Answer:
y = [tex]\frac{1}{3}[/tex] x² - 2x - 2
Step-by-step explanation:
x-coordinate of the vertex of a parabola is ( [tex]- \frac{b}{2a}[/tex] )
y = f(x) = ax² + bx + c
(x, y) ∈ f(x)
~~~~~~~~~
{ (0, - 2), (3, - 5) } ⊂ { (x, y): y = ax² + bx + c }
a(0)² + b(0) + c = - 2 ⇒ c = - 2
a(3)² + b(3) + ( - 2) = - 5
9a + 3b - 2 = - 5 ⇒ 3a + b = - 1
[tex]- \frac{b}{2a}[/tex] = 3 ⇒ b = - 6a
[tex]\left \{ {{3a+b=-1} \atop {b=-6a}} \right.[/tex]
3a + ( - 6a) = - 1
a = [tex]\frac{1}{3}[/tex]
b = - 2
y = [tex]\frac{1}{3}[/tex] x² - 2x - 2
The equation of the parabola for the given values is y = x²/3 - 2x - 2.
What is a parabola?A parabola is the part of the conic section of which the points are equidistant from a fixed line called as directrix and a fixed point known as focus.
The general equation for the parabola is given as,
y = ax² + bx + c
Where c is the y-intercept.
Substitute c = -2 as per the question to obtain,
y = ax² + bx - 2
At (3,-5) the parabola has minimum value which implies y' = 0 as below,
y' = 2ax + b = 0
Substitute x = 3 to obtain,
2a × 3 + b = 0
=> -6a = b
And, y = -5 at x = 3 which gives,
-5 = 3²a + 3b - 2
=> 9a + 3b = -3
Substitute b = -6a to get,
9a - 18a = -3
=> a = 1/3
Which implies b = -6 × 1/3 = -2
Now, the equation for the parabola becomes as below,
y = x²/3 - 2x - 2
Hence, the required equation of the parabola is obtained as y = x²/3 - 2x - 2.
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A loan worth $1000 collects simple interest each year for 6 years. At the end of
that time, $270 of interest has accrued. What was the annual interest rate for
this loan?
a. 4.25%
b. 5.75%
c. 5.5%
d. 4.5%
Answer:
B
Step-by-step explanation:
Use a calculator and do it step by step.
Mr. Vara is designing post caps in the shape of a square pyramid for a fence that he just built in his backyard. The caps are solid wood and each one has a volume of 94.5 cubic centimeters.What is the height, in centimeters, of a wooden post cap?
Answer:
Height of the square pyramid is 6.569 centimeter
Step-by-step explanation:
The volume of the square pyramid is 94.5 cubic centimeters
The height of the square pyramid will be equal to the lengths of the sides of the square.
The volume of the square pyramid is given by
[tex]a^2 * \frac{h}{3}[/tex]
or
[tex]\frac{a^3}{3} = 94.5\\a^3 = 94.5 *3\\a = \sqrt[3]{94.5*3} \\a = 6.569[/tex]centimeter
Height of the square pyramid is 6.569 centimeter
Ms. Ponse knows that only 44% of the pencils she
leis students borrow will be returned to her. She will
let students borrow 125 pencils in the second
semester. How many pencils can Ms. Ponse plan on
getting back?
Answer:
55
Step-by-step explanation:
44% * 125 = 0.44 * 125 = 55
Answer:
She can expect to receive back 0.44(125 pencils) = 55 pencils
Step-by-step explanation:
She loans out 125 pencils. If 44% will likely be returned, then 100% - 44%, or 56%, will not be returned.
She can expect to receive back 0.44(125 pencils) = 55 pencils
Please help.
Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.
Answer:
question 12 is answer B
question 13 is -8x^3
Step-by-step explanation:
exponent rule [tex]\frac{a^m}{a^n} = a^(^m^-^n^)[/tex]
.........help.......me.......please
Answer:
x = 17
Step-by-step explanation:
x + 73 = 90
x = 90 - 73
x = 17
Please help i dont get this serious inquires only...
A quadratic equation is given to us. And we need to plot its graph . Firstly we will make a table . For that substitute different values of x to get different values of y . For graph refer to attachment.
• Here's the table .
[tex]\boxed{\begin{array}{c|c} \underline{\red{\bf{ x}}}&\underline{\red{\bf y}}\\\\ \sf 1 &\sf 0 \\\\\sf 0 & \sf 1 \\\\\sf 2 &\sf 1 \\\\\sf -2 &\sf 9 \end{array}}[/tex]
Calvin practices a 100-meter swim each day. He recorded his finish times, in seconds, in the dot plot below.
