Answers
Step-by-step explanation:
the extreme values (minimum, maximum) of a function are the zero points of the first derivation of the function.
so,
f'(x) = 2x + b
and then
2x + b = 0
we know, x = 20 for the minimum
2×20 + b = 0
40 + b = 0
b = -40
therefore, the actual function is
f(x) = x² - 40x + 164
the target format is
f(x) = (x - h)² + k = x² - 2hx + h² + k
so,
-40x = -2hx
-40 = -2h
h = 20
and
h² + k = 164
20² + k = 164
400 + k = 164
k = -236
Related Questions
Brett owns 236 shares of animite energy co., each of which offers a yearly dividend of $3.59. how much money does brett receive from dividends every year? a. $1,038.85 b. $1,529.59 c. $657.58 d. $847.24
Answers
The total amount of money that Brett receives from dividends every year is $847.24.
What is the total amount of money received from dividends?Dividends are payments made to the shareholders of a public company from the income of a company in a particular period.
Total dividends = dividend per share x total shares owned
236 x 3.59 = $847.24
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Answer:
Step-by-step explanation:
847.24
Using the image above, what is the measure of Angle E? Round to the nearest hundredth
Answers
Answer:
the answer is 30°
Step-by-step explanation:
180°-90°-60°
Complete the table for the equation below
Answers
Answer:
-1
2
4
Step-by-step explanation:
You have to replace x with each number that is given, follow the order of operations, and then you have the correct y value.
What is the length of the hypotenuse of the triangle?
Triangle A B C. Side A C is 7 feet and side C B is 4 feet. Hypotenuse A B is unknown.
StartRoot 22 EndRoot ft
StartRoot 33 EndRoot ft
StartRoot 57 EndRoot ft
StartRoot 65 EndRoot ft
Answers
Answer:
[tex]\sqrt{65}[/tex]
Step-by-step explanation:
[tex]a^{2}+b^{2}=c^{2}[/tex]
[tex]4^{2} +7^{2} =c^{2}[/tex]
[tex]16+49=c^{2}[/tex]
[tex]65=c^{2}\\\sqrt{65}=c[/tex]
Answer:
65
Step-by-step explanation:
WILL GIVE BRAINLIEST PLEASE HELP ASAP
Please answer this in word form and do it fast because I’m running out of time. Will give brainliest
Answers
Step-by-step explanation:
because the distance from O to the other 3 points is the same. each bisector provides a line of points with equal distance to the 2 end points of its base line.
where these 2 bisectors intersect, is the point that has the same distance to all end points.
5. Mickey bought pizza and sodas for himself and four of his friends. The pizza was $17.49,
and 5 sodas were $1.19 each.
If the pizza is sliced into 10 equal slices and each person eats 2 slices and drinks one
soda, what is the cost to each person?
$2.94
® $4.13
$3.50
$4.69
Answers
Answer:
D. is the correct option
Step-by-step explanation:
There is a total of 5 people, so we can either split the pizza cost into 5, or into 10 and multiply by 2 (since each guest ate 2 slices) We'll do the first option since it's simpler.
$17.49 ÷ 5 = 3.489 or rounded up to $3.50
Next, we'll add $1.19 to $3.59 which equals $4.69
Hope this helps!
i could use some help with this question pleaseeeee, i'll give brainliest and an explanation for future reference would be appreciated^^
if L,M are the two roots of the equation : 8x² - 40x + 11 = 0 , then L+M = ...........
a) 40
b) -40
c) 5
d) -5
Answers
Answer:
c) 5
Step-by-step explanation:
we know that,
alpha + beta = -b/a
here, we are given that alpha is L and beta is M (roots of the quadratic equation)
therefore,
L+M = -b/a
L+M = -(-40)/8
L+M = 40/8
L+M = 5
HOPE IT HELPS!!
PLEASE MARK BRAINLIEST... ♡
Answer:
L + M are 5.122 and -0.122 so I am assuming the answer you want is 5 or c.
Step-by-step explanation:
SOME OF THIS I NEEDED TO RESEARCH BECAUSE I FEEL LIKE THIS IS OUT OF MY DEPTH BUT I GUESS HERE YOU GO
STEP
1
:
Equation at the end of step 1
(23x2 - 40x) - 5 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 8x2-40x-5
The first term is, 8x2 its coefficient is 8 .
The middle term is, -40x its coefficient is -40 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 8 • -5 = -40
Step-2 : Find two factors of -40 whose sum equals the coefficient of the middle term, which is -40 .
-40 + 1 = -39
-20 + 2 = -18
-10 + 4 = -6
-8 + 5 = -3
-5 + 8 = 3
-4 + 10 = 6
-2 + 20 = 18
-1 + 40 = 39
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step
2
:
8x2 - 40x - 5 = 0
STEP
3
:
Parabola, Finding the Vertex:
3.1 Find the Vertex of y = 8x2-40x-5
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 8 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C ,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 2.5000
Plugging into the parabola formula 2.5000 for x we can calculate the y -coordinate :
y = 8.0 * 2.50 * 2.50 - 40.0 * 2.50 - 5.0
or y = -55.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = 8x2-40x-5
Axis of Symmetry (dashed) {x}={ 2.50}
Vertex at {x,y} = { 2.50,-55.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-0.12, 0.00}
Root 2 at {x,y} = { 5.12, 0.00}
Solve Quadratic Equation by Completing The Square
3.2 Solving 8x2-40x-5 = 0 by Completing The Square .
Divide both sides of the equation by 8 to have 1 as the coefficient of the first term :
x2-5x-(5/8) = 0
Add 5/8 to both side of the equation :
x2-5x = 5/8
Now the clever bit: Take the coefficient of x , which is 5 , divide by two, giving 5/2 , and finally square it giving 25/4
Add 25/4 to both sides of the equation :
On the right hand side we have :
5/8 + 25/4 The common denominator of the two fractions is 8 Adding (5/8)+(50/8) gives 55/8
So adding to both sides we finally get :
x2-5x+(25/4) = 55/8
Adding 25/4 has completed the left hand side into a perfect square :
x2-5x+(25/4) =
(x-(5/2)) • (x-(5/2)) =
(x-(5/2))2
Things which are equal to the same thing are also equal to one another. Since
x2-5x+(25/4) = 55/8 and
x2-5x+(25/4) = (x-(5/2))2
then, according to the law of transitivity,
(x-(5/2))2 = 55/8
We'll refer to this Equation as Eq. #3.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-(5/2))2 is
(x-(5/2))2/2 =
(x-(5/2))1 =
x-(5/2)
Now, applying the Square Root Principle to Eq. #3.2.1 we get:
x-(5/2) = √ 55/8
Add 5/2 to both sides to obtain:
x = 5/2 + √ 55/8
Since a square root has two values, one positive and the other negative
x2 - 5x - (5/8) = 0
has two solutions:
x = 5/2 + √ 55/8
or
x = 5/2 - √ 55/8
Note that √ 55/8 can be written as
√ 55 / √ 8
Solve Quadratic Equation using the Quadratic Formula
3.3 Solving 8x2-40x-5 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 8
B = -40
C = -5
Accordingly, B2 - 4AC =
1600 - (-160) =
1760
Applying the quadratic formula :
40 ± √ 1760
x = ——————
16
Can √ 1760 be simplified ?
Yes! The prime factorization of 1760 is
2•2•2•2•2•5•11
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 1760 = √ 2•2•2•2•2•5•11 =2•2•√ 110 =
± 4 • √ 110
√ 110 , rounded to 4 decimal digits, is 10.4881
So now we are looking at:
x = ( 40 ± 4 • 10.488 ) / 16
Two real solutions:
x =(40+√1760)/16=5/2+1/4√ 110 = 5.122
or:
x =(40-√1760)/16=5/2-1/4√ 110 = -0.122
It's going 2 by 2 for the paper i couldn't get it all in at a time so the first 2 are one paper and its like that for the next 2 papers but the last paper is the whole paper
Answers
it took I'd :safalbista10 10
PLEASE HELP ASAP !!
A particle moves in a a straight line along the x-axis. Its displacement (distance from 0 along the x-axis) is given by the following equation: f(t) = 3(t)^4 - 5(t)^3 + 6(t) - 7; t >= 0, where t is measured in seconds and f is measured in meters. Find the velocity of the function after 2 seconds.
Answers
The velocity of a particle when it moves on a straight line along the x-axis will be V= 42 m/s
What is velocity?Velocity is defined as the ratio of the distance moved by the object in a particular time. The velocity is a vector quantity so it needs both the magnitude and the direction.
Here we have a displacement function:-
F(t)=3t⁴-5t³+6t-7
So to find out the velocity we will differentiate the above equation with respect to t.
d(F(t)/dt=12t³-15t²+6
V=12t³-15t²+6
Put the value of t=2 seconds
V=12x(2x2x2)-15x(2x2)+6
V=42 meters per second
Hence the velocity of a particle when it moves on a straight line along the x-axis will be V= 42 m/s
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What is the solution to the equation ?
p = –6
p =
p = –4
p =
Answers
The solution to this equation is p = -6
This expression is related to a First Degree Equation.First degree equation is a mathematical expression and sentence, which is defined by having only one unknown. Its representation is given by: ax+b=0.
— To solve this expression, let's eliminate these square root symbols:
√-5p = √24-p
-5p = 24 - p
— Move the p term before the positive sign equality, thus also shifting the 24th term:
-5p = 24 - p
-5p + p = 24
-4p = 24
— Finally, let's divide the second to the first term of this equation:
-4p = 24
p = 24 ÷ (-4)
p = -6
Therefore, the correct result of this expression will be p = -6
I need help with this problem
Answers
solve the system of equations. {2y=6x
x^2+y=4
Answers
X2+y=4
Y=6x/2
X2+y=4
Answer: x=1 y=3, x=-4 y=-12
Answer: (1,3)and (-4,-12)
Step-by-step explanation:
please help me with this
Answers
Answer:
In the explanation
Step-by-step explanation:
AB = line segment
ABC = angle
AB = line segment
CD = intersecting line
AC = line segment
AB = line segment
EBC = angle
BC = line segment
NEED HELPP ASAPP SOMEONE HELP
Answers
Answer:
[tex]\textsf{C)}\quad g(x)=\dfrac{1}{2}(x-8)^2-8[/tex]
Vertex = (8, -8)
Step-by-step explanation:
Standard form: [tex]y=ax^2+bx+c[/tex]
Vertex form: [tex]y=a(x-h)^2+k[/tex]
where (h, k) is the vertex
Intercept form: [tex]y=a(x-p)(x-q)[/tex]
where p and q are the x-intercepts
Therefore, the form that most quickly reveals the vertex is
[tex]g(x)=\dfrac{1}{2}(x-8)^2-8[/tex]
The vertex is (8, -8)
A textbook has 428 numbered pages, starting with 1.
A textbook has 428 numbered pages, starting with 1. You are equally likely to stop on any of the pages if you flip through the book randomly.
What is the probability that you turn to page 45?
Answers
Answer:
1/428 or 0.00233644859% chance
Step-by-step explanation:
Simply because there is only one page 45 use 428 as your denominator and then divide 1 by 428!
Answer: 1/428
Step-by-step explanation: There are 428 pages so that is the denominator. 45 is only one page so 1 is the numerator. Therefore it is a 1 in 428 chance that you would land on 45. Hope this helped!
Which probability is correct? p(a) = three-fifths p(b) = startfraction 16 over 31 endfraction p(a|b) = two-sevenths p(b|a) = startfraction 10 over 21 endfraction
Answers
The correct probability expression is (a) P(a) = three-fifths
How to determine the correct probability ?Using the data in the complete question, we have:
n(A) = 3
n(U) = 5
The probability of A is then calculated using:
P(A) = n(A)/n(U)
This becomes
P(A) = 3/5
Hence, the correct probability expression is (a) P(a) = three-fifths
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Answer:
It’s A my friend
Step-by-step explanation:
i did the quiz
yw :)
hope i helped/ made life easier
How many millimeters are in 27 centimeters? (2 points)
a
27 mm
Ob
270 mm
Ос
2,700 mm
Od
27,000 mm
Answers
Step-by-Step Explanation:
We know,
1 cm = 10 mm
1mm = 1/10 cm
Therefore,
27 cm = 27 * 10 = 270 mm
In an orchard, there are 17 apple trees, 30 orange trees, and a cherry tree. what is the ratio of orange trees to cherry trees? a. 17:30 b. 47:30 c. 30:1 d. 1:30
Answers
Answer: C. 30:1
Step-by-step explanation:
A ratio of x:y is created by taking the number of x and the number of y, plugging them in, and reducing if necessary. In this problem, x is orange trees and y is cherry trees. There are 30 orange trees and only 1 cherry tree, so the ratio is 30:1. It cannot be reduced.
If 6 hotdogs cost $ 18, then what is the cost for each hotdog
Answers
Answer:
each hot dog costs $3
Step-by-step explanation:
$18÷6 hotdogs=$3 or $3×6 hotdogs=$18
do the math please. i need it nowwwwww
Answers
Using algebraic expressions, the value of x in the diagram given is calculated as: x = 4
What is an Algebraic Equation?An algebraic equation is an equation that has an unknown variable (i.e. x) and digits, which can be used to solve a problem.
