Answers
Answer:
The equation of the parabola is [tex]y = \frac{1}{3}\cdot x^{2}-\frac{4}{3}\cdot x -4[/tex], whose real vertex is [tex](x,y) = (2, -5.333)[/tex], not [tex](x,y) = (2, -5)[/tex].
Step-by-step explanation:
A parabola is a second order polynomial. By Fundamental Theorem of Algebra we know that a second order polynomial can be formed when three distinct points are known. From statement we have the following information:
[tex](x_{1}, y_{1}) = (-2, 0)[/tex], [tex](x_{2}, y_{2}) = (6, 0)[/tex], [tex](x_{3}, y_{3}) = (0, -4)[/tex]
From definition of second order polynomial and the three points described above, we have the following system of linear equations:
[tex]4\cdot a -2\cdot b + c = 0[/tex] (1)
[tex]36\cdot a + 6\cdot b + c = 0[/tex] (2)
[tex]c = -4[/tex] (3)
The solution of this system is: [tex]a = \frac{1}{3}[/tex], [tex]b = - \frac{4}{3}[/tex], [tex]c = -4[/tex]. Hence, the equation of the parabola is [tex]y = \frac{1}{3}\cdot x^{2}-\frac{4}{3}\cdot x -4[/tex]. Lastly, we must check if [tex](x,y) = (2, -5)[/tex] belongs to the function. If we know that [tex]x = 2[/tex], then the value of [tex]y[/tex] is:
[tex]y = \frac{1}{3}\cdot (2)^{2}-\frac{4}{3}\cdot (2) - 4[/tex]
[tex]y = -5.333[/tex]
[tex](x,y) = (2, -5)[/tex] does not belong to the function, the real point is [tex](x,y) = (2, -5.333)[/tex].
Related Questions
2 + 2 = ?
please help!
Answers
Answer:
4
Hope that this helps!
PLEASE HELP ASAP ASAP URGENT WILL GIVE BRAINLIEST
Answers
Answer:
for the solve and check:
[tex]2\frac{3}{8}+x=3\frac{1}{4} \\2\frac{3}{8}-2\frac{3}{8}+x=3\frac{1}{4}-2\frac{3}{8}\\\\x=3\frac{1}{4}-2\frac{3}{8}\\\\\\x=\frac{7}{8}[/tex]
----------------------------------------------------
[tex]3\frac{3}{8}+x=4\frac{1}{4} \\3\frac{3}{8}-3\frac{3}{8}+x=4\frac{1}{4}-3\frac{3}{8}\\\\x=4\frac{1}{4}-3\frac{3}{8}\\\\\\x=\frac{7}{8}[/tex]
for the second solve and check:
[tex]4\frac{3}{8}+x=5\frac{1}{4} \\4\frac{3}{8}-4\frac{3}{8}+x=5\frac{1}{4}-4\frac{3}{8}\\\\x=5\frac{1}{4}-4\frac{3}{8}\\\\\\x=\frac{7}{8}[/tex]
----------------------------------------------------
[tex]5\frac{3}{8}+x=6\frac{1}{4} \\5\frac{3}{8}-5\frac{3}{8}+x=6\frac{1}{4}-5\frac{3}{8}\\\\x=6\frac{1}{4}-5\frac{3}{8}\\\\\\x=\frac{7}{8}[/tex]
Answer:
Step-by-step explanation:
Green picture
x = 2.25 ft = 2 1/4 ft
we substitute 2 1/4 for x
x = 2 1/4 ft
3 3/4 ft + 2 1/4 ft = 6 ft
6 ft = 6 ft
Since 6ft is equal to 6ft...
Blue picture
It is 2 1/4 ft long
we substitute 7/8 ft for x
since 2 1/4 ft is equal ...
Yellow picture
2 3/8 ft - 2 3/8 ft + x = 3 1/4 ft - 2 3/8 ft
x = 3 1/4 ft - 2 3/8 ft
x = 7/8 ft
Check
x = 7/8 ft
2 3/8 ft + 7/8 ft = 3 1/4 ft
3 3/8 ft - 3 3/8 ft + x = 4 1/4 ft - 3 3/8 ft
x= 4 1/4 ft - 3 3/8 ft
x = 7/8 ft
check
x = 7/8 ft
3 3/8 ft + 7/8 ft = 4 1/4 ft
red picture
4 3/8 ft - 4 3/8 ft + x = 5 1/4 ft - 4 3/8 ft
x = 5 1/4 ft - 4 3/8 ft
x = 7/8 ft
check
x = 7/8 ft
4 3/8 ft + 7/8 ft = 5 1/4 ft
Divide £9 in the ratio 2 : 1
Answers
Answer:
Step-by-step explanation:
will give brainliest
Answers
Answer:
Step-by-step explanation:
1/48 + 5/6
The LCD of 48 and 6 is 48 so we have:
1/48 + 40/48
= 41/38
Answer:
41/48
Step-by-step explanation:
Please help me out! I really need to get this done.
Answers
B. Range (0,0)
A. Domain All real numbers
B. Domain all real numbers
i’m not too sure about the domain but I’m pretty sure it’s all real numbers because of the arrows at each end of the line
Two gamblers, call them Gambler A and Gambler B flip a coin repeatedly. The coin is unfair and comes up heads 2/3 of the time. Gambler A wins one dollar from Gambler B, when a head is tossed. Conversely Gambler B wins one dollar from Gambler A when a tail is tossed. The coin tosses are independent. The game ends when one of the gamblers runs out of money. There are 5 dollars in the pot. Determine the probability that Gambler A wins the game if he starts with I dollars. Here I
Answers
Answer:
≈ 0.52
Step-by-step explanation:
P( head ) = 2/3 , P( tail ) = 1/3
when a head is tossed ; Gambler A wins $1
when a tail is tossed : Gambler B wins $1
Determine the P( Gambler A wins the game ) if he starts with I dollars
Assuming I = $1
n = 5
p ( head ) = P( winning ) = 0.66
p( losing ) = 0.33
applying the conditional probability in Markov which is ;
Pₓ = pPₓ₊₁ + (1 - p) Pₓ₋₁
P( 1) = 0.66P₂ + 0.33P₀
resolving the above using with Markov probability
P( 1 ) = 0.51613
hence the probability of Gambler A winning the game if he starts with $1
≈ 0.52
15 POINTS**
Write an explicit formula an, the nth term of the sequence 27,-3,-33,-63
Answers
Answer:
The nth term is 27 - 30(n-1) or can be simplified to 57 - 30n.
Step-by-step explanation:
This is an arithmetic sequence (ie. each term equals the previous term with a constant value added (or subtracted from it)
T1 = 27
T2 = -3 = T1 - 30 = 27 - 30
T3 = -33 = T2 -30 = 27 -30 - 30=27-30X(2)
T4= -63 = T3 - 30 =27-30X(2)-30=27-30X(3)
In general, the nth term of this sequence:
S(n) = 27 - 30X(n-1)
Find the solution(s) to the system of equations. Select all that apply.
y=x-4
y = 2x- 5
Answers
Answer:
Y
Step-by-step explanation:
Ashley started washing at 10:28 AM and finished at 10:41 AM.
How long did it take her? Give your answer in minutes.
Answers
Answer:
13 minutes
Step-by-step explanation:
The reason why it is 13 minutes is because you subtract 10:41 AM from 10:28 AM and you get 13 minutes.
Answer:
13
Step-by-step explanation:
41-28= 13
the hours don't change so you just need to subtract the minutes
Which is the best estimate for the weight of a bicycle?
A. 2 ounces
B. 2 pounds
C. 20 ounces
D. 20 pounds
Answers
Answer:
B
Step-by-step explanation:
i know this already from another
Explanation: The dude above me
What is the area of this square?
A= 12
B= 48
C= 72
D= 144
No links, docs, files, drives etc
I will mark the correct answer brainlyest
You earn many points
Answers
========================================================
Explanation:
A square has all four sides that are the same length. So all four sides are 12 cm
area = side*side = 12*12 = 144 cm^2
Or you could say
area = (side)^2 = (12)^2 = 144 cm^2
Squaring a number is the same as multiplying it by itself. Hence the name "square" refers to a side length pairing up with its corresponding area value.
---------
Side note: The perimeter is 4*(side) = 4*12 = 48 cm. It's possible that choice B is put in there as a trick answer.
B
If you do 4x12 you will end up with 48
Please help me solve this problem
Answers
Answer:
90°
Step-by-step explanation:
It's simple, the angle of a line is 180°
∠EFG=90°
Line GD-∠EFG=180°-90°=90°
Please mark brainliest!
Three years ago the sum of the ages of father and his son was
48 years and three years hence father's age will be three times
that of his son. Find the present ages of the father and his son.
Answers
Answer:
The father is 42 years old and the son is 12 years old.
Step-by-step explanation:
Since three years ago the sum of the ages of father and his son was 48 years, and three years hence father's age will be three times that of his are his, to find the present ages of the father and his are his, the following calculations must be performed:
F + S = 48
F + 6 + S + 6 = 3S
34 + 14 = 48 /// 34 + 6 = 40 --- 14 + 6 = 20 (x 3 = 60)
38 + 10 = 48 /// 38 + 6 = 44 --- 10 + 6 = 16 (x 3 = 48)
40 + 8 = 48 /// 40 + 6 = 46 --- 8 + 6 = 14 (x 3 = 42)
39 + 9 = 48 /// 39 + 6 = 45 --- 9 + 6 = 15 (x 3 = 45)
39 + 3 = 42
9 + 3 = 12
Therefore, the father is 42 years old and the son is 12 years old.
The equation below describes a circle. What are the coordinates of the center
of the circle?
(x+ 5)2 + (y + 7)2 = 212
Answers
Answer:Center =(-5,-7)
Step-by-step explanation:
Five friends are sharing 4 fruit bars. Each friend gets the same amount.
How much fruit bar does each friend get?
Answers
Answer:
4/5 of a fruit bar
Step-by-step explanation:
A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1070 and a standard deviation of 204. Scores on the ACT test are normally distributed with a mean of 19.1 and a standard deviation of 5.2. It is assumed that the two tests measure the same aptitude, but use different scales.
(A) If a student gets an SAT score that is the 51-percentile, find the actual SAT score. Round answer to a whole number. SAT score =
(B) What would be the equivalent ACT score for this student? Round answer to 1 decimal place. ACT score =
(C) If a student gets an SAT score of 1417, find the equivalent ACT score. Round answer to 1 decimal place. ACT score =
Answers
Answer:
a) SAT score = 1075
b) ACT score = 19.2.
c) ACT score = 27.9.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
(A) If a student gets an SAT score that is the 51-percentile, find the actual SAT score
SAT scores have mean 1070 and standard deviation 204, so [tex]\mu = 1070, \sigma = 204[/tex]
51th percentile means that Z has a p-value of 0.51, so Z = 0.025. The score is X. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.025 = \frac{X - 1070}{204}[/tex]
[tex]X - 1070 = 0.025*204[/tex]
[tex]X = 1075[/tex]
SAT score = 1075.
(B) What would be the equivalent ACT score for this student?
ACT scores have mean of 19.1 and standard deviation of 5.2, which means that [tex]\mu = 19.1, \sigma = 5.2[/tex]. The equivalent score is X when Z = 0.025. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.025 = \frac{X - 19.1}{5.2}[/tex]
[tex]X - 19.1 = 0.025*5.2[/tex]
[tex]X = 19.2[/tex]
ACT score = 19.2.
(C) If a student gets an SAT score of 1417, find the equivalent ACT score.
Z-score for the SAT:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1417 - 1070}{204}[/tex]
[tex]Z = 1.7[/tex]
Equivalent score on the ACT:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.7 = \frac{X - 19.1}{5.2}[/tex]
[tex]X - 19.1 = 1.7*5.2[/tex]
[tex]X = 27.9[/tex]
ACT score = 27.9.
Bert measured a swimming pool and made a scale drawing. The scale of the drawing was
1 centimeter = 1 meter. What scale factor does the drawing use?
Simplify your answer and write it as a fraction.
Submit
Answers
Each meter is 100 centimeter
NEED THIS BY FRIDAY ! I HAVE MORE UNANSWERED QUESTIONS ON MY PAGE!!
Answers
Answer:
2, 3, 4 (up to down)
Step-by-step explanation:
Rational: can be terminating, repeating, in a fraction
Irrational: Not terminating (ending), doesn't repeat (o.33333....), and you can't put it in a fraction
Hope this helps!!
p.s. brainliest plz
Please look at the image
Answers
Answer:
value for X
3x-4 =41
3x =41+4
3x =45
x =15
PLEASE HELP!!!!!!!!!!!
Answers
Answer:
I think it's 18
Step-by-step explanation:
because I'm looking at 12/8 to be a ratio, that means that the size of the bigger figure had decreased by 12/8 or 1.5
then I divided the 27 by 1.5 to get the area of the small one which was 18.
The Unit Circle
What is the domain of a sine function?
a. positive numbers
b. All real numbers
c. negative numbers
d. positive numbers including zero
Please select the best answer from the choices provided
Answers
Answer:
B. All real numbers
Step-by-step explanation:
I calculated it logically
Answer:
I believe it is all real numbers
Name the circle part L shown in the figure.
