Answers
Equation is: y = 0.5x² + 0.5x - 3
Explanation:
general form of the parabola is:
y = ax² + bx + c
Now, we will need to solve for a, b and c.
To do this, we will simply get points from the graph, substitute in the general equation and solve for the missing coefficients.
First point that we will use is (0,-3).
y = y = ax² + bx + c
-3 = a(0)² + b(0) + c
c = -3
The equation now becomes:
y = ax² + bx - 3
The second point that we will use is (2,0):
y = ax² + bx - 3
0 = a(2)² + b(2) - 3
0 = 4a + 2b -3
4a + 2b = 3
This means that:
2b = 3 - 4a
b = 1.5 - 2a ...........> I
The third point that we will use is (-3,0):
y = ax² + bx - 3
0 = a(-3)² + b(-3) - 3
0 = 9a - 3b - 3
9a - 3b = 3 ...........> II
Substitute with I in II and solve for a as follows:
9a - 3b = 3
9a - 3(1.5 - 2a) = 3
9a - 4.5 + 6a = 3
15a = 7.5
a = 7.5 / 15
a = 0.5
Substitute with the value of a in equation I to get b as follows:
b = 1.5 - 2a
b = 1.5 - 2(0.5)
b = 0.5
Substitute with a and b in the equation as follows:
y = 0.5x² + 0.5x - 3
Hope this helps :)
Related Questions
A parachutist's speed during a free fall reaches 207 kilometers per hour. What is this speed in meters per second? At this speed, how many meters will the parachutist fall during 20 seconds of free fall? Do not round your answers.
Answers
Explanation:
We start out with the ratio 207 km/1 hr.
We know that 1 km = 1000 m; this means 207 km = 207*1000 = 207000 m. This gives us 207000 m/1 hr.
We know that 1 hr = 60 minutes, so we have 207000 m/60 min.
We also know that 1 min = 60 seconds, so 60 min = 60*60 = 3600 sec; this gives us 207000 m/3600 sec.
Dividing this, we get 57.5 m/s.
In 20 seconds, the parachutist will fall 57.5(20) = 1150 m.
Answer:
1150 meters
Step-by-step explanation:
Speed of parachute = 207 kilometers per hour
Speed of parachute in meter /second = (207 x 1000)/ (60 x 60)
= 57.5 meter /second
Parachute fall for 20 seconds with a speed of 57.5 meter /second, Thus the distance covered in 20 seconds
= 57.5 meter /second x 20 seconds
= 1150 meters.
is a simplified version of 5(x+8)-10x =60
Answers
5x + 40-10x = 60
5x-10x = -5x
40-5x = 60
Subtract 40 from both sides
-5x = 20
X= -4
? - 12 = -6
What is the missing number?
Answers
NEED HELP ASAPPP
Figure TUVW is transformed to T’U’V’W’, as shown:
Which of the following sequences of transformations is used to obtain figure T’U’V’W’ from TUVW?
Reflection about the y-axis followed by a translation left by 2 units
Reflection about the x-axis followed by a translation left by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation right by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation left by 2 units
Answers
If you look closely, the reflection was made from the y-axis. The reflection would be above or below the x-axis if the reflection was to be made through the x-axis.
Also, the figure was moved 2 units to the left. Hence the reflection was moved 2 units from where the reflection should originally be which was (-6,-4).
Hope this answer is helpful.
The correct answer is Reflection across the y-axis and then Translation 2 units to the left. In a translation, the sign on the x of every point is changed. The reflected image is too far to the left to be just a reflection or even a rotation. That is why I said it was translated 2 units
Step-by-step explanation:
A bakery supplier receives an order for 2 tons of flour from a bakery chain. The flour is shipped in crates. Each crate holds eight 10-pound bags of flour. How many crates does the supplier need to ship to fulfill the order?
Answers
8 x 10 = 80
4000 \ 80 = 50
The supplier needs to ship 50 crates.
Hope this helps
if the temperature at 9:00 pm was 12 degrees farenheit,and after 6 hours the temperature dropped to 6 degrees Fahrenheit below 0,what was the rate of change in temperature per hour?
Answers
6-6=0
6 is the rate of change in temperature 6 hours
Then 1 is the rate of change in temperature is 1 hour
Write 6 percent as a decimal
Answers
Given the function f(x) = 2x-5/3, which of the below expression is correct?
F^-1(x) = 5-2x/3
F^-1(x) = 3x-5/2
F^-1(x) = 3x+5/2
F^-1(x) = -2x - 5/3
Answers
I think you’re subtracting 5. So now it’s f^-1(x)= 3x+5/2. Not too sure but hope this may help. So, C.
the ratio of the areas of two similar polygons is 81:64. If the perimeter of the first polygon is 32 cm, what is the perimeter of the second polygon? Round to the nearest tenth
Answers
In two similar polygons, the ratio of their areas is the square of the ratio of their sides. If the sides of any polygon are a and b then :
Ratio of area =[tex] a^{2} :b^{2} [/tex]
Given ratio of area =81:64
Or 81:64=[tex] a^{2} :b^{2} [/tex]
Taking root of both sides
9:8=a:b
The ratio of perimeter of any two similar polygon is equal to the ratio of sides.
