write a quadratic equation for the points (2,0) and (12,5). make sure to include the axis and five points used to graph the parabola
Answers
Using the Factor Theorem, the parabola is given by: [tex]f(x) = 0.05(x^2 - 4x + 4)[/tex]
The graph is sketched at the end of this answer.
The Factor Theorem states that a polynomial function with roots is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
In this problem:
The graph is a parabola, which means that the function is of the 2nd degree.One zero, with multiplicity 2, at [tex]x = 2[/tex], hence, [tex]x_1 = x_2 = 2[/tex].Then:
[tex]f(x) = a(x - 2)(x - 2)[/tex]
[tex]f(x) = a(x^2 - 4x + 4)[/tex]
Point (12,5) means that when [tex]x = 12, y = 5[/tex], and this is used to find a.
[tex]f(x) = a(x^2 - 4x + 4)[/tex]
[tex]5 = a(12^2 - 4(12) + 4)[/tex]
[tex]100a = 5[/tex]
[tex]a = \frac{5}{100}[/tex]
[tex]a = 0.05[/tex]
Hence, the parabola is:
[tex]f(x) = 0.05(x^2 - 4x + 4)[/tex]
At the end of this answer, the graph with five points is sketched.
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Related Questions
please help
Jay buys a certain brand of cereal that costs $15 per box. Luke changes to a super-saving brand of the same size. The equation shows the price, y, as a function of the number of boxes, x, for the new brand, y = 10x Part A: How many more dollars is the price of a box of Jay's original brand of cereal than the price of a box of the super-saving brand? Show your work. (5 points) Part B: How much money does Jay save each month with the change in cereal brand if he buys 8 cereal boxes each month? Show your work. (5 points)
Answers
A.
Jay's original brand is $5 more than the price of a box of the super-saving brand.
Since Jay's original brand costs $15 per box and the price of Luke's super-saving brand is y = 10x where x = number of boxes. For one box, x = 1.
So, y = 10x
y = 10 × 1
y = $10
So, Jay's brand costs $15 per box and Luke brand cost $10 per box.
So, the difference in price is per box is $15 - 10$ = $5
So, Jay's original brand is $5 more than the price of a box of the super-saving brand.
B.
Jay saves $40 per month with the change in cereal brand if he buys 8 cereal boxes each month
Since the difference in price for each box bought is $5. Jay saves $5 for every super-saving cereal brand he buys.
So, if he buys 8 cereal boxes per month, he saves $5 per box × 8 boxes per month = $40 per month.
So, Jay saves $40 per month with the change in cereal brand if he buys 8 cereal boxes each month
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please, help!!!! Bussines Calc. I give 20 points. I need a full explanation.
Answers
I believe you are trying to find the most Cheapest cost?
Since the area had to be 1200m^2 the most biggest numbers we could divide with is 30 x 40, which equals to 1200.
30 x 20 (expensive one the lower) = 600 (wall 3) + 20 x 20 = 1000 (wall 3 + wall 1)
40 x 13 (cheapter one the higher) = 520 (wall 4) + 32 x 13 = 936 (wall 4 + wall 2)
Add all together, $1936 to build the whole fence.
(I don't know for sure if I am right. If I am right, can I have a brainliest?)
make your own dish pantry package potluck portfolio
Answers
Answer:
huh??
Step-by-step explanation:
Given loga (m) = 10 and loga (n) = 25 , find loga (m * n ^ 2)
Answers
The result of the log function [tex]log_a (m * n ^ 2)[/tex] is 60
According to the law of logarithm if [tex]log_ab=y[/tex] then [tex]b=a^y[/tex]
Given the following expressions
[tex]log_am=10\\log_an=25[/tex]
This can be expressed as
[tex]m =a^{10} \ and \ n = a^{25}[/tex]
Substitute the value of m and n into the expression [tex]log_a (m * n ^ 2)[/tex] to have:
[tex]log_a (m * n ^ 2) = log_a(a^{10}\times a^{50})\\=log_aa^{60}\\=60log_aa\\=60(1) \\= 60[/tex]
This shows that the result of the log function [tex]log_a (m * n ^ 2)[/tex] is 60
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The police are searching for a bank that has been on the run for two hours. Based on his running speed, the police believe he could be anywhere within an 8.5 mile radius of the bank. Find the area and circumference of the region in which they must search for the suspect. Round to the nearest whole unit.
Answers
Answer:
π is equivalent to 3.14
Circumfrance = 53
area = 227
Step-by-step explanation:
π is equal to 3.14
Circumfrance = 8.5*2*π
So 8.5 * 2 is 17 times π is 53.38
round to nearest whole number is 53
area is π * radius squared so
8.5 * 8.5 =72.25
* π is 226.865
round to the nearest whole number is 227
how do you do this? appreciated for your help
Answers
Answer:
1/20 E
Step-by-step explanation:
11.74 - 11.69 = .05
.05 =1/20
Answer:
E. 1/ 20 seconds
Step-by-step explanation:
The distance covered by both the athletes is the same.
So, calculating the difference between their times:
Bryan completed the race in 11.74 secondsLuis completed the race in 11.69 secondsDIFFERENCE:That means, Luis completed the race before Bryan, and the difference between their times is:
= 11.74 - 11.69
= 0.05 seconds
CONVERSION:To convert this decimal into a fraction we'll multiply and divide the decimal by 100 (as the number of decimal places is "2", the decimal will be handled by 10 exponent "2" )
[tex]=0.05 \times \frac{100}{100}[/tex]
[tex]= \frac{5}{100}[/tex]
5's a common factor in both numerator and denominator hence, it cancels out
[tex]=\frac{1}{20}[/tex]
ANSWER:Therefore, we got [tex]\frac{1}{20}[/tex] seconds. That is option E.
Which equation can be simplified to find the inverse of y = 2x2?
1/y=2x^2
y=1/2x^2
-y=1/2x^2
x=2y^2
Answers
Answer:
D. x = 2y²Step-by-step explanation:
The step in working out the inverse is to swap over the variables.
If we apply same to given equation, we'll have:
y = 2x² → x = 2y²It gives us the option D
Answer:
Option D
Step-by-step explanation:
y=2x²Interchange x and y
x=2y²Hence option D is correct
y²=x/2y=√x/2Assume there are 20 people in a room, including you. You must shake hands with everyone else in the room. How many hands will you shake
Answers
Answer:
19, I'm pretty sure?
find the 6th term of geometric sequence whose common ratio is 3/2 and whose first term is 2
Answers
Answer:
243/16
Step-by-step explanation:
we have a1 = 2
r = 3/2
n = 6
The 6th term of the geometric sequence is 243/16
The given parameters are:
[tex]a = 2[/tex] --- the first term
[tex]r = 3/2[/tex] --- the common ratio
The nth term of a geometric sequence is:
[tex]T_n = ar^{n-1[/tex]
So, the 6th term would be:
[tex]T_6 = 2 \times (3/2)^{6-1[/tex]
Subtract 1 from 6
[tex]T_6 = 2 \times (3/2)^5[/tex]
Evaluate the exponent
[tex]T_6 = 2 \times (243/32)[/tex]
Simplify
[tex]T_6 = 243/16[/tex]
Hence, the 6th term of the geometric sequence is 243/16
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For the following quadratic equation, find the discriminant. –4x² + 24x – 152 = 0
Answers
(12a-9b+7)+(2a-3b-14)
Answers
Answer:
14a - 12b - 7
Step-by-step explanation:
12a - 9b + 7 + (2a - 3b - 14)
collect like terms
14a - 9b + 7 - 3b - 14
solution
14a - 12b - 7
HELP PLEASEE!!!
In Asha's science experiment, her bacteria are dying at a constant rate of $600$ an hour. If she drew a graph of the number of bacteria in her culture where $x$ represented the time in minutes since the start of the experiment and $y$ represented the number of bacteria remaining in the colony, her graph would be a line. What would be the slope of this line?
Answers
Answer:
-10
Step-by-step explanation:
The rate of change is also known as the slope of the function thus the slope will be -600.
What is the slope?A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.
Slope = Tanx where x will be the angle from the positive x-axis at that point.
The slope is also calculated by differentiation for example slope of y = sinx will be y' = cosx.
As per the given,
Bacteria are dying at a constant rate of $600$ an hour.
The rate of change = -600/hour
Slope = y/x = number of bacteria change/time taken
If the graph is a straight line then it will remain constant.
Slope = -600
Hence "The rate of change is also known as the slope of the function thus the slope will be -600".
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SOMEONE PLS HELP ME!!!
Answers
Answer:
refer to the picture attached for steps
In general, as sample size increases: a.the standard error will remain the same regardless of changes in sample size. b.the standard error fluctuates in size. c.the standard error increases in size. d.the standard error is a constant. e.the standard error decreases in size.
Answers
Answer:
With a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the mean
Step-by-step explanation:
List the congruent sides.
Answers
Answer:
PQ≅ST; QR ≅TW; PR ≅SW
Step-by-step explanation:
There are 495 pages in the mathematic book, from this 330 pages are included for the first term. Find the proportion of total pages to allotted pages in simplest form.
Answers
Answer:
330/495 = 2/3
the answer is 2/3
Answer:
3 : 2
Step-by-step explanation:
Total pages : allotted pages = 495 : 330
Find the HCF of 495 and 330
495 = 5 * 3*3*11
330 = 5 * 3 * 2 * 11
HCF = 5 * 3 * 11 = 165
Divide 495 and 330 by 165
495 : 330 = 3 : 2
an online music store sells 15 songs for $12. Another online music store sells 10 songs for $9. Which online store has the lower cost per song?
