hello,
y-coordinate is found by computing f(0)=c
so this is the point (0,c)
the vertex is found for x = -b/(2a)
[tex]f(\dfrac{-b}{2a})=\dfrac{ab^2}{4a^2}-\dfrac{b^2}{2a}+c\\\\=\dfrac{b^2-2b^2+4ac}{4a}\\\\=-\dfrac{b^2-4ac}{4a}[/tex]
So this is the point ( -2(2a), -(b^2-4ac)/(4a) )
thanks
The vertex of the parabolic graph is, [tex]\rm\left ( -4a, \dfrac{-b^2+4ac}{4a} \right ) \\\\[/tex]
Given that,
[tex]\rm f(x) = ax^{2} +bx+c[/tex]
We have to determine,
The y-coordinate of the vertex of the parabolic graph?
According to the equation,
The vertex of a parabola is the point at which the parabola passes through its axis of symmetry.
In case the coefficient of the x² term is positive, and then the vertex will be located at the lowest point on the graph, the point at the base of the “U”-shape.
On the contrary, if the coefficient of the x² term is negative, the vertex will be located at the highest point on the graph, at the top of the “U”-shape.
Therefore,
The vertex of the parabola of the given quadratic equation,
[tex]\rm f(x) = ax^{2} +bx+c[/tex]
The co-ordinate is founded when x = 0,
[tex]\rm f(x) = ax^{2} +bx+c\\\\\rm f(0) = a(0)^{2} +b(0)+c\\\\\rm f(0) = c[/tex]
Then, The vertex is found at point (0, c) at x = -b\2a,
[tex]\rm f \left (\dfrac{-b}{2a }\right) = a\left (\dfrac{-b}{2a }\right) ^2 + b \left (\dfrac{-b}{2a }\right) +c\\\\f \left (\dfrac{-b}{2a }\right) = a \left (\dfrac{b^2}{4a^2 }\right)- \left (\dfrac{b^2}{2a }\right) +c\\\\f \left (\dfrac{-b}{2a }\right) = \left (\dfrac{b^2}{4a }\right)- \left (\dfrac{b^2}{2a }\right) +c\\\\f \left (\dfrac{-b}{2a }\right) = \dfrac{b^2-2b^2+4ac}{4a}\\\\f \left (\dfrac{-b}{2a }\right) = \dfrac{-b^2+4ac}{4a}\\\\[/tex]
Hence, The vertex of the parabolic graph is, [tex]\rm\left ( -4a, \dfrac{-b^2+4ac}{4a} \right ) \\\\[/tex].
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2x + y = 15
Whats the slope
Answer:
-2
Step-by-step explanation:
Y = mx+c
M here being the number in front of x
"The intersection of two planes is a line" is a statement that is generally accepted as true, but
cannot be proven to be true. What type of statement is this?
1. defined
2. undefined
3. postulate
4. proof
A postulate is something that is assumed to be true and there isn't a proof for it as its something foundational to help set up further proofs later down the road. Another example of a postulate is that a line is defined by two distinct points.
A meteorologist is monitoring the atmospheric pressure as his height above sea level varies. The meteorologist determines that the atmospheric pressure decreases by 12% for each additional kilometer the city is above sea level. The atmospheric pressure at sea level is 103 kPa (kilopascals). Define a function, p , that determines the atmospheric pressure (in kPA) in terms of the number of kilometers the city is above sea level, n .
Answer:
The function [tex]p(n)[/tex] is represented by [tex]p(n) = 103\cdot (0.88)^{n}[/tex].
Step-by-step explanation:
Statement indicates that atmospheric pressure decreases exponentially when height above sea level is increased. This fact is represented by the following model:
[tex]p(n) = p_{o}\cdot r^{n}[/tex] (Eq. 1)
Where:
[tex]p_{o}[/tex] - Atmospheric pressure at sea level, measured in kilopascals.
[tex]r[/tex] -Atmospheric pressure decrease rate, dimensionless.
[tex]n[/tex] - Height above sea level, measured in kilometers.
[tex]p(n)[/tex] - Current pressure, measured in kilopascals.
If we know that [tex]p_{o} = 103\,kPa[/tex] and [tex]r = 0.88[/tex], the function [tex]p(n)[/tex] is represented by:
[tex]p(n) = 103\cdot (0.88)^{n}[/tex]
What is the measure of the missing angle?
36°
57°
Answer:
7767788877787887+-77-7
Is 40 cm equal to 4 m?
Answer:
There are 100 centimetres in one metre. Therefore, 4 metres is equal to 4 x 100 = 400 centimetres. This is longer than 40 centimetres.
You own 16 CDs. You want to randomly arrange 5 of them in a CD rack. What is the probability that the rack ends up in alphabetical order?
Answer:
[tex]\frac{1}{524160} or 1.910^{-6}[/tex]
Step-by-step explanation:
In order to solve this, you would need to multiply the probability of you choosing the one that goes first, so 1 in 16 discs, then the next one so 1 in 15, and so on untill the fifth disc.
So you would have to do this:
[tex](\frac{1}{16})(\frac{1}{15})(\frac{1}{14})(\frac{1}{13})(\frac{1}{12})\\\frac{1}{524160}[/tex]
That is the probability that the rack ends up in alphabetical order, if you pull discs randomly, 1 in 524160 chances.
Probabilities are used to determine the chances of an event.
The probability that the rack ends up in alphabetical order is [tex]\mathbf{ \frac{1}{524160}}[/tex]
The given parameters are:
[tex]\mathbf{CD = 16}[/tex]
[tex]\mathbf{r = 5}[/tex] -- CDs to arrange
So, the total number of arrangements of 5 CDs from the 16, is:
[tex]\mathbf{Total = ^{16}P_5}[/tex]
Apply permutation formula
[tex]\mathbf{Total = \frac{16!}{(16 - 5)!}}[/tex]
This gives
[tex]\mathbf{Total = \frac{16!}{11!}}[/tex]
Expand
[tex]\mathbf{Total = \frac{16 \times 15 \times 14 \times 13 \times 12 \times 11!}{11!}}[/tex]
[tex]\mathbf{Total = 16 \times 15 \times 14 \times 13 \times 12 }[/tex]
[tex]\mathbf{Total = 524160}[/tex]
There is only one possibility of the CDs being in alphabetical order.
So, the probability is:
[tex]\mathbf{Pr = \frac{1}{524160}}[/tex]
Hence, the probability that the rack ends up in alphabetical order is [tex]\mathbf{ \frac{1}{524160}}[/tex]
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Which of the following Geometric Objects are defined? Select ALL that apply.
Answer:
[]line
[]plane
[]line segment
BRAIN MEH
Which type of graph is typically not used for quantitative data?
Answer:
bar graph
pie chart
histogram
Step-by-step explanation:
7. Sociologists can get three possible answers to a typical survey question such as "Do you believe in the tooth fairy?" - namely, yes, no and no opinion. With this in mind, the Sociomagnetic Computer Company has decided to build a computer to process survey data. This computer has a trinary memory - that is, each byte (tryte?)consists of 8 trits, with a trit holding a 0, 1, or 2. How many trits are needed to hold a 6-bit number? Give an expression for the number of trits needed to hold n bits.
Answer:
1. n ≥ 4
2. N ≥ nlog(2)÷log3
Step-by-step explanation:
1
1 byte = 8 bits
each byte = 8 trits
a 6 bit number = [tex]2^{6} = 64[/tex]
3n ≥ 64
divide through by3
n ≥ 64/3
we take the logarithm
n ≥ [tex]\frac{log64}{log3}[/tex]
n ≥ 1.8062 ÷ 0.4771
n≥3.785
when approximated, n ≥ 4. So the number of trits needed in the storage of 6 bit is atleast 4
2.
to hold n bits, we can do something similar.
3N ≥ 2n
we take log of both sides
such that;
N ≥ [tex]\frac{nlog(2)}{log(3)}[/tex]
Suppose the manager of your local McDonalds tracks the
monthly sales of their new McBurger, Mini McBurger, and
Choco-Latte Shake. The data is listed below.
For January through December, the sales are as follows.
McBurger: 46, 63, 58, 77, 81, 102, 183, 197, 125, 111, 83, 218.
Mini McBurger: 23, 41, 35, 44, 62, 88, 95, 99, 108, 111, 98, 63.
Choco-Latte Shake: 88, 46, 39, 52, 67, 99, 189, 238, 188, 97,
51, 12
Create a matrix to display the data.
Answer:
Step-by-step explanation:
The question says "Create a matrix to display the data".
The are 3 products:
- McBurger - Mini McBurger - ChocoLatte Shake
The figures represent monthly sales for each product, in a given year. This means 12 figures for each product - represent the 12 months of the year.
These figures will appear on the matrix, with the horizontal arrangement representing each month of the year and the vertical arrangement representing each product's sales.
In that light, you'll have a 12 by 3 matrix.
[tex]\left[\begin{array}{ccc}46&23&88\\63&41&46\\58&35&39\\77&44&52\\81&62&67\\102&88&99\\183&95&189\\197&99&238\\125&108&188\\111&111&97\\83&98&51\\218&63&12\end{array}\right] 12 by 3 matrix[/tex]The first row represents sales in January, the second row represents sales in February, the third row represents sales in March, the fourth row represents sales in April, etcetera.
The first column represents sale of McBurger, the second column represents sale of Mini McBurger, the third column represents sale of Choco-Latte Shake.
HELP PLEASE!!!! WILL MARK BRAINLIEST, AND FRIEND REQUEST!!!!
which expression represents a rational number
5/9 + [tex]\sqrt{18}[/tex]
[tex]\pi + \sqrt{16}[/tex]
2/7+ [tex]\sqrt{121}[/tex]
3/10 + [tex]\sqrt{11}[/tex]
Answer:
hmm easy peasy
Step-by-step explanation:
C
C is the only answer with the square root thats a whole number while the rest of the answers ' square roots are not whole number answers and the numbers after the decimal go on forever making it an irrational number. Also, for B, pi is not a rational number.
Which label on the cone below represents the height?
I think D represents the height, i don't know that for sure but yoy can try?
Answer:
Well d because there is a line going from bottom to top of the cone next to the D
Step-by-step explanation:
Choose an expression for the number of scoops Zack needs to fill both feeders. Will make brainliest if u tell me in under a minute!!!
Answer:
C
Step-by-step explanation:
Please mark brainliest
What is the approximate
area of a circle with a diameter of 7?
Answer:
38.48
Step-by-step explanation:
In terms of the entire bill, which rational number represents the net change to Callie’s bank account? What does the sign on the number mean?
Answer:
Callie has 4 months to pay off the bill. The rational number is +4. The sign is positive because it represents a quantity of something, in this case, months.
Step-by-step explanation:
this is correct...
trust me :)
The sign is positive because it represents a quantity of something, in this case, months.
Callie has 4 months to pay off the bill.
The rational number is +4.
What is the rational number?
A number that can be represented as the quotient p/q of two integers such that q ≠ 0. In addition to all the fractions, the set of rational numbers includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator.
The sign is positive because it represents a quantity of something, in this case, months.
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PLEASE HELP
Select the correct answer from each drop-down menu. Options are (equal to, not equal to)
Answer:
Not equal to.
Step-by-step explanation:
If peter drove for 9 hours at an average speed of 63 miles per hour, how far did he drive?
Answer:
567 miles
Step-by-step explanation:
9 hours x 63 miles per hour = 567 miles total
on the map above.
In the United States, large quantities of oil and natural gas can be found in region
A. 1
B. 2
C. 3
D. 4
Please select the best answer from the choices provided
A
B
С
D
Answer: C
Step-by-step explanation:The top producing states are Texas, Oklahoma, New Mexico, Wyoming, and Louisiana, which produce more than 50 percent of U.S. natural gas.
Answer:
Your answer is C
colleen is searching online for tickets two weeks ago the cost to fly from orlando to hartford was 200$ . Now the cost is 335$ what is the percent increase what would be the percent increase if the airline charges an additional $50 baggage fee with the new price. the percent increase of the airline ticket is...... and i will give a brainlest to the best
The percentage increase for flight tickets to fly from orlando to hartford would be = 67.5% and 92.5% when there is an additional $50 to the new price.
What is percentage Increase?Percentage increase is defined as the rise in the quantity or amount for an object which is converted into percentage.
The formula for percentage increase would be = increase ÷ original amount × 100
The increase of the cost = 335 - 200 = $135
The original amount = $200
The percentage increase = 135/200 × 100
= 13500/200 = 67.5%
But if the increase in cost is 135 + 50 = $185
The percentage increase of the new cost would be;
= 185/200 ×100
= 18500/200
= 92.5%
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divide the complex numbers
Answer:
1/4 - 1/3i
Step-by-step explanation:
(4+3i)(-i) / 12i(-i)
= 3 - 4i / 12
7th grade math help me plzzz
Answer:
11.a) is 15+5.50+3 maybe
11.b) is $3.50 because 15-12=3 3+5.50=8.50 8.50+3=11.50 11.50-8=3.50
Question 2: A researcher plans to examine what butterfly species are present in one acre of prairie land in Alberta, Canada. The data will be collected as a list of the Latin name for the species. This data can be considered: * qualitative nominal qualitative ordinal quantitative discrete quantitative continuous
Answer:
qualitative nominal
Step-by-step explanation:
The data collected while examining the species of butterflies present in a particular area which are represented using Latin names is a non-numeric data type is aimed at separating or making distinction among the species available. These types of data used in classification are called Qualitative variables.
Also, the data is nominal and not ordinal, this is because there is no sort of order or ranking in the groups or species names. Qualitative variables in which does not posses ordering or ranking in the categories are represented on the nominal scale. Whose which implies order or rank are represented on the ordinal scale.
The Carousel at Carowinds has 4 rings of horses. Fred is riding on the inner ring, which has a radius of 7 feet. Juan is riding on the outer ring, which is 10 feet farther out from the center than the inner ring is. In one rotation of the carousel, how much farther does Juan travel than Fred? Use 3.14 for .
