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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Susan needs to buy apples and oranges to make fruit salad. She needs 15 fruits in all. Apples cost $3 per piece, and oranges cost $2 per piece. Let m represent the number of apples. Identify an expression that represents the amount Susan spent on the fruits. Then identify the amount she spent if she bought 6 apples. 30 + 5m; $36 30 + m; $36 30 + 5m; $24 30 + m; $24
Answer:
m + 30 ; $36
Step-by-step explanation:
Given that:
Total fruits needed = 15
Fruits needed :
Apple (m) ; cost = $3 per piece
Oranges (o) ; cost = $2 per piece
Amount spent on fruits :
[(cost of apple * number of apples) + (cost of orange *(total fruits - number of apples)]
3m + 2(15 - m)
3m + 30 - 2m
3m - 2m + 30
m + 30
Amount spent if 6 apples is purchased :
m = 6
m + 30
6 + 30 = $36
Find the dimensions of the rectangular box with largest volume if the total surface area is given as 4 cm2. (Let x, y, and z be the dimensions of the rectangular box).
Dimensions of the rectangular box with largest volume if the total surface area is given as 4 cm² : (√2/3 , √2/3 ,√2/3)
Given, rectangular box with largest volume.
Let f(x , y , z) = xyz
Ф ≡ xy + yz + xz - 2 = 0
[tex]F =[/tex] [tex]f + \lambda[/tex][tex]\phi[/tex]
[tex]F = xyz + \lambda (xy + yz + xz - 2)[/tex]
[tex]F_x = 0\\yz + \lambda(y + z) = 0......1\\\\F_y = 0\\xz + \lambda(x+z)= 0......2\\\\F_z = 0\\xy + \lambda(x + y) = 0..........3[/tex]
xy + yz + xz - 2 = 0........4
Solving the above 4 equations,
[tex]yz + \lambda(y + z) = 0\\\lambda = -yz/(y+z)\\\\xz + \lambda(x + z) = 0\\\lambda = -xz / (x+z)[/tex]
Evaluating the lambda values,
x = y
Similarly, y = z
Therefore, x² + x² + x² - 2 = 0
x = √2/3
y = √2/3
z = √2/3
Hence, Dimensions : (x , y , z) = (√2/3 , √2/3 ,√2/3)
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You are testing fertilizers on plants. One plant is 11 cm tall and growing at a rate of 2 cm/day. Write an equation that can be solved to find the number of days, d, it will take for the plant to be 65 cm tall.
The required equation that can be solved to find the number of days, d, it will take for the plant to be 65 cm tall is d= [tex]\frac{5.5\times 65}{11}\\[/tex]
From the question given, we are told that when testing fertilizers on a plant that is 11 cm tall, it is growing at a rate of 2 cm/day. This can be expressed as:
11cm = 2cm/dayWe can get the number of days it will take the 11cm plant to grow:
11cm = x
2cm = 1 day
[tex]2x = 11 * 1\\2x = 11\\x = 11/2\\x = 5.5 days\\[/tex]
Since it will take 5.5days for 11 cm plant tall to grow, to calculate the number of days 'd' it will take a 65cm plant tall to grow, we can say:
11cm = 5.5days
65cm = "d"
Cross multiply
[tex]11d = 5.5 \times 65\\d = \frac{5.5\times 65}{11}\\[/tex]
Hence the required equation that can be solved to find the number of days, d, it will take for the plant to be 65 cm tall is d= [tex]\frac{5.5\times 65}{11}\\[/tex]
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How do I write 4,332 in scientific notation??
Answer:
4.332 x 10 to the 3 power I do believe
Step-by-step explanation:
Answer:
4.332 times 10^3
Step-by-step explanation:
ion kno if thats right but i tried.
