36\\\\\frac{1}{2} * \frac{36}{1} \\ =\\\frac{36}{2} \\ =\\\frac{18}{1}[/tex]
Therefore, it takes 18 sticks of pepperoni to make 36 pizzas. I hope this helps! Have a lovely day!! :)
College Math- Probability (Help appreciated!!!!) (please no links! :) )
A pair of fair dice is rolled. E is the event that the first dice rolls a 3 and F is the event that the sum of the two dice is 6. Are E and F independent events?
Answer:no they are not independent
Step-by-step explanation:
1) in order for events to be independent the probability of E happening should equal the probability of E happening given that F has already happend
2) P(E)=1/6 (on 6 sided die there is only 1 face that has 3 hence probability of e occurring is 1/6) or .167
3) P(E | F) read as probability of E happening given F has occurred
(Probability of E * probability of F) / total number of outcomes in F
probability of F= 1/6 as there is only one face(3) which will make the sum of the 2 die 6
(1/6)(1/6)/6=0.004
P(E)= .1167
P(E| F) =.004
hence probability aren't equal as making F happen impacts E'E's chances
ANOTHER way to think about this is if E rolls a 3 then the only way to make the sum of the 2 dice equal 3 is if die 2 rolls 3 as well. Hence the pprobability Of the second outcome tht sum of 2 die=6 depends on the number the first die lands
Jamal plans to attend a 4-year private university. He will receive $8,200 in scholarships
and grants each year, and he will earn $1,900 each year through a work study program.
Jamal's family will contribute $21,000 each year. How much will Jamal need to
contribute?
Jamal's family will contribute $21,000 each year. How much will Jamal need to
contribute?
Type your answer.
3.
1 noint
A, b, and c are polynomials, where: a = 3x – 4 b = x 7 c = x2 2 what is a2 – (b c) in simplest form? 8x2 – 25x 7 8x2– 25x 11 10x2 – 25x 7 10x2 – 25x 11
The expression A² – (B + C) in its simplest form is 8x² – 25x + 7
What is the polynomial?A polynomial function is an expression constructed with one or more terms of variables with constant exponents.
Data obtained from the question
A = 3x – 4, B = x + 7, C = x² + 2, A² – (B + C) =?
The simplest form of the polynomial is given by;
(3x – 4)² – (x + 7 + x² + 2)
9x² – 12x – 12x + 16 – (x + x² + 9)
9x² – 24x + 16 – x – x² – 9
9x² – x² – 24x – x + 16 – 9
8x² – 25x + 7
Hence, the simplest form of the polynomial is A² – (B + C) = 8x² – 25x + 7.
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Answer: A: 8x^2 - 25x + 7
Step-by-step explanation: got it right :)
How many milliliters are in 5.25 liters?
Answer: 5250 milliliters
Step-by-step explanation:
i hope this will be helpful
What is the difference of the polynomials? (8r6s3 – 9r5s4 3r4s5) – (2r4s5 – 5r3s6 – 4r5s4) 6r6s3 – 4r5s4 7r4s5 6r6s3 – 13r5s4 – r4s5 8r6s3 – 5r5s4 r4s5 5r3s6 8r6s3 – 13r5s4 r4s5 – 5r3s6
The difference between the polynomials (8r⁶s³ - 9r⁵s⁴+3r⁴s⁵) - (2r⁴s⁵ -5r³s⁶ - 4r⁵s⁴) is (8r⁶s³ - 5r⁵s⁴ + r⁴s⁵ + 5r³s⁶).
What are polynomial?Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.
The difference between the two polynomials can be solved as,
[tex](8r^6s^3 - 9r^5s^4+3r^4s^5) - (2r^4s^5 -5r^3s^6 - 4r^5s^4) \\\\= 8r^6s^3 - 9r^5s^4+3r^4s^5 - 2r^4s^5 +5r^3s^6 + 4r^5s^4\\\\= 8r^6s^3 - 5r^5s^4+r^4s^5 +5r^3s^6[/tex]
Thus, the difference between the polynomials (8r⁶s³ - 9r⁵s⁴+3r⁴s⁵) - (2r⁴s⁵ -5r³s⁶ - 4r⁵s⁴) is (8r⁶s³ - 5r⁵s⁴ + r⁴s⁵ + 5r³s⁶).
