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.
Solve the following system of equations:y=x2−4x+3 y=2x−2
[tex]y = 2x -2 ~~~~.....(i) \\\\y = x^2 -4 x +3 ~~~~ .....(ii) \\\\\\x^2-4x +3 = 2x -2\\\\\implies x^2 -4x -2x +3 +2 =0\\\\\implies x^2 -6x +5 =0\\\\\implies x^2 -5x -x +5 =0\\\\\implies x(x-5) -(x-5) =0\\\\\implies(x-5)(x-1) =0\\\\\implies x = 5 ~~ \text{or}~~ x = 1 \\\\\\\text{Substitute x = 1 in equation (i):}\\\\y = 2 -2 =0\\\\ \text{Substitute x = 5 in equation (i):}\\\\\\y = 2(5) -2 = 10 -2 =8 \\\\\text{Hence,}~~ (x,y) = (1,0) ~ \text{and} ~ (x,y) = (5,8)[/tex]
write the fraction as a decimal use bar notatin if necessary
-2 5/22
Answer:
1.13
Step-by-step explanation:
to turn a fraction to a decimal divide the denomitator by the numerator [tex]\frac{-25}{22}[/tex] can also be written as -25÷22 which equals 1.13 or 1.136 with a line over it
Hope this helps!
The speed of an object is the ratio of its distance traveled to time. If the speed of a bicycle is 4.5 meters per second, what is the distance traveled in 9 seconds?
Answer:
40.5 meters
Step-by-step explanation:
4.5m/s • 9s = 40.5m
Anyone able to help with this?
[tex]W = 23.7°[/tex]
Step-by-step explanation:
The formula given is the statement of Snell's law of refraction. We are given the following:
[tex]I_a = 1.0003[/tex]
[tex]I_w = 1.3[/tex]
[tex]A = 31.5°[/tex]
So we need to find the angle of refraction W. Starting with Snell's law,
[tex]\dfrac{I_w}{I_a} = \dfrac{\sin A}{\sin W} \Rightarrow \sin W = \left(\dfrac{I_a}{I_w}\right)\sin A[/tex]
Plugging in the given values, we get
[tex]\sin W = \left(\dfrac{1.0003}{1.3}\right)\sin{31.5°} = 0.402[/tex]
Solving for the angle W, we then get
[tex]W = \sin^{-1}(0.402) = 23.7°[/tex]
Find the distance between two points in the simplest radical form
Answer:
The answer will be 5.
Step-by-step explanation:
using the formula d=/(x2-x1)2 +(y2-y1)
Evaluate each expression if x = 7, y = 1, and z = 8.
=
19. x + y + 2
20. x + 2z
21. 4y
22. 4x – 3z
23. 4x – 17
24. 62 – 52
shto The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.
25. 9y + (2x + 1)
26. 14 + 2z
27. 2 : 2
28. xz
29. y - x
30. 24y - 2
31. x2 – 2y + 8
32. 2xz
33. 30y - 40x – 1,000
19, 15.5
20, 25
21, 1/16
22, 4
23, 11
24, 8
25, 19.5
26, 30
27, 4
28, 56
29, 6.5
30, 4
31, 21
32, 112
33, 3,200
here are they
Evaluate the expression 8+-9
Answer:
8+-9=-1
Step-by-step explanation:
evaluated
Answer:
8+(-9)=8-9=-1
Step-by-step explanation:
to get -9 you multiply -×+ which is -
Solve the given equations. PLEASE show your work. Tell me if there is no solution or infinite.
17 + 2(1 + 3x) = x - 5(3 - x)
Answer:
x = 17/5
Step-by-step explanation:
17+2+6x = x-15 +5x
19+6x =16x -15
19+15 = 16x-6x
34 = 10x
34/10= 10x/10
17/5 = x
x = 17/5 or 3 2/3
Did I do 11,7 right ?
Answer:
Yes
Step-by-step explanation:
The radius of a circle measures 10 yards what is the circumference of the circle
Answer:
62.8 yards
Step-by-step explanation:
The circumference would just be equal to diameter*3.14, and the diameter is 2 times the radius. 2x10=20, and 20x3.14 would equal 62.8 yards.
What is a circle define and illustrate The following in figures
Answer:
Circle is a closed geometric figure having an infinite number of sides.
Step-by-step explanation:
A circle ⭕ has infinite number of sides want to know how then try and experiment.
First draw a pentagon of five sides, then a hexagon of six sides and keep on increasing the number of sides and then you will notice the shape being close of a circle.
Your deductible expenditures are $8236 for interest on a home mortgage, $3528 for contributions to charity, and $634 for state income taxes. Your filing status entitles you to a standard deduction of $12,200. Should you itemize your deductions rather than claiming the standard deduction? If so, what is the difference?
Answer:
yes 198
Step-by-step explanation:
Choose the correct answer below
Answer: B.
Step-by-step explanation:
brainliest me
Eighteen greater than a number is 159. Find the number. Check your solution
The number is___
Answer:
let the number be x.
[tex]x + 18 = 159 \\ x = 159 - 18 = 141[/tex]
the number is 141
hope helpful <3
the interval [2, 4] is divided into n equal subintervals of length delta x. What is delta x (in terms of k and n)
Each subinterval would have length ∆x = (4 - 2)/n = 2/n
In a particular country, 3% of the population is HIV positive. A test for HIV correctly
diagnoses 95% of those who have the condition, but incorrectly diagnoses 4% of those
who are not HIV positive as being HIV positive. A patient obtains a positive test result,
apparently indicating the presence of HIV. Determine the probability that the patient
really is HIV positive.
Using conditional probability, it is found that there is a 0.4235 = 42.35% probability that the patient really is HIV positive.
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happeningIn this problem:
Event A: positive test.Event B: HIV positive.The percentages involving a positive test are:
95% of 3%(positive)4% of 100 - 3 = 97%(not positive).Hence:
[tex]P(A) = 0.95(0.03) + 0.04(0.97) = 0.0673[/tex]
The probability of both having a positive test and being HIV positive is:
[tex]P(A \cap B) = 0.95(0.03)[/tex]
Then, the conditional probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.95(0.03)}{0.0673} = 0.4235[/tex]
0.4235 = 42.35% probability that the patient really is HIV positive.
A similar problem is given at https://brainly.com/question/14398287
The points (9,21) and (21,49) form a proportional relationship. Find the slope in fraction form or simplest form. Then use the slope to graph the line.
Answer:
I think it's -28/-12
Step-by-step explanation:
y-y/x-x
The sum of two numbers is 48. One numner is 3 times the other. Find the numbers.
Answer:
16 and 3?
Step-by-step explanation:
48÷3=16
hope this helps
Answer:
12 & 36
Step-by-step explanation:
According to the statement:
[tex]x+y=48[/tex]
[tex]x=3y[/tex]
Replace x= 3y:
[tex]3y+y=48[/tex]
[tex]4y=48[/tex]
[tex]y=48/4=12[/tex]
Then:
[tex]x=3y=3(12)=36[/tex]
Hope this helps
A number n is a prime factor of 28 and 63
Answer:
7
Step-by-step explanation:
The factors of 28 and 63 are
28 : 1, 2, 4, 7, 14, 28
63 : 1, 3, 7, 9, 21, 63
The common factors are 1 and 7
7 is a prime factor of both 28 and 63
Calculate the length of the circumference inscribed in the ABCD trapezium using the data shown in the figure
i need help :(
From the given figure,
Subtracting AB and DC, so,
[tex]6 - 3 = 3 \: cm[/tex]
As we know that :-
[tex]d = \sqrt{ {5}^{2} - {3}^{2} }[/tex]
[tex]→d = 4 π cm[/tex]
Since:-
[tex]c = πd[/tex]
[tex]c = 4πd[/tex]
So, Answer is 4 π d
State the rules for multiplying integers.
Answer:
If they are the same integer, then the answer is always positive. However, if the integer are different, the answer is negative.
Find the average rate of change of k(x) = x' over the interval [3, 9].
Answer:
y=6x×2/4
x=7
thanks for the points
Jalisa buys candles in bulk to sell in her store. Her cost for each candle is $9
. She marks up the candles 85%
. How much does Jalisa charge per candle?
Answer:
$16.65
Step-by-step explanation:
To turn percentages into coefficients divide by 100, so 85% become .85. She marks them up or adds a cost of 85% so instead of using .85 we use 1.85. so 1.85 times initial cost of candle is 1.85*9=16.65
6-4x=12+2x
Solve for x
X is the random number of times a coin with heads probability 1/4 is tossed till the first heads appears, find: g
what led to the creation of the free-soil party?
A. To stop immigrants from entering the United States
B. To promote slavery across the West
C. To stop the spread of slavery
D. To achieve Manifest Destiny
Answer:
The answer is C
Step-by-step explanation:
brainliest plss
what is the sum of 6/12 and 1/2
A.3/12
B.9/12
C.12/12
D.13/12
PLZZZZ HELP I WILL GIVE BRAINLIST
Answer:
1/2
Step-by-step explanation:6/12 is 1/2 of the fraction meaning that 6/12 is = to 1/2.
Answer:
12 / 12
Step-by-step explanation:
LCM of 12 and 2 = 12
1 / 2
= ( 1 / 2 ) x ( 6 / 6 )
= ( 1 x 6 ) / ( 2 x 6 )
= 6 / 12
6 / 12 + 1 / 2
= 6 / 12 + 6 / 12
= ( 6 + 6 ) / 12
= 12 / 12
when is a number divisible by 6?
they are sixty four thousand people at a football game 80% of the people were supporting the home team how many people were supporting the home team
Answer:
51200
Step-by-step explanation:
64000×80%=51200
[tex]\huge\mathfrak{question}[/tex]
they are sixty four thousand people at a football game 80% of the people were supporting the home team how many people were supporting the home team
[tex] \huge \mathfrak step \: by \: step[/tex]
First we will look for how much 80% of 64,000 is.
Lets put our equation
[tex]64000 \times 80 \div 100[/tex]
solve it and we get
[tex]{{\boxed{{51200}}}}}[/tex]
as our answer
hi can you please answer this question 20 points if u do
Answer:
Step-by-step explanation
just multiply
like 1x2=2
so 60x2=120
2x5=10
120x5=600
and on and on