Use quadratic regression to find a function that fits the following points. (-2,-16), (3,11), (0,2).
Answers
Answer:
y = -1.2x² +6.6x +2
Step-by-step explanation:
The quadratic regression function of a calculator or spreadsheet can do this for you. The resulting function is ...
y = -1.2x² +6.6x +2
_____
If you want to do this by hand, put the given (x, y) values into the formula ...
ax² +bx +c = y
and solve the resulting system of equations.
The third point tells you c=2, so you can simplify the system of equations to ...
a(-2)² +b(-2) +2 = -16 ⇒ 4a -2b = -18 ⇒ 2a -b = -9
a(3)² +b(3) +2 = 11 ⇒ 9a +3b = 9 ⇒ 3a +b = 3
Adding these equations together gives ...
(2a -b) +(3a +b) = (-9) +(3)
5a = -6 . . . . . . . . simplify
a = -1.2 . . . . . . . divide by 5
b = 3 -3a = 3 -3(-1.2) = 6.6 . . . . from the second equation
Now we know the coefficients are a=-1.2, b=6.6, c=2, so the function is ...
y = -1.2x² +6.6x +2
Related Questions
3y + 2 = 4x , x+ 5y = 3 what is the solution to the system of equations shown above? (in fraction form)
Answers
So 3y+2=4x
<=>3y+2=4(3-5y)
<=>3y+2=12-20y
<=>3y+20y=12-2
<=>23y=10
<=>y=10/23 => x=3-5(10/23)=19/23
Ok done. Thank to me :>
Answer:
19/23, 50/23
Step-by-step explanation:
We can take the first equation and isolate the x:
x + 5y = 3 ⇒ -5y ⇒
x = 3 - 5y.
Then we can substitute the x in the first equation by this:
3y + 2 = 4(3-5y) ⇒
3y + 2 = 12 - 20y ⇒ +20y
23y + 2 = 12 ⇒ -2
23y = 10 ⇒ ÷23
y = [tex]\frac{10}{23}[/tex]
Then we can add the value of y into the equation equaling x we made:
x = 3 - 5([tex]\frac{10}{23}[/tex]) ⇒
x = 3 - [tex]\frac{50}{23}[/tex] ⇒
x = [tex]\frac{19}{23}[/tex]
Hope this helps! :)
Find the measure of
Answers
Answer:
120° , 80° , 90°
Step-by-step explanation:
The sum of the inner angles of a triangle is one hundred and eighty degrees. and as the diagram shows, The AB is equal to AC so angle ABC is equal to angle ACB so Angle A is 180°-(30°×2)=120°
you can get the second follow the above steps
and the third one is 2x+x+x=180°
so 4x=180°
so x=45°
so 2x=90°
Q.17) Given info:- In ∆ABC , AB = AC where, angle A = x°, angle B = 30°and angle C = ?°. Find the value of X in triangle ABC ?
Explanation:
Given that
ABC is a triangle
angle A = x°
angle B = 30°
angle C = ?°
And
AB =AC
We know that
In a triangle Angles opposite to equal sides are equal.
⇛Opposite angle to AB = Opposite angle to AC
⇛angle B = angle C
⇛angle B & C = 30°
We know that
The sum of all angles in a triangle is 180°
⇛ angle A + angle B + angle C = 180°
⇛30° + x° + 30° = 180°
⇛60° + x° = 180°
⇛x° = 180°÷60 = 180°:60
⇛x° = 180°/60
⇛x° = 3°
Now,
⇛angle A = x = 3°
⇛angle B = 30°
⇛angle C = 30°
Answer: The value of x for the given problem is 3°
Q.18) Given info:- In ∆ABC , AB = AC where, angle A = x°, angle B = 50°and angle C = ?°. Find the value of X in triangle ABC ?
Explanation:
Given that
ABC is a triangle
angle A = x°
angle B = 50°
angle C = ?°
And
AB =AC
We know that
In a triangle Angles opposite to equal sides are equal.
⇛Opposite angle to AB = Opposite angle to AC
⇛angle B = angle C
⇛angle B & C = 50°
We know that
The sum of all angles in a triangle is 180°
⇛ angle A + angle B + angle C = 180°
⇛ x° + 50°+50° = 180°
⇛x° + 100 = 180°
⇛x° = 180°÷100° = 180°:100°
⇛x° = 180°/100
⇛x° = 18°
Now,
⇛angle A = x = 18°
⇛angle B = 50°
⇛angle C = 50°
Answer: The value of x for the given problem is 18°
Q.19) Given info:- In ∆ABC , AB = AC and angle A = 2x°, angle B = x°, angle C = x°. Find the value of X in triangle ABC ?
Explanation:
Given that
ABC is a triangle
angle A = 2x°
angle B = x°
angle C = x°
And
AB =AC
We know that
In a triangle Angles opposite to equal sides are equal.
⇛Opposite angle to AB = Opposite angle to AC
⇛angle B = angle C
⇛angle B & C = x°
We know that
The sum of all angles in a triangle is 180°
⇛ angle A + angle B + angle C = 180°
⇛x° + 2x° + x° = 180°
⇛2x° + 2x° = 180°
⇛4x° = 180°
⇛x° = 180°÷4 = 180°:4
⇛x° = 180°/4
⇛x° = 45°
Now,
⇛angle A = 2x = 2(45) = 90°
⇛angle B = 45°
⇛angle C = 45°
Answer: The value of x for the given problem is 45°
can someone please help me
Answers
Answer:
135=9r
Step-by-step explanation:
"product" means multiplication.
Not much needed to be explained
if a temperature is 2 celcious and falls by 7 celcious what is your new temperature
Answers
Answer:
-5°C
Step-by-step explanation:
if you want to subtract a smaller number from a bigger number you can consider the number line attached below. I have marked 2 and -5 with blue ink.
When you use a number line, firstly see where your first number lies on the number line, in this case 2 is your first number. If you have to subtract a number, you have to move left and if you have to add a number you have to move right on the number line.
As you have to subtract 7 from 2, move 7 spaces to the left counting zero as a number. If you count 7 spaces to the left, it will end at -5.
So your answer is -5°C.
Hope this helps!!
A flight from Boston to London only took 5 hours because of a strong tailwind. The flight back to Boston against the same wind took 6 hours. What was the speed of the wind if the speed of the plane in still air is 550 mph?
Answers
If the flight back to Boston against the same wind took 6 hours. The speed of the wind if the speed of the plane in still air is 550 mph is 50 mph.
How to find the speed of the plane?Given data:
Boston to London = 5 hours
Flight back to Boston = 6 hours
Still air = 550 mph
Using this formula
Speed (s) = Distance /Time
We need to formula an equation that will be used to find the speed
Equation: (550 + s)5 = (550 - s)6
So,
Let s represent the speed
(550 + s)5 = (550 - s)6
2750 +5s = 3300 - 6s
Collect like terms
6s +5s = 3300 - 2750
11s = 3300 - 2750
11s = 550
Divide both side by 11s
s= 550/11
s = 50mph
Therefore the speed of the plane is 50mph.
Learn more about speed here:https://brainly.com/question/28439044
#SPJ1
Factor the expression x^2+9+8
Answers
Answer:
2+17
x^{2}+17
x2+17
Step-by-step explanation:
Answer:
[tex](x+1)(x+8)[/tex]
Step-by-step explanation:
Hi there!
[tex]x^2+9x+8[/tex]
We must ask ourselves: What two factors of 8 add up to 9? That would be 1 and 8.
1 × 8 = 8 and 1 + 8 = 9.
Rewrite the expression accordingly:
[tex](x+1)(x+8)[/tex]
I hope this helps!
Rachel withdraws $19 from her bank account once each day for three days. What integer represents the change in the amount in the account? Find the integer that would represent the change in the amount in the account if Rachel deposits $19 into her bank account once each day for three days.
Answers
Answer:
How much did she start with tho???
Step-by-step explanation:
if [tex]a_{1}[/tex]=4 and [tex]a_{n}[/tex]= [tex]5a_{n-1}[/tex]-1 then find the value of [tex]a_{3}[/tex]
Answers
========================================================
Explanation:
The first term is 4 because of the notation [tex]a_1 = 4[/tex]
To get the second term, we'll use the recursive equation [tex]a_n = 5(a_{n-1})-1[/tex] which basically says [tex]\text{nth term} = 5*(\text{previous term})-1[/tex]. To get the second term, we'll multiply the first term by 5, then subtract off 1.
2nd term = 5*(1st term) - 1
2nd term = 5*4 - 1
2nd term = 19
This means [tex]a_2 = 19[/tex]
We repeat this process again to find the third term [tex]a_3[/tex]
[tex]a_n = 5*(a_{n-1})-1\\\\a_3 = 5*(a_{3-1})-1\\\\a_3 = 5*(a_{2})-1\\\\a_3 = 5*(19)-1\\\\a_3 = 95-1\\\\a_3 = \boldsymbol{94}\\\\[/tex]
The third term is 94
Coordinate plane .........
Answers
Answer:
The answer is the blue dot
Step-by-step explanation:
You should remember that the x goes first in (x,y).
What number should go in the space?
Multiplying by 0.51 is the same as decreasing by _____%.
Answers
Answer:
49
Step-by-step explanation:
x multiplied by 0.51 is the same as 49% of x
please help me with this question!!
Answers
Answer:
\(x = 1\)
Step-by-step explanation:
Based on the given conditions, formulate: \(x = 12 \div 12\)
Cross out the common factor:\(x = 1\)
Answer: \(x = 1\)
Which equation represents the sentence?
Six less than a number is half the number.
n−6=n2
n2−6=n
6−n=n2
6−n2=n
Answers
Answer:
It is n-6=n/2.
Step-by-step explanation:
I took the quiz.
Determine if the table represents a linear function, quadratic function, or exponential function.
Answers
Answer:
please no of one is not function so sorry
I need this answer!!