Answers
Answer:
The second store (10 songs for $9)
Step-by-step explanation:
15 songs/$12 = $1.25 per song
10 songs/$9 = $1.11 per song
Answer:
second
Step-by-step explanation:
second bc if you cross multiply 135>120
I need the answers to the ones with an x by them please and thank you guys I really need this It’s home work
Answers
Answer:
Sorry I took so long, I hope I helped though
3) 2.428
5) 5.414
6) 8.29
10) 3.34
11) 42.35
12) 24.276
14) 6.777
17) 17
18) 19
19) 50.6
20) 17
26) basically add them all, I got the answer 1
27) 0.29+0.24 is 0.53
28) your answer is right, one fourth of 1 is .25, so the answer is 0.15+0.08+0.02
There are only 9 counters in a bag. There are 2 red counters 3 green counters 4 blue counters Lethna takes at random a counter from the bag. (a) Write down the probability that she takes
(i) a blue counter,
A white counter
Answers
White counter -0
Given that lines b and c are parallel, and the m<1=4x-30 and m<5=2x+50. Find the measure of angle 1 and measure of angle 7 Explain your reasoning and show your work.
tysm in advance
Answers
+30 +30
4x=2x+80
-2x -2x
2x=80
/2 /2
X=40
4(40)-30=130°
2(40)+50=130°
180-130=50°
Angle 7=50°
The required measure of the angle 1 and 7 is given as 130° and 40° respectively.
Given that,
Lines b and c are parallel, and the m<1=4x-30 and m<5=2x+50. Find the measure of angle 1 and the measure of angle 7 .
The orientation of one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
here,
From the figure,
∠1 = ∠5
4x - 30 = 2x + 50
2x = 80
x = 40
Now,
∠ 1 = 4 [40] - 30
∠1 = 130° = ∠5
∠7 = 180 - ∠5
∠7 = 180 - 130 = 40°
Thus, the required measure of the angle 1 and 7 is given as 130° and 40° respectively.
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5.6 reccuring
as a fraction
Answers
Answer:17/3 or 5 and 2/3
Zoom in so you can see it
I will give you 50 point and brain list
Answers
Answer:
so this is what it should be let me know if this Is wrong
A boat traveled 27 miles in 2 hours. At this rate, how many miles will the boat travel in 1 over 2 hour?
Answers
27/2 = 13,5 miles
In 1/2 hour the boat will travel :
13,5 x 1/2 = 6,75 miles
Ok done. Thank to me:>
There are 48 people in the stands cheering for ——— at the volleyball game and they are wearing white and maroon shirts. The ratio of marron to white is 5:3. How many people were wearing white shirts?
Answers
Which are perfect square trinomials? Select two options.
x2 − 9
x2 −100
x2 − 4x + 4
x2 + 10x + 25
x2 + 15x + 36
Answers
Step-by-step explanation:
An expression obtained from the square of a binomial equation is a perfect square trinomial. An expression is said to a perfect square trinomial if it takes the form ax2 + bx + c and satisfies the condition b2 = 4ac. The perfect square formula takes the following forms: (ax)2 + 2abx + b2 = (ax + b)
Answer:
x2 − 4x + 4
x2 + 10x + 25
Step-by-step explanation:
Use mental math to find the missing number. Enter your answer in the box.42,000 ÷ = 600
Answers
Answer:
7 is the required answer.
Step-by-step explanation:
4200 ÷ 7 = 600
If the price of a particular chocolate bar is increased by 40%, and it used to be $2, what is the new price after the increase?
Answers
Answer:
6$
Step-by-step explanation:
2+4=6
20%+40%=60%
The new price after the increase is $2.8 .
What is percent increase?Percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage. In other words, it is the difference between the final value and the initial value which is divided by the initial value and then multiplied by 100.
According to the question
The price of chocolate bar = $2
The price of a particular chocolate bar is increased by 40%,
i.e
The percent increase in the price of chocolate bar = 40%
Now,
increase prize :
= [tex]2*\frac{40}{100}[/tex]
= $0.8
The new price after the increase
= $2.8
Hence, the new price after the increase is $2.8 .
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cellus If investments double every 7 years and you start with a $600 investment, how much money would you have after 21 years?
Answers
Answer:
4800$
Step-by-step explanation:
1 day = 600
7 years = 600 x 2 = 1200$
14 years = 1200 x 2 = 2400$
21 years = 2400 x 2 = 4800$
10 times 7 + 5^2/2 times 5
Answers
Answer:
132.5
Step-by-step explanation:
10x7=70
5^2=25
70+25/2x5
70+12.5x5
70+62.5=132.5
Can somebody help ????
Answers
Answer:
Answer is 4, explained answer in the comments because I didn't see the answer button, but now I do.