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Write 1.38 as a fraction
Answer:
69/50
Step-by-step explanation:
138/100
69/50
What number should be added to both sides of the equation to complete the square?
x2 - 6x = 5
Answer:
9
Step-by-step explanation:
The given equation is:
[tex]x^{2}[/tex] - 6[tex]x[/tex] = 5
To complete the square you have to add one number to both sides of the equation.
First, divide the coefficient of the term x by 2 and square the result. This number should then be added to both sides of the equation.
For the equation [tex]x^{2}[/tex] - 6[tex]x[/tex] = 5 the coefficient of the term x is -6.
(6 ÷ 2)² = 9
So you'll add 9 to both sides of the equation.
[tex]x^{2}[/tex] - 6[tex]x[/tex] (+ 9) = 5 (+ 9)
↓
[tex]x^{2}[/tex] - 6[tex]x[/tex] + 9 = 14
This can also be written as:
([tex]x[/tex] - 3)² = 14
use a quadratic function to model the area of each function. graph the function. evaluate each function for x = 8
top of square: 2x + 4, side: x +3
(other question)
top: 3x - 9, side: x + 2
HELP
Answer:
A=220 and 150 un^2
Step-by-step explanation:
The area for a square is LxW
you have one square with dimensions 2x+4 by x+3 and another with dimensions 3x-9 by x+2
for your first set: A=LxW= (2x+4)*(x+3)
evaluate at x=8: A= (2(8)+4)*(8+3) = 220
second set: A=LxW = (3x-9)*(x+2)
evaluate at x=8: A= (3(8)-9)*(8+2) = 150
Raylan opened a savings account with $100. After 5 years there is $122. 50 in the account. What is his simple interest rate?
4.5% annually
Step-by-step explanation:Simple interest is the amount of interest added to a singular sum of money at a fixed rate.
Formula
The formula for simple interest is A = P(1+rt). In this formula, A is the total amount of money in the account, P is the original amount deposited, r is the rate of interest as a decimal, and t is the time in years.
Calculations
To find the rate, plug the information we know into the formula above
122.50 = 100(1+r*5)Divide both sides by 100
1.225 = 1 + r*5Subtract 1 from both sides
0.225 = r*5Divide both sides by 5
0.045 = rThis gives us the rate as a decimal. So, to find the rate as a percent. Do this by moving the decimal 2 places to the right (or just multiply by 100, they do the same thing). This means that the rate of simple interest is 4.5%.
rajani says complementary angle of 43° is 37° degree do you agree?
pls fast
Answer:
no
Step-by-step explanation:
complementary angles add up to 90°
supplementary angles add up to 180°.
43 + 37 = 80.
so, they are neither.
Answer:
No
Step-by-step explanation:
Complementary angles add up to 90°The given angles are 43° and 37°43 + 37 ≠ 90They are not complementaryI do not agree with the statementif a person travels 1/4 miles in 1/6 hour,how fast are they traveling in miles per hour
Answer:
3/2 or 1.5 miles per hour
Step-by-step explanation:
Speed Formula:
[tex]\displaystyle \large{s=\dfrac{d}{t}}[/tex]
speed = distance/time
Given:
Distance = 1/4 milesTime = 1/6 hourTherefore:
[tex]\displaystyle \large{s=\dfrac{\dfrac{1}{4}}{\dfrac{1}{6}}}\\\displaystyle \large{s=\dfrac{1}{4}\cdot 6}\\\displaystyle \large{s=\dfrac{6}{4}}\\\displaystyle \large{s=\dfrac{3}{2} \ \tt{miles/hour}}[/tex]
Therefore, they are traveling 3/2 or 1.5 miles per hour.
can I have some help? I don't understand this
Answer:
15
__
28
Step-by-step explanation:
just multiply top by bottom
5*3 15
___ = ____
7*4 28
Answer:
the answer is 15/28
Step-by-step explanation:
if you multiply the numerators 5 and 3, you get 15. then you have to multiply the denominators 7 and 4 to get 28
What is the lateral surface area of this prism? 8 7 7 12
Answer:
The lateral surface area is 12
Step-by-step explanation:
got it right on edu
Answer:
use PH+2B
Step-by-step explanation:
use the perimeter by adding sides, get the height in the corner, and ur base will be multiplied by width times length it should look similar to PxH+2xB
Ms. Sampson tells her class to write an equivalent fraction for 1/2. Lucy writes 3/8 and Tim writes 4/8. Wich student is correct? Explain how you know
Answer:
Tom 4/8
Step-by-step explanation:
if you simplify 4/8 it will give u 1/2
What kind of expression is this?