Suppose the time it takes a certain printer to print a document is an Exponential random variable with an average time of 15 seconds. You send a document to the printer at 1:00pm, and it is the third document in the queue. What is the probability that your printout will be ready by 1:01pm
Answer:
0.8046
Step-by-step explanation:
We're asked to calculate the probability that the job will be ready by 1.01 pm
From the question, we can note that the parameter of an Exponential is E(X)= 15
Next, to calculate the third job probability, we will have to use Poisson Distribution with parameter 1/λ
Therefore, E(Y) = 1/15
Then, The third job will be ready for 1:01 pm, and thus E(Y) = 61/15
Therefore, the required probability is
P(X ≥ 3) = 1 - P(X < 3)
= 1 - Poisson(3,4, true)
= 1 - 0.1954
= 0.8046
The auxiliary equation for the given differential equation has complex roots. Find a general solution. y''-10y' 29y=0
Answer:
[tex]y = Acos5x - Bsin5x[/tex]
Step-by-step explanation:
Given the differential equation y''-10y'+29y=0
First, we need to rewrite it as an auxiliary equation as shown:
Let y'' = m²y and y' = my
Substitute the values into the general equation
m²y-10my+29y = 0
Factor out y:
(m²-10m+29)y = 0 [The auxiliary equation]
Solve the auxiliary equation and find the roots of the equation
m²-10m+29 = 0
m = -b±√(b²-4ac)/2a
a = 1, b = -10, c = 29
m = -10±√(10²-4(1)(29))/2(1)
m = -10±√(100-116)/2
m = -10±√-16/2
m = (-10±4i)/2
m = -10/2 + 4i/2
m = -5+2i
Comparing the complex number with a+bi, a = -5 and b = 2
The general solution for complex solution is expressed as:
[tex]y = Acosax + Bsinax[/tex]
Substitute the value of a in the equation
[tex]y = Acos(-5)x + Bsin(-5)x\\y = Acos5x-Bsin5x[/tex]
Hence the general solution to the differential equation is [tex]y = Acos5x - Bsin5x[/tex]
Put a check mark for each set the number is part of:
1.56432...
Natural
Whole
Integer
U
Rational
Irrational
Real
Answer:
Irrational Number
Step-by-step explanation:
Given
[tex]Number = 1.56432..[/tex]
Required
Determine which set of number it is
The given number is not a natural number, whole number and it is not an integer because it contains decimal point
The given number is not rational because it can not be expressed as a fraction of two whole numbers.
Hence:
The set of the number is irrational
The figure shows the letter W and four of its transformed images—A, B, C, and D:
Which of the four images was formed by a reflection of the letter W?
A
B
C
D
Answer:
The answer is c
Step-by-step explanation:
Beacuse when u the shape is transfrromed that what u get
A pair of $72 sneakers is marked with a sign "$20 OFF or 20% OFF.
The $20 on final price is ________
The 20% Off final price is ________
Which deal will give you the cheaper final price?
Answer:
$52
$57.6
Step-by-step explanation:
$20 off $72 is equal to 72-20=$52
20% of $72 is $14.4 which will then lead to 72-14.4=$57.6
Real Estate Agent:
A woman bought 4 lots for $48,000 each. She then subdivided
them into a total of 7 lots that sold for $33,000 each. What was
her percent of profit? I
Savings and Loan Counselor:
A customer wishes to borrow $30,000, make monthly payments
of interest only, and pay the full amount of the principal at the
end of the term. If the interest rate is 12% annually, what are the
monthly payments for a five-year term?
Step-by-step explanation:
A.
Cost of 4 lots for $48,000= 48000*4
=$192,000
Sales made from all 7 lots = 33000*7
= $213,000
Profit =213,000-192,000
Profit =$39,000
Percent profit =(39000/192000) *100
=0.20*100
=20%
B.
Total interest formula=
Principal Loan Amount x Interest Rate x Time
Interest =30000x0.12x5
Interest = $18,000
Monthly payments for 5 years
= 18000/12*5
=18000/60
=$300
Fraction Multiplication and División:Question 4
Tina has $72 to spend on new t-shirts. If each t-shirt costs $12,
how many different t-shirts can Tina buy? Set up a fraction to
determine how many t-shirts Tina can buy. Then solve.
Answer: 6 T-shirts
Step-by-step explanation:72/12=6
Please answer correctly, will give brainlist.
Answer:
the answer is 77
Step-by-step explanation:
A measures 32 and B measures 109 so you subtract 109 and 32 and your answer will be 77
Sharon wants to open a checking account from which to pay bills. She wants online services, and a debit card, which both banks provide for free. Based upon past experience, she expects to accidentally overdraft the account 1 time per year, due to unexpected charges and miscommunications. She expects no 2nd copies of statements, and to use network ATMs 4 times per month with either bank. She has $3300 in an emergency savings account at First State Bank, and thinks that the balance will be enough to cover overdrafts in the future if automatic transfers are made when needed.
Answer:
a.No, Common Bank will save Sharon more money.
Step-by-step explanation:
There are two banks i.e. first state bank and the common bank that should be compared in the table depend upon the prices of both the banks
On seeing it we get to know that the first state bank would charged a fee on a monthly basis i.e. $4 while on the other hand the common bank has no fee on the monthly basis
Also the unsufficient bonds are more cheaper in the common bank if we compared with the first state bank
Moreover, the $7 is charged in the first state bank and $3 charged in the common bank.
Therefore the common bank would become cheaper
Hence, the correct option is a.
Answer:
Sharon wants to open a checking account from which to pay bills. She wants online services, and a debit card, which both banks provide for free. Based upon past experience, she expects to accidentally overdraft the account 1 time per year, due to unexpected charges and miscommunications. She expects no 2nd copies of statements, and to use network ATMs 4 times per month with either bank. She has $3300 in an emergency savings account at First State Bank, and thinks that the balance will be enough to cover overdrafts in the future if automatic transfers are made when needed.
A 4-column table with 5 rows. Column 1 is labeled First State Bank with entries monthly fee, non-sufficient funds fee, second copy of statement, network A T M usage, non-sufficient funds protection from a First State Bank savings account. Column 2 is labeled Description with entries 4 dollars, 36 dollars, 7 dollars, 3 dollars each transaction, 4 dollars on each day that a transfer occurs to cover an overdraft. Column 3 is labeled Common Bank with entries monthly fee, non-sufficient funds, second copy of statement, network A T M usage, non-sufficient funds protection from a Common Bank savings account. Column 4 is labeled Description with entries 0 dollars, 24 dollars, 4 dollars, 2 dollars each transaction, not offered with this account.
Based on the tables of fees, above, if Sharon chooses First State Bank, will it save her money over choosing Common Bank?
a. No, Common Bank will save Sharon more money. <<<---Correct b. Yes, First State Bank will save Sharon money. c. No, First State Bank and Common Bank would have the same costs for Sharon. d. No, costs cannot be estimated in advance, so this information cannot be used.Step-by-step explanation:
Edge 2021
Same Thing as the first one
Which one doesn't belong? Give me two reasons why. There are no wrong answers. please answer. Picture posted
5/4; it is an inproper fraction in a group of proper ones. it also doesnt have a 2 anywhere.
20/25; it is the only one that isnt simplified. it also has double didgits in both the numerator and denominator
Evaluate the function for the indicated values of x.
[Look at image]
Answer:
f(-10) = -19
f(2) = 4
f(-5) = -9
f(-1) = 1
f(8) = -5
Step-by-step explanation:
The area of a parallelogram is 24 square units. One side of the parallelogramis
36 units long. The other side is 4 units long. Which could be the parallelogram's
height? Choose all the correct answers.
A.1/6
B.2/3
C.3/2
D.6
E.9
The required height of the parallelogram is 2/3. Option B is correct.
Given that,
The area of a parallelogram is 24 square units. One side of the parallelogramis 36 units long. The other side is 4 units long. Which could be the parallelogram's height is to be determined.
A parallelogram is a quadrilateral consisting of pairs of parallel side.
Here,
We have given the area of the parallelogram and the measure of its base. So,
Area of the parallelogram = base * height
24 = 36 * height
height = 2 / 3
Thus, the required height of the parallelogram is 2/3. Option B is correct.
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Suppose you are working with a data set that is normally distributed, with a mean of 350 and a standard deviation of 48. Determine the value of x from the following information.
a. 70% of the values are greater than x.
b. x is less than 10% of the values.
c. 24% of the values are less than x.
d. x is greater than 60% of the values.
Answer:
324.848
288.464
316.112
337.856
Step-by-step explanation:
Given that :
Mean (m) = 350
Standard deviation (σ) = 48
Determine the value of x for the following :
Using the z probability calculator :
a.) 70% of the values are greater than x.
1 - 0.7 = 0.3
P(x < 30%) = P(x < 0.3) = - 0.524 = z
Z = (x - m) / σ
x = (z * σ) + m
X = (- 0.524 * 48) + 350 = 324.848
b.) x is less than 10% of the values.
P(x < 0.1) = - 1.282 = z
X = (- 1.282 * 48) + 350 = 288.464
C.) 24% of the values are less than x
P(x < 0.24) = - 0.706 = z
X = (- 0.706 * 48) + 350 = 316.112
D.) x is greater than 60% of the values
P(x > 0.6) = -0.253 = z
X = (- 0.253 * 48) + 350 = 337.856
In AJKL, JL is extended through point L to point M, mZLJK = (2x + 2)°,
mZKLM = (82 – 16)°, and m/JKL (3x + 6)". Find mZKLM.
Answer:
<KLM = 48 degrees
Step-by-step explanation:
According to the instructions, we construct the triangle JKL and extend the side JL to point M. The information about the angles is shown in the attached image.
Recall that the addition of all internal angles of a triangle must give 180 degrees.
The angles we need to complete the addition is angle <JLK, which happens to be the supplementary angles to angle <KLM
Therefore <JLK = 180 - (8 x - 16) = 180 - 8 x + 16 = 196 - 8 x
The we can now solve for "x" in the equation of addition of internal angles of a triangle:
(2 x + 2) + (3 x + 6) + (196 - 8 x) = 180
Combining like terms on the left
- 3 x + 204 = 180
subtracting 204 from both sides:
- 3 x = 180 - 204
- 3 x = - 24
divide both sides by "-3" to isolate x
x = - 24 / (-3)
x = 8 degrees
Now that we know "x", we can find the measure of angle <KLM via its formula:
<KLM = 8 x - 16 = 8 (8) - 16 = 48 degrees
Maggie makes blankets to sell. The table shows Maggie’s expense, f(x), her revenue, g(x), and her profit, h(x), per unit of yarn used, x.
Which expresses h(x) as a combined function?
h(x) =
x + f(x)
(f+g)(x)
(f-g)(x)
(g-f)(x)
Answer:
(g-f)(x)
Step-by-step explanation:
You have to subtract expenses from revenue and multiply by yarn to equal profit
Suppose an internet marketing company wants to determine the current percentage of customers who click on ads on their smartphones. How many customers should the company survey in order to be 90% confident that the estimated proportion is within five percentage points of the true population proportion of customers who click on ads on their smartphones
Answer:
The value is [tex]n =271[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 5\% = 0.05[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 90 ) \%[/tex]
=> [tex]\alpha = 0.10[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally we will assume that the sample proportion is [tex]\^ p = 0.5[/tex] since we have no information on the proportion of of customers who click on ads on their smartphones
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{1.645 }}{0.05} ]^2 * 0.5 (1 - 0.5 ) [/tex]
=> [tex]n =271[/tex]
Using the z-distribution, as we are working with a proportion, it is found that 271 customers should be sampled.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem:
90% confidence level, hence the critical value is z = 1.645.No prior estimate, hence p = 0.5.Within five percentage points, hence M = 0.05.Then:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.05\sqrt{n} = 0.5 \times 1.645[/tex]
[tex]\sqrt{n} = [10(1.645)][/tex]
[tex](\sqrt{n})^2 = [10(1.645)]^2[/tex]
[tex]n = 270.6[/tex]
Rounding up, 271 customers should be sampled.
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What is the number that comes in 21,7,15,11 times table
Answer:
i think it is 105
but 105 divide by 11 is 9.54
To the nearest megawatt, what is the mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010?
Answer:
7739.5
Step-by-step explanation:
How much will cost to buy beef for a family of 2 if each person gets 1/2 pound of beef and the beef cost 5.99 per pound?
Answer:
it will cost 5.99
Step-by-step explanation:
because each person getting half and there are 2 peeps so add up the meet to make on pound
Three Rivers publishes a catalog each year, last year it had 198 pages back and front. We
print 150 copies. How much does it cost the college if a ream, 500 pages, cost
$7.40 each?
Answer:
$222
Step-by-step explanation:
We need to find how many ream was used in the printing forts, to determine how much the College spent.
The catalog is 198 pages, back and front, which means, 1 leaf will take 2 pages. Therefore, 99 pages were used in printing 1 copy of the catalog.
No of pages that were used in printing 150 copies = 150*99 = 14,850 pages.
If 500 pages = 1 realm, therefore,
14,850 pages = 14,850/500 = 29.7.
Since, it's a full team that is sold, let's approximate the number of reams bought to be 30 reams.
If 1 ream costs $7.40, therefore,
30 reams = 30*7.40 = $222
I’ll mark brainliest tysm
-13 EX: 2(-4) - 5 = -8 -5 = -13
-7
-1
1
3
THESE ARE THE ANSWERS
can somebody please help me with this quesiotion
Answer:
-3
Step-by-step explanation:
sense its between -2 and -4
*question
Choose the letter of the correct answer Write your answer on a separate
sheet
1. What do you call an expression in fraction form in which the numerator and
the denominator are polynomials?
A. rational algebraic equation
C. rational algebraic expression
B. linear algebraic expression
D. finear algebraic equation
2. In a rational algebraic expression written in the form of where P and Q are
polynomials, the polynomial Q must not be equal to
AO
C 2
B.
D. 3
3. Which of the following is a rational algebraic expression?
Answer:
1. Rational Algebraic Expression
2. 0
3. See explanation
Step-by-step explanation:
Solving (1):
From the list of given options, Option C. Rational Algebraic Expression answers the question.
And it is always of the form P/Q where P and Q are polynomials
Take for instance
P = x² - x + 2 and Q = x² + 2x - 4
P/Q = (x² - x + 2)/(x² + 2x - 4)
The above expression is a perfect example of a Rational Algebraic Expression
Solving (2): The denominator of a rational algebraic expression must not equal 0
Hence, option A answers the question
Solving (3): The options are missing.
However, a perfect example has been sighted on (1) above
If the polygon is rotated 90' clockwise about the origin, the measure of angle W' is
Answer:
If you are referring to the angle of the polygon, than it is the same, if you are referring to the angle between the initial and final point about the origin, than it's a right angle. If there is a point(x,y) rotated about the origin(0,0), then the new point will be (y,-x).
The following is the correct way to show the product for 0.297×7.1:
Answer:
2.1087
Step-by-step explanation:
0.297
7.1 +
2.1087