Algebraic expression for Mat A is: 4x + 3
Algebraic expression for Mat B is: 2x + 11
We would have the following algebraic equation:
4x + 3 = 2x = 11
Solve for the value of x
4x - 2x = 11 - 3
2x = 8
x = 8/2
x = 4
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A box contains 20 uckets mmbered from 1 to 20 tetor de candowm. find the probability it is divisible by 3 and 4
Answers
Answer:
that 2 out of 20 ratio you have 18 to 1 odds of getting these
Solve for x in the equation
Answers
Answer:
x = -1 + ⟌17
Step-by-step explanation:
You want to solve the equation for x by finding a, b, and c of the quadratic formula
write an equation in point-slope form for the given point and slope: point: (-7, 5) slope: 3
Answers
Answer:
y - 5 = 3(x + 7)
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = 3 and (a, b ) = (- 7, 5 ) , then
y - 5 = 3(x - (- 7) ) , that is
y - 5 = 3(x + 7)
i need help to solve this
Answers
Step-by-step explanation:
(6+r)^2 = 81 + r^2
36 + 12r+ r^2 = 81 + r^2
12r = 81-36 = 45
r = 15/4 = 3.75
The nearest-known exoplanet from earth is 4.25 light-years away.
about how many miles is this?
give your answer in standard form.
Answers
Answer:
24 trillion miles. The nearest-known exoplanet is a small, probably rocky planet orbiting Proxima Centauri – the next star over from Earth. A little more than four light-years away, or 24 trillion miles.
The number of miles in 4.25 light-years will be 24.986 × 10¹² miles.
What is conversion?Conversion means to convert the same thing into different units.
The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The nearest-known exoplanet from the earth is 4.25 light-years away.
We know that 1 lightyear = 5.879 × 10¹² miles.
Then the number of miles in 4.25 light-years will be
⇒ 4.25 light-years
⇒ 4.25 × 5.879 × 10¹² miles
⇒ 24.986 × 10¹² miles
The number of miles in 4.25 light-years will be 24.986 × 10¹² miles.
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Answer with steps pls
Answers
Answer:
A) 2¹²
Step-by-step explanation:
Given :
3x - y = 12Equate the equation to y :
3x - y + y = 12 + y12 + y = 3x12 + y - 12 = 3x - 12y = 3x - 12Substituting in the expression :
[tex]\frac{8^{x} }{2^{y} }[/tex][tex]\frac{2^{3x} }{2^{3x-12} }[/tex][tex]{2^{3x-3x+12}}[/tex]2¹²Which is an example of stratified random sampling created from each given population? A. Deciding who should be the president of the senior class by tossing a coin to choose between two candidates. B. C. Surveying members of a political party by calling people listed in the telephone directory whose last names begin with the letter A. D. Surveying subscribers to a magazine by separating the list of subscribers into four age groups and choosing a sample from each group proportional to its size in the population.
Answers
Answer:
the answer is D
Step-by-step explanation:
i just did the test
Answer:
D
Step-by-step explanation:
Here are the driving scores of 40 new drivers. make a relative frequency table for their scores:
48, 67, 62, 74, 42, 62, 60, 75, 91, 88, 48, 60, 51, 63, 57, 85, 69, 75, 97, 72,
71, 79, 84, 65, 63, 73, 46, 55, 62, 72, 80, 55, 55, 56, 83, 80, 64, 72, 83, 92
in creating the table, you will need to make some choices about how to bin the data: how many bins,
and how wide the bins should be. you may also need to make some decisions about what to do with numbers that fall in the boundary between two bins in writing up your answers be clear about how you are making these choices there is more than one reasonable way to do it so you need to be clear about which decisions you are making.
Answers
The relative frequency table is:
Class Frequency Relative frequency
40 - 50 4 0.1
50 - 60 6 0.15
60 - 70 11 0.18
70 - 80 9 0.23
80 - 90 7 0.18
90 - 100 3 0.08
What is the relative frequency table?The relative frequency measures how often a value appears relative to the sum of the total values. The class width is 10. The class width is the difference between the upper and lower boundary (e.g. 100 - 90).
Frequency is the number of times the numbers in the class interval appear in the data set. Relative frequency is the frequency of a class interval divided by the total frequency of the data set.
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A swimming pool in a certain resort is enjoyed by people because it has a floor measurement of 8 ft by 12 ft and a depth of 9 ft. How much water can it contain?
Answers
Answer:
864 ft3
Step-by-step explanation:
length = 12 ft
width = 8 ft
depth = 9 ft
Volume = ? = length * width * depth
how is it no explain why
Answers
Answer:
the top answear
Step-by-step explanation:
the top aka 16^15/5 it should be 16^15 not that 5
Answer:
The answer is "no" because when two numbers with the same bases are divided, their powers are subtracted.
This should have been done instead:
[tex]\frac{6^{15} }{6^5}[/tex] = 6¹⁵ ⁻ ⁵
= 6¹⁰
Hope this helps!
