Answer:
[tex]\alpha + \beta = -\frac{b}{a}[/tex]
[tex]\alpha \beta = \frac{c}{a}[/tex]
Step-by-step explanation:
Given
[tex]ax^2 + bx + c = 0[/tex]
[tex]Roots: \alpha \& \beta[/tex]
Required
Show that:
[tex]\alpha + \beta = -\frac{b}{a}[/tex]
[tex]\alpha \beta = \frac{c}{a}[/tex]
[tex]ax^2 + bx + c = 0[/tex]
Divide through by a
[tex]\frac{a}{a}x^2 + \frac{b}{a}x + \frac{c}{a} = \frac{0}{a}[/tex]
[tex]x^2 + \frac{b}{a}x + \frac{c}{a} = 0[/tex]
The general form of a quadratic equation is:
[tex]x^2 - (Sum)x + (Product) = 0[/tex]
By comparison, we have:
[tex]-(Sum)x = \frac{b}{a}x[/tex]
[tex]-(Sum) = \frac{b}{a}[/tex]
Sum is calculated as:
[tex]Sum = \alpha + \beta[/tex]
So, we have:
[tex]-(\alpha + \beta) = \frac{b}{a}[/tex]
Divide both sides by -1
[tex]\alpha + \beta = -\frac{b}{a}[/tex]
Similarly;
[tex]Product = \frac{c}{a}[/tex]
Product is calculated as:
[tex]Product = \alpha * \beta[/tex]
So, we have:
[tex]\alpha * \beta = \frac{c}{a}[/tex]
[tex]\alpha \beta = \frac{c}{a}[/tex]
Answers of these two questions??
Answer:
1:second ans
2:fourth ans!
Step-by-step explanation:
brainlist
how to write 970 014 in words
THE FUNCTION! f(x) = x^2+4 is defined over the interval (-2,2). If the interval is dived into n equal parts what is the height of the right endpoint of the kth rectangle?
f(x) = x^2+4 is defined over the interval (-2,2). If the interval is dived into n equal parts the height of the right endpoint of the kth rectangle is mathematically given as
H endpoint = -2+k x5/n. Option A is correct
what is the height of the right endpoint of the kth rectangle?
Generally, the equation for the function is mathematically given as
f(x) = x^2+4
interval is divided = 5/n
endpoint =k x 5/n
therefore,
H endpoint = -2+k x5/n
In conclusion, the height of the right endpoint of the kth rectangle is
H endpoint = -2+k x5/n
Read more about rectangle
https://brainly.com/question/16167300
#SPJ1
The graph of the quadratic function y=-x^2-2x+3.What statement about the graph is true.select all that apply.
Answer:
the graph has an x intercept at 1, 0 has a vertex of -1,4 axis of symmetry x = -1 relative min of -1, 4has the roots of 3 and 1Can you help me solve this it’s pretty easy but for you guys
Answer:
x - 81 = 321
adding 81 on both sides
x-81+81= 321+81
x= 402
Answer:
402
Step-by-step explanation:
81+321=402-321=81 n=402
please say this question answer please
Answer:
4
Step-by-step explanation:
Its 4 because x= 4
Find area using law of sines
Answer:
4
Step-by-step explanation:
HOPE THIS HELPED!!! I TRIED AND REMEMBERED
) Jolie draws a map of her neighborhood on a
coordinate plane. She draws her house at a point in
Quadrant II.
OU
Select all the points that could represent the location of
Jolie's house?
a.) (0,5)
b.) (1, -4)
c.) (-2, 0)
d.) (-4.71
Pls help and explain if you can
Can some one please help me and explain how you got the answer?
Answer:
Yes number 5 is, they are proportional because y is coresponding to x by multiplying by 1/5
No number 6 isn't, you can't go from 3 to 1 and 7 to 3
Answer:
5. Proportional & 6. Not Proportional
Step-by-step explanation:
Proportional relationships = x and y increase at the same rate
5. all increases by x2
6. increases at different rates
Ο Α.
B.
C.
D.
