Answer:
a = 3
b = 2
c = 0
d = -4
Step-by-step explanation:
Form 4 equations and solve simultaneously
28 = a(2)³ + b(2)² + c(2) + d
28 = 8a + 4b + 2c + d (1)
-5 = -a + b - c + d (2)
220 = 64a + 16b + 4c + d (3)
-20 = -8a + 4b - 2c + d (4)
(1) + (4)
28 = 8a + 4b + 2c + d
-20 = -8a + 4b - 2c + d
8 = 8b + 2d
d = 4 - 4b
Equation (2)
c = -a + b + d + 5
c = -a + b + 4 - 4b+ 5
c = -a - 3b + 9
28 = 8a + 4b + 2c + d (1)
28 = 8a + 4b + 2(-a - 3b + 9) + 4 - 4b
28 = 6a - 6b + 22
6a - 6b = 6
a - b = 1
a = b + 1
220 = 64a + 16b + 4c + d (3)
220 = 64(b + 1) + 16b + 4(-b - 1 - 3b + 9) + 4 - 4b
220 = 60b + 100
60b = 120
b = 2
a = 2 + 1
a = 3
c = -3 - 3(2) + 9
c = 0
d = 4 - 4(2)
d = -4
Step-by-step explanation:
Step 1: Solve using the first point
(2, 28)
[tex]28 = a(2)^3 + b(2)^2 + c(2) + d[/tex]
[tex]28 = 8a + 4b + 2c + d[/tex]
Step 2: Solve using the second point
(-1, -5)
[tex]-5 = a(-1)^3 + b(-1)^2 + c(-1) + d[/tex]
[tex]-5 = -a + b - c + d[/tex]
Step 3: Solve using the third point
(4, 220)
[tex]220 = a(4)^3 + b(4)^2 + c(4) + d[/tex]
[tex]220 = 64a + 16b + 4c + d[/tex]
Step 4: Solve using the fourth point
(-2, -20)
[tex]-20 = a(-2)^3 + b(-2)^2 + c(-2) + d[/tex]
[tex]-20 = -8a + 4b - 2c + d[/tex]
Step 5: Combine the first and fourth equations
[tex]28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d[/tex]
[tex]8 = 8b + 2d[/tex]
[tex]8 - 8b = 8b - 8b + 2d[/tex]
[tex](8 -8b)/2 = 2d/2[/tex]
[tex]4 - 4b = d[/tex]
Step 6: Solve for c in the second equation
[tex]-5 + 5 = -a + b - c + d + 5[/tex]
[tex]0 + c = -a + b - c + c + d + 5[/tex]
[tex]c = -a + b + d + 5[/tex]
Step 7: Substitute d with the stuff we got in step 5
[tex]c = -a + b + (4 - 4b) + 5[/tex]
[tex]c = -a + b + 4 - 4b + 5[/tex]
[tex]c = -a - 3b + 9[/tex]
Step 8: Substitute d and c into the first equation
[tex]28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)[/tex]
[tex]28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b[/tex]
[tex]28 - 22 = 6a - 6b + 22 - 22[/tex]
[tex]6 / 6 = (6a - 6b) / 6[/tex]
[tex]1 + b = a - b + b[/tex]
[tex]1 + b = a[/tex]
Step 9: Substitute a, b, and c into the third equation
[tex]220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)[/tex]
[tex]220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b[/tex]
[tex]220 - 100 = 60b + 100 - 100[/tex]
[tex]120 / 60 = 60b / 60[/tex]
[tex]2 = b[/tex]
Step 10: Find a using b = 2
[tex]a = b + 1[/tex]
[tex]a = (2) + 1[/tex]
[tex]a = 3[/tex]
Step 11: Find c using a = 3 and b = 2
[tex]c = -a - 3b + 9[/tex]
[tex]c = -(3) - 3(2) + 9[/tex]
[tex]c = -3 - 6 + 9[/tex]
[tex]c = 0[/tex]
Step 12: Find d using b = 2
[tex]d = 4 - 4b[/tex]
[tex]d = 4 - 4(2)[/tex]
[tex]d = 4 - 8[/tex]
[tex]d = -4[/tex]
Answer: [tex]a = 3, b = 2, c = 0,d = -4[/tex]
a boat travels 3600 meters in 12 minutes what is the boats speed
Answer:
300 meters per minute
Step-by-step explanation:
If the boat travels 3600 meters in 12 minutes, it travels 300 meters in 1 minute. Hope this helps!
Please help me out! i have a few more of these questions, about 5
Answer: You could plot the points (0,-2) ( 1,0) ( 2,2) (3,4) ( 4,6) (5,8) ( -1,-4) (-2.-6)
Step-by-step explanation:
y= 2x - 2
x y
0 -2
1 0
2 2
3 4
4 6
5 8
-1 -4
-2 -6
In algebra, we use an(n)___ to represent a variable.
Answer:
A letter.
You can use any letter of the alphabet, but the ones that are most commonly used are x, y, and z.
Can someone help and explain A and B please...
