Graph the function. Identify the vertex and axis of symmetry.
f(x)=-2x^2+2x-1
Answers
y = a(x - h)² + k, where the vertex is (h , k)
y = -2(x² - x + 1/2)
y = -2(x² - x + 1/4 - 1/4 + 1/2)
y = -2(x² - 1/2) - 1/2
Vertex = (1/2 , -1/2)
Axis of symmetry: x = 1/2
Answer:
Part A) The vertex is the point [tex](0.5,-0.5)[/tex]
Part B) The axis of symmetry is [tex]x=0.5[/tex]
Part C) The graph in the attached figure
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
(h,k) is the vertex of the parabola
and the axis of symmetry is equal to the x-coordinate of the vertex
so
[tex]x=h[/tex] -----> equation of the axis of symmetry
In this problem we have
[tex]f(x)=-2x^{2}+2x-1[/tex]
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]f(x)+1=-2x^{2}+2x[/tex]
Factor the leading coefficient
[tex]f(x)+1=-2(x^{2}-x)[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]f(x)+1-(1/2)=-2(x^{2}-x+(1/4))[/tex]
[tex]f(x)+(1/2)=-2(x^{2}-x+(1/4))[/tex]
Rewrite as perfect squares
[tex]f(x)+(1/2)=-2(x-(1/2))^{2}[/tex]
[tex]f(x)=-2(x-(1/2))^{2}-(1/2)[/tex] -----> equation in vertex form
The vertex of the parabola is the point [tex](0.5,-0.5)[/tex]
Is a vertical parabola open downward
The axis of symmetry is equal to
[tex]x=0.5[/tex]
see the attached figure to better understand the problem
Related Questions
PLEASE HELP.
The polynomial 16x + 2 is a ___ . Adding the term ____ to the polynomial would make it a trinomial.
1. a) monomial b) binomial c) trinomial
2.) a) xy b) 5 c) 3x
Answers
~Shadow
The polynomial 16x+2 is a binomial.
Adding the term xy to the polynomial would make it a trinomial.
What is monomial?A polynomial with exactly a single term is called monomial.What is trinomial?A polynomial with three terms is called trinomial.Hence, the polynomial 16x+2 is a binomial.
Adding the term xy to the polynomial would make it a trinomial.
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What times what equals 80.73
Answers
find all the zeros of the function y=x^3+6x^2+x+6
Answers
The zeros of a function are the values of x for which the function equals zero. The function given here is a cubic function, and finding its zeros can be complex, often requiring numerical methods or advanced mathematical approaches like the cubic formula.
Explanation:This problem deals with finding the zeros of the cubic function y=x^3+6x^2+x+6. A zero of a function is a value of x for which the function equals zero. You can find the zeros of this function by setting the equation equal to zero and solving for x.
Unfortunately, this particular cubic equation does not have an easy solution using basic algebraic methods. We can't factor it in an easy and straightforward manner. However, you can use numerical methods, or online calculator tools, to get an approximate value for the zeros. Alternatively, you can use the cubic formula (somewhat similar to the quadratic formula), but this requires knowledge of more advanced mathematics.
Please consult your teacher or textbook for more detailed instructions on how to use higher level methods to solve cubic equations. Remember that each method has its own level of accuracy and complexity, so choose the method that best suits your abilities and the requirements of your task.
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How are mc091-2.jpg and mc091-3.jpg related?
Answers
Can someone solve this and show me the work √5k+2 +8=11
Answers
you have: [tex] \sqrt{5k} +2+8=11[/tex]
-->>Isolate the variable...
[tex] \sqrt{5k} +2+8=11[/tex]
[tex] \sqrt{5k} +10=11[/tex]
[tex] \sqrt{5k} +10=11[/tex]
-10 -10
[tex] \sqrt{5k} =1[/tex]
What is the opposite of square root? [tex] (x)^{2} [/tex]
[tex] \sqrt{5k} ^{2} = 1^{2} [/tex]
5k=1
Now simply divide-->>
k=[tex] \frac{1}{5} [/tex]
Thus, your answer.
