The maximum value of the quadratic function f(x)=-3(x-4)(x-6) is -72.
Given data:
To determine whether the quadratic function f(x) = -3(x-4)(x-6) has a minimum or maximum, analyze the leading coefficient, which is -3.
Since the leading coefficient is negative (-3), the quadratic function opens downward, indicating that it has a maximum point.
To find the minimum or maximum value of the function, we can look at the vertex of the parabola. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic function in the form [tex]ax^2 + bx + c[/tex].
In our case, the quadratic function is f(x) = -3(x-4)(x-6), so the coefficient of [tex]x^2[/tex] is -3, and there is no linear term (b = 0).
Using the formula x = -b / (2a):
x = -0 / (2*(-3))
x = 0
Substituting this x-coordinate back into the quadratic function, find the corresponding y-coordinate (minimum or maximum value).
f(0) = -3(0-4)(0-6)
f(0) = -3(-4)(-6)
f(0) = -3(24)
f(0) = -72
Hence, the quadratic function f(x) = -3(x-4)(x-6) has a maximum value of -72.
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A large quantity of waste material contains metal. At the successive passes through a recovery
process the mass of the metal recovered is:
32kg at the first pass,
24kg at the second pass;
18kg at the third pass;
13,5kg at the fourth pass, and so on, to form a geometric sequence,
1. How much metal would be recovered at the eighth pass?
(Round off the answer to TWO decimal places)
Answer:
The amount of metal recovered at the eight pass is approximately 4.27 kg
Step-by-step explanation:
The mass of metal recovered formed the following geometric sequence;
32 kg, 24 kg, 18 kg, 13.5 kg
∴ The first term, a = 32 kg
The common ratio in the geometric sequence is found as follows;
r = a·r/a = 24 kg/(32 kg) = 0.75
r = a·r²/a·r = 18 kg/(24 kg) = 0.75
r = a·r³/a·r² = 13.5 kg/(18 kg) = 0.75
The mass of the metal recovered in the eight pass will be the 8th term of the geometric series given as follows;
nth term = a·rⁿ⁻¹
a = 32, r = 0.75, n = 8
∴ 8th term = 32·(0.75)⁸⁻¹ = 32·0.75⁷ = 2187/512 ≈ 4.27
The amount of metal recovered at the eight pass ≈ 4.27 kg.
The eight term of the geometric sequence is 4.27.
Geometric sequenceA geometric sequence is in the form:
aₙ = ar⁽ⁿ⁻¹⁾
where aₙ is the nth term, a is the first term and r is the common difference.
Given that a = 32, r = 24/32 = 0.75
The eight term is a₈ = 32(0.75)⁸⁻¹ = 4.27
The eight term of the geometric sequence is 4.27.
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***WILL MARK BRAINLEST***
Find the y-intercept for the parabola defined by this equation: y = -x^2 - 2x + 3 separate the values with a comma
Answer:
y-intercept is (0, 3)
Step-by-step explanation:
To find the y-intercept, substitute in 0 for x and solve for y.
If Measure of angle a is 155°, what is Measure of angle c? Line l intersects line m to form 4 angles. Clockwise, from the top, the angles are: a, b, c, d. 25° 35° 155° 180°
Answer:
c. 155
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
I took the test. Im sorry for the late response.
The volume of the rectangular pyramid is ___ cubic units.
Answer:
600 cubic units.
Step-by-step explanation:
The formula for a rectangular pyramid is[tex]V=\frac{lwh}{3}[/tex] or volume is equal to length x width x height divided by 3. The length is 15, the width is 10, and the height is 12. This equals to 1800, then we divide it by three for the answer.
will mark the best awnser :)
Answer:
15 square feet
Step-by-step explanation:
HELP PLEASE!!!!!!!!!!
Volunteers at Sam's school use same of the student council's savings for a special project. They buy 3 backpacks for $6 each and fill each backpack with paper and pens that cost $6. By how much did the students council's savings change because of this project?
ill mark brainlist plss help
Answer:
60%
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
3/5 is the same as 6/10. All percentages are out of 100% so you have to change the denominater to 100. Do do that you just add a 0 to the numerator and demoninator. i.e. 60/100. which is translated to 60%.
I NEED HELP WIT DIS ASSIGNMENT ASAP
Find the time.
I = prt
Principal: $500
Rate: 5%
Interest earned: $25
Time: ?
Answer:
1 year
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 5%/100 = 0.05 per year,
then, solving our equation
t = 25 / ( 500 × 0.05 ) = 1
t = 1 years
The time required to
accumulate simple interest of $ 25.00
from a principal of $ 500.00
at an interest rate of 5% per year
is 1 year.
Lincoln invested $2,800 in an account paying an interest rate of 5\tfrac{3}{8}5
8
3
% compounded continuously. Lily invested $2,800 in an account paying an interest rate of 5\tfrac{7}{8}5
8
7
% compounded quarterly. After 15 years, how much more money would Lily have in her account than Lincoln, to the nearest dollar?