Answer:
the third one hope it helps:)
Elshaun Works as a painter he charges $25 for each hour he works he also has to buy 100 $ worth of paint if the number of hours worked is represented by H which expression the total amount of money he would charge for his painting work
Answer:
Step-by-step explanation:this is a very hard question
Hi! I want to solve exercise 13. The question is to say Wich one is not a monomial. Thank you
Answer:
A monomial is any expression that only contains one term, and terms can only be divided by a plus and a minus sign
So the answer is B and C are not monomials rather they are binomial expressions
Which of the following is an odd function? f(x) = 3x2 x f(x) = 4x3 7 f(x) = 5x2 9 f(x) = 6x3 2x
If the condition f(-x) = -f(x) is satisfy then the function is an odd function. Then the odd function is f(x) = 6x³ + 2x.
What is an odd function?Odd Function - A true function f(x) is said to be an odd function if the output value of f(-x) is the same as the negative of f(x) for all values of x in the domain of f.
The equation should be stored in an odd function:
f(-x) = -f(x)
Then the functions are given below.
f(x) = 3x² + x
f(x) = 4x³ + 7
f(x) = 5x² + 9
f(x) = 6x³ + 2x
Then replace x with the negative x, then we have
f(x) = 3(-x)² + (-x) = 3x² - x =
f(x) = 4(-x)³ + 7 = -4x³ + 7
f(x) = 5(-x)² + 9 = 5x² + 9
f(x) = 6(-x)³ + 2(-x) = -6x³ - 2x = - (6x³ + 2x)
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Answer: D
Step-by-step explanation:
Ryan's friends have organized a treasure hunt. He is using the map below to find the clues. The position of the last clue, which
leads to the treasure, is located at point (-2,4).
6
+
2
2
-2
He figures that the treasure is 3 units either to the east or south of the location of the last clue. Which of these could be the
location of the treasure?
OA. point (1, 4) or point (-2, 1)
OB. point (-5, 4) or point (-2, 1)
OC. point (1, 1) or point (-5,7)
OD. point (1, 4) or point (-2,7)
Using translation concepts, it is found that the location of the treasure could be given by these following points:
A. point (1, 4) or point (-2, 1)
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
We consider that he is at point (-2,4), hence:
A shift east 3 units leads to point (1,4).A shift south 3 units leads to point (-2,1).Hence option A is correct.
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An object falls from a window. the distance the object has traveled, d, varies jointly with the acceleration due to gravity and the square of the time elapsed. the object has fallen 5.929 meters in 1.1 seconds, and the acceleration due to gravity is 9.8 meters per second squared. assuming the object continues to fall and the acceleration due to gravity remains the same, what is the total distance the object travels in 2 seconds? 10.8 m 19.6 m 21.6 m 39.2 m
The total distance the considered fallilng object travels in 2 seconds is given by: Option C: 19.6 m
What are equations of motion?There are three equation of motions that can be used when motion of the object is under constant acceleration and on a straight path.
They are listed below as:
[tex]v = u + at\\\\s = ut + \dfrac{1}{2} at^2\\\\v^2 = u^2 + 2as[/tex]
where the symbols have following meanings:
u = initial velocity of the considered objectv = final velocity of the objecta = acceleration of the objects = distance traveled by the object in 't' time.Here, assuming negligible air resistance, and ideal situations, the free fall of the considered object can be modeled by these equations of motion.
Here, according to sign convention, we have:
[tex]a = -g = -9.8 \: \rm m/s^2[/tex]
Due to free fall, we have: [tex]u = 0[/tex]
Thus, the net displacement (taking the window as origin) is given by equation:
[tex]s = \dfrac{-gt^2}{2}[/tex]
The distance that object traveles in 2 seconds is the absolute displacement it gets in 2 second of freefall.
This is obtained as:
[tex]D_2 =|s|_2 = \left| \dfrac{-9.8 (2)^2}{2} \right| = 19.6 \: \rm m[/tex]
Thus, the total distance the considered fallilng object travels in 2 seconds is given by: Option C: 19.6 m
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