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]
is it true that energy never moves
Answer:
False
Step-by-step explanation:
Energy is transferred from one object to another when a reaction takes place. Energy comes in many forms and can be transferred from one object to another as heat, light, or motion, to name a few.
Solve 6-x=4(5+x)-4 what would the answer be
Answer:
x = -2
Step-by-step explanation:
For the data set 6, 5, 10, 11, 13, the mean, X, is 9. What is the standard
deviation?
Answer:
standard deviation = 3.0331
Step-by-step explanation:
You can solve for this two different ways.
If you have a TI-84 calculator or something similar, type all the data into list 1. Then click the stat button, then the calc button, then 1-vars stats. This will give you mean, standard deviation, median, mode, etc.
If you are solving by hand, find the different between each data point and the mean. Square these numbers and find the average. Then take the square root of that.
3^2 + 4^2 + 1^2 + 2^2 + 4^2 = 46
46/5 = 9.2
square root of 9.2 = 3.0331
Hope this is helpful!!!!!!!!!!! :)
Jaira is having pizza for her birthday party. She can make two small pizzas, each with a radius of 6 inches, or one large pizza with a radius of 12 inches. Which option will give her more square inches of pizza?
Answer: One large pizza with a radius of 12 inches
Step-by-step explanation:
Hi, to answer this question we have to calculate the area of each option.
Area of a circle: π r^2
Option 1: two small pizzas, each with a radius of 6 inches.A = π r^2 = π 6^2 = 113.1 in2
Since there are 2 small pizzas we have to multiply the area by 2:
113.2 x 2 = 226.2 in2
Option2 = one large pizza with a radius of 12 inchesA = π r^2 = π 12^2 = 452.38 in2
Since 452.38 in2 > 113.1 in2
Option 2 (one large pizza) will give her more square inches of pizza
Feel free to ask for more if needed or if you did not understand something.
I need help with this please ASAP!!!
Answer:
11.3
Step-by-step explanation:
i used the theorem of Pythagoras
Answer:
11.3
Step-by-step explanation:
In a right angled triangle: the square of the hypotenuse is equal to
the sum of the squares of the other two sides.
[tex]8^{2} + 8^{2} = x^{2}[/tex] (x is the hypotenuse)
64 + 64 = [tex]x^{2}[/tex]
[tex]x^{2}[/tex] = 128
=> x = [tex]\sqrt{128}[/tex] = 11.3137085 = 11.3
Can I please get help with this math problem?
If P(A) = 0.25, P(B) = 0.60 and P(A and B) = 0.15, are the event A and B independent? Explain/show work.
Answer:
event A and B are independent because P(A and B) = P(A) x P(B) = 0.15
Step-by-step explanation:
When two events are independent, the probability of both occurring is the product of their separate probabilities, as expressed below;
P(A and B) = P(A) x P(B)
Given;
P(A) = 0.25
P(B) = 0.60
P(A and B) = 0.15
Now, let's check if P(A and B) will be equal to P(A) x P(B)
P(A) x P(B) = 0.25 x 0.60 = 0.15
P(A and B) = P(A) x P(B), thus event A and B are independent.
Find area of trapezoid
Answer:
The area of the trapezoid would be 115 inches.
help me answer this question
Answer: Sorry i whould help but I cant see it can you put it more bigger
Step-by-step explanation:
Kyle spends $32.35 on a bag of soil and x tomato plants. The price of soil is $9.85 and the plants cost $1.25 each. How many plants did Kyle buy? Write and solve an equation.
please and thank you!
Use the graph or table to write a linear function that relates to y to x.