Answer: 445
Step-by-step explanation:
Lincoln’s Final Amount:
Compounded Continuously: A=Pe^rt
P= 2800
r= 0.05375
t=15
A=2800e^0.05375(15)
A=2800e^0.80625
A=6270.5833
Lily’s final amount:
Compounded quarterly:
A=P(1+r/n)^nt
P=2800
r=0.05875
t=15
n=4
A=2800(1+ 0.05875/4)^4(15)
A=2800(1.0146875)^60
A=6715.7829
How much more money does Lily have?
6715.7829-6270.5835
=445.1994
The money would Lily have in her account than Lincoln, to the nearest dollar 445.
We have to determine the compound interest Lincoln’s final amount
Compounded Continuously
A=Pe^rt
P= 2800
r=0.05375
t=15
A=2800e^0.05375(15)
A=2800e^0.80625A=6270.5833
What is the formula for compound interest?
A=P(1+r/n)^nt
P=2800
r=0.05875
t=15
n=4
A=2800(1+ 0.05875/4)^4(15)
A=2800(1.0146875)^60
A=6715.7829
=6715.7829-6270.5835
=445.1994
Therefore money would Lily have in her account than Lincoln, to the nearest dollar 445.
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Solve and
graph this
inequality.
-3x>15
Answer:
x > -5
Step-by-step explanation:
-3x > 15
divide by -3
x > -5
Answer: x<-5
Step-by-step explanation:
First, we must isolate x in order to graph the inequality properly. To solve for x, you must divide each side by -3. Because you are dividing by a negative number, you must switch the side around. So, the inequality would be [tex]x<-5[/tex]t.To graph this, you must put a veritcal dotted line (since the equation has a less than symbol) and shade to the left (this shows all the possiblilties of what x could be. Or, if you were to graph it on a number line, put an open circle on -5 and draw an arrow left from the dot. Hope this helps!
An item is regularly priced at $83. It is now priced at a discount of 55% off the regular price.
Answer:
$45.65 total
Step-by-step explanation:
Answer:
45.65
Step-by-step explanation:
Find the value of a, b, c,
and d.
76
to the document will
32
go to (1,1)
go to (-5, 1)
a a = 32, b = 26, C = 104, d = 90
b) a = 76, b = 52, c = 90, d = 90
c) a = 38, b = 52, c= 90, d = 90
d) a = 38, b = 52, c = 104, d = 90
e) a = 76, b = 26, C = 104, d = 180
go to (0, 2)
go to (7,0)
go to (-3,2)
Answer:
The answer is D
Step-by-step explanation:
1.Angle D is 90 becuase any angle inscribed in a semi circle is a right angle.
2.Since c and 76 form a semi-circle. They add up to 180 so c=104.
3.Angle A is a inscribed angle of arc 76. So that means angle A is half of the arc 76.
Angle A=38.
4. Angle B can be found two ways,
Using triangle interior theorem, since we know 90 and 38 as our given degree, a triangle has 180 degrees, so our third angle ,b will add up to 180 so it will be 52.Angle b is a inscribed angle of arc c so it is half of arc C or 104. Angle B=52D is the answer
Can someone help? Will mark Brainliest
Answer: The answer is the 3rd one
Step-by-step explanation:
9514 1404 393
Answer:
(d) AE = (32√6)/3
Step-by-step explanation:
The side length ratios in a 30-60-90 triangle are 1 : √3 : 2. In a 45-45-90 triangle, they are 1 : 1 : √2.
So, we have the side length ratios ...
CE : CD = 2 : √3
BE : CE = √2 : 1
AE : BE = 2 : √3
Then the ratio AE : CE is ...
[tex]\dfrac{AE}{CD}=\dfrac{2}{\sqrt{3}}\cdot\dfrac{\sqrt{2}}{1}\cdot\dfrac{2}{\sqrt{3}}=\dfrac{4\sqrt{2}}{3}[/tex]
Multiplying by the length of CD, we have ...
AE = (8√3)(4√2)/3
AE = (32√6)/3 . . . . . matches the last choice
Anyone know the correct answer to this?
Answer:
It should be y=4x-7
Step-by-step explanation:
M is the slope meaning Δx over Δy or rise over run
So if you look at (2,2) and count up to (3,6) the rise is 4 and the run is 1 meaning the slope is 4.
B is the y- intercept so then it would just be -7.
9514 1404 393Answer:
y=4x-6
Step-by-step explanation:
The line intersects the y-axis at y=-6, so that is the value of 'b' in the slope-intercept form.
The horizontal difference between marked points is 1 unit; the vertical difference is 4 units. That means the slope is . . .
m = rise/run = 4/1 = 4
Filling in these values (m=4, b=-6), we get ...
y = 4x -6
Is 14 19 23 a right triangle
Answer:no
Step-by-step explanation: because it is an acute triangle
what is a decimal that is equivalent to the fraction 9/100
Answer:
0.09
Step-by-step explanation:
9/100 as a decimal is 0.09.
