The maximum or minimum of a quadratic function is found evaluating the polynomial at [tex]x = -\frac{b}{2\cdot a}[/tex].
A quadratic function is an algebraic function of the form:
[tex]y = a\cdot x^{2}+b\cdot x + c[/tex], [tex]\forall \,x, y, a, b, c\,\in \mathbb{R}[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.[tex]y[/tex] - Dependent variable. [tex]a,\,b,\,c[/tex] - Coefficients.The maximum/minimum of a quadratic function is represented graphically by the vertex, which is the only point that has no a "twin" point by any means of symmetry. We can get the x-coordinate of the vertex by means of the quadratic formula:
[tex]a\cdot x^{2} + b\cdot x + (c- y) = 0[/tex] (2)
[tex]x = \frac{-b\pm \sqrt{b^{2}-4\cdot a\cdot (c-y)}}{2\cdot a}[/tex], where [tex]b^{2}-4\cdot a\cdot (c-y) = 0[/tex].
Hence, the x-coordinate of the vertex is:
[tex]x = -\frac{b}{2\cdot a}[/tex] (3)
And the y-coordinate of the vertex is determined by evaluating (1) at (3):
[tex]y = f\left(-\frac{b}{2\cdot a} \right)[/tex] (4)
The maximum or minimum of a quadratic function is found evaluating the polynomial at [tex]x = -\frac{b}{2\cdot a}[/tex].
We kindly invite to check this question on maxima and minima: https://brainly.com/question/12870574
5x+3x-6=6x+12 what is the answer
Answer:
x=9
Step-by-step explanation:
1. Combine like terms
2. Add 6 to both sides
3. Simplify
b)Using the formula from part a, calculate the retail price for each quantity range.
( Hope this helps guys )
ANSWER:
$45.00
$41.40
$37.80
$34.20
$30.60
EXPLANATION:
Ok so the first box is 25.00 your going to multiply .80 whatever your awnser is for that which is 20 then you take that and add the 25 from the box and get 45 and that’s your awnser and just repeat the process for the other boxes .
Answer:
man, thanks alot really helped me I was struggling with this one. Couldnt find any answers
Step-by-step explanation:
what is 1760 rounded to the nearest hundred
Answer:
1800
Step-by-step explanation:
Ethan, Caleb, and Jayden went to a bakery to buy desserts. Ethan bought 2 cupcakes, 2
brownies and a pie for $20. Caleb bought 4 cupcakes, 4 brownies and a pie for $44, Jayden
bought 5 cupcakes and 6 brownies for $40. Write a system of equations to represent is
situation. Convert the system to a matrix and find the cost of 1 cupcake, 1 brownie, and 1
pie to the nearest cent.
Answer:
x = 32
y = -20 and
z = -4
Step-by-step explanation:
Cupcakes = X
Brownies = Y
Pies = Z
Ethan = 2x+2y+z = 20
Caleb = 4x+4y+z = 44
Jayden = 5x+6y = 40
-1(2x+2y+z=20) =
(-2x - 2y - z = -40) + (4x+4y+z=44)
= 5x + 6y = 40
-3(2x+2y=24 =
(-6 - 6y = -72) + (5x + 6y = 40)
= - x = - 32
= x = 32
5 (32) + 6y = 40
= 160 + 6y = 40
6y = 40 - 160
y = 120/6
y = - 20
2(32) + 2(-20) + z = 20
64 - 40 + z = 20
z = 20 - 24
z = -4
The owner of a food truck determines a location for the operation. The owner maps out two office buildings on a coordinate plane. Office Building
1 is located at (−4,10), and Office Building 2 is located at (2,6). If the food truck is located halfway between Office Building 1 and Office Building 2, what is the y-coordinate of the food truck’s location?
somebody please explain and answer this!!
Answer:
y coordinate: 8
Step-by-step explanation:
middle of the two areas have the y as 8
Very urgent!!!!!
The first term of an AP is 6 and the 5th term is 18.find the number of terms in the series having a sum of 162....
With workings
And explanation
Thanks
Answer:
number of terms=9
Step-by-step explanation:
[tex]t_{1}=6\\t_{5}=18\\\\t_{n}=t_{1}+(n-1)d\\18=6+(5-1)d\\18-6=4d\\4d=12\\d=12/4=3\\s_{n}=162\\s_{n}=\frac{n}{2}[2t_{1}+(n-1)d]\\162=\frac{n}{2}[2(6)+(n-1)3]\\162 \times 2=n(12+3n-3)\\324=n(3n+9)\\3n^2+9n-324=0\\n^2+3n-108=0\\n^2+12n-9n-108=0\\n(n+12)-9(n+12)=0\\(n+12)(n-9)=0\\n=-12,9\\n=-12 (rejected)[/tex]
as number of terms can't be negative.