Answer:
e
Step-by-step explanation:
Answer:
D.)
E.) and
A.)
Step-by-step explanation:
Find the mean of 7, 1, 1, 4, 1, 4 graphically. What is the sum of the number???
Answer:
The mean is 3. The sum of the number is 18.
Step-by-step explanation:
1+1+1+4+4+7 = 18
18 divided by 6= 3
Please help I’ll make you the brainiest
Answer:
Jesse is correct
step by step explanation:
Answer:
The best bet would be Jesse.
Step-by-step explanation:
What type of association is shown in the following scatter plot?
Day of the Week
O A. No Association
OB. Strong Negative
O C. Strong Positive
O D. Weak Negative
Find all solutions of the equation in the interval [0, 2pi)
cosx (2 sinx+1)=0
Answer:
x = pi/2 and 11pi/6
Step-by-step explanation:
Given the trigonometry expression
cosx (2 sinx+1)=0
This can be written in two forms as;
cosx = 0 and 2sinx + 1 = 0
If cos x = 0
x = arccos0
x = 90degrees
x = pi/2
Similarly
2sinx + 1 = 0
2sinx = -1
sinx = -1/2
sinx =-0.5
x = aarcsin(-0.5)
x = -30
Since sin is negative in the third and 4th quadrant
x = 270 + 30
x = 330degrees
x = 330pi/180
x = 11pi/6
Brianna planted daffodils and tulips in her garden she planted 4 daffodils for every 3 tulips if Brianna planted 28 flowers in all how many tulips did she plant
Answer:
Step-by-step explanation:
It means if she planted 12 tulips then 4 daffodils for every 3 tulips = 16 daffodils
Total = 12 + 16 = 28
Answer:
12 Tulips
Step-by-step explanation:
16 daffodils and 12 tulips for 28 flowers in all
You pick a card at random, put it back, and then pick another card at random. What is the probability of picking a 3 and then picking a number less than 3? (Write answer as a percentage)
Answer: 37.5%
Step-by-step explanation:
multiply. write your answer as a fraction in simplest form: 4 x 5/14
Answer:
Most simplified version is 1 3/7
Step-by-step explanation:
First step is turn everything into a fraction 4 into a fraction is 4/1
4/1 times 5/14 is 20/14 or 1 and 6/14 or 1 and 3/7
Here we have a problem with the multiplication of fractions.
We will find that:
[tex]4 \cdot\frac{5}{14} = \frac{10}{7}[/tex]
First, two things we need to remember:
[tex]\frac{x}{y} \cdot\frac{a}{b} = \frac{x \cdot a}{y \cdot b}[/tex]
Also, an integer number N can be written as:
[tex]N = \frac{N}{1}[/tex]
Now we want to solve:
[tex]4 \cdot\frac{5}{14}[/tex]
Using the above relations we get:
[tex]4 \cdot\frac{5}{14} = \frac{4}{1} \cdot\frac{5}{14} = \frac{4 \cdot5}{1 \cdot14} = \frac{20}{14}[/tex]
Now we need to simplify this, to do it, we need to divide both numerator and denominator by the same number.
We can see that both are multiples of 2, so if we divide both by 2 we get:
20/2 = 10
14/2 = 7
Then we have:
[tex]\frac{20}{14} = \frac{10}{7}[/tex]
Now 7 and 10 do not have common factors, so we can't simplify it anymore.
Concluding, we get:
[tex]4 \cdot\frac{5}{14} = \frac{10}{7}[/tex]
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Select the correct answer.
Drake owns 100 stocks of Balancia, Inc. He had bought these stocks at a face value of $10. The market price of these stocks is now $50 each.
Balancia has declared a dividend of 20% this year. Balancia's retained earnings for the year is $2,000,000 and it has 1,000,000 outstanding
stocks. What is the P/E Ratio?
Answer: 25
Step-by-step explanation:
The Price to Earnings ratio, AKA, the P/E ratio, is calculated by dividing the Market price of the stock by the Earnings per share.
Earnings per share = Net earnings for the year / Number of shares
= 2,000,000 / 1,000,000
= $2 per share
P/E ratio = Market price of shares/ Earnings per share
= 50 / 2
= 25
Find the missing angle.
Select one:
85°
180°
158°
32°
Answer:
missing angle 32 ...........
Can anybody tell me what’s going on here?