336 students enrolled in a freshman-level chemistry class. By the end of the semester, 6 times the number students passed as Find the number of students who passed and the number who failed
Figure A below is translated 4 units left and 1 unit down and then reflected over the y-axis. On a coordinate plane, triangle A has points (5, negative 2), (5, negative 3), (2, negative 4). Triangle B has points (negative 1, negative 3), (negative 1, negative 4), (2, negative 5). Which best explains whether figure B is the image of figure A under the specified transformations?
Figure B is not the image of figure A because the triangles are not congruent.
Figure B is not the image of figure A because the transformations were performed in an incorrect order.
There is not enough information to determine whether figure B is the image of figure A after the transformations.
Figure B is the image of figure A. The transformations were performed correctly.
Answer:
D
Step-by-step explanation:
I took the test.... Hope this helps!!!
Answer:
D
Step-by-step explanation:
please help me with this
Answer:
D
Step-by-step explanation:
the answer should be D
Help Me! I'm not good at this! I will mark brainliest!
Answer:
1.61 * 10 ^8
3.3 * 10^-7
Step-by-step explanation:
Multiply the numbers and then add the exponents
2.3 * 10^1 * 7 * 10^6
2.3 *7 * 10^(1+6)
16.1 * 10^7
We need to make this scientific notation by moving the decimal one place to the left and adding 1 to the exponent
1.61 * 10 ^8
Multiply the numbers and then add the exponents
1.1* 10^-5 3*10^-2
1.1 *3 * 10^(-5+-2)
3.3 * 10^-7
Answer:
1. B
2. C
Step-by-step explanation:
1. 2.3 × 10¹ × 7 × 10⁶
2.3 × 7 × 10^(1+6)
16.1 × 10⁷
1.61 × 10⁸
2. 1.1 × 10^-5 × 3 × 10^-2
1.1 × 3 × 10^(-5-2)
3.3 × 10^-7
Please help!!! i attached the problem.
Answer:
y>7.5
line under inequality sign.
Step-by-step explanation:
What is the solution to the equation below? Round your answer to two
decimal places
e^x = 5.9
Answer:.1.77
Step-by-step explanation:
e^x = 5.9
Take the natural logarithm of both sides
x = ln (59/10)
x = 1.77
Answer: x=1.77
Step-by-step explanation:
A P E X
What type of triangle is shown below?
isosceles triangle
scalene triangle
right triangle
obtuse triangle
Answer:
scalene
Step-by-step explanation:
Its a scalene triangle
Simplify x 2 − 4x + 4 x 2 − 4
Look at the attached picture
Hope it will be helpful to you..
PLZ HELP I’M TIMED!! I’LL GIVE BRAINLIEST- FIND THE VALUE OF Y
Answer:
131
Step-by-step explanation:
25+24=49
180-49=131
Amy must choose a number between 55 and 101 that is a multiple of 3, 6, and 7. Write all the numbers that she could choose. If there is more than one number, separate them with commas.
Answer:
84
Step-by-step explanation:
L.C.M. of 3,6,7=42
42×1=42
42×2=84
42×3=126
55<84<101
last month he sold 50 chickens and 30 ducks for $550. this month he sold 44 chickens and 36 ducks for $532. how much does a chicken cost and how much does a duck cost ?
Answer:
cost of one chick:$8 Cost of one duck:$5
Find the area of the trapezoid by decomposing it into other shapes.
A) 25 cm2
B) 27 cm2
C) 30 cm2
D) 35 cm2
Answer:
35 cm2
Step-by-step explanation:
Answer:
The area of the trapezoid would be 30 cm squared.
Step-by-step explanation:
Convert: 15,940 feet = how many miles and feet
Answer:
3.02 miles
Step-by-step explanation:
y=6x+15 what is y, when x=5
Answer:
Answer:45
6 x 5+15=45
Step-by-step explanation:
Hope this helped!
Answer:
Look at explanation
Step-by-step explanation:
First, plug in x=5 into the equation y=6x+15 for x.
[tex]y=6(5)+15[/tex]
Solve.
[tex]y=6(5)+15\\=30+15\\=45\\y=45[/tex]
find the vertex of the parabola represented by the function f(x)= -2x^2
Ms. Augustine is playing a game with her class. When a student tells her a number, she uses a rule to determine the new number. Ms. Augustine always uses the same rule. The table below shows some of the results.
What would the number be when the student says 8?
A. 58
B. 56
C. 54
D. 50
Answer:
When a student tells her a number, she uses a rule to determ
Step-by-step explanation:
Get the answers ... When a student tells her a number, she uses a rule to determine the new number. Ms. Augustine always uses the same rule. The table below shows some of the results. What would the number be when the student says 8? A. 58. B. 56. C. 54
Answer:
58
Step-by-step explanation:
Suppose you deposit $1500 in a savings account that pays interest at an annual rate of 6% if no money is added or withdrawn from the account answer the following questions how much will be in the account in four years how much will be in the account after 16 years how many years will it take for the account to contain $2000 How many years will it take for the account to contain $2500
Answer:
In 4 years = $1,893.72
In 16 years = $3,810.53
years to contain $2,000 = 4.9371454128
years to contain $2,500 = 8.766692911
Step-by-step explanation:
In 4 years
A = 1,500 (1 + 0.06)^4
= $1,893.72
In 16 years
A = 1,500 (1 + 0.06)^16
= $3, 810.53
to find number of years
t = ln (A/P) / ln (1+r)
when A = 2,000
t = ln(2,000/1,500) / ln(1+0.06)
= 4.9371454128 years
when A = 2,500
t = ln(2,500/1,500) / ln(1+0.06)
= 8.766692911 years
PS: You can also use log in place of ln
The number of years it will take for the account to contain $2000 is 4.94 years while it will take 8.77 years to contain $2500.
Calculation of future value and the number of years it takesLet:
PV = Present value = $1,500
r = Interest rate = 6%, or 0.06
n = number of years
FVn = Future value after a certain number of years
Therefore, we have:
The amount that will be in the account in four years can be calculated using the future value (FV) formula as follows:
FV4 = PV * (1 + r)^n = $1,500 * (1 + 0.06)^4 = $1,893.72
Therefore, the amount that will be in the account in four years is $1,893.72.
The amount that will be in the account after 16 years can also be calculated using the future value (FV) formula as follows:
FV16 = PV * (1 + r)^n = $1,500 * (1 + 0.06)^16 = $3,810.53
Therefore, the amount that will be in the account after 16 years is $3,810.53.
The number of years will it take for the account to contain $2000 can be calculated using the following formula:
n = (log(FV/PV)) / (log(1+r)) = (log($2,000/$1,500)) / (log(1+0.06)) = 0.1249387366083 / 0.0253058652647703 = 4.94 years
Therefore, the number of years it will take for the account to contain $2000 is 4.94 years.
The number of years it will take for the account to contain $2500 can be calculated using the following formula:
n = (log(FV/PV)) / (log(1+r)) = (log($2,500/$1,500)) / (log(1+0.06)) = 0.221848749616356 / 0.0253058652647703 = 8.77 years
Therefore, the number of years it will take for the account to contain $2000 is 8.77 years.
Learn more about future value here: https://brainly.com/question/13504821.
#SPJ2
pls help A round trip to your favorite aunt's house is 412 miles. You went to your favorite aunt's house 2 times last week. How many miles did you travel in total?
824 miles
Step-by-step explanation:
412×2=824 miles
or you could do 412+412=824 miles
Hope that helps! If you need any further clarification then please comment down below or message me. Good luck!
A bag contains 4 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, find the
probability that a blue marble will be drawn.
a. 1/3
b. 1/11
c. 1/7
d. 3/14
Answer:
The probability should be 3/14
Answer:
3/14
Step-by-step explanation:
If you want to find the probability of a blue marble being drawn, I would add up the total amount of marbles, which is 4+3+7=14. There are 3 blue marbles out of the 14 total marbles, and as a fraction, that would be 3/14.
Hope this helps!
PLS HELP I WILL MARK BRAINLIEST (EDITED) I ONLY HAVE 20 MORE MINS HELP
Step 2: Finding the area of triangles
a) The International Space Station has small cupboards that are used for storage. A cupboard door is drawn below.
a rectangle with a line going from the upper left corner to the down right corner. at the left corner, under the line is 60. under the right corner, is 30. there is a square at the down left corner
What is a formula that can be used to find the area of one triangular section of the door? How do you know the formula will work? (3 points)
Answer:
60 times 30 divided by 1/2
Step-by-step explanation:the formula will work because you will multiply to find the square amount of the square. Then divide by 2 to get back to the triangl. Hope it helps. Sry if it is wrong.
V62 is between what pair of consecutive integers?
10 and 11
8 and 9
7 and 8
6 and 7
Answer:
7 & 8.
Step-by-step explanation:
√62 = 7.87400787401.
Can someone pls answer the question plss
Answer:
the first one
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The y axis or interval (0,Infinity) is forever going more lower and the x is forever going to the negatives
Remember: Use ALL numbers below or above
the true median (which was 55)
What is the UPPER quartile?
64.5
69
73
65
Answer:
upper:65 lower:44
Step-by-step explanation:
Please help me with this problem.
Answer:
1
Step-by-step explanation:
Find the value of x
146° (9x + 20)°
Answer:
x = 14
Step-by-step explanation:
146° = 9x + 20°
146° - 20° = 9x
126° = 9x
x = 126°/9
x = 14
The standard New York state license plate has three letters followed by four digits. How many different
license plates are possible if the digits can't be repeated and letters can be repeated?
a
1,560,000 possible license plates
175,760,000 possible license plates
88,583,040 possible license plates
90,283,340 possible license plates
с
d
Answer:
175,760,000 possible license plates
Step-by-step explanation:
There are 3 spots where there are 26 choices each
= 26 ^3
and 4 spots where there are 10 choices each (the digits 0 through 9,
= 10 ^4
This gives:
26^3*10^4=175,760,000
Hope this Helps...!!