Ratio of perimeter = a:b
Perimeter of first polygon is 32 cm.
Let the perimeter of second polygon be x.
32:x=a:b
Or, 32:x=9:8
[tex] \frac{32}{x} =\frac{9}{8}
[/tex]
Cross multiplying
9x= (32)(8)
9x=256
Dividing both sides by 9
x=28.4.
The perimeter of second polygon is 28.4cm.
Carissa also has a sink that is shaped like a half-sphere. The sink has a volume of 2000/3[pie] in^3. One day, her sink clogged. She has to use one of two conical cups to scoop the water out of the sink. The sink is completely full when Carissa begins scooping.
(a) One cup has a diameter of 4 in. and a height of 8 in. How many cups of water must Carissa scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number.
(b) One cup has a diameter of 8 in. and a height of 8 in. How many cups of water must she scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number.
Help ASAP!
Please Be Sure Answer is 100% CORRECT!
Answers
A: 1/3 x 3.14 x 2*2 x 8 = 32/3 = 2000 divided by 32 = 63 scoops
The formula is 1/3 x 3.14 x r*2 x h
B: 1/3 x 3.14 x 8*2 x 8 = 128/3 = 2000 divided by 128 = 16 scoops
Last week, you finished Level 2 of a video game in 32 minutes. Today, you finished Level 2 in 28 minutes. What is your percent of change?
Answers
The first step to solve this problem is to compute how much change in minutes were you able to have today compared to the last week.
32 minutes – 28 minutes = 4 minutes faster than last week
To compute the percent of change you have to divide the change in minutes to the duration in minutes for the last week:
4 minutes / 32 minutes = 0.125 or 12.5% faster than last week
What is the volume of the composite figure ?
Answers
HELP WILL MARK BRAINLIEST!!!!!!!!!!!!!!!!!!
Give me 5 fun facts about Octogons!
Answers
They have 8 sides.
They can be constructed with a straightedge and a compass
They form patterns on some oriental rugs.
Janggi ( a game uses octagonal pieces). Look this up.
3×1 1/2=3×6/3=18/3=6
Answers
3*1 2/3 = 3 *6/3=18/3=6
Possible explanation: Hannah did not write the mixed number, 1 2/3, as a fraction correctly, 1 2/3 is not equal to 6/3
5 cups: explanation: first 1 wrote 1 2/3 as a fraction. 1 2/3 = 3/3+2/3=5/3, then I multiplied 3 x 5/3 = 15/3=5 = True
Thus: Hannah needs 5 cups for 3 batches of bars
The original price of an item is $130. The item is on a discount of 1/5 off the original price. You then pay a sales tax of 10%. What is the amount you paid for the item?
Answers
First, find 1/5 of $130, and then subtract that from the original price of the item, because it is a discount.
Divide the price of the item by 5.
130 ÷ 5 = 26
130 - 26 = 104
So, the price of the item (not including tax) is $104. Now, we must calculate the sales tax and then add that onto the price of the item, as tax is money collected by the government.
To calculate the tax, multiply the discounted price of the item by the percentage of tax, and then add it.
104 × 10% = 10.4
104 + 10.4 = 114.4
ANSWER:
The amount of money you paid fot the item is $114.4.
Last summer, Mike received a tip from 35% of his babysitting customers. If he had 20 customers, how many customers gave Mike a tip?
Answers
35/100 = x/20
cross multiply.
100x = 700
Now divide by 100.
x = 7
For your party you purchased balloons for $.79 each. You spent a total of $11.85. About how many balloons were purchased?
Answers
Let us suppose the number of balloons purchased is x in number.
It is given balloons are purchased for $.79 each
Cost of x balloons = .79x.
Total amount spent on purchasing balloons = $11.85
Cost of x balloons = Total cost of balloons.
.79x=11.85
With x .79 is multiplied .Opposite of multiplication is division.
We perform the opposite operation both sides
Dividing both sides by .79
x=11.85÷.79
x=15
Total number of balloons purchased is 15.
Can anyone solve this?
Answers
then multiply 3 by 2 to get 6 so you would have (3,6)
Mr. Nelson is buying property in the shape of a triangle to build a new house. If the property costs $42.50 per square foot, how much will he pay?
Answers
a=h(b/2)
a=47(98/2)
a=47(49)
a=2303
Now, you multiply that by $42.50 to find out how much he will pay.
2,303x42.50=97,877.50.
He will pay $97,877.50.
