Answer: a = -2, b = -2, c = 1.
Step-by-step explanation:
We know that:
y = a*x^2 + b*x + c.
Then:
y' = 2*a*x + b
y'' = 2*a.
Then we can write the equation:
y′′ + y′ − 2y = 4x^2.
as:
2*a + 2*a*x + b - 2*(a*x^2 + b*x + c) = 4*x^2
To solve this, the first step is moving all the terms to the same side:
2*a + 2*a*x + b - 2*a*x^2 - 2*b*x - 2*c - 4*x^2 = 0
Now let's group terms with the same power of x.
(-4 - 2*a)*x^2 + (-2*b + 2*a)*x + (-2c + b) = 0
Now, this must be zero for all the values of x, then the parenthesis must be equal to zero:
-4 - 2*a = 0
-2*b + 2*a = 0
-2*c + b = 0
From the first equation:
-4 - 2*a = 0
-4 = 2*a
-4/2 = a
a = -2
And from the second equation:
-2*b + 2*a = 0
2*a = 2*b
a = b
b = -2.
From the third equation we have:
-2c + b = 0
-2c = b
c = b/-2 = -2/-2 = 1.
c = 1
Then our equation is:
y = -2*x^2 - 2*x + 1.
A package of 24 trading cards sells for $4.99 Based on this price, what is the price per card
Answer:
4.80961924
Step-by-step explanation:
Write the number in
standard form
6 tens+7=
Answer:
60 + 7 =
Step-by-step explanation:
its correct lol omg sjsjsjjsjsjsssjsjsnsnssn
Answer:
Answer: 67
10 x 6 + 7 = 67
RS = 4x – 9, ST = 19, RT = 80 – 14
Equation:
82 – 14
RS
RT
Step-by-step explanation:
The expressions are not properly written
Given
RS = 4x – 9
ST = 19
RT = 8x – 14
Based on the given parameters, the addition postulate below is true
RS+ST = RT
Substitute
4x-9+19 = 8x-14
collect like terms
4x-8x = -14-19+9
-4x = -33+9
-4x = -24
x = -24/-4
x = 6
Get RS:
RS = 4x-9
RS = 4(6)- 9
RS = 24-9
RS = 15
Get RT:
RT = 8x - 14
RT = 8(6)-14
RT = 48-14
RT = 34
f(x) = 5x3 + 2x2
35x
14
-
Answer:
651
Step-by-step explanation:
f(x) = 5×3 + 2×2
35x
14
= 5×3 = 15
= 2×2 = 4
= 15 + 4
= 19
35(19) - 14
= 665 - 14
= 651
Find the distance between the two points rounding to the nearest tenth (if necessary). (-6,5) and (3,-7)
The distance between points (-6,5) and (3,-7) is 15 units.
How to find the distance between two points?In the coordinate plane, the points are denoted by coordinate and the distance means the physical distance between them.
Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
Given the points (-6,5) and (3,-7)
Here x₁ = -6 , x₂ = 3
y₁ = 5 and y₂ = -7
So,
[tex]d = \sqrt {\left( {-6 - 3 } \right)^2 + \left( {5 +7 } \right)^2 }[/tex]
d = √225
d = 15 units.
Hence "The distance between points (-6,5) and (3,-7) is 15 units".
To learn more about the distance between two points,
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Find the smallest whole number multiple of 2 that leaves a remainder of 1 when divided by either 3 or 7.
Answer:
2 times 8 = 16 divided by 3 leaves a remander of 1
Step-by-step explanation:
The smallest whole number is 22.
What is Least Common Multiple?Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.
For example, L.C.M of 16 and 20 will be 2 x 2 x 2 x 2 x 5 = 80, where 80 is the smallest common multiple for numbers 16 and 20.
Given:
First find the LCM of 7 and 3 .
LCM = 3 x 7 = 21
So, we will add remainder 1 (as given) to the LCM .
= 21+ 1
= 22
Learn more about LCM here:
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Two sides of a rectangle iPhones are five and 5/8 feet long other two sides of 6 1/4 feet long what is the perimeter
Answer:
Here it is!
Step-by-step explanation:
The radius of a volleyball is 0.05 m, calculate its volume.
Answer:
0.00052m
Step-by-step explanation:
Step-by-step explanation:
radius of volleyball= 0.05m
volume = ?
we know,
volume=4/3πr^3
=4/3×0.00039
=0.0005m^3 #
Which of the following numbers can be expressed as repeating decimals?