SUBMIT
Plzzzz helpppp
Answer:
c
Step-by-step explanation:
Create two equivalent fractons for 3/4
Answer:
6/8 and 9/12
Step-by-step explanation:
You can find any by multiplying numerator and denominator by any given number. The number multiplied has to be the same for the top and the bottom
1. Number is 2
3/4 * 2/2 = 6/8 (3*2 = 6 and 4*2 = 8)
2. Number is 3
3/4*3/3 = 9/12 (3*3 = 9 and 3*4 = 12)
A company has a new process for manufacturing large artificial sapphires. In a trial run, 37 sapphires are produced. The mean weight for these 37 gems is 6.75 carats, and the sample standard deviation is 0.33 carat. Obtain a 95% confidence interval for the true mean weight of all sapphires produced by the new process. Interpret your results in the context of the problem. State the margin of er
Answer:
The margin of error is of 0.11 carats.
The 95% confidence interval for the true mean weight of all sapphires produced by the new process is between 6.64 and 6.86 carats. The interpretation is that we are 95% sure that the true weight of all sapphires produced by the company using the new process is between these two values.
Step-by-step explanation:
We have the standard deviation for the sample, which means that we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 37 - 1 = 36
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 36 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.05}{2} = 0.975[/tex]. So we have T = 2.0281
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.0281\frac{0.33}{\sqrt{37}} = 0.11[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The margin of error is of 0.11 carats.
The lower end of the interval is the sample mean subtracted by M. So it is 6.75 - 0.11 = 6.64 carats
The upper end of the interval is the sample mean added to M. So it is 6.75 + 0.11 = 6.86 carats.
The 95% confidence interval for the true mean weight of all sapphires produced by the new process is between 6.64 and 6.86 carats. The interpretation is that we are 95% sure that the true weight of all sapphires produced by the company using the new process is between these two values.
2. [5pts] The Pew Research Group conducted a poll in which they asked, "Are you in favor of, or opposed to, executing persons as a general policy when the crime committed while under the age of 18?" Of the 580 Catholics surveyed, 180 indicated they favored capital punishment; of the 600 seculars surveyed, 238 favored capital punishment. Is there a significant difference in the proportion of individuals in these groups in favor of capital punishment for persons under the age of 18? Use the ???? = 0.01 level of significance. Show all work.
Answer:
See below for answers and explanations
Step-by-step explanation:
Here, we are comparing two proportions of a large sample size. Therefore, conducting a 2-proportion z-test is appropriate. Conditions are already assumed, so we can conduct the test.
We are testing our null and alternate hypotheses which are:
H: p1=p2 (there is no difference)
Ha: p1≠p2 (there is a difference)
Given:
x1=180
n1=580
x2=238
n2=600
p1=180/580=0.31
p2=238/600=0.4
p=(180+238)/(580+600)=418/1180=0.35
Use the formula to calculate the z-statistic:
[tex]Z=\frac{p_1-p_2}{\sqrt{p(1-p)(\frac{1}{n_1}+\frac{1}{n_2})}}[/tex]
[tex]Z=\frac{0.31-0.4}{\sqrt{0.35(1-0.35)(\frac{1}{580}+\frac{1}{600})}}[/tex]
[tex]Z=-3.24[/tex]
Calculate p-value (note that this is two-sided):
1) normalcdf(-1e99,-3.24)=5.977105194*10^-4
2) Since this is a two-sided test, we double it to get p=0.001195421
Conclusion: Since 0.0012<0.05, we reject the null hypothesis and conclude that there is a significant difference in the proportion of individuals in these groups in favor of capital punishment for persons under the age of 18 because our p-value is extremely low.
JKLM is a rectangle. Find the value of x.
Help me fast please
Answer:
x = 10
Step-by-step explanation:
3x + 38 = 7x - 2
subtract 3x from both sides ogf the equation:
38 = 4x - 2
add 2 to each side:
40 = 4x
divide both sides by 4:
x = 10
e^2=36. solve for e
e = ± ( )
Answer:
solution given:
e^2=36
e=±√36=±6 is your answer
Barbara was asked to create a set of numbers that contained only natural numbers. Which of the sets
does NOT contain only natural numbers?
24
А
{31, 15, 23, 4, 300,
20
B
19, 100, 4, 12, 6,
c {5, 3, 8, 14, 0,
1, 21
D 22, 7, 9, 11, 28, 4.0)
Answer:
D
Step-by-s:
Ya que el 4.0 no es un número natural, es un número decimal (Z - número entero).
Since 4.0 is not a natural number, it is a decimal number (Z - whole number).
Evaluate 12 ÷ 2 × 6.
Answer:
[tex]36[/tex]
Step-by-step explanation:
1) Simplify 12 ÷ 2 to 6.
[tex]6 \times 6[/tex]
2) Simplify.
[tex]36[/tex]
therefor, the answer is 36.
The center of a circle is at (–4, 2) and its radius is 9.
What is the equation of the circle?
(x−4)2+(y+2)2=3
(x+4)2+(y−2)2=3
(x−4)2+(y+2)2=9
(x+4)2+(y−2)2=9
(x−4)2+(y+2)2=81
(x+4)2+(y−2)2=81
Answer: fourth choice
Step-by-step explanation:
Answer:
formula for circle is
(x-h)^2+(y-k)^2=r^2
so the answer is sixth
The multiplicative inverse of -2¹/₇ is
In the diagram, KLMN is a rectangle, and the two shaded regions are squares. If the length of KL is 6 centimeters, and the length of KN is 14 centimeters, which is closest to the length of ST in centimeters?
Answer:
15.2cm
Step-by-step explanation:
From the given diagram;
KN = SN = 14cm
KL = NT = 6cm
Required
ST
Using the Pythagoras theorem;
ST² = SN² + NT²
ST² = 14² + 6²
ST² = 196 + 36
ST² = 232
ST = √232
ST = 15.2cm
Hence the length of ST is 15.2cm
Pls help with this question! Its due today!
Answer:
down below.
Step-by-step explanation:
straight lines are always 180.
[tex]x+34+2x+2=180\\3x+36=180\\3x+36-36=180-36\\3x=144\\3x/3=144/3\\x=48[/tex]
6789 divided by 89.65
Step-by-step explanation:
75 . 727 is your answer
hope it is helpful to you
Find the 9th term of the geometric sequence 10, 40, 160,
ANSWER ASAP 50 points
Step-by-step explanation:
[tex]U _{ {9}^{th} } \: term = U _{ {1}^{st} } {r}^{(n - 1)} \\ = 10 \times {4}^{(9 - 1)} \\ = 655360 \\ {9}^{th} \: term \: is \: 655360[/tex]
f(x)=2x^ 2 +9x Find f(10)
X+4y=8 and 3x+4y=0 find the slope-intercept form
Answer:
Step-by-step explanation:
Slope intercept form: y =mx + c
1) x + 4y = 8
4y = -x + 8
Divide the equation by 4
[tex]\frac{4y}{4}=\frac{-x}{4}+\frac{8}{4}\\\\y = \frac{-1}{4}x + 2[/tex]
Here, m = -1/4 and y-intercept = 2
2) 3x + 4y = 0
4y = -3x
Divide the equation by 4
y = [tex]\frac{-3}{4}x[/tex]
If ZP and ZQ are complementary angles,
mZP = 7x + 3, and mZQ = 16x – 5, find mZP.
A. 31°
B. 34°
C. 56
D. 59°
A lawyer has 4 clients to meet. In how many different ways can he make
his rounds if he meets each client once?
Answer:24
Step-by-step explanation: 4x3x2x1
The product of a whole number 'n' with every whole number until 1 is called the factorial. The number of ways the lawyer can meet the client is 24 or 4!.
What is a factorial?The product of a whole number 'n' with every whole number until 1 is called the factorial. The factorial of 4 is, for example, 43221, which equals 24.
A lawyer has 4 clients to meet. The number of ways the lawyer can meet the client is 4!.
Number of ways = 4! = 4×3×2×1 = 24
Hence, the number of ways the lawyer can meet the client is 24 or 4!.
Learn more about Factorial:
https://brainly.com/question/16674303
#SPJ2
Wesley walked 11 miles in 4
hours.
If he walked the same distance every hour,
how far did he walk in one hour?
Write your answer:
Using a whole number of miles and a whole number of feet
Answer:
3 miles
58080 feet
Step-by-step explanation:
Could someone please do this for me ASAP this is for math!
Answer:
Step-by-step explanation:
[tex]x^{2}[/tex]+x-20
use FOIL
(x - 4)(x+5)
x-4=0
x+5=0
4 and negative 5 are the factors
plz help me on this geometry i suck plz i will give brainly
Answer:
The shed that Vicky and Jim will use is the second shed (length | 4 [] width | 2 1/4), because the height length is 7.
4 x 2.25 = 9
63 divided by 9 = 7
(First Shed) 5 x 2.20 = 11
66 divided by 11 = 6
7 > 6
7 = Height of First Shed
The first shed will be used to store the new lawnmower since it is the taller shed.