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]
Equivalent expression 5x-3x for x=2
Answer: 16
Step-by-step explanation:
Plug 2 in for x.
5^2-3^2
25-9= 16
Answer:
16
Step-by-step explanation:
[tex]5^{x}[/tex]-[tex]3^{x}[/tex] x=2
[tex]5^{2}[/tex]=25
[tex]3^{2}[/tex]=9
25-9=16
find the volume of the following comes with the given dimensions. round your answer to the nearest hundredth. diameter=4ft height=1ft
Answer:
4
Step-by-step explanation:
Question 1:
Which ordered pairs are a solution to the equation y=2x+6
Select all that apply
(0,6)
(-1,4)
(-1,-4)
(3,12)
Question 2:
Which ordered pairs are a solution to the equation y=4-2x
Select all that apply
(-1,2)
(0,4)
(-1,6)
(1,6)
Answer:
1.
(0,6)
(-1,6)
(3,12)
2.
(0,4)
(-1,6)
Step-by-step explanation:
The rule for the first question is y = 2x + 6
We can substitute the numbers for each equation.
6 = 2(0) + 6
6 = 6
So (0,6) is correct.
4 = 2(-1) + 6
4 = 4
So (-1,4) is correct as well.
-4 = 2(-1) + 6
-4 ≠ 4
(-1,-4) is incorrect.
12 = 2(3) + 6
12 = 12
So this answer is correct as well.
The second question‘s rule is that y = 4 - 2x. So we can substitute the numbers.
2 = 4 - 2(-1)
2 ≠ 6
This is incorrect.
4 = 4 - 2(0)
4 = 4
This answer is correct.
6 = 4 - 2(-1)
6 = 6
This answer is correct as well.
6 = 4 - 2(1)
6 ≠ 2
This answer is incorrect as well.
SAT scores are normally distributed, with a mean of 1000 and a standard deviation of 200.
a) If you scored 950, what would be your percentile?
b) If you scored 1100, what percent of students scored better than you?
c) If your percentile was 92%, what did you score on the SAT?
Answer:
My sister is getting ready to prepare, I would say 1100 it means you are above.
Step-by-step explanation:
wesley. is very particular about his salad He must have 10 leaves of lettuce for every 4 pieces of carrots If he has 50 leaves of lettuce in his salad how many pieces of carrots will he have
Answer:
20 carrots
Step-by-step explanation:
4/10
x/50
10 x 5 = 50
4 x 5 = x
x = 20
20/50
Help me please. Im giving 20 points
A telephone pole is 8 meters tall and a pigeon is standing on the ground 6 meters
from the pole. If the pigeon flies from where it is standing to the top of the
telephone pole, how far will it fly?
Your answer will be 10m.
We can picture this question as a right-angled triangle, where the pole is one leg, and the distance from the pole to the pigeon on the ground is another leg. Using this, the hypotenuse would be the distance that the pigeon would travel to get from the ground to the top of the pole, presuming it flies in a straight line, and so we can use Pythagoras’ Theorem to find the length of the hypotenuse.
a² + b² = c²
(6)² + (8)² = c²
36 + 64 = c²
100 = c²
10 = c
I hope this helps! Let me know if you have any questions :)
!! NEED RN, MARKING BRAINLIST !!
What is the value of x?
Answer:
5 sqrt(3)
Step-by-step explanation:
Since this is a right triangle
sin theta = opposite side/ hypotenuse
sin 60 = x /10
10 sin 60 = x
10 sqrt(3) /2 =x
5 sqrt(3) =x
Answer:
5√3
Step-by-step explanation:
The sine function ties together the information at hypotenuse = 10, opposite side = x and angle of elevation = 60 degrees:
sin 60 degrees = opp side / hypotenuse = x/10.
Therefore, x = 10 sin 60 degrees = √3/2, and so x = 10√3/2 = 5√3 (equal to the third answer choice).
Y=4×^2-13×+10 what is the quadratic function by factoring?
Answer:
(4x-5)(x-2)
Step-by-step explanation:
factors of 10: 1,10, &2,5
factors of 4: 1,4 &2,2
(4x-5)(×-2)
Will mark brainliest.
Answer:
23.6
20characyersnx xmxm
Step-by-step explanation:
Area=bh=5.9*4=23.6in.²
6,291 DIVIDED BY 3 = ?
its easy i know lets see if your smart.
Answer:
6,291÷3=2,097
Hope this helped :)
the answer is 2,097
Step-by-step explanation:
6,291 divided bt 3= 2,097
A surgical technique is performed on eight patients. You are told there is an 80% chance of success. Find the probability that the surgery is successful for fewer than two patients. Please show your work.
Answer:
20.31%
Step-by-step explanation:
a) Construct a binomial distribution.
P = nCx* p%5Ex%2Aq%5E%28n-x%29 p= .8 and q = .2 and n = 8
b) Find the
mean = np = 8%2A.8+=+6.4
variance = npq = 6.4%2A.2+=+1.28
standard deviation of the probability distribution.sqrt%281.28%29
c) P(x = 6) = 28+%2A%28.8%29%5E6%28.2%29%5E2 = .2936 or 29.36%
d) P(x < 6) = 1 - P(x = 8) - P(x = 7) - P(x = 6)
= 1 - .1678 - .3355 - .2936 = .2031 or 20.31%
HOPE THIS HELPS PLZ MRK BRAINLIEST
A human blinks 9,460,800 times per year. A dog blinks 1,861,440 times per year. About how many more times does a human blink than a dog?
A. 2
B. 8
C. 10
D. 5
Sorry, I can't change the number of points you get.
Please answer this fast I need it!
Answer:
The answer is D.
Step-by-step explanation:
In order to find how many times human blink more than the blink of a dig, you have to divide it :
[tex]9460800 \div 1861440[/tex]
[tex] = 5 \: times[/tex]
14)
Write an equation of the line that is perpendicular to the line y = 4x - 10 that passes through the point (-16, 2).
A)
y = - 3x - 2
y = -4x+6
y=-3x+2
y = 4x + 2
Answer:
y = -1/4x -2
Step-by-step explanation:
the perpendicular slope would be -1/4
2 = -1/4 (-16) + b
b = -2
the equation should be y = -1/4x -2
None of the answers you typed could be correct.
Plz I need help with this problem. I'm dumb
Answer:
V_rectangular_box = width x height x length
V = V_big_one + V_small_one
= (1/3)x(1/4)x(5/8) + (1/6)x(1/4)x(1/4) = 1/16 (ft3)
Answer:
fjdjdkhfidkfjsidmi
Step-by-step explanation:
irufusidjf9sodf8wpud8dkdhd8idhddh
help guys!!! i have deadline!!!!
number 20!! mark brainliest and give 30 points!!!
or more if you want.
A caterer combines 3 quarts of orange juice, 5 pints of milk, and 5 cups of pineapple juice to make smoothies. How many cups can be filled with smoothies? Explain
Answer:
27 cups
Step-by-step explanation:
(3 quarts = 12 cups) (5 pints = 10 cups) (plus 5 cups) = 27 total
Joe's Painting charges $100 plus $20 per hour to paint the exterior of your home. Steve's Painting charges $120 plus $15 per hour to paint the exterior of your home. How many hours do Joe and Steve have to work for their models to be equal to each other? Which of the following systems is correct for this situation if "x" = hours worked and "y" = total income.
Joe's Painting: 20x + 100 = y
Steve's Painting: 15x + 120 = y
x = hours worked
y = total income
We can find when the two equations intersect by making them equal to each other. That means we put an equal sign in the middle. So, it would look something like this:
20x + 100 = 15x + 120
First, we have to move the 100 by subtracting it from both sides.
20x = 15x + 120 - (100)
20x = 15x + 20
Then, we need to move the 15x by subtracting it from both sides.
20 - (15x) = 20
5x = 20
Lastly, we need to divide 5 from both sides.
5x = 20/5
x = 4
Therefore, Joe and Steve would have to work for 4 hours in order for their models to be equal to each other.
What is the median of the data set represented by the dot plot?
Answer:
The median is 5.
Step-by-step explanation:
To find the median you have to do steps, (they are really easy):
The median is like the middle of the graph so just try finding the middle, ( i could explain this in a different way but it's hard to explain) Hope this helps.
Hey, I know you already found the median, but if you need help with anything else like that I'll show you!
Mean:
Step 1: Add up all data values to get the sum
Step 2: Count the number of values in your data set
Step 3: Divide the sum by the count
Mode:
Mode is the value or values in the data set that are the most common. To remember what mode is, think of most. Mode, Most.
Range:
The Range is the difference between the lowest and highest values. So, if we had a data set that read 5 5 3 6 9, you would have to find the lowest and highest number. For this set, thats 3 and 9. subtract them to get the sample range. 9 - 3 = 6.
Which expressions show repeated multiplication? Check all that apply.
(1)(9)
(one-half) (one-half) (one-half)
(7)(7)(7)(7)
(2)(3)(4)(5)(6)
(9)(9)(9)(9)(9)(9)
Answer:
2 ,3 and 5 show repeated multiplication
Step-by-step explanation:
Repeated multiplication : When we multiply any integer by itself many times then it is called repeated multiplication
1) (1)(9)
By definition it is not repeated multiplication
2) (one-half) (one-half) (one-half)
By definition it is repeated multiplication
3) (7)(7)(7)(7)
By definition it is repeated multiplication
4) (2)(3)(4)(5)(6)
By definition it is not repeated multiplication
5) (9)(9)(9)(9)(9)(9)
By definition it is repeated multiplication
Hence 2 ,3 and 5 show repeated multiplication
Answer:
its 2 3 5
Step-by-step explanation:
Use the zero product property to find the solutions to the equation x2 + x – 30 =12
Answer:
x = -7, x = 6
Step-by-step explanation:
x² + x - 30 = 12
x² + x - 42 = 0
- 42 = 7*(-6)
7+(-6) = 1
(x+7)(x-6) = 0
x+7 =0, x = -7
x - 6 = 0, x = 6
Answer:
It's A :D
Step-by-step explanation:
find the area of this triangle. pls help
Answer:
area is 24
Step-by-step explanation:
Eduardo has purchased a home with an assessed value of $179,000. The
property tax rate in his area is 2.3%. What is his monthly tax payment?
O A. $343.08
O B. $341.98
C. $345.76
O D. $348.67
Answer: A. 343.08
Step-by-step explanation:
with the property tax rate and monthly tax payment is what were looking for
Which of the following are characteristics of the graph of the absolute value
parent function?
Check all that apply.
PLEASE HELP
The graph of the absolute value parent function will be V-shaped. Then the correct option is C.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
The absolute function is given as
f(x) = | x – h | + k
The graph of the absolute value parent function will be V-shaped.
Then the correct option is C.
More about the absolute function link is given below.
https://brainly.com/question/10664936
#SPJ5
Answer:
A,C,D
Step-by-step explanation:
just took the test
Find the equation of the line that passes through the point (3,14) and is parallel to the following line y = 2/3x + 4
Answer:
y = 2/3x + 12
Step-by-step explanation:
Parallel means the same slope.
Using point-slope formula, you can find the new equation.
y-14 = 2/3 (x-3)
y-14 = 2/3x - 2
y = 2/3x + 12
(PLEASE HELP I WILL GIVE BRAINLIEST!!)
D. At what number of hours do both companies charge the same amount?
E. Look at your answer for Part D. How much money does each company charge for this number of hours?
Answer:
D. 8
E. 130
Step-by-step explanation:
D. set the equations equal to each other than solve and try to get one side with the x's.
10x+50=5x+90
-5x -5x
5x+50=90
-50 -50
5x=40
divide 5 on both sides
x=8
E. plug in 8 as x for either equation
=5(8)+90
=40+90
=130
=10(8)+50
=80+50
=130
I NEED HELP PLEASE!!!!
I NEED HELP PLEASE!!!!
I NEED HELP PLEASE!!!!
I NEED HELP PLEASE!!!!
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Given f(x)=(2x-3)(3x+7), what is the y-intercept
Answer:
(0,-21)
Step-by-step explanation:
The x value of a y intercept is always 0
So we can plug in 0 to the equation to solve for the y intercept
(2*0-3)(3*0+7)
-3*7= -21
y intercept: (0,-21)
Answer:
-21
Step-by-step explanation:
f(x)=(2x-3)(3x+7)
The y intercept is when x=0
f(0) = (0-3) (0+7)
-3*7
-21
The y intercept is -21
Identify the different methods used by the U.S. to deal with international 100 points
conflicts. Cite evidence from the lesson activities to explain each
method. *
Given data set:
6, 2, 7, 12, 6, 1, 7, 1, 9, 7, 8
Find the mean, median, and mode of the data set.
Answer:
see below
Step-by-step explanation:
6, 2, 7, 12, 6, 1, 7, 1, 9, 7, 8
First put the numbers in order from smallest to largest
1,1, 2,6,6, 7, 7, 7, 8, 9, 12
The mean is adding all the numbers and dividing by the number of numbers
( 1+1+ 2+6+6+ 7+ 7+ 7+ 8+ 9+ 12 )/11
66/1 =6
The mean is 6
The median is the middle
There are 11 terms
11/5 = 5.5 so 6 is the middle number
1,1, 2,6,6, 7, 7, 7, 8, 9, 12
7 is the median
Mode is the most often
7 appears three times so it is the mode
A cylinder has a base diameter of 20 meters and a height of 10 meters. What is its
volume in cubic meters, to the nearest tenths place?
