Answer:
α² + β² = 5
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 ( a≠ 0 ) , then
sum of roots = - [tex]\frac{b}{a}[/tex]
product of roots = [tex]\frac{c}{a}[/tex]
x² - x - 2 = 0 ← is in standard form
with a = 1, b = - 1, c = - 2 , then
α + β = - [tex]\frac{-1}{1}[/tex] = 1
αβ = [tex]\frac{-2}{1}[/tex] = - 2
Using the identity
(α + β)² = α² + β² + 2αβ , then
α² + β² = (α + β)² - 2αβ = 1² - 2(- 2) = 1 + 4 = 5
[tex] \large \boxed{ \boxed{\mathrm{ \alpha }^{2} + { \beta }^{2} = 5}}[/tex]
Given : [tex] \alpha + \beta = 1[/tex][tex] \alpha \times \beta = - 2[/tex]let's solve for :
[tex] { \alpha }^{2} + { \beta }^{2} [/tex][tex] { \alpha }^{2} + { \beta }^{2} + 2 \alpha \beta - 2 \alpha \beta [/tex][tex]( \alpha + \beta ) {}^{2} - 2 \alpha \beta [/tex]let's plug the values,
[tex](1) {}^{2} -2 \times ( - 2)[/tex][tex]1 + 4[/tex][tex]5[/tex][tex] \mathfrak{best \: \: of \: \: luck \: \: for \: \: your \: \: assignment}[/tex]
find the volume of the cone. the radius is 5 and the height is 3
Answer:
V= 78.54
Step-by-step explanation:
Which statement has the same information that is given for the proof below
Answer:
D. TU is a midsegment
Step-by-step explanation:
30) Find the sine, cosine, and tangent of
Answer:
sin < C = c/a
cos < C = b/a
tan < C = c/b
Which number could represent point Z
Find each product.
1. 2x(x^2-6x+3)
2. 2a^2(5b^2 + 3ab + 6a + 1)
Given:
The expressions are:
[tex]2x(x^2-6x+3)[/tex]
[tex]2a^2(5b^2+3ab+6a+1)[/tex]
To find:
The product of each expression.
Solution:
According to the distributive property of multiplication over addition, we get
[tex]a(b+c)=ab+ac[/tex]
The first expression is:
[tex]2x(x^2-6x+3)[/tex]
Using distributive property of multiplication over addition, we get
[tex]2x(x^2-6x+3)=(2x)(x^2)+(2x)(-6x)+(2x)(3)[/tex]
[tex]2x(x^2-6x+3)=2x^3-12x^2+6x[/tex]
Therefore, the product of [tex]2x(x^2-6x+3)[/tex] is [tex]2x^3-12x^2+6x[/tex].
The second expression is:
[tex]2a^2(5b^2+3ab+6a+1)[/tex]
Using distributive property of multiplication over addition, we get
[tex]2a^2(5b^2+3ab+6a+1)=(2a^2)(5b^2)+(2a^2)(3ab)+(2a^2)(6a)+(2a^2)(1)[/tex]
[tex]2a^2(5b^2+3ab+6a+1)=10a^2b^2+6a^3b+12a^3+2a^2[/tex]
Therefore, the product of [tex]2a^2(5b^2+3ab+6a+1)[/tex] is [tex]10a^2b^2+6a^3b+12a^3+2a^2[/tex].
The solution to the system below is (1, -3).
2y + x = -5 and y - 3x = -6
Which graph correctly represents this?
The graph correctly represents this system is attached below.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We are given system of equation as;
2y + x = -5
y - 3x = -6
The solution to the system of equations is given as (x, y) = (1, -3).
The solution to the system of equations ploted on the graph is the point where the lines intersect.
The coordinates of the point of where the lines cross are (1, 3).
Learn more about equations here;
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Which expression is equivalent to
(3m² + 5m - 2) + (-2m +18)?
Someone answer ASAP
3m^2 +5m-2-2m+18
3m^2 +3m+16
Answer:
3m² + 3 m + 16
Step-by-step explanation:
( 3 m ² + 5 m - 2 ) + ( - 2m + 18 )
Remove the unnecessary parantheses and rewrite
3 m ² + 5 m - 2 - 2 m + 18
combine like terms
3m² + 5 m - 2 m + 18 - 2
calculate the sum
3m² + 3 m + 16
what is 0.8 divided by 62 as a decimal please help this is a finals
0.8 divided by 62 equals 0.80 or 80 percent (%)
Answer:
0.0129032258
Step-by-step explanation:
I simply did long division.
0.8 divided by 62 = 0.0129032258
PLEASE HELP! WAYYY OVERDUE!!!
Look at the box plots and decide whether each team's distribution is symmetric or skewed negatively or positively.
Answers:
Red = negative skewYellow = symmetricBlue = positive skew================================================
Explanation:
A symmetric distribution is where we have the left half be a mirror copy of the right half. In other words, we have symmetry going on.
For the yellow team, note the distance between Q1 and the median is 1 unit (47-46 = 1), and so is the distance from the median to Q3 (48-47 = 1). So the box portion has perfect symmetry. You should find that the whiskers are also perfectly symmetric as well using a similar technique of finding the distances and comparing them.
Overall, the entire box-and-whisker plot for the yellow team is perfectly symmetric.
---------------
If a distribution isn't symmetric, then it's skewed in some way. If the right side is pulled longer than the left, then we consider it "skewed to the right" aka "positively skewed". So that applies to the blue team. The red team has negative skew because its left tail is longer than the right tail.
Helppp me pleaseee ASAP
Answer:
$856.91 after 7 years
Step-by-step explanation:
Initial investment, P = 500
Interest rate, i = 8% (compounded once a year, i.e. annually)
Number of years, t = 7
Substitute in compound interest formula
Future value,
A = P (1 + 0.08/1) ^(1*7)
= 500 (1.08)^7
= 856.91 (to the nearest cent)
A package of cups contain exactly 6 blue cups.The probability of choosing a blue cup from the package is 3/5.How many of the cups in the package are not blue?
Answer:
There are 4.
Step-by-step explanation:
If there are 6 blue cups, and the blue cups make up 3/5th of the total cups, you can divide 6 by 3/5 to find the total amount of cups, which is 10. Then, you do 10-6 to find how many cups in the package are not blue.
4. Convert the following fractions to decimals
1. 23/100
Answer:
0.23
Step-by-step explanation:
Using either long division or a calculator, divide 23 by 100; you will get the result 0.23.
Answer:
0.23 hope tbis helps :)
Step-by-step explanation:
In 2009, a school population was 1,700. By 2017 the population had grown to 2,500. Assume the population is changing linearly.
Find an equation for the population, P, of the school t years after 2009.
Answer:
P(t) = 100t + 1900
Step-by-step explanation:
∆P = 2500 - 1700 = 800
∆t = 2017 - 2009 = 8
m = ∆p/∆t = 800/8 = 100
b = initial pop = 1900
using slope intercept form
P(t) = 100t + 1900
PLZ HELP IF RIGHT THEN YOU'LL GET BRAINLIEST
One year, the population of a city was 346,000. Several years later it was 339,080. Find the percent decrease.
Answer:
2% decrease
Step-by-step explanation:
Steps to find percent decrease:
- Subtract starting value minus final value
- Divide that amount by the absolute value of the starting value
- Multiply by 100 to get percent decrease
Help pleaseeeeeeeeeeeeeeeeeeeeee ASAP
If charlie bikes at an average speed of 7miles per hour how many hours will take to ride 28 miles
Answer:
It will take him 4 hours.
Step-by-step explanation:
7x4= 28 miles
Find the slope of a line through (4, 5) and (4, -5). Determine if the line is vertical, horizontal, or neither.
Answer:
Its a straight line
Step-by-step explanation:
Question 2 : Two lines meet at a point that is also the endpoint of a ray. Set up and solve an equation to find the value of a.
Answer:
you should draw it in your graph sis
give me some points i have question two
Step-by-step explanation:
[(4096)⁰]⁻⁴ =
a)1/(4096)⁴
b)-4
c)4096
d)1
[(4096)⁰]⁻⁴ = (4096)⁰ = 1
OPTION D
Brainliest goes to whoever answers correctly and explains also if you want extra points answer my other questions
Answer:
Step-by-step explanation:
126 + 44 = 170 ( total for under 25s)
186 - 56 = 130 (online for 25s - 50s)
154 - 58 = 96 ( in stores for aboves 50s)
314 for ONLINE TOTAL
196 for IN STORES TOTAL
510 for TOTAL TOTAL
A = 170
B = 56
C = 96
D = 96 - 58 = 38
E = 314 - 196 = 118
F = 510
Complete the square of the quadratic equation x^2 - 2x - 35 = 0. What is the vertex of the equation?
( )( )
Answer:
Step-by-step explanation:
x^2 - 2x - 35 = 0
Solve for x over the real numbers:
x^2 - 2 x - 35 = 0
Add 35 to both sides:
x^2 - 2 x = 35
Add 1 to both sides:
x^2 - 2 x + 1 = 36
Write the left hand side as a square:
(x - 1)^2 = 36
Take the square root of both sides:
x - 1 = 6 or x - 1 = -6
Add 1 to both sides:
x = 7 or x - 1 = -6
Add 1 to both sides:
Answer: x = 7 or x = -5 as for the vertex plane curve | Cartesian equation x^2 - 2 x - 35 = 0 | vertex (not a possible affine variety)
There are 1,597 souvenir paperweights that need to be packed in boxes. Each box will hold 16 paperweights. How many boxes will be needed?
Answer:
99.8125, or 100
Hope that this helps!
This negative when developed will produce a 4” by 6” photograph. What is the length of each negative, if the width is 24 millimeters
Helpppppppppppp..!!!!!’nnnnmmmm
Step-by-step explanation:
heyYYYYYYYY I HAVE AGREAT APP FOE U. it's called algebrator use that and it'll help ya
no files just type it in thank you.
Answer:
True
Step-by-step explanation:
[tex]3[/tex] · 10 = 30
30 = (3 · 5) + (3 · 5)
30 = (15) + (15)
30 = 30
True
Which values of a and b make the equation true?
Answer:
a=3
b=3
Step-by-step explanation:
(2xy)^4
----------------
4xy
Expand the numerator
2^4 x^4 y^4
---------------------
4xy
Simplify
16 x^4 y^4
---------------------
4xy
We know that a^b / a^c = a^(b-c)
16/4 * x^(4-1) y^(4-1)
4 x^3 y^3
Answer:
a = 3 & b = 3
Step-by-step explanation:
[tex] \small \sf \: \frac{ ( 4 xy )⁴ }{4xy }= 4x {}^{a} y {}^{b} \\ [/tex]
2⁴ x⁴ y ⁴ / 4 xy
simplify
16 x⁴ y⁴ / 4 xy
[tex] \small \sf \frac{a {}^{b} }{a {}^{c} } \: = a {}^{b - c} [/tex]
16 / 4 × x⁴ - x × y⁴ - y
4 x³ y³
Therefore , a = 3 and b = 3
If a test consists of ten multiple choice questions with each permitting a possible answers. How many ways are there in which a student give his answer?
The question isn't correctly given, a possible format is in the comment below, however, the explanation will cover then concept which can be applied to different but similar
Answer:
10048576 ways
Step-by-step explanation:
We are given a question, from which we can choose aby of 4 options, this gives ua 4 possible choices for 1.
This will also apply if we have more than 1 question with the same number of options.
This can be called the product rule, as each possibility is the same of each question given :
Therefore, given 10 questions:
. We have
4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 4^10 = 10048576 ways
Given the function g(x) = 3x² - 5, find the values of t such that g(x) = -7/2t.
Answer:
Step-by-step explanation:
-7/2t = 3x^2 - 5
t = -2(3x^2 - 5)/7
The value of t is given by the equation t = [2/7](5 - 3x²) if the function g(x) = 3x² - 5.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The function:
g(x) = 3x² - 5
To find the value of such that g(x) = -(7/2)t
Equate both the equations:
3x² - 5 = -(7/2)t
After simplification:
t = [2/7](5 - 3x²)
The above equation represents the value of t.
Thus, the value of t is given by the equation t = [2/7](5 - 3x²) if the function g(x) = 3x² - 5.
Learn more about the function here:
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what is the answer pleaseee
Answer:
7
Step-by-step explanation:
In most cases the first step is to create an equation to solve for the missing variable
But in this case we are already given the equation
(7.25h + 5 = 6.5h + 10.25)
All we have to do is solve for h
7.25h + 5 = 6.5h + 10.25
Step 1 subtract 5 from both sides
7.25h = 6.5h + 5.25
Step 2 subtract 6.5h from both sides
0.75h = 5.25
Step 3 divide both sides by .75
h = 7
So at 7 hours the cost will be the same for both instructors
What is the value of u?
Answer:
you on the games
Step-by-step explanation:
Answer:
I think its 58
Step-by-step explanation: