Answers
Question 16:
[tex]\alpha[/tex] and [tex]\beta[/tex] are the roots of the equation.
That means [tex](x-\alpha )(x-\beta ) = 2x^{2} -6x+5 = 0\\[/tex]
[tex](x-\alpha )(x-\beta ) = 2x^{2} -6x+5 = 0[/tex]
[tex]2x^{2} -6x+5 = 0\\x^{2} -3x+\frac{5}{2} =0[/tex]
[tex](x-\alpha )(x-\beta ) =x^{2} - (\alpha +\beta )x +\alpha \beta[/tex]
So,
[tex]x^{2} - (\alpha +\beta )x +\alpha \beta = x^{2} -3x+\frac{5}{2}[/tex]
Compare coefficient
[tex]\alpha +\beta = 3\\\alpha \beta = \frac{5}{2}[/tex]
Consider [tex]\frac{\beta }{\alpha } + \frac{\alpha }{\beta }[/tex]
[tex]\frac{\beta }{\alpha } + \frac{\alpha }{\beta } =\frac{ \alpha ^{2} +\beta ^{2}}{\alpha \beta }[/tex]
[tex]= \frac{(\alpha +\beta )^{2} -2\alpha \beta }{\alpha \beta } \\= \frac{3^{2} -2*\frac{5}{2} }{\frac{5}{2} } \\= 4*\frac{2}{5} \\=\frac{8}{5}[/tex]
Ans: 8/5
Question 19:
[tex]f(x+2) = 2x^{2} +5x-3\\[/tex]
Substitute x with -1
So,
[tex]f(1) = 2(-1)^{2} +5(-1)-3\\=2-5-3\\=-6[/tex]
Ans: -6
Related Questions
Acafeteria has two sizes of pizza to serve students during lunch.
The smaller pizza has a 4-inch diameter. What is the area of the smaller pizza?
What did a the area of the smaller pizza
Answers
Answer:
pointsss
Step-by-step explanation:
Answer: 12.56 inches^2 or 4π inches^2 (depending on what format your answer needs to be in)
Step-by-step explanation:
The formula for the area of a circle is [tex]\pi r^{2}[/tex].
To find the radius (r), divide the diameter of 4 inches by 2. The radius is 2 inches.
Plug this into your equation to get [tex]\pi (2^{2} )[/tex], which can be simplified to 4π inches^2.
If you need your answer as a decimal, input 3.14 for [tex]\pi[/tex] to get an equation of 4 * 3.14. Multiply to get a final answer of 12.56 inches^2.
-8 Find the slope of the line y = -8/2x+1/5 Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
The slope is -4.
Because:
-8/2 is -4, which is the slope.
A planet has a circular orbit around a star. It is a distance of 65,000,000 km from the centre of the star. It orbits at an average speed of 65,000 km/h. How many Earth days does it take the planet to orbit the star? Give your answer to 2 sf.
Answers
Answer:
42
Step-by-step explanation:
65000000/65000=1000
24hrs=1 day
1000/24=125/3
125/3 times 1000= 42
Solve the inequality f – 4 ≤ 9 for f
help me.
Answers
Answer:
13
Step-by-step explanation:
Have a great day!! :)
5m - 2 represents the statement two less than five times a number
Answers
Answer:
yes
Step-by-step explanation:
Please give atleast two answers 20 POINTS
Answers
Answer:
3x^3
Step-by-step explanation:
First: you multiply the exponents inside the parenthesis with the one outside.
12*1/3= 4
3*1/3=1
you get 81x^(4)/3x
divide everything by 3: 27x^(4)/x
now subtract exponents (when dividing), you get: 27x^3
Now 1/3 is the same thing as cube root, so cube root of 27 is, thus the answer is: 3x^3
HELP please guys ................
Answers
Answer:
2nd choice
Step-by-step explanation:
Peter says, "If you subtract 16 from my number and multiply the difference by - 2, the result is
- 34." What is Peter's number?
Answers
P minus 16 and the answer times -2 is -34
-2(P-16) = -34
-2P+32 = -34
-2P = -66
Divide by -2
P is 33.
Check: 33-16 is 17 and 17*-2 is -34. So
P is 33.
Answer:
33
Step-by-step explanation:
Let the number be x,
=> (x - 16) -2 = - 34
=> -2x + 32 = -34
=> -2x = - 34 - 32 (by transposing)
=> -2x = -66
=> x = -66/-2 = 33
Peter's number is 33.
Hope you understood.
Make x the subject of the formula x/a 2 + 3 b = 2 c
Answers
Answer: x=-3ab/2+ac
Step-by-step explanation:
Multiply to remove the fraction, then set equal to 0 and solve.