Step-by-step explanation:
We are given a theta degree measure of sin in a specific interval. We are asked to find half of that degree measure.
The interval it ask us to find it in is between 2 pi and 5 pi over 2.
That is 360 degrees to 450 degrees. If you use reference angles, that is between the 0 degrees and 90 degrees. So that means our measure is going to be in the 1st quadrant.
Replace x with theta
[tex] \sin( \frac{x}{2} ) = + - \sqrt{ \frac{1 - \cos(x) }{2} } [/tex]
We dont know cos x but we can use the pythagorean trig theorem to find cos x.
[tex] \sin {}^{2} (x) + \cos {}^{2} (x) = 1[/tex]
[tex] \sin {}^{2} ( \frac{4}{5} ) + \cos {}^{2} (x) = 1[/tex]
[tex] \frac{16}{25} + \cos {}^{2} (x) = 1[/tex]
[tex] \cos {}^{2} (x) = 1 - \frac{16}{25} [/tex]
[tex] \cos {}^{2} (x) = \frac{9}{25} [/tex]
[tex] \cos(x) = \frac{3}{5} [/tex]
Cosine in 1st quadrant is positive so 3/5 is cos x.
Replace 3/5 for cos x.
[tex] + - \sqrt{ \frac{1 - \frac{3}{5} }{2} } [/tex]
[tex] + - \sqrt{ \frac{2}{10} } [/tex]
The answer is
[tex] + - \sqrt{ \frac{2}{10} } [/tex]
the distance time graph shows information about part of a bicycle journey. Use the graph to estimate the speed in m/s at time 6 seconds
NEED ASAP WILL MARK AS BRAINLIEST IF CORRECT
Answer:
2.16
Step-by-step explanation:
if x is seconds on the graph and y is the distance then you just look for what is y in the coordinate (6, _ ), in which the line on the graph shows it is 13
hope this helps!!
edit:
it seems i was incorrect, ahh im sorry
so you do have to divide the answer in the end, so 13/6 which is equaled to 2.16
What is the mean of 82, 4, 94, 4, 60, 91
and what is n2 = 81 ; What is the value of n?
-4n = 16; What is the value of n?
Answer:
1. The mean is 55.83
2. when n2=81 then n=40.5
3. when -4n=16 then n = -4
Step-by-step explanation:
1. you add all the numbers together then divide the sum by 6
2. divide both sides by 2
3. divide both sides by -4
help please ? i need help
Answer:y
Step-by-step explanation:
select all the expressions that equal.. *see picture for problem*
Answer:
Step-by-step explanation:
oknjbgfkdfrgn jnfbfl
Which expression represents the volume of the prism?
Answer:
Option A 1/2x³ is your answer
Answer:
Step-by-step explanation:
Options
1. 13
2. 15
3. 16
4. 18
Answer:
16 units.
Step-by-step explanation:
Using the hypotenuse formula (a^2 + b^2 = c^2) we can determin that AB and BC is 5 units long, now we add AB, BC and AC together and we get 16.
I'm confused on this
(this is 12 year old math)
Answer: the top box can be the linear equation y=40x+15 and the bottom box is 40
Step-by-step explanation:
If you swim 15 more minutes than your friend and your swam 55 minutes, that means your friend only swam 40 minutes. The set amount of time that your friend swims for x is 40 minutes. So the additional time you swim is b, 15 minutes.
The solutions to a cubic function are x = 4 , x = 3 and x = - 3 . What is a possible cubic function with those solutions?
Answer:
12x
Step-by-step explanation:
Find the value of X.
Answer:-
x=110 degree
Step-by-step explanation:
It's quadrilateral so it's total sum degree is 360
then 40+82+128+x=360
360-(128+82+40)=X
x=360-250
x=110 degree
brad buys a pack of 12 energy drinks for £9.25
he sells all 12 for £1
work out the percentage profit
give your answer correct to 2 significant figures
Answer:
I dont I know i want points
i need help i am in middie school
Answer:
45/51 is:
Step-by-step explanation:
make it a whole:
1 6/51
GCF:
1 2/17 is ur answer. Please consider marking me as brainliest if you can! Have an amazing day lovely! <3
Answer:
I think it would be 9/17
For the second one
Factor completely x2 − 49. (1 point) (x − 7)(x − 7) (x + 7)(x − 7) (x + 7)(x + 7) Prime
Answer:
(x + 7)(x - 7)
Answer:
b is right
Step-by-step explanation:
equivalent fractions for 2 1/5 and 1 5/6