Answer:
the answer to the question is D
Complete the following ratios:
Answer:
700/821, 429/821, 700/429
Step-by-step explanation:
SOH, CAH, TOA
Sin= opp/hyp
Cos= adj/hyp
Tan= opp/adj
elijah's credit card statement showed these items: Last Balance Payments Finance Rate New Charges $152.58 $45.00 1.5% $213.40 What is Elijah's new balance? $320.98 $322.59 $323.27 $397.51
Answer:
Option A,$320.98 is correct
Step-by-step explanation:
The new balance on Elijah's credit is the sum of the last balance plus new charges minus payments made.
last balance as shown by the statement was $152.58
new charges were $213.40
payment made by Elijah was $45
new balance=$152.58+$213.40-$45=$320.98
The rationale for this is that the new charges on the card account add to previous balance owed by Elijah while the payment of $45 made reduces overall balance.
Answer:
Other answer is incorrect. Elijah's new balance would be $322.59
Your welcome.
(DO NOT GIVE ANSWER!
Please just explain how to get the answer, thank you! )
The probability of winning a game is 25%. How many times should you expect to win if you play 36 times?
Answer:
----
Step-by-step explanation:
My answer was wrong...
No way to delete...
What is the rank of Brazil. (Percentile wise)
Answer:
I dont know it this is the answer u r looking for but out of everything on the list, brazil has 2.2222222222222 percent
Answer:
3.9%
Step-by-step explanation:
add up all the Olympic medals =485
Brazil = 19
to get the rank of Brazil 19/ 485 =0.039175..... multiply by 100 to get %
In the following credit card statement, what is the balance?
A. $10
B. $130.23
C. 5-13-2010
D. $259.67
Answer:
I wanna say its D. $259.67
Step-by-step explanation:
Some one should back my answer but I hope this helps you
Answer:
for odyessyware users, the option is 202.23 instead og 259.67 if that helps anyone
Step-by-step explanation:
peace and good luck ya'll =)
I will mark brainliest! The question is the image attached, please help!
Answer:
x=20 and y=128.Option 2
Step-by-step explanation:
Since,the angles are vertically opposite,they are equal(property)
Therefore,
(3x-8)=(2x+12)
3x-8=2x+12
3x-2x=12+8
x=20,
Now,
Since,the angles are formed in a straight line,their sum is equal to 180(property)
Therefore,
y+(2x+12)=180
y+2×20=180-12
y=168-40
y=128
Therefore,x=20 and y=128
option 2 would be your answer because it explains the missing part where y is.
Find the surface area of the figure. Round the the nearest hundredth.
Answer:
Step-by-step explanation:
surface area of cylinder=2πrh
SA=1/2×2×π×3×25+2 ×(1/2×π×3²)=75π+9π=84π≈84×3.14≈263.76 cm²
if lowerside is also counted then area of lower side=25×6=150
total surface area=263.76+150=413.76 cm²
if we take π=22/7
84 π=84×22/7=12×22=264 cm²
if base is also counted then area=264+150=414 cm²
The loudness, L. measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as
L - 10log , where lo - 10- and is the least intense sound a human ear can hear. Jessica is listening to soft music at a
sound intensity level of 109 on her computer while she does her homework. Braylee is completing her homework while
listening to very loud music at a sound intensity level of 10 on her headphones. How many times louder is Braylee's music
than Jessica's?
Answer:
Option A is correct.
Braylee's music is 3 times louder than Jessica's.
Step-by-step explanation:
Full Complete Questions
The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as
L = 10log (I/I₀), where lo = 10⁻¹² W/m²
and is the least intense sound a human ear can hear.
Jessica is listening to soft music at a sound intensity level of 10⁻⁹ W/m² on her computer while she does her homework.
Braylee is completing her homework while listening to very loud music at a sound intensity level of 10⁻³ W/m² on her headphones. How many times louder is Braylee’s music than Jessica’s?
times louder
3 times louder
30 times louder
90 times louder
Solution
The loudness of a sound intensity is given as
L = 10 log (I/I₀)
For Jessica
I = 10⁻⁹ W/m²
I₀ = 10⁻¹² W/m²
L = 10 log (10⁻⁹/10⁻¹²)
L = 10 log (10³)
L = 10 × 3 = 30 dB
For Braylee
I = 10⁻³ W/m²
I₀ = 10⁻¹² W/m²
L = 10 log (10⁻³/10⁻¹²)
L = 10 log (10⁹)
L = 10 × 9 = 90 dB
How many times louder is Braylee's music than Jessica's?