Answer:
0.09!
Step-by-step explanation:
Convert the fraction to a decimal by dividing the numerator by the denominator.
0.09 is your answer!
Hope this helped.
Signed ~Jaz~
Find the missing sides of the triangle. Leave your answers in simplest radical form.
Answer5
34
Step-by-step explanation: 45
Ap calculus need help please
Answer:
[tex]\displaystyle \int\limits^1_0 {[2f(x) - g(x)]} \, dx = 11[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationCalculus
Integrals
Definite IntegralsIntegration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int\limits^1_0 {f(x)} \, dx = 4[/tex]
[tex]\displaystyle \int\limits^1_0 {g(x)} \, dx = -3[/tex]
[tex]\displaystyle \int\limits^1_0 {[2f(x) - g(x)]} \, dx[/tex]
Step 2: Find
[Integral] Rewrite [Integration Property - Subtraction]: [tex]\displaystyle \int\limits^1_0 {[2f(x) - g(x)]} \, dx = \int\limits^1_0 {2f(x)} \, dx - \int\limits^1_0 {g(x)} \, dx[/tex][1st Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^1_0 {[2f(x) - g(x)]} \, dx = 2\int\limits^1_0 {f(x)} \, dx - \int\limits^1_0 {g(x)} \, dx[/tex]Substitute in integral values: [tex]\displaystyle \int\limits^1_0 {[2f(x) - g(x)]} \, dx = 2(4) - (-3)[/tex]Multiply: [tex]\displaystyle \int\limits^1_0 {[2f(x) - g(x)]} \, dx = 8 - (-3)[/tex]Subtract: [tex]\displaystyle \int\limits^1_0 {[2f(x) - g(x)]} \, dx = 11[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
don’t answer if you don’t know
Which statement is true about the expression 4 (9+6)?
A: the expression has two factors
B: the expression has three coefficients
C: the expression has one variable
D: the expression has two variable terms
(YOULL BE MARKED BRAINLIST PLSSSS HELP)
How do you find an exponential growth model
Answer:
When the line of the graph is going up
Step-by-step explanation:
When the line is going down that means its a exponential decay :)
melanie is using the spinner to play a card game. the spinner has six sections of equal size. What is the probability that melanie will have to take cards when she spins the spinner. A.1/6. B.1/4. C. 1/3. D.2/3. E.3/4
Answer:
The answer is very clear is 2/3
Step-by-step explanation:
100 points. Can someone help
If a set of parallel lines contains the two points, (-2, 3) and (8, -5). If the lines are rotated 180 degrees clockwise, what would the two coordinates be after the rotation? Show or explain your work.
The two coordinates after the rotation are (2,-3) and (-8,5)
How to determine the coordinates after rotation?The points are given as:
(-2,3) and (8,-5)
The rule of 180 degrees clockwise rotation is:
(x,y) = (-x,-y)
This means that:
(2,-3) => (-2,3)
(-8,5) => (8,-5)
Hence, the two coordinates after the rotation are (2,-3) and (-8,5)
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Answer:
(2, -3) and (-8, 5)
Step-by-step explanation:
If a point is rotated 180° clockwise about the origin (0, 0) then:
(x, y) → (-x, -y)
Therefore,
(-2, 3) → (-(-2),-3) = (2, -3)
(8, -5) → (-8, -(-5)) = (-8, 5)
So the two coordinates after rotation would be (2, -3) and (-8, 5).
How does Reflection work in real-life situations?
Answer:
reflection is defined as the change in the direction of a wavefront at the interface between two different media, bouncing the wavefront back into the original medium. A common example of reflection is reflected light from a mirror or a still pool of water, but reflection affects other types of waves beside light.
Step-by-step explanation:
Answer:
I think it's help uu
Step-by-step explanation:
if wrong then sry
Middle school Math!!!
Multiple choice!! ONLY ONE Question!!
Look at the picture these are the answers:
y=2x-1
y=1x+2
y= -1x+2
y= -6/4x+2
Inez has $72 to buy video games each game costs $9 how many video games can Inez buy
Answer:
8
Step-by-step explanation:
1 video game = 9
? = 72
72/9=8
Answer:
8
Step-by-step explanation:
y/6 - 7 = 4 please explain how to solve
Answer:
y=66
Step-by-step explanation:
screenshot attached on the bottom
Answer: 1st circle 0.42n
Step-by-step explanation:
Answer:
p=0.42n
Step-by-step explanation:
Im not sure but if you do 2.52 divided by 6 you get 0.42 so my answer is A (p=0.42n)
i need help due asap
Step-by-step explanation
the third one
Step-by-step explanation:
Let's solve for y.
8x−3y>11
Step 1: Add -8x to both sides.
8x−3y+−8x>11 −8x −3y>−8x+11
Step 2: Divide both sides by -3.
−3y/−3 > −8x+11/−3
y<8/3x−11/3
Answer:
y<8/3x−11/3