O Arc
O Sector
O chord
O radius
Answers
Answer:
Step-by-step explanation:
Which pair of inequalities is equivalent to 0
Choose the correct answer below.
Answers
Answer: D is correct
Step-by-step explanation:
Answer:
C. x > 0 and x ≤ 3
Step-by-step explanation:
0 < x ≤ 3
when 0 < x then x > 0
Example: 0 < 2 then 2> 0
Therefor
x > 0 and x ≤ 3
Trying to finish this test at 3:30 am plz help
Answers
Given:
The given sum is:
[tex]\sum _{k=4}^9(5k+3)[/tex]
To find:
The expanded form and find the sum.
Solution:
We have,
[tex]\sum _{k=4}^9(5k+3)[/tex]
The expanded form of given sum is:
[tex]\sum _{k=4}^9(5k+3)=(5(4)+3)+(5(5)+3)+(5(6)+3)+(5(7)+3)+(5(8)+3)+(5(9)+3)[/tex]
[tex]\sum _{k=4}^9(5k+3)=(20+3)+(25+3)+(30+3)+(35+3)+(4+3)+(45+3)[/tex]
[tex]\sum _{k=4}^9(5k+3)=23+28+33+38+43+48[/tex]
[tex]\sum _{k=4}^9(5k+3)=213[/tex]
Therefore, the correct option is C.
On cold days Leah likes to make hot chocolate. She uses 8 tablespoons of cocoa and 2 tabelspoons of sugar, what ratio is equivalent to 8 to 2? Complete the statement. The ratio 8 to 2 is equivalent to the ratio ? To ?
Answers
Answer:
4 to 1
Step-by-step explanation:
The greatest common factor between 8 and 2 is 2. So 2 will go into 8, 4 times. And 2 will go into 2, 1 time. So simplified the equivalent ratio is 4:1.
please xplain and help with answers
Answers
Step-by-step explanation:
for mixed number to a improper fraction you take the whole number and times that by the denominator and add the numeriator
for example
[tex]8 \frac{3}{8} [/tex]
8 x 8 = 64
64 + 3 = 67
and after you get your last number (67) you put that over your original denominator which is 8 so it would be
[tex] \frac{67}{8} [/tex]
for the improper to mixed you see how many times you denominator goes into your numerator
another example is
[tex] \frac{13}{7} [/tex]
7 goes into 13 twice so your whole number is 2 and you have a remaining 1 so it would look like
[tex]2 \frac{1}{7} [/tex]
Answer:
A) 9/4
B) 67/8
C) 17/6
D) 9/2
E) 16/3
F) 127/12
G) 37/4
H) 41/6
Q) Whole Number: 1 Fraction: 6/7
R) Whole Number: 4 Fraction: 1/2
S) Whole Number: 1 Fraction: 8/9
T) Whole Number: 2 Fraction: 1/3
U) Whole Number: 2 Fraction: 3/7
V) Whole Number: 3 Fraction: 1/3
W) I am not 100% sure for this one but I think it's right.
Mixed Number - Whole Number: 1 Fraction: 5/8
Improper fraction - 13/8
Step-by-step explanation:
With improper fractions the first thing that you want to do is multiply the whole number with the denominator (the number on the bottom of the fraction), then add the numerator (the number on the top of the fraction). You also want to keep the denominator the same in both fractions.
When working with converting mixed fractions into improper fractions it is kind of the opposite, but it is a little harder to explain. Let's take letter Q as an example. If you know that you cannot divide the numerator and the denominator in anyway to make a whole number, the whole number will become a one and the numerator is how many are left. so in this case the answer for Q would be 1 6/7, 1 being the whole number and 6 from 6+7=13. now let's look at letter R, you know you can divide 2 four times into 9, the whole number will be 4 and the fraction will be 1/2, 4x2+1=9. You can also double check that you did it right by turning it back into a improper fraction from the mixed number state by multiplying the denominator with the whole number, then adding the numerator. Hope that made sense, send me a DM if you need more help!
Help please
(Worth 10 points)
Please respond with a actual answer
*No robots no bad links*
Answers
What choice is the range of f(x)=√x-3-1
Answers
Answer:
its not loading
Step-by-step explanation:
Can you help me with Math
Answers
Answer:
42+106=x
148=x
Step-by-step explanation:
Plsss help. giving extra points if correct.
Answers
Answer:
98?
Step-by-step explanation: