Answer:
y = 2x² − 12x + 8
Step-by-step explanation:
FIRST METHOD :
y = 2x² − 12x + 8
= (2x² − 12x) + 8
= 2 (x² − 6x) + 8
= 2 (x² − 6x + 9 − 9 ) + 8
= 2 (x² − 6x + 9) − 2×9 + 8
= 2 (x² − 6x + 9) − 18 + 8
= 2 (x² − 6x + 9) − 10
= 2 (x − 3)² − 10
Then ,the equation has a extremum value of (3,-10)
Since the number 2 in the equation y = = 2 (x − 3)² − 10 is greater than 0
(2 > 0) , the graph (parabola) opens upward
Therefore ,the extremum (3,-10) is a minimum.
SECOND METHOD :
the graph of a function of the form f(x) = ax² + bx + c
has an extremum at the point :
[tex]\left( -\frac{b}{2a} ,f\left( -\frac{b}{2a} \right) \right)[/tex]
in the equation : f(x) = 2x² − 12x + 8
a = 2 ; b = -12 ; c = 8
Then
[tex]-\frac{b}{2a} = -\frac{-12}{2 \times 2} = 3[/tex]
Then
[tex]f\left( -\frac{b}{2a} \right) = f(3) = 2(3)^2- 12(3) + 8 = 18 - 36 + 8 = -18 + 8 = -10[/tex]
the graph of a function f(x) = 2x² − 12x + 8
has an extremum at the point (3 , -10)
Since the parabola opens up ,then the extremum (3,-10) is a minimum.
Finding a percentage of a total amount: Real-world situations
A file that is 258 megabytes is being downloaded. If the download is 13.3% complete, how many megabytes have been downloaded? Round your answer to the
nearest tenth.
Answer: 34.3 megabytes
Step-by-step explanation:
To find how many megabytes have been downloaded you must multiply 13.3% by 258. 13.3% can be written as the decimal 0.133
Now let's multiply
[tex]258[/tex]×[tex]0.133[/tex]=34.314
Rounded to the nearest tenth that is 34.3
Three books are what percent of four books?
If four books are 100%, then 3 books are how much percent of total books?
[tex]\frac{3}{4}[/tex] × 100 = 3 × 25 = 75%
Hope it helps!
The answer is 75%.
To find the percentage, divide the number of given books by total books and multiply by 100%.
(3 ÷ 4) × 100%0.75 × 100%75%For what value of x is the rational expression below undefined?
3x+15/6-x
Let the function be (3x+15)/(6-x) then the value of x exists at -5.
What is the value of x?Given: Rational Expression (3x+15)/(6-x)
To find the value of x when given a rational expression equivalent to 0.
To estimate the value of x, convey the variable to the left side and convey all the remaining values to the right side. Simplify the values to estimate the result.
Consider, (3x+15)/(6-x) = 0
3x + 15 = 0(6-x)
3x + 15 = 0
Subtract 15 from both sides of the equation, e get
3x + 15 - 15 = 0 - 15
simplifying the above equation, we get
3x = 0 - 15
3x = -15
Divide both sides by 3, then we get
x/3 = -15/3
x = -5
Therefore, the value of x exists at -5.
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Supervisor: "Last week, you spoke with 800 customers in 40 hours."
Employee: "That is an average of ____ customers every 30 minutes."
Answer: 10
Step-by-step explanation: 800/80 = 10
sin theta =-(1)/(\sqrt(17))and (3\pi )/(2)<=\theta <=2\pi then tan\theta =
Using a trigonometric identity, and considering that the angle is in the fourth quadrant, the tangent of the angle is given as follows:
tan(theta) = -1/4
Which trigonometric identity relates the sine and the cosine of an angle?The following identity is used to relate the measures, considering an angle [tex]\theta[/tex]:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
For this problem, the sine is given as follows:
[tex]\sin{\theta} = -\frac{1}{\sqrt{17}}[/tex]
Then the cosine, which we need to find the tangent, is found as follows:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
[tex]\left(-\frac{1}{\sqrt{17}}\right)^2 + \cos^2{\theta} = 1[/tex]
[tex]\frac{1}{17} + \cos^2{\theta} = 1[/tex]
[tex]\cos^2{\theta} = \frac{16}{17}[/tex]
[tex]\cos{\theta} = \pm \sqrt{\frac{16}{17}}[/tex]
Since the angle is in the fourth quadrant, the cosine is positive, hence:
[tex]\cos{\theta} = \frac{4}{\sqrt{17}}[/tex]
What is the tangent of an angle?It is the sine of the angle divided by the cosine of the angle, hence:
[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}} = \frac{-\frac{1}{\sqrt{17}}}{\frac{4}{\sqrt{17}}} = -\frac{1}{4}[/tex]
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3. Complete the table (showing work) and draw a graph of the logarithmic function f(x) = log 1/5 x
Answer:
Step-by-step explanation:
What is the name for a mathematical phrase? O A. An inequality OB. An operation OC. An expression OD. An equation
22. Kim earns x dollars per hour for the first 40 hour she works in a week
and 1-
1¹/1/12 times as much for each hour over 40. If she worked 52 hours
last week, how much, in dollars, did she earn?