20 is 30% of what number
Answers
Let 20 be 30%
Convert to 100%, 20/30*100 = 66.666
20 is 30% of 66.67 or 67 (whole number)
20 is 30% of *67*
Tell whether the sequence is arithmetic. If it is identify the common difference
30. -15,-5,5,15….
Answers
a triangle has a side length of 4 inches and an area of 18 square inches and a larger similar triangle has a corresponding side length of 8 inches. Find the area of the larger tringle ?
...?
Answers
The area of the larger similar triangle can be calculated using the proportion of the squares of the lengths of the corresponding sides. Using this principle, we find that the area of the larger triangle is 72 square inches.
Explanation:In mathematics, the area (Area) of similar triangles is proportional to the square of their corresponding sides. Given that the side length of the smaller triangle is 4 inches and the side length of the larger similar triangle is 8 inches, we can set up an equation relating the side lengths and areas of the two triangles. The smaller triangle has an area of 18 square inches, and we'll call the area of the larger triangle A.
The equation is (Area of larger triangle / Area of smaller triangle) = (Side of larger triangle / Side of smaller triangle)2. Substituting the given values, we get (A / 18) = (8 / 4)2. Simplifying the right side of the equation gives us (A / 18) = 4. Multiplying each side of the equation by 18 allows us to solve for A, indicating that the area of the larger triangle is 72 square inches.
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The area of the larger triangle is 72 square inches.
Given that the smaller triangle has a side length of 4 inches and an area of 18 square inches, and the larger triangle has a corresponding side length of 8 inches, we can calculate the ratio of the side lengths:
[tex]\[ \text{Ratio of side lengths} = \frac{\text{Side length of larger triangle}}{\text{Side length of smaller triangle}} = \frac{8}{4} = 2 \][/tex]
Now, we can find the ratio of the areas of the two triangles by squaring the ratio of their side lengths:
[tex]\[ \text{Ratio of areas} = \left(\frac{8}{4}\right)^2 = 2^2 = 4 \][/tex]
Since the area of the smaller triangle is 18 square inches, we can find the area of the larger triangle by multiplying the area of the smaller triangle by the ratio of the areas:
[tex]\[ \text{Area of larger triangle} = \text{Area of smaller triangle} \times \text{Ratio of areas} \] \[ \text{Area of larger triangle} = 18 \times 4 \] \[ \text{Area of larger triangle} = 72 \text{ square inches} \][/tex]
Therefore, the area of the larger triangle is 72 square inches.
if your mother has 3 cows how many cows do you need to make 5 cows
Answers
allyson and adrian have decided to connect their ankles with a bungee cord; one end is tied to each person's ankle. the cord is 30 ft long but stretches to 90 ft. they both start from the same location. allyson moves 10 ft/sec and adrian moves 8 ft/sec in the directions indicated. a) after 2 seconds will the slack in the cord be used up? b)determine when the bungee cord first becomes tight, where are the girls located? c) when will the bungee cord first touch the corner of the building? (using similar triangles)
Answers
Final answer:
Allyson and Adrian have a 30 ft long bungee cord that stretches to 90 ft. After 2 seconds, the slack in the cord will not be used up. The bungee cord first becomes tight after 3 seconds, when Allyson reaches the end of the cord and Adrian has stretched it completely. The bungee cord first touches the corner of the building when Adrian has traveled twice the height of the building.
Explanation:
Physics - Elasticity and Motion:
a) After 2 seconds, Allyson would have moved a total distance of 10 ft/sec × 2 sec = 20 ft. Adrian would have moved a total distance of 8 ft/sec × 2 sec = 16 ft. Since the cord is 30 ft long and stretches to 90 ft, after 2 seconds, the slack in the cord would not be used up.
b) To determine when the bungee cord first becomes tight, we need to find the time it takes for one person to reach the end of the cord and the other person to stretch the cord completely. Allyson will take 30 ft ÷ 10 ft/sec = 3 sec to reach the end, while Adrian will take 30 ft ÷ 8 ft/sec = 3.75 sec to stretch the cord completely. Therefore, the bungee cord first becomes tight after 3 seconds, when Allyson is at the end of the cord and Adrian has stretched it completely.
c) To determine when the bungee cord first touches the corner of the building, we can use similar triangles. The ratio of the stretched length of the cord to the original length is the same as the ratio of the horizontal displacement to the height of the building. Let's assume the height of the building is H. Then, (90 ft - 30 ft) ÷ 30 ft = x ÷ H, where x is the horizontal distance traveled by Adrian. Solving for H, we find H = (90 ft - 30 ft) ÷ 30 ft × x = 2x. Therefore, the bungee cord first touches the corner of the building when Adrian has traveled twice the height of the building.
dy/dx ln(xy)=e^(x+y)
Answers
(xy)'/xy = (x+y)' e^(x+y)
(x'y + xy')/xy = (1+y') e^(x+y)
(y + xy')/xy = (1+y')e^(x+y) and simplify
Hope this helps
Use the Laplace transform to solve differential equation
dx/dt + 7x = 5cos(2t)
Initial conditions: x(0) = 4, x'(0) = -4
Assume forcing functions are 0 prior to t = 0- ...?
Answers
=> L(x) = -(4s^2 - 5s +16)/(s^2+4)(s+7)
now the boring part, using partial fractions we separate 1/(s^2+4)(s+7) that is:(7-s)/[53(s^2+4)] + 1/53(s+7). So:
L(x)= (1/53)[(-28s^2+4s^3-4s^2+35s-5s^2+5s)/(s^2+4) + (-4s^2+5s-16)/(s+7)]L(x)= (1/53)[(4s^3 -37s^2 +40s)/(s^2+4) + (-4s^2+5s-16)/(s+7)]
denoting T:= L^(-1)and x= (4/53) T(s^3/(s^2+4)) - (37/53)T(s^2/(s^2+4)) +(40/53) T(s^2+4)-(4/53) T(s^2/s+7) +(5/53)T(s/s+7) - (16/53) T(1/s+7)
x-intercept=2; containing the point (-5,4), using either the general form or the slope-intercept form of the equation of a line.
...?
Answers
y - 0 = (4 - 0)/(-5 - 2) (x - 2)
y = -4/7 (x - 2)
7y = -4(x - 2)
7y = -4x + 8
4x + 7y = 8
The present value of $12,000 for six years compounded at 6% semiannually is
Answers
Then, it would be: P * R * T /100
12000 * 6 * 12 / 100 = 8640
So, your final answer is $8640
Hope this helps!
what is the recursive rule for the sequence f(n)=2+(-3)(n-1)?
Answers
The recursive rule for the sequence f(n) = 2 + (-3)(n-1) is f(1) = 2 and f(n) = f(n-1) - 3 for n > 1, where each term is 3 less than the previous term.
The given sequence can be expressed as a recursive formula. A recursive formula defines each term of a sequence using the preceding term(s). To find the recursive rule for the sequence f(n) = 2 + (-3)(n-1), let's write out the first few terms:
f(1) = 2 + (-3)(1-1) = 2f(2) = 2 + (-3)(2-1) = -1f(3) = 2 + (-3)(3-1) = -4f(4) = 2 + (-3)(4-1) = -7Examining the pattern, each subsequent term is 3 less than the previous term. Thus, the recursive rule is:
f(1) = 2f(n) = f(n-1) - 3 for n > 1This means that, to get the next term in the sequence, we subtract 3 from the previous term, starting with the second term.
Six times the sum of a number and twelve is forty.
Which equation represents this?
6N + 12N = 40
6N + 12 = 40
6(N + 12) = 40
Answers
6(N+12)= 40
six times the sum of (a number and twelve) or six times the sum of a number and than plus 12 equal 40.
In first case answer is:
6(N + 12) = 40 and in second
in second:
6N + 12 = 40
Zach is 4 years older than twice his sister Maya’s age.
Let m represent Maya’s age.
Which expression represents Zach’s age?