5 over 7 , 4 over 5 , 7 over 9 , 5 over 8 help plz
Answer:
7/9
Step-by-step explanation:
When 7/9 is put as a decimal then its 0.777777. This makes it a repeating decimal.
(PLS HELP 50 PTS + BRANLIEST)
A={2, 3, 5, 7, 10} B={1, 4, 6, 8, 9, 10}, C={5, 6, 7}. The universal set U={1, 2, 3, 4, 5, ...10} List the elements of the following:
AUC=
A⋂U=
A⋂Ø=
Ā=
ĀUB=
Answer:
AUC= {2,3,5,6,7,10}
The second one=A
The third one= empty
I'm sorry. I don't know the others.
LUCILLE'S PENCIL POUCH WOULD HOLD 3/8
OF THE 48 PENCILS THAT SHE PURCHASED AT
THE BEGINNING OF THE NEW SCHOOL YEAR. How many pencils will fit in her pouch
HOW MANY PENCILS WILL FIT IN HER POUCH?
Answer:
The pouch would be able to hold 12.8 pencils :)
Step-by-step explanation:
because 3/8 is 37.5 and if you do that divided by 48 and add a decimal infront of the eight you will get your answer
question 16 i mark as brainliest
Answer:
A
Step-by-step explanation:
Day
Distance
(miles)
1
Tuesday
Wednesday
Thursday
214
1%
Jesse is training for his track meet on Saturday. This chart shows the number of miles he ran on Tuesday, Wednesday, and Thursda
How many mites did Jesse run on these 3 days
Answer:
This is very unclear however if your miles are 214 and you need 1% of the miles you can multiply it by 0.01 and the answer would be 2.14 miles
The base of a triangle is one third of its height. If the area of the triangle is 24 square inches, what are the base and height of the triangle?
A. 3in, 9 in
B. 8in, 24 in
C. 2in, 6in
D. 4in, 12in
Answer:
D. 4in, 12in
Step-by-step explanation:
Area of triangle = 24in²
Unknown:
Base and height of the triangle = ?
Solution:
The area of a triangle = [tex]\frac{1}{2}[/tex] x base x height
From the problem,
base = [tex]\frac{1}{3}[/tex] x height
let the base = b
height = h
b = [tex]\frac{1}{3}[/tex]h
h = 3b
Input into the formula of area;
24 = [tex]\frac{1}{2}[/tex] x b x 3b
Mulitply through by 2;
48 = 3b²
b² = 16
b = √16 = 4
So, h = 3b= 3 x 4 = 12in
Answer these two questions correctly and I’ll give brainlist ❤️.
Last month , Carter ran 48 miles. This was 60% of his goal. How many miles did cater set as his goal.
Lily wants to buy a tablet that cost $88. Her dad said that he would pay 25% of the cost. How much money will her father contribute towards the tablet?
I will be giving out brainlist if the answer you submitted was correct❤️.
Posting this again please only answer if you actually know the answer and stop stealing my points :((
Answer:
1. 80 miles
2. $22
Step-by-step explanation:
1. i did 48 divided by 60 and got .8
then i multiplied .8 by 100 and got 80
2. i did 88 multiplied by .25
Explaining the Multiplication and
Explain the rules for multiplication and division comet
units. How do you know when to multiply and when
divide to convert units of measurement
Write three to four sentences
sample response: To convert larger units to smaller units, multiply. When the units are smaller, you need more of them to express the same measure. To convert smaller units to larger units, divide. When the units are larger, you need fewer of them to express the same measure.
A $60 skateboard is only $51 after a sale. Find the percent of discount
Answer:
15% off
Step-by-step explanation:
The third-grade chorus performs a musical for the school. The musical lasts 42 minutes. It ends at 1:59 p.m. What time did the musical start?
Answer:
1:17 pm
Step-by-step explanation:
Answer:
1:17pm
Step-by-step explanation:
59 - 42= 17
Carmen creates the ratio table above based on one 8-ounce serving of juice.
How many total calories will 4 servings of juice contain?
420
520
650
780
I’ll give you brainiest!
Answer:
520. Becuase with each serving added the total calories go up by 130, 130+390=520.
3. Simplity: 1-7721
a. -772
b. - 7
c. 772
d. 72
Answer:
1 - 7721 = -7220 so i don't really see the answer in the choices you gave.
