Determine the equation of the graph and select the correct answer below. parabolic function going down from the left through the point negative five comma zero and turning at the point negative four comma negative one and going up through the point negative three comma zero and through the point zero comma fifteen and continuing towards infinity Courtesy of Texas Instruments y = (x + 4)2 + 1 y = (x + 4)2 − 1 y = (x − 4)2 + 1 y = (x − 4)2 − 1
Solution: The correct option is second option, i.e., [tex]y=(x+4)^2-1[/tex].
Explanation:
The standard form of the parabola along the y-axis with vertex (h,k) is [tex]y=a(x-h)^2+k[/tex].
Since the turning point is given as [tex](-4,-1)[/tex].
Put these values in the standard form of the parabola.
[tex]y=a(x+(-4))^2+(-1)[/tex]
[tex]y=a(x+4)^2-1[/tex] .....(1)
The parabola passes through the points (-5,0), (-3,0) and (0,15). It means each point will satisfy the above condition.
Put x = 0 and y = 15 in the equation (1).
[tex]15=a(0+4)^2-1\\16=4^2a\\16=16a\\a=1[/tex]
Put a = 1 in equation (1).
[tex]y=1(x+4)^2-1[/tex]
Therefore, the The correct option is second option, i.e., [tex]y=(x+4)^2-1[/tex].
a jazz concert brought in 122,000 on the sale of 8,000 tickets .if the tickets sold for $10 and $20 each, how many of each type of tickets were sold?
What is the value of y in the equation 3(3y – 12) = 0? (5 points)
4
5
6
9
4.
How many solutions does the equation 5p – 4p – 8 = –2 + 3 have? (5 points)
One
Two
None
Infinitely many
The greatest common factor of a number n and 6 is 3. What are all of he possible whole-number values for n?
Answer: Odd multiple of 3.
[tex]3,\ 9,\ 15,\ 21, \ 27, \ 33, \ 39,\ 45,...........[/tex]
Step-by-step explanation:
Given : The greatest common factor of a number n and 6 is 3.
Then, it is clear that n should be a multiple of 3.
Prime factorization of 6 :
[tex]6=2\times3[/tex]
So for n a even number then the greatest common factor will be 6.
Thus , the possible choice for n is a odd multiple of 3.
Hence, the possible whole-number values for n are :
[tex]3,\ 9,\ 15,\ 21, \ 27, \ 33, \ 39,\ 45,...........[/tex]
Solve for b.
d = 3a + 3b
A)b=d−3a
B)b=d−3a/3
C)b=3a−d/3
D)b=d−3a/a
What's 755,082 rounded to the nearest 10,000
(1, -1) parallel to y= 2/5x-3
What is 2.085×106 in standard form?
208,500
285,000
2,085,000
2,850,000
2.085 x 10^6 =
move the decimal 6 places to the right: 2,085,000
Maryann is testing the effectiveness of a new acne medication. There are 100 people with acne in the study. Fifty-five patients received the acne medication, and 45 other patients did not receive treatment. Thirty of the patients who received the medication reported clearer skin at the end of the study. Twenty-two of the patients who did not receive medication reported clearer skin at the end of the study. What is the probability that a patient chosen at random from this study took the medication, given that they reported clearer skin?
Answer: 58 %
Step-by-step explanation:
Let M represents the event of taking medicine, M' represents the event of not taking medicine and C represents the event of clearing skin,
Thus, according to the question,
n(M) = 55,
n(M') = 45,
n(M∩C) = 30,
n(M'∩C)= 22,
⇒ n(C) = n(M∩C) + n(M'∩C) = 30 + 22 = 52
Let S shows the total number of people,
⇒ n(S) = 100
Hence, the probability of cleared skin,
[tex]P(C)=\frac{n(C)}{n(S)}=\frac{52}{100}=0.52[/tex]
And, the probability of cleared skin of that people who took the medicines,
[tex]P(M\cap C)=\frac{n(M\cap C)}{n(S)}=\frac{30}{100}=0.3[/tex]
Thus, the probability that a patient chosen at random from this study took the medication, given that they reported clearer skin,
[tex]P(\frac{M}{C})=\frac{P(M\cap C)}{n(C)}=\frac{0.3}{0.52}=0.57692307692\approx 0.58 = 58\%[/tex]
Answer: 0.58
Step-by-step explanation:
Let A = Event that the patients received the acne medication.
B = Event that the patients did not receive the acne medication.
C = Patient reported reported clearer skin.
Now,
[tex]P(A)=\dfrac{55}{100}=0.55\ \ ,P(B)=\dfrac{45}{100}=0.45[/tex]
[tex]P(C|A)=\dfrac{30}{55}\ \ , P(C|B)=\dfrac{22}{45}[/tex]
Using Bayes theorem, The probability that a patient chosen at random from this study took the medication, given that they reported clearer skin:
[tex]P(A|C)=\dfrac{P(A)\cdot P(C|A)}{P(A)\cdot P(C|A)+P(B)\cdot P(C|B)}\\\\=\dfrac{0.55\cdot\dfrac{30}{55}}{0.55\cdot\dfrac{30}{55}+0.45\cdot\dfrac{22}{45}}=0.576923076923\approx0.58[/tex]
Hence, the required probability : 0.58
5^2-11 over 6(3). Evaluate the expression. A. 7. B. 2/9. C.-1/63. D. 7/9
How many inches tall is a 7 foot basketball player?
Daniel Plays Videogames for 2/3 (Fraction) of an hour every night before dinner. hos many hours if videogames does he play altogether after 5 days.
How do you turn -13 into an improper fraction
A company’s profits (P) are related to increases in a worker’s average pay (x) by a linear equation. If the company’s profits drop by $1,500 per month for every increase of $450 per year in the worker’s average pay, what is the slope of the graph of the equation?
What is 23.66 times 2.03
Alex spend 3/4 of his money. He gave 1/4 of the remainder to his sister. He had $120 left. How much did have in the beginning?
use distributive property to find the product of (m+3)(m+7)
Answer:
m² + 10m + 21
Step-by-step explanation:
(m + 3)(m + 7)
m(m + 7) + 3(m + 7)
m² + 7m + 3m + 21
m² + 10m + 21
whats the answer to z−4/9−1/3=5/9
PLEASE HELP!!!!!
What is 4.2 as a mixed number?
What is 7.5 as a mixed number?
What is 8.8 as a mixed number?
What is 18.5 as a mixed number?
What is 10.5 as a mixed number?
Answer:
#1) 4 1/5
#2) 7 1/2
#3) 8 4/5
#4) 18 1/2
#5) 10 1/2
Step-by-step explanation:
In order to convert to a mixed number, place the numbers to the right of the decimal over 10. Reduce the fraction.
I hope this helped!
Write 0.12*10-3 as a decimal
which of these numbers are square numbers 25 36 48
Steven wants to buy a $565 bicycle. Steven has no money saved, but will be able to deposit $30 into a savings account when he receives his paycheck each Friday. However, before Steven can buy the bike, he must give his sister $65 that he owes her. For how many weeks will Steven need to deposit money into his savings account before he can pay back his sister and buy the bike?
The sales tax rates from 4 different countries are shown in the table. Convert each sales tax rate to a decimal. Then sort the countries from least to greatest tax rates.
Hamilton: 9/160
Oakland: 5.75%
Green: 5 7/8%
Campbell: 11/200
Converting Sales Tax Rates and Sorting by Rate
Convert Fractions to Decimals:
Hamilton: 9/160 = 0.05625
Oakland: 5.75% = 5.75 / 100 = 0.0575
Green: 5 7/8% = 47/8 / 100 = 0.05859375
Campbell: 11/200 = 0.055
2. Sort Countries by Tax Rate:
1. Campbell: 0.055
2. Hamilton: 0.05625
3. Oakland: 0.0575
4. Green: 0.05859375
Therefore, the countries sorted from least to greatest tax rates are:
1. Campbell (0.055%)
2. Hamilton (0.05625%)
3. Oakland (0.0575%)
4. Green (0.05859375%)
what is the difference between bisectors and perpendicular bisectors?
Final answer:
A bisector cuts a line segment or angle into two equal parts, while a perpendicular bisector not only does that but also intersects the line segment at a right angle.
Explanation:
In mathematics, a bisector is a line segment or line that divides an angle or segment into two equal parts. It cuts the angle or segment into two congruent angles or segments. For example, if you have a line segment AB and its bisector is a line segment CD, then CD divides AB into two congruent segments AC and CB.
A perpendicular bisector is a type of bisector that not only divides a line segment into two equal parts, but it also intersects the line segment at a right angle (90 degrees). So, in addition to being equidistant from the two endpoints of the line segment, the perpendicular bisector is perpendicular to the line segment as well.
what is 15%, 0.015, and 1/5 from least to greatest
Need help on my math homework
200 +6m = 500-6m
add 6m to each side
200+12m = 500
subtract 200 from each side
12m = 300
divide both sides by 12
m = 300/12 = 25
25 minutes
check:
200+ 25*6 = 200 +150 = 350
500 - 25*6 = 500-150 = 350
Okay So I just a question that I don't even know what it means, So if someone could help that would be awesome!
see attached picture for solution:
38 points!
Please do #11 and #12
In return:
Brainliest
Special Thanks
60 + 84
the sum of the numbers as a product of their GCF is?
Final answer:
The sum of 60 and 84 expressed as a product of their Greatest Common Factor is 144. You determine this by first finding the GCF, which is 12, and then adding the other factors (5 and 7) together and multiplying by the GCF.
Explanation:
To find the sum of the numbers 60 and 84 as a product of their Greatest Common Factor (GCF), you first need to calculate the GCF of the two numbers. The GCF of 60 and 84 is 12. You can divide each number by 12 to find the other factors, which are 5 for 60 and 7 for 84. Therefore, the sum of the numbers can be expressed as the product of their GCF and the sum of these other factors:
60 + 84 = (12 × 5) + (12 × 7)
GCF × (sum of other factors) = 12 × (5 + 7)
Now you can add the other factors:
5 + 7 = 12
Then multiply by the GCF:
12 × 12 = 144
So, the sum of the numbers expressed as a product of their GCF is 144.
What is the midpoint of AB if A = (−2, 2) and B = (3, −1)? Enter your answer in the boxes below.
Answer:
[tex](\frac{1}{2}, \frac{1}{2})[/tex]
Step-by-step explanation:
Since, the coordinates of the midpoint of a line segment having the endpoints [tex](x_1,y_1)[/tex] and [tex](x_2, y_2)[/tex] are,
[tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
Here,
[tex]x_1=-2, y_1=2, x_2 = 3, y_2=-1[/tex]
Hence, the coordinates of the midpoint of segment AB are,
[tex](\frac{-2+3}{2},\frac{2-1}{2})[/tex]
[tex](\frac{1}{2}, \frac{1}{2})[/tex]