2m
2m + 4
m + 4
4m + 2
Answers
Answer:
It's 2m + 4
Step-by-step explanation:
Kurt johnson delivers packages for a delivery company. he receives $7.50 for every package delivered. what does kurt earn in a week if he delivers 48 packages? 360.00 405.00 555.00 640.00
Answers
48 packages.....so x = 48
y = 7.50(48)
y = 360.....so if he delivers 48 packages, he earns $ 360
Answer:
He earned $ 360.00.
Step-by-step explanation:
Given,
The amount he gets for a package of delivery = $ 7.50
The number of packages he delivered in a week = 48,
Hence, the amount he earned in the week = The amount he gets for a package of delivery × The number of packages he delivered
= 7.50 × 48
= $ 360.00
The slope of the line below is 2. use the coordinates of the labeled point(3,10) to find the point-slope equation of the line
A. y-10=-2(x-3)
B. y+10=2(x+3)
C. y-10=2(x-3)
D. y+10=-2(x+3)
Answers
The point-slope equation of the line is option (C), y-10 = 2(x-3) is the correct answer.
What is slope of a line?The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.
For the given situation,
The slope of the line, m = 2
The coordinates of the labeled point, (x1, y1) = (3,10)
The point-slope equation of the line is
[tex](y-y1)=m(x-x1)[/tex]
On substituting the above values,
⇒ [tex]y-10=2(x-3)[/tex]
Hence we can conclude that the point-slope equation of the line is option (C), y-10 = 2(x-3) is the correct answer.
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(x+y^2)(2x+3y^2) what is the product
Answers
After the foil method, you get - 2x^2 + 3xy^2 + 2y^2 + 3y^4
You combine like terms and put them in order by exponent number:
5y^6 + 2x^2 + 3xy^2
=2x^2 + 3xy^2 +2xy^2 +3y^4
=2x^2 + 5xy^2 +3y^4
A total of 333 tickets were sold for the school play. they were either adult tickets or student tickets. the number of student tickets sold was two times the number of adult tickets sold. how many adult tickets were sold?
Answers
111 adult tickets
That checks out...
2x + x = 333
3x=333
x=111
After setting up a system of equations to represent the total number of tickets and the relationship between student and adult tickets, the equations were solved to find that 111 adult tickets were sold.
The question involves solving a numerical problem where we are given that 333 tickets were sold for a school play, consisting of adult tickets and student tickets. The number of student tickets is twice the number of adult tickets sold. We can express this with two equations and solve for the number of adult tickets.
Let A be the number of adult tickets and S be the number of student tickets. The following equations represent the system we need to solve:
A + S = 333 (Total number of tickets)
S = 2A (Number of student tickets is twice the number of adult tickets)
To solve for A, we can substitute the second equation into the first:
A + 2A = 333
3A = 333
A = 333 / 3
A = 111
Therefore, 111 adult tickets were sold.
Chloe rolls two six-sided number cubes and adds the numbers showing on the cubes. What is the probability that the sum of the number cubes is even or five?
A)22/36
B)18/36
C)4-36
D)72/1296
Answers
Answer:
you would be right if you × it then it would be D but you always + so if you do 4/36 + 18/36= 11/18 is your answer
What is another way to write 250,000 ml?
Answers
_______________________
(Note that "mL" is another way to write "ml"; or "milliliters".
____________________________
Lengthy explanation:
_________________________________
One other way to write 250,000 mL is to convert that value to "L" (Liters).
_________________________________
Note the exact version: 1000 mL = 1 L
_________________________________
So:
_______________
250,000 mL * ([tex] \frac{1 L}{1000 mL} [/tex] ) = ? L ;
___________________________________________
Note: The "mL" notations "cancel out") ; and we are left with:
_________________________________________________
250,000 mL =
___________________________________
([tex] \frac{250,000}{1000} [/tex] L ;
__________________________________
250,000 ÷ 1000 = ? L
______________________
Take: "250,000" and move back the last 3(three) decimal places:
_____________________________
250,000 ÷ 1000 = 250 L
_____________________________
hope this helps you
Which of the following are zero-dimensional or one-dimensional figures.? (Check all that apply)
A. Point
B. Angle
C. Ray
D. Plane
E. Segment
F. Line
Answers
One-dimensional figure = C.) Ray E.) Segment F.) Line
Hope this helps!