(A) 52X
0+1=1/x
(C) 52x+1-¹-x
(B) 40+1
(D) 52x-1-x
(E) 58x
40+1 in dollars per hour
A _____ is a solid consisting of a suite a point not in the same plane as the square and all points between them
Answer:
Square Pyramid
Step-by-step explanation:
Thats what a Square Pyramid is
Find the value of B - A if the graph of Ax + By = 3 passes through the point (-7,2), and is parallel to the graph of x + 3y = -5
Answer: -6
Step-by-step explanation:
[tex]x+3y=-5\\\\3y=-x-5\\\\y=-\frac{1}{3}x-\frac{5}{3}[/tex]
So, since parallel lines have the same slope, the slope of the line we need to find is -1/3.
Substituting into point-slope form, the equation is
[tex]y-2=-\frac{1}{3}(x+7)\\[/tex]
Converting to the required form,
[tex]y-2=-\frac{1}[3}x-\frac{7}{3}\\\\\frac{1}{3}x+y=-\frac{1}{3}\\\\-3x-9y=3[/tex]
So, B-A is equal to -6.
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The statements which are correct about the equation of circle [tex]x^{2} +y^{2}-2x-8=0[/tex] are 1) The radius of the circle is 3 units,2) The center of the circle lies on the x axis,5) The radius of this circle is the same the radius of the circle whose equation is [tex]x^{2} +y^{2} =9[/tex].
Given the equation of circle be [tex]x^{2} +y^{2}-2x-8=0[/tex].
We are required to find the appropriate statements related to the equation [tex]x^{2} +y^{2}-2x-8=0[/tex].
[tex]x^{2} +y^{2}-2x-8=0[/tex] can be written as under:
[tex]x^{2} +y^{2} -2x+1-9=0[/tex]
[tex]x^{2} +1^{2}-2x+y^{2} -9=0[/tex]
[tex](x-1)^{2}+y^{2}[/tex]-9=0
[tex](x-1)^{2} +y^{2} =9[/tex]
[tex](x-1)^{2}+y^{2} =3^{2}[/tex]
Equation of a circle usually in the form [tex]x^{2} +y^{2} =a^{2}[/tex] in which a is radius.
From the comparison of both the equations we get that radius is 3 units.
From the equation point will be (1,0). It is on the x axis.
Hence the statements which are correct about the equation of circle [tex]x^{2} +y^{2}-2x-8=0[/tex] are 1) The radius of the circle is 3 units,2) The center of the circle lies on the x axis,5) The radius of this circle is the same the radius of the circle whose equation is [tex]x^{2} +y^{2} =9[/tex].
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Answer: 1,2,5 on edge
Step-by-step explanation:
see above ans for work
A number cube is rolled three times. An outcome is represented by a string of the sort OEE (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). The outcomes are listed in the table below. Note that each outcome has the same probability.
The probability of occurrence for the events A, B and C is; 1/4.
What is the probability of occurrence of.the described events?For the first event A in which case, there's no odd number on the first two rolls, the possible events are; EEE and EEO. Consequently, the required probability is;
Event A = 2/8 = 1/4.
For the event B in which case, there's an even number on both the first and last rolls; the possible events are; EEE and EOE. Consequently, the required probability is;
Event B = 2/8 = 1/4.
For the event C in which case, there's an odd number on each of the first two rolls; the possible events are; OOO and OOE. Consequently, the required probability is;
Event C = 2/8 = 1/4.
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9e-6(-2e+7)= please help me solve this problem
[tex]\bold{Answer:} \small\boxed{21e-42}[/tex]
Step-by-step explanation:
[tex]To\ solve\ : \ 9e-6(-2e+7)[/tex]
we first must use the distributive property. You can think about solving this like this:
[tex]=9e-(6)(-2e+7)[/tex]
Notice how we are not distributing -6, but only 6. Now we can solve normally:
[tex]=9e-(-12e+42)[/tex]
Now we distribute the '-' sign to the terms in parenthesis.
[tex]=9e+12e-42[/tex]
[tex]\longrightarrow \large\boxed{21e-42}[/tex]
The decimal form is 15.08 rounded.
[tex]h(x) = x -1 + \frac{1+ ln {}^{2} (x) }{x}[/tex]
[tex]\displaystyle \lim_{x\to0} h(x)= \: ? \\ \displaystyle \lim_{x\to \infty } h(x)= \: ?[/tex]
Apply L'Hôpital's Rule if possible
Answer:
[tex]\lim_{x\rightarrow +\infty } x-1+\frac{1+ln^{2}x}{x} = + \infty[/tex]
[tex]\lim_{x\rightarrow 0 } x-1+\frac{1+ln^{2}x}{x} = + \infty[/tex]
Step-by-step explanation:
[tex]\lim_{x\rightarrow +\infty } x-1+\frac{1+ln^{2}x}{x}[/tex]
[tex]= [\lim_{x\rightarrow +\infty } (x-1)]+[ \lim_{x\rightarrow +\infty } (\frac{1+ln^{2}x}{x})][/tex]
= +∞ + 0
= +∞
[tex]\lim_{x\rightarrow +\infty } x-1+\frac{1+ln^{2}x}{x}[/tex]
[tex]= [\lim_{x\rightarrow 0 } (x-1)]+[ \lim_{x\rightarrow 0 } (\frac{1+ln^{2}x}{x})][/tex]
= -1 + +∞
= +∞
A garrison has provision for 10 days. At the end of 2 days 1/2 of the men left the garrison. how long the food will now last?
Please answer with explanation?
After half of the men go away, the provisions will last for another 16 days.
how long the food will now last?
First, we know that the garrison has provisions for 10 days.
2 days after that, the garrison has provisions for another 8 days. Here we know that the number of men on the garrison is reduced to its half. Then, the time that the provisions in the garrison will last is multiplied by 2.
So we just need to solve the product:
2*8 days = 16 days.
After half of the men go away, the provisions will last for another 16 days.
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a. Use the adjusted trial balance to prepare the December 31 year-end income statement. b. Use the adjusted trial balance to prepare the December 31 year-end statement of owner's equity. The E. Happ, Capital account balance was $69,623 on December 31 of the prior year, and there were no owner investments in the current year. c. Use the adjusted trial balance to prepare the December 31 year-end balance sheet.
It should be noted that a trial balance is a report which lists the balances of the ledger accounts of a company.
How to illustrate the information?It should be noted that the information is incomplete. Therefore, an overview will be given. It should be noted that the accounts that are reflected on a trial balance are related to the accounting items.
The adjusted trial balance simply lists the general ledger account balances after the adjustments have been made. In such a case, these adjustments typically include prepaid and accrued expenses, and non-cash expenses such as depreciation.
Furthermore, a trial balance is a list of the closing balances of ledger account while adjusted balance is a list of general account. An adjusted trial balance is typically prepared by creating a series of journal entries which are designed to account for any transactions that haven't been completed.
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solve for x in the diagram
sorry its a little messy!! not good at drawing with a finger haha. all you need to do is follow pedmas and isolate, knowing that a right angle=90°. hope this helps!<3<3
Answer: [tex]\Large\boxed{x=12}[/tex]
Step-by-step explanation:
Given information
∠1 = x + 42°
∠2 = 3x°
Total Angle = 90° (Right Angle)
Derived formula from the given information
∠1 + ∠2 = Total Angle
Substitute values into the given formula
(x + 42) + (3x) = (90)
Combine like terms
x + 3x + 42 = 90
4x + 42 = 90
Subtract 42 on both sides
4x + 42 - 42 = 90 - 42
4x = 48
Divide 4 on both sides
4x / 4 = 48 / 4
[tex]\Large\boxed{x=12}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
(1,-2) and (2,-4) exponential formula f(x)=ab^x
We conclude that the exponential function is:
f(x) = -1*(2)ˣ
How to find the exponential function?Here we know that we have an exponential function of the form:
f(x) = a*b^x
And we know two points on the function, that are:
f(1) = -2 = a*b^1 = a*b
f(2) = -4 = a*b^2
Then we have a system of equations to solve, which is:
-2 = a*b
-4 = a*b^2
From the first equation we can solve:
-2/a = b
Replacing that in the other equation we can get:
-4 = a*(-2/a)^2 = 4/a
a = 4/-4 = -1
Now that we know the value of a, we can get the value of b:
-2/a = b
-2/-1 = 2 = b
In this way, we conclude that the exponential function is:
[tex]f(x) = -1*(2)^x[/tex]
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IF THE ODDS AGAINST A PARTICULAR CANDIDATE WINNING AN ELECTION ARE 9
TO 5, WHAT IS THE PROBABILITY THAT THE CANDIDATE WILL WIN?
The probability that the candidate will win is P = 0.357
How to find the probability?
We know that the odds against the particular candidate are 9 to 5.
The the odds for the candidate are 5 to 9, this means that in 5 cases the candidate will win, and in 9 cases the candidate will lose.
Then the candidate wins in 5 out of 14 cases, then the probability that the particular candidate wins the elections is given by the quotient:
P = 5/14 = 0.357
The probability that the candidate will win is P = 0.357
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A recipe for a single batch of cookies calls for 3 eggs.
Step 1. Write an equation that represents the total number of eggs we need (n) for some batches (b) of this recipe.
Step 2. How many eggs do we need to make 6 batches of this recipe?
The total number of eggs needed for b batches is n = 3b
The total number of eggs needed for 6 batches is 18.
How many eggs are needed?
Multiplication is one of the basic mathematical operation that is used to determine the product of two or more numbers. The sign used to denote multiplication is x. Other mathematical operations include addition, subtraction and division.
In order to determine the total number of eggs needed, multiply the number of eggs needed for one batch by the total number of batches.
Total eggs needed = eggs needed for one batch x total number of batches
n = 3 x b
n = 3b
6 x 3 = 18
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Please hurry quick I need an answer
Answer:
slope is 4
Step-by-step explanation:
Slope is rise/run
for every 4 units it rises it runs 1 unit
4/1=4
First dispensed is 1/3 of a quart, later 1/4and then you dispensed 3 1/2 quarts. What’s the total volume that is dispensed
Answer:4 1/12.
Step-by-step explanation: First, you add 3 and a half with a quarter. A half equals two quarters so it equals 3 and 3/4. Then, you add 3 3/4 with 1/3. A common denominator here is 12. 3/4 times 3/3 = 9/12. 1/3 times 4/4 = 4/12. 9+4 = 13. The answer is more than one so we carry and get 4 and 1/12.
Two regular 6-sided dice are tossed. Compute the probability that the sum of the pops on the upward faces of the 2 dice is the following. 1
Answer: 0
Step-by-step explanation:
What is (43/7÷ x+32/9) ÷25/6=4/3
The value of x in the equation (43/7 ÷ x + 32/9) ÷ 25/6 = 4/3 is 43/14
How to solve for x in the equation?The equation is given as:
(43/7 ÷ x + 32/9) ÷ 25/6 = 4/3
Rewrite as a product
(43/7 ÷ x + 32/9) x 6/25 = 4/3
Multiply both sides of the equation by 25/6
(43/7 ÷ x + 32/9)= 4/3 x 25/6
Evaluate the product
(43/7 ÷ x + 32/9)= 50/9
Rewrite the equation as:
43/7x + 32/9= 50/9
Subtract 32/9 from both sides
43/7x = 2
Multiply both sides by 7x
14x = 43
Divide by 14
x =43/14
Hence, the value of x in the equation (43/7 ÷ x + 32/9) ÷ 25/6 = 4/3 is 43/14
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3
Select the correct answer.
What is the inverse of the function f(x)=19/x2
If [tex]$&f(x)=\frac{19}{x^{2}} \\[/tex] then the inverse function exists [tex]$&f^{-1}(x)=\sqrt{\frac{19}{x}}[/tex].
What is the meaning of inverse function?An inverse function in mathematics exists function which "reverses" the another function.
Let f(x) = y, then the inverse function, [tex]$x=f^{-1}(y)$[/tex]
[tex]$&f(x)=\frac{19}{x^{2}} \\[/tex]
[tex]$&y=\frac{19}{x^{2}} \\[/tex]
[tex]$&x^{2}=\frac{19}{y} \\[/tex]
simplifying the equation, we get
[tex]$&x=\sqrt{\frac{19}{y}} \\[/tex]
[tex]$&x^{-1}=f^{-1}(y)=\sqrt{\frac{19}{y}} \\[/tex]
[tex]$&f^{-1}(y)=\sqrt{\frac{19}{y}},[/tex] then [tex]$&f^{-1}(x)=\sqrt{\frac{19}{x}}[/tex].
If [tex]$&f(x)=\frac{19}{x^{2}} \\[/tex] then the inverse function exists [tex]$&f^{-1}(x)=\sqrt{\frac{19}{x}}[/tex].
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Select the common ratio and the 4th term of the geometric series: 9, -6,4...
The given geometric sequence has the common ratio, r = -2/3, and the value of the 4th term, a₄ = -8/3.
A geometric sequence is a special series where every term is the product of the previous term and a common ratio.
The first term of a geometric sequence is represented as a, the common ratio as r, and the n-th term as aₙ, which is calculated as, aₙ = a.rⁿ⁻¹.
In the question, we are asked to find the common ratio and the 4th term of the geometric sequence, 9, -6, 4, ........
The first term of the sequence, a = 9.
The second term of the sequence, a₂ = -6.
By the formula of the n-th term, aₙ = a.rⁿ⁻¹, we can show that:
a₂ = a.r²⁻¹.
Substituting the values, we get:
-6 = 9(r²⁻¹),
or, r²⁻¹ = -6/9,
or, r = -2/3.
Thus, the common ratio of the given geometric sequence is -2/3.
The 4th term can be calculated using the formula of the n-th term, aₙ = a.rⁿ⁻¹ as:
a₄ = a.r⁴⁻¹ = a.r³.
Substituting the values, we get:
a₄ = 9(-2/3)³,
or, a₄ = 9.(-8/27),
or, a₄ = -8/3.
Thus, the 4th term of the given geometric sequence is -8/3.
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A man can take a same time to row 13km downstream and 7km upstream.His speed in still water is 5km/hr.The speed of stream is
Answer:
0.6 km/hr
Step-by-step explanation:
Speed downstream: 13/5= 2.6 km/hr
Speed upstream: 7/5= 1.4 km/hr
Therefore, Velocity of current is: 1/2 (2.6-1.4) km/hr = 1/2(1.2) km/hr
Write all possible values of y if y is a multiple of 9: 248
The possible values of y are 9n where n is an integer greater than 0 equal to 0
How to determine the possible values of y?The statement is given as;
y is a multiple of 9
The above means that
The number y can be divided by 9 without remainder
The numbers in this category are:
Numbers = 9, 18, 27, 36, 45......
This can be rewritten as:
Numbers = 9n where n is an integer greater than 0 equal to 0
Hence, the possible values of y are 9n where n is an integer greater than 0 equal to 0
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[tex] \: \: \: \: \: \: \: \: \: \: \: n\\ evaluate \: \: \: \: \: Σ \: (nCi)\\ \: \: \: \: \: \: \: \: \: \: \: \: i = 0[/tex]
Evaluate the summation
Assuming you mean
[tex]\displaystyle \sum_{i=0}^n {}_nC_{i}[/tex]
where
[tex]{}_n C_i = \dbinom ni = \dfrac{n!}{i! (n-i)!}[/tex]
we have by the binomial theorem
[tex]\displaystyle (1 + 1)^n = \sum_{i=0}^n {}_nC_{i} \cdot 1^i \cdot 1^{n-i}[/tex]
so that the given sum has a value of [tex]\boxed{2^n}[/tex].
Which of the LCM (40,120,150)?
Answer:
2400
Step-by-step explanation:
40 = 2^3 * 5
120 = 2^5 * 5
150 = 2 * 3 * 5^2
LCM = 2^5 * 3 * 5^2