Answer:
a: [tex]f(t)=(t+2)^2-18[/tex]
b: vertex: (-2, -18)
minimum
c: x = -2
Step-by-step explanation:
Completing the square is difficult to explain in words. but I'll try my best. Let me know if you need any more information.
Part A ===============
Start with the given function in this form:
[tex]f(x)=ax^2+bx+c\\t^2+4t-14[/tex]
We need an additional number, d, and we'll calculate it like this:
[tex]d=(\frac{b}{2a})^2 \\\\d=(\frac{4}{2(1)} )^2\\d=2^2\\d=4[/tex]
d needs to be added and subtracted at the same time. That way we do not change the value of the expression:
[tex]ax^2+bx+d-d+c\\\\t^2+4t+4-4-14[/tex]
And you can separate them like this to make it easier to read:
[tex](t^2+4t+4) + (-4-14)\\(t^2+4t+4)-18[/tex]
Finally, we need to factor the trinomial in the parenthesis. Because we've completed the square, it's now a perfect square trinomial. The factored form is just:
[tex](x+e)^2[/tex]
where e is half of b, or the square root of c. That looks like this in our case, and you can also expand it to make sure.
[tex](t+2)^2\\\\(t+2)(t+2)\\t^2+2t+2t+4\\t^2+4t+4[/tex]
Put that all together and you get the answer:
[tex]f(t)=(t+2)^2-18[/tex]
Part B ===============
Vertex form is this:
[tex]f(x)=a(x-h)^2+k[/tex]
where (h, k) is the vertex and a is the scale factor.
In part A, we converted the given function into vertex form. Looking at that, you can see the vertex is at (-2, -18), and the scale factor is 1. When the scale factor is positive, the parabola faces upwards. When it's negative, the parabola faces downwards.
The scale factor is a positive 1 in this case, and if you picture that in your mind, the vertex is at the very lowest point, or the minimum, of the parabola.
Part C ==============
The axis of symmetry is always on the vertex, and that is because the vertex is the exact point where the parabola changes direction from positive to negative, or negative to positive.
The vertex of this parabola is (-2, -18), so the axis of symmetry is at x = -2.
Sorry if that got too long and hard to follow, I can clarify any part of it if needed.
36,000÷?=90 PLS HELP
Answer:
Easy
Step-by-step explanation:
Answer: 36,000 divided by 90 is 400
Answer:
400
Step-by-step explanation:
Write an algebraic expression for the verbal expression: "7 times the sum of a squared and b minus 4 times the sum of a squared and b".
Expand and simplify.
(x + 1)(2-6)
Incredibly, Enzo wins 5 tickets from every game, and Beatriz wins 11 tickets from every game. When they stopped playing games, Enzo and Beatriz had won the same number of total tickets.
What is the minimum number of games that Enzo could have played?
Answer:
Enzo must have played 11 games.
Step-by-step explanation:
Since Enzo earns 5 tickets from every game and Beatriz wins 11 tickets from each game, we have to find the LCM (Least Common Multiple) since they earned the same amount of tickets when they stopped.
The LCM of 11 and 5 is 55.
To see how many games they both played we have to divide the amount of tickets they earn each time from the LCM (55).
Since Enzo earns 5 tickets from each game and both Enzo and Beatrice earned 55, Enzo must've played 11 games.
(If that makes sense lol)
A camera is on sale for $130. After a 7.875% sales tax is added, what is the total cost of the camera?
Solve this system using the substitution method: 9x – 2y = 4; 3x – 5 = y
I need help please please whoever gets it correct I’ll give bairnlast
Answer:
(-1,-1)A
B (1,-3)
C (-2,-4)
I need help ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
4
Step-by-step explanation:
10. Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 3 liters of natural oil for every 4
liters of synthetic oil. In order to make 518 liters of Petrolyn oil, how many liters of natural oil are needed?
Step by step please
you have the ratio of natural:synthetic so;
3:4
3+4=7
357/7=51
3*51:4°51
153:204
therefore, it'd be 204 litres of synthetic oil!!
i hope this helps you!!
Last year, wind turbines along a hilly ridge had an average output of 390 kilowatt hours per year. The turbines were upgraded, and now their average annual output is 30% more.
What is the new average yearly output?
kilowatt hours=
30% × 390 = 117
= 390 - 117
= 507 kw/h
Is there a proportional relationship between a planet’s diameter and its distance from the sun? Explain.
Answer:
Yes there is a proportional relationship
Step-by-step explanation:
If we look at earth and the sun, the diameter of the sun is 108 times that of the diameter of earth, and the average distance between the earth and sun is 108 times the suns diameter.
Solve for x.
100°
(2x+3)
51°
Answer:
23
Step-by-step explanation:
Exterior angle property: Exterior angle equals sum of opposite interior angles
51 + 2x +3 = 100
2x + 54 = 100
2x = 100 - 54
2x = 46
x = 46/2
x = 23
A cable is 40 decimeters long. How long is the cable in meters?
Be sure to include the correct unit in your answer.
Answer:
4 Meters
Step-by-step explanation:
Formula
divide the length value by 10
thanks in advance ill mark brainliest
Answer:
i
Step-by-step explanation:
i think it is a. ..........
Original price of shorts $53.95 Discount 30% Tax:4.5%
Answer:157.35
Step-by-step explanation: multiply then add the tax
to pass this school year i need more time on my computer, more time on edmentum, the thing is im all caught up with my work and all i need is to find a way to get more time, if someone could find out how long it takes before im "off task" so i can just touch my computer to start the time again, or if theres a different way plz plz lmk
Answer:
you could start by making a definite timetable for yourself and try to get away so as to differentiate the time between your work your Edmonton and a time is spending a computer don't try to spend much more time when your computer because it's mainly due to procrastinating in during other work
joey enter a hot dog eating competition. He ate 30 1/2 hot dogs in 3/4 minutes. How many hot dogs did he eat in one min.
