[tex] \rm \color{lime}(2,10)[/tex]
step-by-step explanation:
[tex]\rm \color{lime}y = - {x}^{2} + 4x + 6[/tex]
identify the coefficients[tex]\rm \color{lime}a = - 1,b = 4[/tex]substitute the coefficient into the expressionfind the x-coordinate of the vertex by substituting a = - 1 and b=4 [tex] \tt \tiny \: x = - \frac{b}{29} [/tex][tex]\rm \color{lime}x = - \frac{4}{2x( - 1)} [/tex]
solve the equation for Xfind the y-coordinate of the vertex by evaluating the function for x = 2[tex]\rm \color{lime}y = - {x}^{2} + 4x + 6,x = 2[/tex]
calculate the function value for x = 2[tex]\rm \color{lime}y = 10[/tex]
since the value of the function is 10 for x = 2 the vertex of the graph of the quadratic function is a (2,10)[tex] = \rm \color{hotpink} (2,10)[/tex]
hope it helps
Answer:
y = - (x - 2)² + 10
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square
y = - x² + 4x + 6 ( factor out - 1 from the first 2 terms )
y = - (x² - 4x) + 6
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² - 4x
y = - (x² + 2(- 2) + 4 - 4) + 6
y = - (x - 2)² + 4 + 6
y = - (x - 2)² + 10 ← in vertex form
. I am a factor of 120. • I am a multiple of 2. . I am a multiple of 3. . I am 1 away from a multiple of 5. Who am I?
Answer: 30
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
Answer:
30 is the correct answer
i need help with this question
Answer:
60
Step-by-step explanation:
10x = (21x - 3)/2
20x = 21x - 3
x = 3
measure of arc HF = 21x - 3 = 21(3) - 3 = 60
What is the answer to 4-(-6)+(-4)+3x0
Answer:
9
Step-by-step explanation:
Follow PEMDAS
[tex]4-(-6)+(-4)+3x\\4+6-4+3x\\6+3x\\6+3=9[/tex]
Answer:
6
Step-by-step explanation: [tex]4-\left(-6\right)+\left(-4\right)+3\times0[/tex]
Apply the Inverse Property of Addition
[tex]-\left(-6\right)+3\times0[/tex]
Apply Zero Property of Multiplication
[tex]-\left(-6\right)[/tex]
Determine the sign
[tex]6=YOUR\ ANSWER[/tex]
I hope this helps you
:)
the smiths spend 11% of their budget on entertainment. their total budget this year is $1,000 more than last year, and this year they plan to spend $4,620 on entertainment. what was their total budget last year?
Answer: $41000 Was the Smiths family budget last year.
Step-by-step explanation:
First you take $4620 and DIVIDE it by .11 you will get $42000 and since last year had $1000 less to spend you subtract $1000 from $42000 to get $41000 for the budget last year.
4. Compute the inverse Laplace transform of
[tex]F(s)= \frac{1}{{s}^{4} } + \frac{3s}{{s}^{2} + 9 } [/tex]
[tex]F(s)= \frac{7}{s} + \frac{6}{{s} + 4} - \frac{5}{ {s}^{2} + 16} [/tex]
[tex]F(s)= \frac{1}{(s - 2)(s + 1)(s - 3)} [/tex]
[tex]F(s)= \frac{s + 2}{ {s}^{2} (s + 1)(s - 1)} [/tex]
[tex]F(s)= \frac{s + 1}{ {s}^{2} (s + 1)} [/tex]
Answer:
See below for all answers and explanations
Step-by-step explanation:
1st Problem
[tex]F(s)=\frac{1}{s^4}+\frac{3s}{s^2+9}\\\\f(t)=\frac{t^3}{6}+3cos(3t)[/tex]
2nd Problem
[tex]F(s)=\frac{7}{s}+\frac{6}{s+4}-\frac{5}{s^2+16}\\ \\f(t)=7+6e^{-4t}-\frac{5}{4}sin(4t)[/tex]
3rd Problem
[tex]F(s)=\frac{1}{(s-2)(s+1)(s-3)}\\\\\frac{1}{(s-2)(s+1)(s-3)}=\frac{A}{s-2}+\frac{B}{s+1}+\frac{C}{s-3}\\ \\1=(s+1)(s-3)A+(s-2)(s-3)B+(s-2)(s+1)C[/tex]