Step-by-step explanation:
Round 543,982 to the nearest hundred thousand
Answer:
500,000
Step-by-step explanation:
Please give brainleist
Answer:
500,000
Step-by-step explanation:
The hundred thousands place is bold so you can tell where it is. 543,982
To round you look at the 4 since it is below 5 you round down and it'll remain as 500,000
Hope that helps and have a great day!
what is the greatest common factor of 20, 50, and 25
Answer:
Step-by-step explanation:
The greatest common factor of 20, 50, and 25 is 5.
Given that,
The numbers are 20,50 and 25.Based on the above information, the calculation is as follows:
[tex]20 = 5\times 4\\\\ 50 = 5\times 10\\\\ 25 = 5\times 5[/tex]
So here the common factor is 5
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Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank's Visa cardholders reveals that the amount is normally distributed with a mean of 2525 dollars and a standard deviation of 88 dollars. (Round all decimals to at least 3 places.) (a) What proportion of the bank's Visa cardholders pay more than 2828 dollars in interest
Complete Question
Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank's Visa cardholders reveals that the amount is normally distributed with a mean of 25 dollars and a standard deviation of 8 dollars. (Round all decimals to at least 3 places.) (a) What proportion of the bank's Visa cardholders pay more than 28 dollars in interest
Answer:
0.354
Step-by-step explanation:
We solve for z score in this question.
The formula is given as:
z = (x-μ)/σ, where
x is the raw score = $28
μ is the population mean = $25
σ is the population standard deviation = $8
z= 28 - 25/8
z = 0.375
P-value from Z-Table:
P(x<28) = 0.64617
P(x>28) = 1 - P(x<28)
= 1 - 0.64617
= 0.35383
Approximately to 3 decimal places = 0.354
The proportion of the bank's Visa cardholders pay more than 28 dollars in interest is 0.354.
Can you give me an answer to this problem? 100m + 60m + ?m
Pythagorean thereon
Answer:
116.62m
Step-by-step explanation:
[tex]c= \sqrt{a^2+b^2} = \sqrt {100^2+60^2} approx. 116.61904[/tex]
The altlas v rocket could go 1 full mile in just 1/10 of a second. How fast did it travel?
Answer:
10 miles per second
Step-by-step explanation:
The computation of the fastage did it travel is shown below:
As per the question, it is mentioned that
1 full mile for just 1 by 10 of a second
Based on the above information
If 1 by 10 seconds is equivalent to one mile,
So, 10 by 10 (1) second would be equivalent to 10 miles per second.
hence, it could be fast by 10 miles per second
I’m stuck on this question, can someone help me please?
Answer:
I think its 110
Step-by-step explanation:
PLS HELP QUICKLY WILL GIVE BRAINLIEST
Answer:
the first one
Step-by-step explanation: it is your answer because when you solve it i gt that answer i calculated it in a calculator and then showed to the teahcre and said that it was crrect please mark me as brainlist
The growth of a sample of bacteria can be modeled by the function b(t) =100(1.06)^t where b is the number of bacteria and t is the time in hours. What is the number of total bacteria after 3 hours? Round to the nearest whole number.
Answer:
There are 119 bacteria after 3 hours.
Step-by-step explanation:
Let be [tex]b(t) = 100\cdot 1.06^{t}[/tex], where [tex]t[/tex] is the time, measured in hours, and [tex]b(t)[/tex] is the number of total bacteria, dimensionless. The number of total bacteria after 3 hours is found after evaluating the function at given function:
[tex]b (3) = 100\cdot 1.06^{3}[/tex]
[tex]b(3) = 119.102[/tex]
We rounded to the nearest preceeding whole number, since number of bacteria represents a discrete set. There are 119 bacteria after 3 hours.
Please help.. I’m stuck on this question
Answer: The answer is 1
Step-by-step explanation: The distance between -7 and -3 is 4 then half the distance in between -7 and -3 is going to be -5 because we just clarified that the distance between -7 and -3 is 4 so we did 4/2 and got 2 so we can figure out whats the distance between each point. Now that we figured that out we can determine what value the blue dot is if the value between each point is 2 then we can make out what the rest of the points on the line. If we from -3 to the blue point that would be 1.
Help please for brainliest