The figure shows a base of 98 ft and a height of 47 ft.
[tex] A = \dfrac{bh}{2} [/tex]
[tex] A = \dfrac{98~ft \times 47~ft}{2} [/tex]
[tex] A = 2,303 ~ft^2 [/tex]
Now that we know the area, we multiply it by the cost of the land per square foot.
2,303 ft^2 * $42.50/ft^2 = $97,877.50
He must pay $97,877.50
Please help asap
The table below shows which sports events have sold out and which have not.
Answers
B. To answer this, you need to find the number of predicted outcomes over the total number of possible outcomes. In this case it is 6/10 or 3/5 chance/probability. Between the 2 sports events there were 6 sold out compared to the total of 10.
What is the value of x?
Enter your answer in the box.
Answers
2x + 2 = 3x - 52 Vertical angles are congruent
2x = 3x - 54 Subtract 2 from both sides
-x = -54 Subtract 3x from both sides
x = 54 Divide both sides by -1
Answer:
x = 54
find the surface of the area of the rectangular prism 16m 5m 14m
Answers
Total Surface Area = 160 + 140 + 448
Total Surface Area = 748 m²
------------------------------
Answer: 748 m²
------------------------------
What do you draw to show that 50,000 pennies is equivalent to 100 five dollar bills?
Answers
PLEASE HELP
If a student is chosen at random find the probability the student is male given that its a senior. Round to the nearest while percent.
Answers
=========================================
Work Shown:
"given that it's a senior" is an important piece of info that tells us to only focus on the "seniors" column. The word "given" is an indication that we know this information 100%
There are 5 seniors (2+3 = 5) and 2 of them are male. So 2/5 = 0.40 = 40% of the seniors are male. The probability of selecting a male, if we know this person is a senior, is 40%
The probability that a randomly selected senior student is male is 40%.
Given Data:
We have a two-way table representing the number of students by gender and grade level.
The relevant information is that there are 2 male seniors.
Event Definitions:
Let’s define the following events:
A: Student is male.
B: Student is a senior.
Conditional Probability:
We want to find the probability that a student is male given that they are a senior: (P(\text{Male}|\text{Senior})).
We can use the formula for conditional probability: [tex][P(\text{Male}|\text{Senior}) = \frac{P(\text{Male and Senior})}[/tex][tex]{P(\text{Senior})}][/tex]
Calculations:
From the table, we know:
Number of male seniors (A and B): 2
Total number of seniors (B): 5
Therefore: [[tex]P(\text{Male}|\text{Senior}) = \frac{2}{5} = 0.4][/tex]
Rounded Answer:
Rounding to the nearest whole percent:
([tex]0.4 \times[/tex]100% = 40%)
Summary: The probability that a randomly selected senior student is male is 40%.
Find two ratios equal to the given ratio : 1/5:1 3/5
Answers
To find two ratios equal to the given ratio, all we need to do is multiply both sides of the ratio by the same number.
1:3 is an equal ratio because we multiply both sides of it by 5.
2:6 is also an equal ratio because we multiply both sides by 10.
Hope this helps!
Pedro wants to paint his room, which is 12.5 feet by 11.5 feet, with an 8-foot-high ceiling. How many total square feet will Pedro need to paint?
Answers
Radius is 8 what is the area of the circle then ?
Answers
We must use a certain formula to find the area of a circle. The formula is:
A = pi × r^2
Pi = Approximately 3.14
Radius = 8 cm
Substitute:
A = pi × r^2
A = 3.14 × 8^2
A = 3.14 × 64
A = 200.96
ANSWER:
The area of the circle is approximately 200.96 cm^2.
Using 3.14 itll be 200.96
Using actual pi it be 201.0619298 then it depends where to round
In a survey of 398 students, 52% said they loved music. Use estimation to explain how many students loved music. PLZ HELP I HAVE THIS FOR HOMEWORK RIGHT NOW AND I NEED TO FINISH IT!!!!!
Answers
S= total number of students in the survey
M= music lovers
S• (52/100)=M
We have to divide the percentage by 100 because that allows use to calculate under 1, so there isn’t an increase in anyway, it should be less than the initial number. So if we multiply 398 by 52, we would get more than 100 percent, using 1 as 100 for percentages allow for an increase or decrease.
398•.52=206.96
For estimation, we can say there are about 400 students and we have to find 50%. Half of 400 is 200, which is a close estimate. So around 200 students in the school share a love of music.
A solid right pyramid has a square base. The base edge length is 2 cm longer than the height of the pyramid. If the height is 6 cm, the volume of the pyramid is cm3.
Answers
Height = 6
Base length = 8
Volume of pyramid = width x length x height /3 = 8 x 8 x 6/3 = 128 cm³
Answer:
128
Step-by-step explanation:
Just did the test ;)
Estimate how many 12 inch rulers will be about the same length as a sheet of paper