Answer:
PLS MARK BRAINLIEST
Step-by-step explanation:
Sn = n/2(2a+(n-1)d)
a=6
a+ 4d= 18
6 +4d= 18
4d = 12
d = 3
162= n/2(12+(n -1)3)
324=n(12 + 3n-3)
324=12n + 3n^2 - 3n
3n^2 + 9n-324=0
3n^2+ 36n-27n -324 =0
3n(n+12) -27(n+12)= 0
3n-27 =0; n+ 12=0
n=9 ; n= -12
since n can't be negative n=9
The number of terms is 9
Madison needs to buy a new laptop for her music production. She borrows $2,100 and must pay the money back in equal amounts for 7 months. She must also pay $4 interest each month. What is her monthly payment, including interest?
Answer:
304
Step-by-step explanation:
2100÷7=300
300+interest=300+4
=304
Express this ratio in simplest form. 600cents : $10.50
helpppppppppppppppppppppppppppppp meeeeeeeeeeeeeeeeeee plsssssssssssssssssssssss there is more but plss help mee
I’m confused I’ll give brainlist it’s either a b c or d
Answer:
C.
Step-by-step explanation:
She needs 160 for a free ticket and get 85 for signing up.
Every time she goes, she get 12.5 points
160=85+12.5v
The answer would be C
Reason:
We eliminate B and D as they do not have a total of 160 points.
We are now left with A and C
A shows that she would need to earn 85 points three times which is incorrect as she receives 85 points 1 time after signing up. Therefore we eliminate A.
We are now left with C
C shows that the total amount of points she would need to earn a free ticket are 160 points.
It also shows that she would receive 85 points 1 time after signing up.
It also shows that the remaining points she would get are from strictly visiting the movie theater.
C is your answer
In the xy-plane, the midpoint M of segment AB has coordinates (-1,3), and point A has coordinates
(-3,0). What is the x-coordinate of point B?
-1
1
2
3
11 3 ×3 4 1 =
Help please
Answer:
Exact Form:
77/ 3
Decimal Form:
25.6
Mixed Number Form:
25 2/3
Step-by-step explanation:
the thing is 11/3 times 3 4/1
if i read 50 pages in 40 minutes how many pages do i read a minute
Answer:
You are reading 1 1/4 page/minute.
Step-by-step explanation:
REALIZAR CADA ELERCICIO POR LOS TRES METIDOS EXPLICADOS EN CLASE
1.EJERCICIO 1 .
2X-Y-4Z=12
3X-4Y+2Z=-11
-5X+2Y-Z=2
EJERCICIO 2.
X+2Y+Z=1
7X+3Y-Z=-2
X+5Y+3Z=2
Hello!
Answer:
1. x= 1 / y= 2 / z= -3 / (1 ; 2 ; -3)
2. x= 3 / y= -5 / z= 8 / (3 ; -5 ; 8)
Step-by-step explanation:
Rosa says she can break this array into 3 different sets of two smaller arrays . Is Rosa correct ? Explain . The array is a 6 by 8.
Answer:
yes
Step-by-step explanation:
because 6X8=48 and 48 dived by 3 equals 16
Arrays are dataset that are represented in rows and columns. Rosa's claim is correct.
What is an array?An array is a linear data structure that collects elements of the same data type and stores them in contiguous and adjacent memory locations.
From the question, we have:
6 rows and 8 columns
The number (n) of elements in the array is: n = Rows × Columns.
So, we have: n = 6 × 8 =48
Express as sum of three numbers, that is n=12+16+20
Express each term as a product, that is n=2 × 6 + 4 × 4 + 4 × 5
The above expression means that, the array can be split to:
An array of 2 by 6
An array of 4 by 4
An array of 5 by 4
Hence, Rosa is correct.
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To make papier-mâché, Emma uses 3/4 cup of white school glue for each batch. For a big project, she will make 11 batches of papier-mâché. Emma has half of 1-gallon bottle of white school glue. Does Emma have enough glue?
Emma will not have enough glue since she'll have 10 2/3 rather than 11 batches.