In geometry, zero-dimensional figures do not extend in any direction and include 'points', while one-dimensional figures extend in one direction and include 'lines', 'segments', and 'rays'. Therefore, the zero or one-dimensional figures in the given options are 'point', 'line', 'segment', and 'ray'.
Explanation:In geometry, quantities can be zero, one, two, or three dimensional. Zero-dimensional figures are those that do not extend in any direction. The only such geometric figure is a point (Option A). One-dimensional figures, on the other hand, extend in one direction. These include a line (Option F), a segment (Option E), and a ray (Option C), all of which have length but no breadth or height. Therefore, the zero-dimensional or one-dimensional figures from the given options are point, line, segment, and ray.
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Gracie Shay wants to buy a new Hummer in 5 years. Gracie estimates the cost of the Hummer will be $28,000. If she invests $12,000 now, at a rate of 6 percent compounded semiannually, she:
1.Will have enough money
2.Will have exactly $16,000
3.Will have $18,000
4.Will have $16,126.80
5.None of these
...?
Answers
The answer is no. 4 "Will have $16,126.80". Below is the solution:
12000 ( 1 + 6/200)^10 = 16,126.80 $
Answer:
Option 4 - She will have $16,126.80
Step-by-step explanation:
Given : Gracie Shay wants to buy a new Hummer in 5 years. Gracie estimates the cost of the Hummer will be $28,000. If she invests $12,000 now, at a rate of 6 percent compounded semiannually.
To find : Which option she will have ?
Solution :
Using compound interest formula,
[tex]A=P(1+r)^t[/tex]
Where, A is the amount
P is the principle P=12,000
Compounded semiannually,
r is the rate 6%=0.06
[tex]r=\frac{0.06}{2}=0.03[/tex]
t is the time 5 years
[tex]t=5\times 2=10[/tex]
Substitute the value,
[tex]A=P(1+r)^t[/tex]
[tex]A=(12000)(1+0.03)^{10}[/tex]
[tex]A=12000\times (1.03)^{10}[/tex]
[tex]A=12000\times 1.3439[/tex]
[tex]A=16126.99[/tex]
The amount she will have $16126.99.
Therefore, Option 4 is correct.
Solve. 3x2 + 4x = –5
using quadratic equation ...?
Answers
x = [-b ±√(b^2 - 4ac)]/2a
a = 3
b = 4
c = -5
x = [-4 ±√(16 + 60)]/6
x = [-4 ±√76]/6
x = [-4 ±√(2^2 * 19)]/6
x = [-4 ±2√19]/6
x = [-2 ±√19]/3
x = [-2 + √19]/3
x = [-2 + 4.35]/3
x = 2.35/3
x = 0.78 (rounded to the nearest hundredth)
x = [-2 - ±√19]/3
x = [-2 - 4.35]/3
x = -6.35/3
x = -2.12 (rounded to the nearest hundredth)
∴ x = -2.12 , 0.78 (rounded to the nearest hundredth)
the function f is defined by f(x)=x2+3x-10
if f(x+5)=x2+kx+30, k=____________(<<
Answers
Help With Number 8 Please?
Answers
Because, ↓
Unit Rate = [tex] \frac{I}{1300 * 0.0425 } [/tex] which is equal to → [tex] \frac{450}{1300 * . 0425} [/tex]
and that's how I found out that my answer is 8.14 years
If arc CE= 40°, and m∠CDE = 30°, what is arc AB ?
A) 70°
B) 100°
C) 140°
D) 20°
Answers
Answer:
B is the right answer [tex]100^{o}[/tex]
Step-by-step explanation: Hope This Helps ;)
A percent is the result of a number being expressed as a fraction of 100. True or False? ...?
Answers
Answer:
True
Step-by-step explanation:
Percentage is expressed as the part from 100.
Thus, Percentage sign means divide by 100.
Also, it is the resultant number when divided by 100.
Thus, the given statement is absolutely true.