Answers
[tex] \rm \frac{2}{36} = \frac{3}{x} [/tex]
[tex] \rm\frac{1}{18} = \frac{3}{x} [/tex]
[tex] \rm x = 3 \times 18[/tex]
[tex] \rm x = \bold{54(d.)}[/tex]
3/7×2 5/6=
i just dont know what the answer is like my brain is really bad in the mornings
Answers
Answer:
3/7*2 5/6= 17/14 = 1 3/14 ≅ 1.2142857
Step-by-step explanation:
Conversion a mixed number 2 5/6 to a improper fraction: 2 5/6 = 2 5/6 = 2 ·6+ 5/6 = 12 + 5/6 = 17/6 1) Multiply the whole number 2 by the denominator 6. Whole number 2 equally 2 * 6/6 = 12/6
2) Add the answer from previous step 12 to the numerator 5. New numerator is 12 + 5 = 17
3) Write a previous answer (new numerator 17) over the denominator 6.
Two and five-sixths is seventeen sixths Multiple: 3/7 * 17/6 = 3 · 17/7 · 6 = 51/42
= 17 · 3/14 · 3 = 17/14. then you simplify.
I hope this helps
Mr. Holland is leaning a ladder against the side of his house to repair the roof. The top of the ladder reaches the roof, which is 3 meters high. The base of the ladder is 4 meters away from the house, where Mr. Holland's son is holding it steady. How long is the ladder? meters
Answers
Answer:
use Pythagoras theorem a^2+b^2 = c^2 where c is the longest side of the triangle (hypotenuse)
3^2 + 4^2 = c^2 (c is the length of the ladder)
9 + 16 = c^2
25 = c^2
c = √25 (square root)
c = 5
Answer:
blahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Step-by-step explanation:
what goes around always come back around
For f(x) = -5x+10, what us the value of x for which f(x) = 35
Answers
Answer:
x= -5
Step-by-step explanation:
f(x)= -5x +10
35= -5x +10
35-10 =-5x
25/-5 =x
x= -5
HUrrryyy i need help!!!!!
Answers
Answer:It is D Step-by-step explanation:
I need help a I don't know what to do
Answers
Answer:
Look at my solution
Researchers will conduct a study of the television-viewing habits of children. They will select a simple random sample of children and record the number of hours of television the children watch per week. The researchers will report the sample mean as a point estimate for the population mean. Which of the following statements is correct for the sample mean as a point estimator?
(A) A sample of size 25 will produce more variability of the estimator than a sample of size 50.
(B) A sample of size 25 will produce less variability of the estimator than a sample of size 50.
(C) A sample of size 25 will produce a biased estimator, but a sample size of 50 will produce an unbiased estimator.
(D) A sample of size 25 will produce a more biased estimator than a sample of size 50.
(E) A sample of size 25 will produce a less biased estimator than a sample of size 50.
Answers
Using the Central Limit Theorem, it is found that the correct option is:
(A) A sample of size 25 will produce more variability of the estimator than a sample of size 50.
By the Central Limit Theorem, for a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], considering the sampling distribution of sample means of size n, the measure of variability is the standard error, which is given by:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
Hence, the higher the sample size, the lower the variability, and option A is correct.A similar problem is given at https://brainly.com/question/24663213
Help me pls I don't get it
Answers
Answer:
maybe A
Step-by-step explanation:
Use point-slope form to write the equation of a line that passes through the point
(-3, -16) with slope – 2/1
Answers
Answer:
y= -2x-22.
Step-by-step explanation:
1) the slope-interception common form is y=s*x+i, where 's' and 'i' are the slope and interception, unknown numbers;
2) if x₁= -3; y₁= -16, and s=-2, then the equation of the required line can be written in the point-interception form y-y₁=s(x-x₁); ⇔ y+16= -2(x+3);
3) the required equation in slope-interception form is:
y+16= -2x-6; ⇒ y= -2x-22.
note, the provided solution is not the only and shortest way.
Help please I really don’t understand due in 3 days
Answers
Answer:
x < 4
Step-by-step explanation:
3x - 3 < 9 ( add 3 to both sides )
3x < 12 ( divide both sides by 3 )
x < 4
Answer:
x < 4.
Step-by-step explanation:
3x - 3 < 9
Add 3 to both sides:
3x < 9 + 3
3x < 12
Divide both sides by 3:
x < 4.
28 is less than 35 by what %?
35 is greater than 28 by what %?
Answers
Answer:
28 is less than 35 by 20%
35is greater than 28 by 20%
At what values of x, does f(x) = 0?
A. 2
B. 8
C. -4
D. 0
E. -1
F. 4
Answers
Answer:
D : 0
Step-by-step explanation:
f(0) = 0
1) Round 26.728 to the nearest integer
What
Answers
What is the answer to this question?
Answers
–3x + 4y = 8
-4x + 3y=-6
are these Graphs perpendicular, parallel, or niether.
Answers
Answer:
Step-by-step explanation:
Q.no 21 solve it.
Plz. Plz
Answers
Answer:
Hamm i don't know sorry a want yo help You Buy a can't because a don't know sorry
can somebody help like rn
Answers
Answer:
4
Step-by-step explanation:
(25-18+5)/4=4
(insert the variables)