8 and 2/15
TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT
please help me solve this problem
2 (3m + 1)²
Expand and simplify
[tex]\huge\text{\bf Hey there!}[/tex]
[tex]\large\boxed{\mathsf{2(3m + 1)^2}}\\\large\boxed{\mathsf{\rightarrow 2\times (3m + 1)\times 3(3m + 1)}}\\\large\boxed{\text{\bf SIMPLIFY IT}}\ \large\boxed{\ \uparrow}\\\large\boxed{\mathsf{\rightarrow 18m^2+ 12m + 2}}\\\\\\\huge\boxed{\text{Therefore, your answer is: \boxed{\mathsf{18m^2 + 12m + 2}}}}\huge\checkmark[/tex]
[tex]\huge\text{\bf Good luck on your assignment \& }\\\huge\text{\bf enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Help please write and solve the equation in the comments
Answer:
x=34
Step-by-step explanation:
2x-5=3(1/2x+4)
2x-5=3/2x+12
1/2x-5=12
1/2x=17
x=34
Answer:
x=34
Step-by-step explanation:
what is the numerical answer?
Answer:
x = 3
Step-by-step explanation:
In a parallelogram the diagonals bisect each other , then
6x + 11 = 5x + 14 ( subtract 5x from both sides )
x + 11 = 14 ( subtract 11 from both sides )
x = 3
Can someone please help me
Answer: i don''t know the answer im sorry i hope someone helps you :)
Step-by-step explanation:
Write x^2+3x-8 in the form of (x+p) ^2+q
Answer:
(x+1.5)^2 -10.25
Step-by-step explanation:
1)first, we half 3 to give us 1.5
(x+1.5)^2
2)square 1.5=2.25
so far we have (x+1.5)^2 - 2.25 --- the negative sign from 2.25 is part of the formula
3)we subtract 8 from -2.25. the 8 comes from here shown in bold ----- x^2+3x-8
4) (x+1.5)^2 -2.25 - 8
5)simplify the last part by doing -2.25 - 8= -10.25
6)answer is (x+1.5)^2 - 10.25
In 20Pg how many choices are
there for the eighth batter for a
line-up of 9 out of 20?
A. 20
B. 14
C. 13
Answer:
13
Explanation-
It is 13 because it is the only one out of all of them that makes sense.
For the ²⁰ P ₉ the required number of choices are 6.0949324 x 10¹⁰.
What is permutation and combination?Permutation and combination are ways to arrange values in a set. In permutation the order of arrangement matters, but in combination the order of arrangement does not matter,
In the given question,
In ²⁰ P ₉, the number of choices are to be found.
To find the choices,
Expand ²⁰ P ₉ by using a formula,
[tex]\rm ^nP_r = n!/(n-r)![/tex]
The number of choices
= 20!/ (20 -9)!
= 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11!/ 11!
= 6.0949324 x 10¹⁰
The required number of choices are 6.0949324 x 10¹⁰.
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The complete question is given below.
Explain how you can multiply to find equivalent fractions
Answer:
One example for an equivalent fraction would be 2/5 = 4/10
Step-by-step explanation:
It is equivalent because in both the denominator and the numerator you multiply by 2 which means that if you would divide 4/10 by 2 top and bottom, you would get 2/5. If you were to but these fractions on a number line; one on top of the other; they would equally have one under the other.
*** I hope this helps (brainly if possible)
What would you do if you found out that you wrote a cheque of $78 but it was recorded as $98 in check register?
Answer:
I will cryy because I only want to write 78 why it recorded as 98
Need help with thissss!!
Answer:
f(5) = 38
Step-by-step explanation:
f(a) = 7(a + 1) - 4
f(5) = 7(5 + 1) - 4
f(5) = 7(6) - 4
f(5) = 42 - 4
f(5) = 38
How to divide 4 divided by 2/3
According to your question, (4 divided by 2/3):-
[tex] \frac{4}{ \frac{2}{3} } [/tex]
By reciprocal, it. becomes:
[tex]4 \times \frac{3}{2} [/tex]
As we know that 2×2 is 4, cancel 4. Then we get:-
[tex]2 \times 3[/tex]
[tex]→6[/tex]
Therefore, the answer is 6
Una chompa cuesta 112 bs ¿a como debo venderla para tener una ganancia de 15%?
Answer:
746
Step-by-step explanation:
112 dividir 15
Y por el resultado lo multiplicas x 100
y esas va ser tu respuesta
A sunflower is 13 inches tall and grows 41 inches each month. The
sunflower's height is a linear function of time. Which statement best
describes the rate of change and initial value of this function?
A. The rate of change is the number of inches grown per month, and
the initial value is the first month.
B. The rate of change is the number of inches grown per month, and
the initial value is the starting height.
C. The rate of change is the starting height, and the initial value is the
number of inches grown per month.
D. The rate of change is the number of months per inch grown, and
the initial value is the first month.
Answer:The rate of change is the number of inches grown per month, and
the initial value is the starting height.
Step-by-step explanation:
The rate of change is the starting height, and the initial value is the
number of inches grown per month.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept
Given,
A sunflower is 13 inches tall and grows 41 inches each month.
The sunflower's height is a linear function of time.
A linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
y=13+41x.
Here x represents the number of months
13 is the initial height of the sunflower.
In the given options, The rate of change is the starting height, and the initial value is the number of inches grown per month is the statement best describes the rate of change and initial value of this function
Hence, The rate of change is the starting height, and the initial value is the number of inches grown per month
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