[tex]1=(-1+1)(-1-3)A+(-1-2)(-1-3)B+(-1-2)(-1+1)C\\1=12B\\\frac{1}{12}=B[/tex]
[tex]1=(3+1)(3-3)+(3-2)(3-3)B+(3-2)(3+1)C\\1=4C\\\frac{1}{4}=C[/tex]
[tex]1=(2+1)(2-3)A+(2-2)(2-3)B+(2-2)(2+1)C\\1=-3A\\-\frac{1}{3}=A[/tex]
[tex]F(s)=\frac{-\frac{1}{3}}{s-2}+\frac{\frac{1}{12}}{s+1}+\frac{\frac{1}{4}}{s-3}\\ \\f(t)=-\frac{1}{3}e^{2t}+\frac{1}{12}e^{-t}+\frac{1}{4}e^{3t}[/tex]
4th Problem
[tex]F(s)=\frac{s+2}{s^2(s+1)(s-1)}\\ \\\frac{s+2}{s^2(s+1)(s-1)}=\frac{A}{s}+\frac{B}{s^2}+\frac{C}{s+1}+\frac{D}{s-1}\\\\s+2=s(s+1)(s-1)A+(s+1)(s-1)B+s^2(s-1)C+s^2(s+1)D\\ \\s+2=s^3A-sA+s^2B-B+s^3C-s^2C+s^3D+s^2D\\\\s+2=s^3(A+C+D)+s^2(B-C+D)-sA-B[/tex]
[tex]\begin{cases} A + C + D = 0\\B - C + D = 0\\- A = 1\\- B = 2 \end{cases}[/tex]
[tex]A+C+D=0\\(A+C+D=0)+(B-C+D)=0\\A+B+2D=0\\-1-2+2D=0\\-3+2D=0\\2D=3\\D=\frac{3}{2}[/tex]
[tex]A+C+D=0\\-1+C+\frac{3}{2}=0\\ \frac{1}{2}+C=0\\ C=-\frac{1}{2}[/tex]
[tex]F(s)=\frac{-1}{s}+\frac{-2}{s^2}+\frac{-\frac{1}{2}}{s+1}+\frac{\frac{3}{2}}{s-1}\\ \\f(t)=-1-2t-\frac{1}{2}e^{-t}+\frac{3}{2}e^{t}[/tex]
5th Problem
[tex]F(s)=\frac{s+1}{s(s^2+1)}\\\\\frac{s+1}{s(s^2+1)}=\frac{A}{s}+\frac{Bs+C}{s^2+1}\\\\s+1=(s^2+1)A+s(Bs+C)\\\\s+1=s^2A+A+s^2B+sC\\\\s+1=s^2(A+B)+sC+A[/tex]
[tex]\begin{cases} A + B = 0\\C = 1\\A = 1 \end{cases}[/tex]
[tex]A+B=0\\1+B=0\\B=-1[/tex]
[tex]F(s)=\frac{1}{s}+\frac{-s+1}{s^2+1}\\ \\F(s)=\frac{1}{s}+\frac{1-s}{s^2+1}\\\\F(s)=\frac{1}{s}+\frac{1}{s^2+1}+\frac{-s}{s^2+1}\\\\f(t)=1+sin(t)-cos(t)[/tex]
Evaluate the following expression for x = 11, y =
3. Enter only the final result.
x + 4
y +2
Answer:
3
Step-by-step explanation:
If x=11 then the top line would equal 11+4, which is 15
If y=3 then the bottom line would equal 3+2, which is 5
So, you end up with 15/5, which equals 3
Min50 , Q1 62, median 84, Q3 96, Max 99
Using the interquartile range, which of the following are outliers? Select all correct answers.
Select all that apply:
3
6
21
60
Answer:
3 and 6
Step-by-step explanation:
IQR = Q3-Q1=96-62=34
Lower Outlier = Q1 - 1.5*IQR = 62 - 1.5*34 = 11
Any Value under 11 is Considered as Outlier
Then 3 and 6 are Outliers
Upper Outlier = Q3 + 1.5*IQR = 96 + 1.5*34 = 147
Any Value Above 147 is Considered as Outlier
There is no Value above 147
The Only Outliers are 3 and 6
Find the surface area of a triangular prism
Answer:
The formula that is used to calculate the surface area of a triangular prism is, Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 + S2+ S3)L + bh; where 'b' is the bottom edge of the base triangle, 'h' is the height of the base triangle, L is the length of the prism and S1, S2 and S3 are the edges of the base triangle.
Find the area of the polygon
Answer:
Area of a regular polygon formulas
Step-by-step explanation:
area = n * a * ri / 2 , having ri - incircle radius (it's also an apothem - a line segment from the center to the midpoint of one of its sides)
area = perimeter * ri / 2 , given ri and polygon perimeter.
area = n * (ri)² * tan(π/n) , given ri.
How do you know when the Solve box has more than one page of information? A) The page indicator shows 1/4. B) There is an answer box. C) There is a Check Button. D) The words are set apart in a box. Will Mark Brainliest if answered correctly.