Answer:
Juan travel 31.4 feet farther than Fred in one rotation.
Step-by-step explanation:
In this problem we need to determine the change in linear position of Fred and Juan, whose formula is:
[tex]s=\theta \cdot r[/tex] (Eq. 1)
Where:
[tex]r[/tex] - Radius, measured in feet.
[tex]\theta[/tex] - Angular arch, measured in radians.
[tex]s[/tex] - Change in linear position, measured in feet.
If both makes one rotation in the carousel, we obtain the change in linear position of each player:
Fred ([tex]r = 7\,ft[/tex], [tex]\theta = 2\pi[/tex])
[tex]s= 2\pi\cdot (7\,ft)[/tex]
[tex]s = (3.14)\cdot (7\,ft)[/tex]
[tex]s = 21.98\,ft[/tex]
Juan ([tex]r = 17\,ft[/tex], [tex]\theta = 2\pi[/tex])
[tex]s= 2\pi\cdot (17\,ft)[/tex]
[tex]s = (3.14)\cdot (17\,ft)[/tex]
[tex]s = 53.38\,ft[/tex]
And the difference between both travelled distances is:
[tex]\Delta s = 53.38\,ft-21.98\,ft[/tex]
[tex]\Delta s = 31.4\,ft[/tex]
Juan travel 31.4 feet farther than Fred in one rotation.
The scale on a map is 1 :50000.
The area of a field on the map
is 1.2square centimetres.
Calculate the actual area of the field in square kilometres.
Answer:
The actual area of the field in square kilometers is [tex]30000000 km^2[/tex]
Step-by-step explanation:
Scale : 1 cm = 50000 km
Area of field on map = [tex]1.2 cm^2[/tex]
Now , 1 cm = 5000 km
[tex]1 cm^2 = (5000 km)^2[/tex]
We are supposed to find the actual area of the field in square kilometers.
So, the actual area of the field in sq. km =[tex]1.2 \times (5000)^2[/tex]
Actual area of the field in sq. km [tex]=30000000 km^2[/tex]
Hence the actual area of the field in square kilometers is [tex]30000000 km^2[/tex]
A chemist is performing an experiment by observing the effects when she combines two solutions. She monitors the temperature of the combined solution over the course of eight hours and records it in this table below.
The chemist can model the temperature with a polynomial function. During these eight hours, over what interval is the temperature decreasing?
A. From hour 0 to hour 8
B. From hour 5 to hour 8
C. From hour 0 to hour 5
D. From hour 2 to hour 6
Answer:
A. From hour 0 to hour 5
Step-by-step explanation:
For all Plato users
Interval of the temperature decreasing is from hour 0 to hour 5.
What is interval?
an interval is defined as a group of numbers which includes all numbers between the beginning and the end.
According to given data is showing that the temperature decreasing zero hour to 1 hour , then 1 to 2 hour, then 2 to 3 hour, then 3 to 4 hour, then 4 to 5 hour.
So the interval of the temperature decreasing is from hour 0 to hour 5.
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Solve the inequality. Graph the solution. -4s<6s +1
Answer:
Step-by-step explanation:
First solve the inequality by writing it.
-4s < 6s + 1
Now subtract -1 on both sides.
-4s - 1 < 6s
Now add 4s on both sides to combine like terms.
-1 < 10s
Now divide 10 on both sides.
-0.1 < s
Now flip it over properly.
s > -0.1
Hope this helped! <3
Use the figure for exercises 1-4
Name the intersection of plane S and line j
Each costume needs 46 centimeters of red ribbon and 3 times as much yellow ribbon. What is the total length of the ribbon needed for 64 costumes? Express your answer in meters.
Answer:
I think its 117.76 meters
Step-by-step explanation:
you multiply the 46 x 3 then you get 138 yellow ribbon then 138 + 46 then its 184 then 184 x 6 = 11776
Answer:
117.76 meters
Step-by-step explanation:
46x64=2,944 (red ribbon)
46x3=138x64=8,832 (yellow ribbon)
8,832+2,944=11,776 (all ribbon)
11,776 centimeters converted into meters is 117.76 meters
HELPPPPPP
Giving that you already know what your grades are on your report card. Please write 1 paragraph on how you would like to improve your grade in math and what steps you plan to take to do so.
my grades are A's and B's and one C. my grade in her class is a B!! help me!!!!
Answer:
I would study more, dedicate more time. I would NOT give up at all. Take constant breaks to reset your brain. Do practice problems and more.
Step-by-step explanation:
Find the midpoint of the segment with the following endpoints. (6, 4) and (9, 1)
Answer:
[tex](\frac{15}{2},\frac{5}{2})[/tex]
Hope this helps!