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]
synthetic division problem... pls help asap
El profesor Héctor y sus alumnos organizaron una excursión a
la Ciudad de México. Visitarán el Centro Histórico, el Castillo de
Chapultepec y el Museo de Antropologia. El costo del transporte
por alumno es de $310.75 y no incluye alimentos.
a) Para pagar el transporte, el profesor Héctor tiene que juntar
el dinero de los 37 alumnos que participaran en la excursion
¿Cuánto dinero debe reunir?
Answer:
$8.39 por pe rsona
Step-by-step explanation:
If the terminal point of ø is (1,0), what is tan ø?
Given:
The terminal point of [tex]\phi[/tex] is (1,0).
To find:
The value of [tex]\tan\phi[/tex].
Solution:
If the terminal point of [tex]\theta [/tex] is (x,y), then
[tex]\tan \theta=\dfrac{y}{x}[/tex]
It is given that the terminal point of [tex]\phi[/tex] is (1,0).
Here, x-coordinate is 1 and the y-coordinate is 0. Using the above formula, we get
[tex]\tan \phi=\dfrac{0}{1}[/tex]
[tex]\tan \phi=0[/tex]
Therefore, the value of [tex]\tan \phi[/tex] is 0.
Find two integers whose sum is 5 and product is -66 TWO INTEGRES
NOT 1 TWO
Answer:
-6 and 11
Step-by-step explanation:
The only factors of 66 are 11, 6, 2 and 3
11*6 is the only pair whose product is 66
The difference betwen 11 and 6 is 5
11 must be positive and 6 negative since the sum is positve
Use the completing the square method to transform the equation x2 + 2x = 13 into an equation of the form (x + a)2 = b, where ɑ and b are real numbers What are the values of ɑ and b?
Answer:
(x+1)² = 14
a = 1, b = 14
Step-by-step explanation:
Given the equation, x² + 2x = 13
We are to use the completing the square method to express in the form
(x + a)² = b
x² + 2x = 13
Add the square of half of the coefficient of x to both sides
Coefficient of x = 2
Half of the coefficient of x = 2/2
Square of the result = (2/2)²
Square of the result = 1²
Add (1/2)² to both sides
x² + 2x + (1)² = 13 + (1)²
(x+1)² = 13 + 1
(x+1)² = 14
Compare with (x+a)² = b
a = 1 and b = 14
ABCD is a trapezium in which AB ∥ CD, AD ⊥ DC, AB = 4 cm, BP = 7 cm and DC = 25 cm, then area of the trapezium is 45.
Question:
ABCD is a trapezium in which AB ∥ CD, AD ⊥ DC, AB = 4 cm, BP = 7 cm and DC = 25 cm, then area of the trapezium is ____.
Answer:
101.5cm²
Step-by-step explanation:
The figure for the trapezium ABCD is attached to this response.
To find the area of the trapezium, we use the formula for calculating the area of a trapezium given as follows;
A = [tex]\frac{1}{2}[/tex] x (a + b) x h ------------------(i)
Where;
A = area of the trapezium
a and b are the parallel sides of the trapezium
h = height of the trapezium.
As shown in the figure,
AB and CD are parallel
Therefore, we can say that;
a = AB
b = CD
Also, from the figure,
The height of the trapezium is BP
Therefore, we can say that;
h = BP
We know that;
a = AB = 4cm
b = CD = 25cm
h = BP = 7cm
Substitute these values of a, b and h into equation (i) as follows;
A = [tex]\frac{1}{2}[/tex] x (4 + 25) x 7
A = [tex]\frac{1}{2}[/tex] x (29) x 7
A = 101.5
Therefore, the area of the trapezium is 101.5cm²
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
Math help please FAST
Answer:
180
60
40
Step-by-step explanation:
Angles in a triangle add up to equal 90 degrees
Equilateral - has all congruent angles and congruent sides
If a triangle has 3 angles and the angles add up to equal 180 then the measure of one angle in an equilateral = 180 / 3 = 60
Bisect means to split into to equal parts
So if you bisect an 80 degree angles you will have two 40 degree angles. ( Because 80/2 = 40 )
Answer:
40°
Step-by-step explanation:
bisecting an angle gives equal angles equivalent to half the size of the bisected angle for each of them
Write an equation of a line that passes through (3, -1) and is perpendicular to y = 6x - 4. Show work.
I NEED THIS FAST LIKE PLEASEE HELP
Answer:
y = -1/6x - 1/2
Step-by-step explanation:
y = -1/6x + b
-1 = -1/6(3) + b
-1 = -1/2 + b
-1/2 = b
Which type of function best models the given data?
Answer:
3)
Step-by-step explanation:
Draw the graph and youll see
Answer:
Exponential growth function
Step-by-step explanation:
It multiplies by 3 each time
The formula for centripetal acceleration, a, is given by this formula, where v is the velocity of the object and r is the object’s distance from the center of the circular path: a=v^2/r . Solve the formula for r.
Answer:
r = V^2/a
Step-by-step explanation:
Here, we want to write the formula for r
What this simply mean is that we want to make r the formula subject
We have this as follows;
a = V^2/r
r = V^2/a
Min had some cards
He gave 1/2 of them to bill.
Bill gave 1/3 of those to Sam.
Sam gave Min 2 cards back and kept 6.
How many cards did Min have in the end?
Answer:
26 cards
Step-by-step explanation:
Sam:
⅓=2+6
=8
Bill:
3/3=3×8
=24
3/3=½
24+2=26
Now ,Min have 26 cards.
hope it help
The function C(x) = 400x - 0.2x ^ 2 represents the total costs for a company to produce a product, where in dollars and x is the number of units sold. Which statement is true? is the total cost
Answer: it b y’all
Step-by-step explanation: I took the test
Answer:
B
Step-by-step explanation:
To determine the maxima and minima of the polynomial, differentiate the given based on x and equate to 0. C(x) = 400x - 0.2x² dC(x) / dt = 400 - 0.4 x = 0 The value of x is 1000. This is the value of the maxima. As the value of C(x) continously becomes lesser as the value of x is set higher, the minima is not identified. Substitute x to the original equation, C(x) = (400)(1000) - 0.2(1000²) = $ 200,000Thus, the answer is letter B.
Which one is it?
a) <
b) =
c) >
Answer:
A: less that
Step-by-step explanation:
4( 14)+3
36+3= 39
39 (2+9)6-7
(11)6-7
66-7
59
39<59
factorize: 9x^2 - 24xy + 16y^2
9x²-24xy+16y²
(3x)²-2.(3x)(4y) +(4y)²
(3x-4y)²
(3x-4y)(3x-4y)
Answer:
[tex](3x -4y)^2[/tex]
Step-by-step explanation:
[tex]9x^2 - 24xy + 16y^2 = (3x)^2 - 24xy + (4y)^2[/tex]
[tex]=(3x)^2 -2(3x \times 4y) + (4y)^2\\[/tex]
a = 3x , b = 4y . The expression [tex]a^2 - 2ab + b^2 = (a-b)(a-b) =(a-b)^2[/tex]
[tex]=(3x -4y)(3x - 4y)[/tex]
[tex]9x^2 - 24xy + 16y^2 = (3x -4y)^2[/tex]
Find the surface area of the prisms below to create a riddle then scan the qr code to answer the riddle round the nearest tenth if necessary
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete, as the prisms and the riddle are not given.
The riddle aspect of the question cannot be attempted, else there are clues.
So, I will give a general rule on how to calculate the surface areas of prisms.
For rectangular prisms, the surface area is:
[tex]Area = 2*(Length * Width + Length * Height + Width * Height)[/tex]
For the attached rectangular prism, the area is:
[tex]Area = 2 *(10*11 + 11 * 15 + 10 * 15)[/tex]
[tex]Area = 2 *(425)[/tex]
[tex]Area = 850m^2[/tex]
For triangular prisms, the surface area is:
[tex]Area = L + 2 * B[/tex]
Where
[tex]L \to[/tex] Lateral Area
[tex]B \to[/tex] Base Area
The area of the attached triangular prism is:
[tex]L = (a + b + c) * h[/tex]
[tex]L = (6 + 8 + 10) * 12[/tex]
[tex]L = 24 * 12[/tex]
[tex]L = 288[/tex]
[tex]B = \frac{1}{2} * bh[/tex]
[tex]B = \frac{1}{2} * 6 * 8[/tex]
[tex]B = 24[/tex]
So, we have:
[tex]Area = L + 2 * B[/tex]
[tex]Area = 288 + 2 * 24[/tex]
[tex]Area = 288 + 48[/tex]
[tex]Area = 336ft^2[/tex]
write the standard form of the equation of a circle with a radius of 1 and a center of (-7,1)
Answer:
(x + 7)² + (y - 1)² = 1
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (- 7, 1) and r = 1 , then
(x - (- 7) )² + (y - 1)² = 1² , that is
(x + 7)² + (y - 1)² = 1
What is the value of f(5) in the function below?