Answer:
A) The page indictor shows 1/4
Step-by-step explanation:
Because 1 is out of a multiple 4 pages.
Hope it helps.
Slope: Tutorial
у
11
10
9
8
7
6
5
4
3
2
2
3
4
6
7
8
9
10 11
The slope of the line in the graph is
(If your answer is a fraction, write it in simplified terms.)
I’m
Answer:
Step-by-step explanation: just write from 2 to 11 one by one
Aaliyah is a salesperson who sells computers at an electronics store. She makes a base pay of $70 each day and then is paid a $1.25 commission for every computer sale she makes. Write an equation for P,P, in terms of x,x, representing Aaliyah's total pay on a day on which she sells xx computers.
Answer:
p = 1.25x + 70
Step-by-step explanation:
We know she makes $70 each day and we know she makes $1.25 for each computer she sells.
With that we can add it into an equation because we can add 70 + 1.25, but the amount for each computer she sells in unknown so we give it an x which makes it 1.25x.
So, we do 1.25x + 70, but the amount total is missing so that is our p.
This finally completes our equation, p = 1.25x + 70 or 1.25x + 70 = p
If b-10 = 5, what is the value of b-6?
The answer is 21. Hope this Helps!
Beginning with the graph of f(x) = x2, what transformations are needed to form g(x) = -(x - 6)2 + 3?
O The graph of g(x) opens upward and is shifted to the right 6 units and up 3 units.
The graph of g(x) opens upward and is shifted to the left 6 units and up 3 units.
The graph of g(x) opens downward and is shifted to the right 6 and up 3 units.
The graph of g(x) opens downward and is shifted to the left 6 units and up 3 units.
The graph of [tex]g(x)[/tex] opens downward and is shifted to the right 6 and up 3 units.
How to apply rigid transformations on a given function
Let be [tex]f(x) = x^{2}[/tex], we need to apply the following three rigid transformations on [tex]f(x)[/tex] to obtain [tex]g(x)[/tex]:
Reflection around the x-axis: [tex]f'(x) = -x^{2}[/tex]Translation in the +x semiaxis: [tex]f''(x) = -(x-6) ^{2}[/tex]Translation in the +y semiaxis: [tex]g(x) = -(x-6) ^{2}+3[/tex]Hence, the graph of [tex]g(x)[/tex] opens downward and is shifted to the right 6 and up 3 units. [tex]\blacksquare[/tex]
To learn more on rigid transformations, we kindly invite to check this verified question: https://brainly.com/question/1761538
Answer:
The graph of opens downward and is shifted to the right 6 and up 3 units.
At the end of an accounting period a company total assets equaled $535,000 and liabilities equaled $210,000 how much was the companys owners equity
What is the name of our number system?
decimal system is the name of our number system.
Answer:
Our Number System is Hindu Arabic Number System.
The digits are: 0,1,2,3,4,5,6,7,8,9
How would I solve for X and Y?
Answer:
x = 10
y = 5√3
Step-by-step explanation:
SOLVE FOR X :
ABC = 90°
ABC + ACB + BAC = 180°
90° + ACB + 30° = 180°
ACB = 60°
cos(ACB) = BC/AC
cos(60°) = 5/x
x = 10
SOLVE FOR Y:
tan(BAC) = BC/AB
tan (30°) = 5/y
y = 5√3
PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)
A number is greater than or equal to three times another number. what are the numbers?
Answer:
THE AWNSWER IS A≥3B
Step-by-step explanation:
A≥3B
3. Consider the straight line x + y = 1 and the family of straight lines that pass
through the origin given by y = mx. As m changes the line rotates about the
origin. Solve these two systems of linear equation and find their points of inter-
section. Is there always a solution - If yes, briefly explain why. If not - for what
a
values of m is there no solution.
Answer:
solution: (1/(1+m), m/(1+m))no solution for m = -1 (lines are parallel)Step-by-step explanation:
Two distinct lines will always have a point of intersection, provided they are not parallel. That is, the system of equations {x +y = 1, y = mx} will have a unique solution as long as m ≠ -1.
The solution to the system can be found by substitution:
x +mx = 1
x(1 +m) = 1 . . . . factor out x
x = 1/(1+m) . . . . . divide by the coefficient of x; we must have m ≠ -1
y = m/(1+m) . . . . find the y-coordinate of the solution
The point of intersection is (1/(1+m), m/(1+m)).
__
The above solution is undefined when the denominator is zero: m = -1. There is no solution for m = -1.
How much of a premium do you pay for a steel house worth $190,000 with $49,000 worth of content in a suburban area?
A. $1258.70
B. $1372.70
C. $1589.90
D. $2304.70
Answer:
D. $2304.70
Step-by-step explanation:
a typical 2000 square foot house may cost anything from $200000 to $300000
Hope it helps!!!brainliest pls!!!!Step-by-step explanation:
How much of a premium do you pay for a steel house worth $190,000 with $49,000 worth of content in a suburban area?
B. $1372.70
How many different 4 letter passwords can be created if the letters can be
repeated?
Answer:358800
Number of dispositions of 4 letters without repetitions of the alphabet (26 letters): 26*25*24*23=358800
Step-by-step explanation:
Kiki's cat eats 23 cups of food twice a day.
How many cups of food does her cat eat each day?
Enter your answer in the box as a mixed number in the simplest form.
cups
Find the area of the yellow region, and no the answer to this exact question before was not correct. Thank you!
Answer:
39 sq.in
Step-by-step explanation:
find area of circle then subtract
Answer:
3.9 in²
Step-by-step explanation:
The shape is constructed of 2 semicircles (with diameter of 6 in) inside a square. Therefore, to calculate the yellow region, subtract the area of the semicircles (which form a circle) from the area of the square, then halve the answer.
Area of a square = [tex]x^2[/tex] ([tex]x[/tex] is the length of one side)
Given:
side length = 6 in⇒ area of the square = 6² = 36 in ²
Area of a circle = [tex]\pi r^2[/tex]
Diameter of a circle = 2r
(where r is the radius)
Given:
diameter = 6 in ⇒ r = 3 in⇒ area of the circle = [tex]\pi[/tex] × 3² = 9[tex]\pi[/tex] in²
Area of yellow region = (area of square - area of circle) ÷ 2
= (36 - 9[tex]\pi[/tex]) ÷ 2
= 3.9 in² (nearest tenth)
the whale swims down 150 more feet more. what is the whales elevation now
Answer:
i think it's 22500 deep down to the ocean
8 times the difference between b and 4 in a variable expression
Answer:
8( b - 4 )
Step-by-step explanation:
8 x ( b - 4 )
8( b - 4 )
I hope this helps!
Write the equation which is the sum of the three numbers y, y l and y 2.
Answer:
3y + 3 or 3(y+1)
Step-by-step explanation:
y + y + 1 + y + 2
= 3y + 3
= 3(y+1)
Consider the line y=9x-5. Find the equation of the line that is perpendicular to that line and passes through the point (-3,-3)
Answer:
y=(-1/9)x-(10/3)
Step-by-step explanation:
Since the line is perpendicular to y=9x-5, the slope of that line would be the opposite of the reciprocal of the original slope value. In this case, the slope of the line would be -1/9. So we have y=(-1/9)x+? Since we know a point, (-3, -3), we can input this back into our original equation and we have: -3=(1/3)+? We simplify and we have ?=-10/3. Therefore the final equation of the line that is perpendicular to that line and passes through the point (-3,-3) is y=(-1/9)x-(10/3).
Saraid is dividing 1/4 pound of cashews into 5 plastic bags. What
fraction of a pound of cashews will be in each plastic bag?
Draw a model to help you solve.
(Please draw a model )
Answer: 20 Pounds
Step-by-step explanation:
1/4 X 5 = 1/20 then reverse it
20/1 = 20 Pounds
(may not be correct!!!)
Trishia is 4 years older than Caila now. The sum of their ages in 8 years from now will be 38. How old are Caila and Trisha now?
Answer: 13 and 9
Step-by-step explanation:
because since there are two people 38-(8x2)=22
The only numbers that add up to 22 that have a difference of 4 are 13 and 9
Another way:
T=C+4
T+8+C+8=38
C+4+C+8=
A promissory note for $3600.00 dated May 15, 2012, requires an interest payment of $370.00 at maturity. If interest is at 9.6% compounded monthly, determine the due date of the note. (hint: find n then convert it into days and use excel sheet to add it to issue date)
In the box below show these parameters:
PV=....., FV=.....
The due date of the promissory note is May 24th 2013.
Data;
Present Value (PV) = $3600Interest = $370Future Value (FV) = PV + I = $3600 + $370 = $3970Due Date of the NoteTo calculate the due date of the note, we can use the formula of future value of the note.
[tex]FV = PV (1 + \frac{r}{n})^d\\ 3970 = 3600 (1 + \frac{9.6}{12})^d\\3970 = 3600(1+0.008)^d\\\frac{3970}{3600} =(1.008)^n[/tex]
Let's take the natural log of both sides
[tex](1.008)^n = (\frac{3970}{3600})\\ n\ln(1.008) = \ln(\frac{397}{360})\\ n = 12.28[/tex]
This is approximately 12 months and 9 days.
The due date of the promissory note is May 24th 2013.
Learn more on promissory note here;
https://brainly.com/question/25793394
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