The factor by which Braylee's music is louder than Jessica's = (90/30) = 3
Braylee's music is 3 times louder than Jessica's.
Hope this Helps!!!
Answer:
3 times louder
Step-by-step explanation:
Question 27
.........................................................
Answer:
B
Step-by-step explanation:
for which value of x is the row in the table of values incorrect? the function is the quadratic function y=-1/2x^2
A.)x = 0
B.)x = 3
C.) x = 2
D.)x = 5
Answer:
D. x = 5
Step-by-step explanation:
At x = 5
y = -½(5)²
y = -½ × 25 = -25/2 = -12½
Answer: x=5
Step-by-step explanation:
Calculate:|a|−|b|+|c|, if a=−8; b=−5; c=1
Answer:
The answer is 4.
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
|x| just means positive x so the equation turns into 8-5+1
8-5 = 3
3+1 = 4
Students in grade 7 and 8 were asked which food they liked best the results are shown in the table below?
Answer:
55% if the students like hotdods
Answer:
55%
Step-by-step explanation:
will give brainliest plz helppp!!!!
Answer:
A. True
B. False
C. False
D. False
Step-by-step explanation:
There are 10 shirts in a drawer. Eight of the shirts have short sleeves. Two shirts have long sleeves. Estimate the probability that you get a short-sleeved shirt if you select one out without looking.
Answer:
4/5
Step-by-step explanation:
8/10=4/5
Which two terms are interchangeable
Answer:
C hope this helped :D if not plz let me know..
The terms that are interchangeable are axioms and postulates.
What are Axioms and Postulates ?"In mathematics or logic, an axiom is an unprovable rule or first principle accepted as true because it is self-evident or particularly useful. “Nothing can both be and not be at the same time and in the same respect” is an example of an axiom"
"The term is often used interchangeably with postulate, though the latter term is sometimes reserved for mathematical applications (such as the postulates of Euclidean geometry). It should be contrasted with a theorem, which requires a rigorous proof."
By the definition of Axiom and postulates,
It is clear that Axiom and postulates are interchangeable, since they both used as a unprovable rule.
Hence A is the correct option.
To know more about axioms and postulates here
https://brainly.com/question/10665597
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A number is multiplied by 4. That results is added to 12. The final number is 40. What is the original number.
A.) 2
B.) 7
C.) 13
D.) 22
Answer:
B.) 7
Step-by-step explanation:
7 x 4 = 28
28 + 12 = 40
:)
Using multiplication, the original number is 7.
What is multiplication?Multiplication is "the process multiplying that the integer is multiplied by number of time".
According to the question,
A number is multiplied by 4. The results is added to 12. The final number is 40. In order to find original number.
4x + 12 = 40
4x = 40 -12
4x = 28
x = 28/4
x = 7.
Hence, using multiplication, the original number is 7.
Learn more about multiplication here
https://brainly.com/question/9813637
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need help mark brain 30 points
Answer:
(6000)(0.03)(5)=$900
(1500)(0.0425)(4)=$255
(580)(0.02)(6)=$69.60
(1200)(0.039)(2.5)=$117
Which of the following represents the additive inverse of h?
Answer:
B or -h
Step-by-step explanation:
i took the quiz
What is the slope of the line represented by y=3/4x-1 ? A. –1 B. -3/4 C. 3/4 D. 1
Answer:
3/4
Step-by-step explanation:
In the above equation the y-intercept is -1 and the slope of the equation is 3/4
Answer:
The answer is C or 3/4.
Step-by-step explanation:
This equation is in point-slope form or Y= mx+b. The variable m represents slope. So, just look for the number that stands in place of m. Hope this helps! Please mark Brainliest! :)