f(x) = 1/4 •2x
A. 32
B. 16
C. 8
D.5/2
Which expression represents the algebraic phrase “nine times a number plus thirteen”?
9 minus y + 13
9 + y minus 13
9y + 13
13y + 9
Answer:
9y + 13
Step-by-step explanation:
a number would best represent as a variable (doesn't matter which letter)
plus thirteen would represent an addition to 13
please help! 10 points, thank you
Answer:
261.5 ft^2
Step-by-step explanation:
Surface Area of a rectangular prism = Length x Width x Height
= 8.5ft x 6ft x 5.5ft
= 261.5 ft
Simplify the radical.
Answer:
See below for answers
Step-by-step explanation:
Problem 7: [tex]\sqrt{125}=\sqrt{25*5}=\sqrt{25}\sqrt{5}=5\sqrt{5}[/tex]
Problem 8: [tex]\sqrt{200}=\sqrt{100*2}=\sqrt{100}\sqrt{2}=10\sqrt{2}[/tex]
PLEASE I NEED THE ANSWER DON'T IGNORE MY QUESTION!!! Solve for X for the following
Answer:
1. 51
2. 8
3. √2 or 1.41
Step-by-step explanation:
using pythagorean theorem
Answer:
1) x = 51
2) x = 8
3) x = [tex]\sqrt{2}[/tex] or approximately 1.4142
Step-by-step explanation:
These are simple Pythagorean theorem questions. Remember, the Pythagorean theorem states that [tex]a^2+b^2=c^2[/tex], where a and b represent the legs of the triangles, and c represents the hypotenuse, the side opposite to the 90 degree angle in the triangle. Now simply use the values of a, b, or c, depending on what is given, to solve for the missing side x.
In question 1, you have two legs with sides 45 and 24. Therefore use the Pythagorean theorem where a and b equal 45 and 24 respectively.
[tex]45^2+24^2 = x^22025+576 = x^22601 = x^2x = 51[/tex]
So the answer to question 1 is 51. Repeat this process for the rest of the questions.
In question 2, we are given the hypotenuse and 1 leg, and are missing the other leg. So set your equation up like so, and then solve,
[tex]x^2+6^2=10^2x^2+36=100x^2=64x=8[/tex]
So the answer to question 2 is 8. Now one last time for the 3 and final question. We are given two legs, and are missing the hypotenuse. So set your equation up similar to the first question.
[tex]1^2+1^2=x^21+1=x^22 = x^2x = \sqrt{2}[/tex]
So the answer to question 3 is [tex]\sqrt{2}[/tex], or approximately 1.4142
Hope this helped
Write [4^ squareroot 81] 5^
Answer:
(⁴√81)⁵
= [tex]81^{\frac{5}{4} }[/tex]
[tex]81^{\frac{5}{4} }[/tex]
= 243
Step-by-step explanation:
(⁴√81)⁵
(3)⁵
= 243
Answer:
the answer is B 81^4/5 I HOPED THIS HELPED
HELP PLEASE ALSO NO LINKS THANK YOU
Answer:
21
Step-by-step explanation:
(base1+base2)2/ height
Evaluate the equation y=2x2 - 2x + 7 for x=-3
Answer:
31
Step-by-step explanation:
y=2x^2 - 2x + 7
Let x= -3
y=2(-3)^2 - 2(-3) + 7
=2 (9) +6 +7
= 18 +6+7
= 31
[tex]\tt{y = 2 {x}^{2} } - 2x + 7 \: ,when \: x \: = \: - 3[/tex]
Let's try![tex]\quad \quad \quad \quad \tt{y = 2 {x}^{2} } - 2x + 7[/tex]
[tex]\quad \quad \quad \quad \tt{y = 2 {( - 3)}^{2} } - 2( - 3)+ 7[/tex]
[tex]\quad \quad \quad \quad \tt{y = 2(9) +6 + 7}[/tex]
[tex]\quad \quad \quad \quad \tt{y = 18 +6 + 7}[/tex]
[tex]\quad \quad \quad \quad \tt{y = 24 + 7}[/tex]
[tex]\quad \quad \quad \quad \tt{y = 31}[/tex]
Hence, the answer is:[tex]\quad \quad \quad \quad \boxed{\tt{\color{green}y = 31}}[/tex]
_______
#LetsStudy
Se ha determinado que la población P (t) de una colonia de bacterias, t horas después de iniciar la observación, tiene una razón de cambio de P'(t) = 350 e0.18t + 220 e-0.3t. Si la población era de 250,000 bacterias cuando se inició la observación, ¿Cuál será la población20 horas después?
Answer:
La población 20 horas después será de 321,161 bacterias.
Step-by-step explanation:
t horas después de iniciar la observación, tiene una razón de cambio de P'(t) = 350 e0.18t + 220 e-0.3t.
Esto implica que la población después de t horas viene dada por:
[tex]P(t) = \int P^{\prime}(t) dt[/tex]
[tex]P(t) = \int (350e^{0.18t} + 220e^{-0.3t}) dt[/tex]
Teniendo en cuenta que
[tex]\int e^{at} dt = \frac{1}{a}e^{at}[/tex]
[tex]P(t) = \int (350e^{0.18t} + 220e^{-0.3t}) dt[/tex]
[tex]P(t) = \frac{350}{0.18}e^{0.18t} - \frac{220}{0.3}e^{-0.3t} + K[/tex]
En que k es la población inicial, o sea, [tex]K = 250000[/tex]. Entonces
[tex]P(t) = 1944.44e^{0.18t} -733.33e^{-0.3t} + 250000[/tex]
¿Cuál será la población 20 horas después?
Esto eres P(20). Entonces:
[tex]P(20) = 1944.44e^{0.18*20} -733.33e^{-0.3*20} + 250000 = 321161[/tex]
La población 20 horas después será de 321,161 bacterias.
What is the missing number? I’ll mark brainly
Answer:
I think it is 4
I am not sure about it
A ratio is equal to 3:8 if the antecedent is 21 find the consequent
Answer:
56
Step-by-step explanation:
To find the "consequent," write out and solve an equation of ratios:
3 x
------- = ------
8 21
Through cross-multiplication, this yields 8x = 63, so that x must be x = 63/8.
Alternatively, solve this modified version of the original equation for x:
3 21
------- = ------
8 x
Then 3x = 8(21), or x = 8(7), or x = 56.
Note that 21 and 56 are in the ratio 3:8
Please help thank you.
Step-by-step explanation:
AAA are the correct answer.
It is related to congurency.
Answer:
AAA
Step-by-step explanation:
You have 2 of angles. Add them together and subtract them by 180. That is how to got AAA.
If you rolled two dice, what is the probability
that you would roll a sum of 12?
Give your answer as a simplified fraction, Enter
the number that belongs in the green box.
second
first
1 2 4 5 6
11,1 1,2 1,3 1,4 1,5 1,6
212,1 2,2 2,3 2,4 2,5 2,6
33,1 3,2 3,3 3,4 3,5 3,6
44,1 4,2 4,3 4,4 4,5 4,6
5 5,1 5,2 5,3 5,4 5,5 5,6
6 6,1 6,2 6,3 6,4 6,5 6,6
Probability is 1/36.
What is probability?The probability is defined as the possibility of an event to happen is equal to the ratio of the number of outcomes and the total number of outcomes.
Two dices were rolled.
Total outcomes in sample space: S = 36
Outcomes which have sum as 12 are E = {(6,6)}
Required Probability: P(E)= 1/36
Hence, Probability is 1/36 of which have sum as 12
Learn more about Probability
https://brainly.com/question/14210034
#SPJ2
Answer:
1/36
Step-by-step explanation:
