Answer:
2x^2- 3x - Y= -5 -x + Y = 5
there is no solve because it already is solved.
Step-by-step explanation:
Write the equation of the following parabolae in their canonical form and hence find their vertices, foci and directrix.
1.
[tex] {y}^{2} - 6y - 2x + 19 = 0[/tex]
2.
[tex] {x}^{2} + 4x + 4y + 16 = 0[/tex]
Given:
y² - 6y - 2x + 19 = 0This is a horizontal parabola.
Canonical form of horizontal parabola is:
4a(x - h) = (y - k)², where (h, k) is vertexFocus is:
F(h + a, k)Directrix is:
x = h - aConvert the equation:
y² - 6y - 2x + 19 = 0y² - 6y + 9 - 2x + 10 = 0(y - 3)² = 2x - 10(y - 3)² = 4(1/2)(x - 5)We got:
h = 5, k = 3, a = 1/2Focus is:
F(5 + 1/2, 3) = F(5.5, 3)Directrix is:
x = 5 - 1/2 = 4.5#2Given:
x² +4x + 4y + 16 = 0This is a vertical parabola.
Canonical form of vertical parabola is:
4a(y - k) = (x - h)², where (h, k) is vertexFocus is:
(h, k + a)Directrix is:
y = k - aConvert the equation:
x² + 4x + 4y + 16 = 0x² +4x + 4 + 4y + 12 = 0(x + 2)² = -4y - 12(x + 2)² = 4(-1) (y + 3)We got:
h = - 2, k = -3, a = - 1Focus is:
F(-2, -3 - 1) = F(-2, - 4)Directrix is:
y = -3 - (-1) = - 2-2x^3+5x^2-3x-12 for x=2
Thank you.
-14
plug in #2 in the spots with an x
good luck :)
What is the next term in the sequence 58, 47, 36, 25,. ? –58 –8 14 69.
Answer:
14
Step-by-step explanation:
58, 47, 36, 25,. ?
Each term is 11 less than the preceding term
the term after 25 will be
25 - 11 = 14
Which function has the graph shown below? *
a. f(x) = x² - 4
b. f(x) = x² + 4
c. f(x) = (x + 4)²
d. f(x) = (x - 4)² opps dont forget to change the sign
Answer:
C
Step-by-step explanation:
yeah-ya......... right?
Guided Practice
Type your answer and then click or tap Done.
Use the ^ symbol (Shift+6 on the keyboard) to signify an exponent. For example, for 2 to the third power, enter 2^3.
Identify the quadratic term in the function.
f(x)=2x^2−3x+5
Answer:
2x^2
Step-by-step explanation:
Q:
identify the quadratic term in the function f(x)=2x^2-3x+5
A:
The quadratic term is 2x^2.
Answer:
2x2-3x-5=0
Step-by-step explanation:
(2x2 - 3x) - 5 = 0
Answer:
The quadratic term in the function is
Step-by-step explanation:
Given : Function
To find : Identify the quadratic term in the function ?
Solution :
The quadratic form of the function is
Where, is quadratic term.
On comparing with given function,
is the quadratic term.
Therefore, the quadratic term in the function is
Which of the following equations has one real solution?
2x2+x+3=0
x2+5x−3=0
x2−5x+4=0
4x2−12x+9=0
Answer:
4x2−12x+9=0
Step-by-step explanation:
The equation, 2x2+x+3=0, does not have a solution
The equation, x2+5x−3=0, equals -5/2+1/2√37 and -5/2+-1/2√37
The equation, x2−5x+4=0, equal 1 and 4
The equation, 4x2−12x+9=0, equals only 3/2
Hope this Helps
Help me asap plssssssss
Answer:
B) 20
Step-by-step explanation:
c = √b2 + c2 - 2bc·cos(A) = 20
Have a nice day! :-)
HELP!! Highschool math
Answer:
What does this mean?
Step-by-step explanation:
So you need to divide the m by 234 and after you got your answer you would need to times it by 156
If A(2, 3) and B(-4, -6), find AB.--
[tex] \huge \bf༆ Answer ༄[/tex]
The distance between points can be solved using Distance formula (similar to Pythagoras theorem)
[tex] \boxed { \sf D = \sqrt{(x2 - x1) {}^{2} + {(y2 - y1) {}^{2} } }}[/tex]
Put the values : -
[tex] \sf D = \sqrt{ (2 - ( - 4)) {}^{2} + (3 - ( - 6)) {}^{2} } [/tex][tex] \sf \: D = \sqrt{ {(6)}^{2} + (9) {}^{2} } [/tex][tex] \sf D = \sqrt{36 + 81} [/tex][tex] \sf D = \sqrt{117} [/tex][tex] \sf D = 3 \sqrt{13} [/tex]Distance between the points = 3√13 units
[tex]꧁ \: \large \frak{Eternal \: Being } \: ꧂[/tex]
Answer:
If you are trying to find the line, simply use a graph.
Step-by-step explanation:
HELP!!! IM CONFUSED
Answer:
2/3Step-by-step explanation:
If we want to find the slope, the most easiest way to find the slope is to use 'Rise/Run'. Two points are given, lets use those points and find the slope.
=> We see that the rise is 2. So 2 will be our numerator,
=> We can also see that the run is 3. So 3 will be our denominator.
What do we get?
We get 2/3 as our slope. Therefore, B is our answer. Hoped I helped.
Work out Sarah's total pay for the last week
Answer:
190
Step-by-step explanation:
Attached picture...
Factor
1
out of
2x+6.
.
The factored expression is
Answer:
the factored expression: 2(x + 3)
Jessica and her brother collects stamps. When Jessica gives her brother 1% of her stamps, she has 2,475 stamps left. Calculate how many stamps Jessica had originally.
Answer:
2500
Step-by-step explanation:
2475 stamps is 99% of her original number of stamps.
SO,
[tex]2475 \div 99\% = 2500[/tex]
She originally had 2500 stamps
Sully built a shelf 8 5/8 inches wide for his DVD collection. If each DVD is 3/8 inches
wide, how many can he fit on the new shelf?
Answer:
23
Step-by-step explanation:
8 5/8 = 69/8
Each DVD is 3/8 inches
Ignore the denominators
We have 69 and 3
69 is 23 times bigger than 3, so 23 DVD's can fit
Simplify.
x2+2x−3/
x−4/
2x2+5x−3/
x^2−16
x2−x−12/2x−3
x2−5x−4/2x−1
x2+3x−4/2x−1
x2+x−12/2x−3
Answer:
x^2 + 7x- 3/x - 3/x^2 -16
Step-by-step explanation:
Key: ( ^ ) means exponent
= x^2 + 2x- 3/x -2x^2 + 5x- 3/x^2 -16
= x^2 - 2x^2 + 2x+5x - 3/x- 3/x^2 -16
= x^2 - 2x^2 = -x^2
= -x^2 + 2x + 5x- 3/x- 3/x^2-16
As you see you add 2x and the 5x and got 7x
= Answer : x^2 + 7x- 3/x - 3/x^2 -16
Answer:
I think the answer is x^2+3x-4/2x-1
Please help me solve this problem ASAP!
Answer:
im pretty sure the answer is 90°
hi please help me with part b and can you see if i did a correctly pls?
a is right its 58
and in my opinion i think b would be 58*5=290 cents, since nickel is worth 5 cents.
but gotta check other people's answers
Lin's bike travels 100 meters when her wheels rotate 55 times. What is the circumference of her wheels? Round your answer to the nearest hundredth.
Thank You!!!
Answer:
Using formula to calculate the circumference of wheel:
where
D is the distance bike travel
n is the number of times rotation
C is the circumference of the wheel
As per the statement:
Lin’s bike travels 100 meters when her wheels rotate 55 times.
here, n = 55 rotation and D = 100 meter.
then by definition:
meter
Therefore, the circumference of her wheel is, 1 9/11
Step-by-step explanation:
A landscaper is planting a tree that is now 48 cm tall. The tree will grow 2 cm per month for x months,
The tree will grow to be less than y cmn tall. Write an inequality showing this relationship.
Answer:
y > 2x + 48
Step-by-step explanation:
Si al doble de un número, se le adiciona 4 resulta 10 ¿Cuál es el número?
Answer:
3
Step-by-step explanation:
Hice una ecuación: 2x+4=10. Luego, reste 4 de cada lado para obtener: 2x = 6, lo que resulta en: x = 3.
what is the correct Answer?!
Answer:
B
Step-by-step explanation:
2⁶
2³
2⁶
2³
then add the ⁶+³+⁶+³ =18
2¹⁸
digital root of 5307
Answer:
15 hegevwyegecceccr
Step-by-step explanation:
5+3+0+7=15
Answer:
The digital root of 5307 is 6
Step-by-step explanation:
5 peppers for $5.50 how much is each
Answer:
$1.10
Step-by-step explanation:
5.50 divided by 5, take a way the decimal in order to divide. 550/5=110
55 divided by 5 is 11 just add a zero
please help with statistic 20
Part A
p = 0.32 = probability of someone voting by internet
n = 13 = sample size
x = 10 = number of people who voted by internet
Apply the binomial probability formula.
[tex]P(x) = (_n C _x)*(p)^{x}*(1-p)^{n-x}\\\\P(10) = (_{13} C _{10})*(0.32)^{10}*(1-0.32)^{13-10}\\\\P(10) = (286)*(0.32)^{10}*(0.68)^{3}\\\\P(10) \approx 0.0010124942242\\\\P(10) \approx \textbf{0.00101}\\\\[/tex]
Note: the [tex]_n C_x[/tex] refers to the combination formula.
Answer: 0.00101=============================================================
Part B
We could apply the binomial theorem for the following values of x: {10,11,12,13}. Then would add up the results.
However, such a task is fairly tedious and it's more efficient to use computer software (or a graphing calculator). Also, there's the element of limited time that you'll need to consider. I showed the steps for part A above because your teacher may have wanted you to list them. Usually it's better to rely on software for that task as well. At the very least, it's useful to have software to check your answer.
Whichever method you use, you should find the following:
P(10) = 0.00101P(11) = 0.00013P(12) = 0.00001P(13) = 0The last value isn't exactly 0, but it's so small that it's effectively zero. This is because we only have 5 decimal places to work with.
Add up those four values to get:
[tex]P(x \ge 10) = P(10)+P(11)+P(12)+P(13)\\\\P(x \ge 10) \approx 0.00101+0.00013+0.00001+0\\\\P(x \ge 10) \approx 0.00115\\\\[/tex]
A faster shortcut is to use your calculator's binomCDF function.
This result of 0.00115 is fairly small. The usual distinction we make between whether a probability is small or not is to set up some kind of threshold. This threshold is known as the significance level. By default, it's set to 0.05 unless your teacher specifies otherwise. Another common significance level is 0.01, but it's usually mentioned.
Since 0.00115 is smaller than 0.05, and even 0.01, we consider the probability of getting 10 or more internet voters to be a significant event. It's fairly unusual to get 10 or more people voting by internet in this sample of n = 13 people.
Answer: Choice A) Yes, because the probability of 10 or more is 0.00115, which is low.=============================================================
Part C
Like with part B, we could find the binomial probability values for x = {1,2,3,...,11,12,13}. We could add up the values like I did, or use the binomCDF function which is faster.
Another approach is to use the complement of the event "at least 1". If x is some number in the set {0,1,2,..,12,13}, then either [tex]x = 0[/tex] or [tex]x \ge 1[/tex]
From this, we can say
[tex]P(x=0) + P(x \ge 1) = 1\\\\P(x \ge 1) = 1-P(x=0)\\\\P(x \ge 1) \approx 1-0.00665\\\\P(x \ge 1) \approx 0.99335\\\\[/tex]
This then rounds to 0.993
Answer: 0.993what is the solution to the system of equations
Solve for n.
n + 24 = 99
n =
Answer:
[tex]n + 24 = 99 \\ \\ n = 99 - 24 \\ \\ n = 75[/tex]
show me how to do the work please
[tex]\large\boxed{\mathsf{\dfrac{x}{-4}\leq 12}}\\\\\large\text{MULTIPLY -4 to BOTH SIDES}\\\\\large\boxed{\mathsf{-4\times -\dfrac{1}{4}x \leq -4 \times 12}}\\\\\large\text{CANCEL out: }\rm{-4 \times-\dfrac{1}{4}}\large\text{ because it gives you 1}\\\\\large\text{KEEP: }\rm{-4\times 12}\large\text{ because it helps solve for what is being compared to the }\\\large\text{x-value}\\\\\large\text{NEW EQUATION: }\rm{x \geq\ -4 \times 12}\\\\\large\text{SIMPLIFY IT}\uparrow[/tex][tex]\huge\text{Therefore, your answer is: \boxed{\mathsf{x\geq-48}}}\huge\checkmark[/tex]
[tex]\large\boxed{\mathsf{It\ is\ an\ CLOSED\ circle\ shaded\ to\ the\ right}}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
HELP DUE IN 1 MINUTE 5x^3 + 20x^2-160x
Which values are solutions to the inequality -3x - 4 < 2? Check all of the boxes that apply.
-4
-2
0
3
Answer:
-2
Step-by-step explanation:
You would add 4 to 2 inorder to get 6, then divide by 3 to get -2
YES I WILL BE GIVING A BRANLIST
Which function has the greater rate of change? What is that value?
Answer:
To find the rate of change you use the formula, Y2-Y1/X2-X1.
Function A:
You can substitute in any two points. The points I will use are (0,0) and (1,1).
1-0/1-0
1/1
1
The rate of change for Function A is 1.
Function B:
The points I will use are (2,1) and (4,2).
2-1/4-2
1/2
The rate of change for Function B is 1/2.
Since 1 is larger than 1/2, Function A has a larger rate of change. The value is 1.
Hope this helps! :)