Note that 1 gallon = 16 cups
Since Emma has half of 1-gallon bottle of white school glue, this means that she has 1/2 × 16 = 8 cups
Since Emma uses 3/4 cup of white school glue for each batch, therefore the number of batches that van be made with 8 cups will be:
= 8 ÷ 3/4
= 8 × 4/3
= 10 2/3
Therefore, Emma will not have enough glue since she'll have 10 2/3 rather than 11 batches.
Read related link on:
https://brainly.com/question/24963824
Can someone help me with this??
Answer:
son: 12 daniel: 32
Step-by-step explanation:
daniel is 26 in 6 years he would be 32
son is 3x younger in 6 years so 32 divided by 3 would be 10.6 (11 if estimated)
I need help with this question
x + 3 + -3 = -6 please help me on this
Answer:-6
Step-by-step explanation:
X=-6
3 and -3 cancel out.
Answer:
-6
Step-by-step explanation:
The positives and negatives added cancel eachother out.
-6+3=-3
-3+-3=-6
A baker needs 2 pounds of flour to make 76 cookies.
How many pounds of flour would the baker need to
make 190 cookies?
Answer:
5 pounds
Step-by-step explanation:
2=76
76/2=38
38x5=190
5 pounds because it takes one pound to make 38 cookies
The value of the digit in the thousands place is_______ times as much as the digit in the hundredths place
3. In a figure a small square is cutting out from the largesquare. The area of the remaining part is 91 cm². The sum of Sides equal to 52cm.
(a). If the side of large square is x and the side of smallest square is y then find the area of the remaining part?
(b). Find the sides of the smallest square?
(c). Find the areas of the two squares?
Step-by-step explanation:
[tex]\large\underline{\sf{Solution-}}[/tex]
Given that,
ABCD is a square of side x cmEFGH is a square of side y cmFurther given that,
Sum of all sides = 52 cmIt means
Perimeter of square ABCD + Perimeter of square EFGH is 52 cmWe know,
[tex] \purple{\rm :\longmapsto\:\boxed{\tt{ Perimeter_{[square]} \: = \: 4 \times side \: }}}[/tex]
So, using this, we have
[tex]\rm :\longmapsto\:4x + 4y = 52[/tex]
[tex]\rm :\longmapsto\:4(x + y) = 52[/tex]
[tex]\rm\implies \:\boxed{\tt{ x + y = 13}} - - - - (1)[/tex]
Now, Further given that,
If square EFGH is cutting out from square ABCD, the area of remaining part is 91 square cm.
It means
[tex]\rm :\longmapsto\:Area_{[ABCD]} - Area_{[EFGH]} = 91[/tex]
We know,
[tex] \purple{\rm :\longmapsto\:\boxed{\tt{ Area_{[square]} = 4 \times side}}}[/tex]
So, using this, we get
[tex]\rm :\longmapsto\: {x}^{2} - {y}^{2} = 91[/tex]
can be further rewritten as using algebraic Identity,
[tex]\rm :\longmapsto\:(x + y)(x - y) = 91[/tex]
[tex]\rm :\longmapsto\:13(x - y) = 91[/tex]
[tex]\red{ \bigg\{ \sf \: \because \: using \: equation \: (1) \bigg\}}[/tex]
[tex]\rm\implies \:\boxed{\tt{ x - y = 7}} - - - - (2)[/tex]
On adding equation (1) and (2), we get
[tex]\rm :\longmapsto\:2x = 13 + 7[/tex]
[tex]\rm :\longmapsto\:2x = 20[/tex]
[tex]\rm\implies \:\boxed{ \: \bf \: \: x \: = \: 10 \:cm \: \: }[/tex]
On substituting the value of x in equation (1), we have
[tex]\rm :\longmapsto\:10 + y = 13[/tex]
[tex]\rm :\longmapsto\:y = 13 - 10[/tex]
[tex]\rm\implies \:\boxed{ \: \bf \: \: y \: = \: 3 \:cm \: \: }[/tex]
So,
[tex]\rm\implies \:\boxed{Side_{[square \: EFGH]} = y \: = 3 \: cm}[/tex]
and
[tex]\rm\implies \:\boxed{Side_{[square \: ABCD]} = x \: = 10 \: cm}[/tex]
Also,
[tex]\rm :\longmapsto\:\boxed{Area_{[square \: ABCD]} = {10}^{2} = 100 \: {cm}^{2} }[/tex]
[tex]\rm :\longmapsto\:\boxed{Area_{[squareEFGH] }\: = {3}^{2} = 9 \: {cm}^{2} }[/tex]
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
[tex]\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}[/tex]
Which of the following functions best describes this graph?
10
Answer:
A
Step-by-step explanation:
vertex = (-4, -4)
vertex form:
y = a(x-h)^2 + k
__________
y = (x- (-4))^2 + (-4)
y = (x+4)^2 -4
y = (x+4)(x+4) - 4
y = x^2 + 8x + 16 - 4
y = x^2 + 8x + 12
answer: A
What is the slope of the line that passes through the given points?
(-1, -5) and (-12, -5)
Watch out for those negative signs!
Select one:
a.
0
b.
undefined (this means you get an answer like 5/0, you CANNOT divide a number by 0!)
c.
10/13 fraction
d.
13/10 fraction
Answer:
The answer is A. 0
Step-by-step explanation:
If you graph the equation it shows a straight horizontal line and that makes it zero
Answer:
A) 0
or m = 0
Step-by-step explanation:
Slope is zero, because it's just a straight horizontal line.
You can tell when you graph it or by the fact that they both have the same y-value, in this case -5.
I hope this helps :)
23 What is the solution to this equation?
2x + 3 = x - 4
Answer:
x = -7
Step-by-step explanation:
2x + 3 = x - 4
~Subtract 3 to both sides
2x = x - 7
~Subtract x to both sides
x = -7
Best of Luck!
Answer:
Hello!!
Solving for the equation [tex]2x+3=x-4[/tex] ... the correct answer would be
[tex]x=-7[/tex]
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolate the variable
Hope this helps!!
The formula for the volume, V, of a sphere with radius r is V=(43)πr3. If the radius of a baseball is 113 inches, what is the volume to the nearest cubic inch?
A. 6
B. 8
C. 10
D. 14
15
The volume of the baseball, to the nearest cubic inch, is A. 6 inches³
The volume of a sphere is calculated by the formula:
= 4/3 x π x radius ³
A baseball is a sphere and in this case its radius is 1.13 inches.
The volume of the baseball is:
= 4/3 x 22/7 x 1.13³
= 4/3 x 22/7 x 1.442897
= 6.0464 inches³
To the nearest inch it is:
= 6 inches ³
In conclusion, the volume of the baseball is 6 inches.
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What is m∠JNM? Line J L and line M K slightly inclined with horizontal intersects at N. The upward and downward angles of the intersecting lines are obtuse. The left and right angles of the intersecting lines are acute. The measure of angle J N M is labeled as left parenthesis 4 x plus 6 right parenthesis degrees. The measure of angle L N K is labeled as left parenthesis 7 x minus 21 right parenthesis degrees.
Answer:
JNM=42
Step-by-step explanation:
JNM is equal to LNK so you can set the equations equal to each other.
7x-21=4x+6, subtract 4x from both sides
3x-21=6, add 21 to both sides
3x=27, divide by 3
x=9, then you plug it into an equation
4 times 9 + 6
36+6
42
<JNM = [tex]42[/tex] degrees.
What is horizontal angle?The angle made by two ground lines is measured horizontally , and is called a horizontal angle.
According to the question
Line J L and line M K slightly inclined with horizontal intersects at N.
<JNM = <LNK
[tex]4x + 6 = 7x - 21[/tex]
Subtract 4x from both sides
[tex]6 = 3x -21[/tex]
[tex]3x=27[/tex]
Divide by 3
[tex]x=\frac{27}{3}[/tex]
[tex]x =9[/tex]
<JNM = [tex]4x+6[/tex]
<JNM = [tex]4(9)+6[/tex]
<JNM = [tex]42[/tex] degrees
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The equation of line j is y =-5/8x+4/9. Line k is parallel to line j. What is the slope of line k?
Answer:
using the formula
y= mx+ c
comparing these;
m= -5/8
when two lines are parallel they are always equal
so the slope of line k= -5/8
Step-by-step explanation:
PLS MARK BRAINLIEST
Helpppppp me brainlest math
Answer:
what do you need help with?
Step-by-step explanation:
100 POINTS & BRAINLIEST!!
Answer:
b
Step-by-step explanation:
Total hours for biweek or 2 weeks
2(20)40hoursHourly pay=$18.25
Total home pay
18.25(40)$730Atleast $255 per week you can easily acquire 1000 also by toil