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]
HELP HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The first one dividing the number by 100
Step-by-step explanation:
Justin played a game with 24 floating plastic ducks each with a colored sticker on the bottom. There are an equal number of red blue and green stickers on the set of ducks. What is the probability that one duck chosen at random will have a red or blue sticker
Answer:
Because there are 24 ducks total and they are separated equally into three categories, we can figure out that there are 24 / 3 = 8 ducks of each color. This makes the probability of pulling a red/blue duck would be (8*2)/24 or 16/24. If we want this to be a percentage we can just solve 16/24*100 and it will give us 66.66...%
(x + 4)
110°
3x
Measure of
Answer:x=57
Step-by-step explanation:
Answer:
30.5
Step-by-step explanation:
Measure of angle A and B equals 110 because of how triangles work
Therefore 3x + x + 4 = 110
4x + 4 = 110
Subtract 4 from each side
4x = 106
Divide both sides by 4
x = 26.5
Measure of angle ABC equals 26.5 + 4 = 30.5
I WILL MARK THE BRAINLIEST THE SECOND I GET IT CORRECT. PLEASE HELP.
(3)/(10) x- (5)/(7) y-4 (5)/(6) y-2 (4)/(5) x
Answer:
is there a mulitply choice or no because i think i have the answer
Step-by-step explanation:
one and a half miles in one hour
Answer:
I don't get your question but if you are asking. How long is 1 hour and a half?
The answer for this question is 15 minutes.
Step-by-step explanation:
How long is 1 hour and a half?
15 minute is the right answer
Big ideas math 6th grade chapter 5 test
Answer:
I'm not sure if you need help but...
Step-by-step explanation:
6+6=12
Can you help me find MAD for this
Answer:
5
Step-by-step explanation:
(3+15+21+13)/4 = 13
13 - 3 = 10
15 - 13 = 2
21 - 13 = 8
13 - 13 = 0
(10+2+8+0)/4 = 5
Each side of a square name tag is 7 centimeters long. What is the name tag's area?
Answer:
49 cm²
Step-by-step explanation:
The area for a square is Area = length x width, and if the square name tag is 7cm long on "each side", that means that both the length and the width are 7cm.
Plug this into the formula to get A = 7cm x 7cm.
This can be simplified to A = 49cm².
Answer: 49 cm^2
Step-by-step explanation:
7 x 7 = 49
What is the total area, in square units, of the
figure shown below?
a. 6
b. 12
c. 24
d. 30
Answer:
30 !
Both are right triangles so you can do 4*3= 12 and then 12/2= 6
then 6*8=48 and 48/2=24
24+6 =30!
hope this helps ! :)
The temperature in a greenhouse should be 65 degrees or higher. One morning, the heater stopped working. The temperature dropped 2 degrees before someone fixed the heater. The temperature was still at least 65 degrees when the heater started working again. How can you best describe the temperature in the greenhouse before the heater stopped working?
12. For angle A it is known that sin(A)>0 and tan (A) <0. If A is drawn in standard position, in which quadrant
does its terminal ray lie?
Answer:
Quadrant 2
Step-by-step explanation:
Sin = opp/hyp and opp is positive in quadrants 1 & 2.
Tan = opp/adj - we need one of these values to be positive and the other negative. adj is negative in quadrants 2 & 3.
Quadrant 2 is found in both of the scenarios that we need to occur.
What number can be used to complete the volume statement for the cone?
4 m
3 m
Volume =
sm
Answer:
V=πr2h /3
Step-by-step explanation:
Answer:
V=πr2h /3
Step-by-step explanation:
a rectangular field has side lengths that measure 9/10 mile and 1/2 mile. What is the area of the field
Answer:
9/20, or 0.45 mile.
Step-by-step explanation:[tex]\\[/tex]
To find the area of a rectangle, multiply length times width. In this problem we are given both the length and width.
[tex]\frac{9}{10}[/tex] × [tex]\frac{1\\}{2}[/tex] is just 9/20, which is 0.45.
Find the 76th term of the arithmetic sequence 17, 19, 21, ...
Answer: 167
Step-by-step explanation: To find the 76th term of this arithmetic sequence, we will be using our explicit formula which is shown below.
[tex]^{a}n = ^{a}1 (n - 1)d[/tex]
Since we want to determine the 76th term, we are going
to substitute 76 in for n in our explicit formula.
Then, [tex]^{a}1[/tex] will be our first term in our sequence which is 17.
Lastly, d is our common difference or the difference between each of the terms in our arithmetic sequence which is 2.
So we have [tex]^{a} 76 = 17 + (76 - 1)(2)[/tex].
Now we have all the information we need. Just simplify from here.
Make sure to apply order of operations because this is where many
students make mistakes. Inside the parentheses first!
(76 - 1) is going to be 75.
So we have [tex]^{a} 76 = 17 + (75)(2)[/tex].
Then, we have to make sure we multiply before we add.
So (75)(2) is going to give us 150.
So we have [tex]^{a} 76 = 17 + 150[/tex].
Now just add to find that [tex]^{a} 76 = 167[/tex].
So the 76th term is 167.
Find the value of c that makes each trinomial a perfect square.
x² + 3x+c
Answer:
2
Step-by-step explanation:
Plug in 2 for c in the equation:
x² + 3x + 2
x 2
x 1
(x + 2)(x + 1)
Check. Use the FOIL method:
(x)(x) = x²
(x)(1) = x
(2)(x) = 2x
(2)(1) = 2
x² + x + 2x + 2
Combine like terms:
x² + (x + 2x) + 2
x² + (3x) + 2
2 can be a answer for c.
~
Which of the following line is moving at a faster speed
Answer:
a. it's a steep line covering more distance over time
A circle with a radius of 1 unit and center C at (-2, 1) is reflected across the x-axis. What are the coordinates of C?
(2, 1)
(2,-1)
(-2,4)
(-2,-1)
Answer: b
Step-by-step explanation:
I NEED HELP PLEASE!!!!
I NEED HELP PLEASE!!!!
I NEED HELP PLEASE!!!!
I NEED HELP PLEASE!!!!
I NEED HELP PLEASE!!!!
I NEED HELP PLEASE!!!!
Answer:
B is correct
You can double check it! :)
Hope this helps!
Tips:
Select a condition, check the 4 tables and eliminate 2 tables at once.
Then check the remaining 2 tables.
:)
Answer:
B. W
Step-by-step explanation:
College & university: 6
College & not university: 17
Not college & university: 28
Not College & not university: 9
PLZZZ HELP ME I NEED HELP AND I HAVE A TIMER AND I WILL GIVE YOU BRAINLEST
On a coordinate plane, 2 lines intersect around (3.8, negative 1.5).
Given the graph of a system of equations, which statements are true about the solution? Check all that apply.
The x-value is an integer.
The x-value is between 3 and 4.
The y-value is between –2 and –1.
The x-value is positive.
The x- and y-values have the same sign
Answer:
b,c,d
Step-by-step explanation:
I just did the assignment
Answer:
b, c. d
Step-by-step explanation:
PLEASE HELP MEEEE--Identify the coefficient and exponent of these very large and very small numbers represented in scientific notation
Identify how each number would be represented in scientific notation.
5,890,000 = 2 x 106
a= 7
b =
0.0000521 = 100
c=
d=
Answer:
A= 5.89
b = 6
c= 5.21
d= -5
you deposit $2000 into an account which pays 4.5% annual intrest compounded quarterly. How long will it take the account to double in value?
Answer: She could have the same future value and invest less than $2,000 initially if she could earn more than 64.5 percent interest.
Step-by-step explanation:
please help! desperateee
Answer:
52
Step-by-step explanation:
This is an isosceles triangle, so the base angles will be the same. Then you know that all of your angles will add up to 180.
Your equation can be:
2(2x+2) + (3x + 1) = 180
x = 25
S = 2(25) + 2
S = 52 degrees
Answer:
52
Step-by-step explanation:
Because SR = TR, ∡S =∡T= 2x+2
For any triangle sum of all angles = 180°.
2x+2 +2x+2+3x+1= 180
7x + 5 =180
x = 25°
∡S =2x+2=2*25+2 = 52°
Naomi used 100 tiles to create a design. Blue tiles make up 1/2 of the design. Another 15 tiles are green, and 1/5 of the tiles are yellow. The rest of the tiles are red. How many red tiles did Naomi use in her design?
A. 15 tiles
B. 25 tiles
C. 65 tiles
D. 85 tiles
Answer:
Naomi used 15 red tiles in her design.
Step-by-step explanation:
We need to add the total number of tiles that we know to find out the unknown value of red tiles. The blue tiles make up 1/2 of the design, or 50 tiles. Next we will add the green tiles, which Naomi used 15 of, as stated.
So far, we have figured out how many blue and green tiles we have. (50 blue, and 15 green, which is a total of 65).
Now we need to calculate the number of yellow tiles, which equal 1/5 of the design. 1/5 of 100 is 20.
Now we add all of our tiles that we already know. We have 50 red + 15 green + 20 yellow which = 85.
Now to find the unknown value of red tiles, we subtract our 85 other tiles from the 100 total tiles, and the ends us up with 15 red tiles.
Hope this helps!!
stay safe :0)
Find the probability that a point chosen at random will lie in the shaded region.
I don't understand what to do here :(
Step-by-step explanation:
In the 1st question
Total boxes = 6
Shaded boxes = 2
Probability = 2/6 = 1/3
What is the net change in the temperature relative to when lko woke up
Complete question:
Between the time iko woke up and lunchtime, the temperature rose by 11°. Then by the time he went to bed, the temperature dropped by 14°.
What is the net change in the temperature relative to when lko woke up?
Answer:
The net change in the temperature relative to when lko woke up =
[tex]\bold{-3}[/tex] °
Step-by-step explanation:
Given that between his wake up time and lunch time, temperature rose by 11°. Let the new temperature be [tex] \bold{T1} [/tex] and let the initial temperature(temperature before wakeup time) be [tex] \bold{T} [/tex]
Since the temperature rose by 11°, the new temperature after Iko woke up, T1, would be derived by adding 11° to the initial temperature.
i.e, T1 = T + 11......................(1)
At bed time the temperature dropped by 14°. Therefore, the temperature would now be 14 less than the new temperature T1. It is expressed as:
T1 + (-14).......................... (2)
Let's substitute T + 11 for T1 in equation 2, we have:
T + 11 + (-14)
To find the expression for the net change in temperature, let's subtract the initial temperature T, from (T+11 -14) i.e,
ΔT = (T + 11 - 14) - T
Solving further, we have:
ΔT = T - T + 11 - 14
ΔT = 11 - 14
ΔT = -3°
Therefore, the net change in the temperature relative to when lko woke up is = -3°
The likelihood that Steph makes a free throw in basketball is 60%. The likelihood he makes a 3-point shot is 0.345.
Which event is more likely, Steph making a free throw or making a 3-point shot?
Drag the different shots to the correct location on the number line?
which on is first on the number line free throw or making a 3-point shot?
which on is second on the number line free throw or making a 3-point shot?
Answer:
A free throw is more likely
First: 0.345
Second: 60%
Step-by-step explanation:
For placement:
0.345 would be behind 0.5
And
60% would be ahead of 0.5
60% = 0.6
0.345 < 0.6
Answer:
A free throw
Step-by-step explanation:
I need help plzzzz I’m nearly done
Answer:
≈ 70.4 cm
Step-by-step explanation:
The circumference (C) of a circle is calculated as
C = 2πr ( r is the radius ) , thus
C = 2 × 3.142 × 11.2 ≈ 70.4 ( to 1 dec. place )
I need help with this question thank u
Answer:
The answer is C.
[tex]n = 2t - 1[/tex]
Step-by-step explanation:
You can simply determind the answer by placing all pair of value n and t in the equation, one by one.
First, try the answer A, you should get as following;
[tex]n = t + 2 \\ 1 = 1 + 2[/tex]
and try to see if it is true or not,
in this case,
1 will never equal 1 + 2 (1 ≠ 1 + 2)
Therefore A is not the Answer. Try going through all other choices, and you will find the answer. The calculation is very simple, you probably won't need a calculator!
[EDIT]
i just realize this answer is wrong sorry
In the figure angle a measures 41 degrees and angle d measures 32. What is the measurement of angle E?
Answer:
it is c
Step-by-step explanation:
A survey was done to investigate the relationship between liking math and learning a musical
instrument. The results are shown in the Venn diagram below. If a person was selected at
random from this survey, which of the following would be the probability of liking math given
that they don't take music?
A) 0.22
Likes Math
Takes Music
B)
0.28
C)
0.33
22
80
45
D)
0.37
38
The probability of liking math given that they don't take music is 0.37 option (D) 0.37 is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.
The probability:
P(Math/Music') = P(Math∩Musci')/P(Music')
Total number of sample = 22+80+45+38 = 185
Probability of liking math:
P(Math) = (22+80)/185 =0.55
Probability:
P(Music) = (45+80)/185 = 0.68
P(Music') = 1-0.68 = 0.32
Probability of liking math and liking music:
P(Math∩Music) = 80/185 = 0.43
Now, P(Maths/Music) = (0.55 - 0.43)/0.32 = 0.375 ≈ 0.37
Thus, the probability of liking math given that they don't take music is 0.37 option (D) 0.37 is correct.
Learn more about the probability here:
brainly.com/question/11234923
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