16. You and a friend are going shopping. You leave school and drive 10 miles
due west on 26th Street. You then drive 7 miles NW on Raspberry Street to the
grocery store. Your friend leaves school and drives 10 miles due east on 26th Street.
He then drives 7 miles SE on Cascade Street to the movie store. Each of you has
driven 17 miles. Which of you is farthest from your school?
Answers
Answer:
My friend is farthest from my school
Step-by-step explanation:
Let the distance from the movie store to school be x and the distance from the grocery store to school be y
Using Cosine rule,
x²= 10²+7² - 2×10×7Cos120
x²= 149 -140(-0.5)
x²= 149+70
x²= 219
x= √219
= 14.8miles
y²= 10²+7² - 2×10×7Cos100
y²= 149 -140(-0.1736)
y²=149+24.2704
y²=173.2704
y=√173.2704
y=13.4miles
What is the solution to the system of equations?
y = -2x – 6
4x - y = -36
A (15, 24)
B (-7, 8)
C (-5, 4)
Answers
Derek and Jeannine buy a car for a total price, including tax, of $19,795. The price of the car was $18,500. What is the tax rate.
Answers
Answer:1.07
Step-by-step explanation:
Mai biked 6 3/4 miles today, and Noah bikes 4 1/2 miles. How many times the length of Noah’s bike ride was Mai’s bike ride?
Answers
Answer:
Mai's ride is 1.5 times longer than Noah's
Step-by-step explanation:
EASY 9TH GRADE MATH
Write an equation in point-slope form that passes through the point (1,-10) and
is perpendicular to y = -1/3 x + 5.
Do NOT type spaces between numbers and symbols.
Til
ALE
11
SE
Answers
Answer:
y = 3x - 13
Step-by-step explanation:
determine if the two triangles are congruent.If they are state how u know
Answers
Answer:
17) Congruent because two sides are congruent and so is the 90 degree vertical angle.
18) Congruent because they have a congruent leg and congruent angle, and they share a side which is congruent to itself. (SAS)
19) Congruent because all three sides are congruent (SSS)
20) congruent, all three sides are the same (SSS)
QUICK I NEED HELP….PLZ Hurry!! ;-;
Which equation represents a liner function
Equation 1: Y=2x+1
Equation 2: Y^2= 3x+1
Equation 3: y=5x^5-1
Equation 4: Y= 4x^4-1
Answers
Answer: Equation 1: Y=2x+1
Step-by-step explanation:
On a certain hot summer's day, 421 people used the public swimming pool. The daily prices are $1.75 for children and $2.00 for adults. The receipts for admission totaled $788.50. How many children and how many adults swam at the public pool that day?
There were _ children at the public pool.
There were _ adult at the public pool
Answers
Answer:
214 children and 207 adults
Step-by-step explanation:
214 x 1.75=374.5
207 x 2 = 414
414 + 374.5 = 788.5
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.
Answers
Answer:
The test has 10 3-point questions and 14 5-point questions.
Step-by-step explanation:
x + y = 24
3x + 5y = 100
From the first equation:
3x + 3y = 72
Subtracting:
3x - 3x + 5y - 3y = 100 -72
2y = 28
so y = 14
x + 14 = 24 so x = 10.
10*3 + 5*14
= 30 + 70 = 100 points.
What is the degree of 5x^5+8x^2+2x-3x^9-8x^4-4x^5
Answers
Answer:
9
Step-by-step explanation:
It is the greatest exponent.
15+25 distributive property
Answers
Answer:
(5 x 3) + (5 x 5)
Step-by-step explanation:
hope thats what your looking for
Which is correct? I wanna make sure im right
Answers
it is letter C. 3.9
hope it helps
#Chloe919
#thanks for the points
#carry on learning
hi guys need some help with this one question thanks
Answers
Take two co-ordinates
(-2,0)(0,4)[tex]\\ \sf{:}\Rrightarrow m=\dfrac{4-0}{0+2}=\dfrac{4}{2}=2[/tex]
Equation in point slope form
[tex]\\ \sf{:}\Rrightarrow y-y1=m(x-x1)[/tex]
[tex]\\ \sf{:}\Rrightarrow y-4=2(x-0)[/tex]
[tex]\\ \sf{:}\Rrightarrow y=2x+4[/tex]
please help me with this also jjodlask
Answers
Answer:
1. 15, 2. -23, 3. 220, 4. 4x-5
Step-by-step explanation:
f(x) = 4x + 3 g(x) = x - 2
1. f(g(5)): Put 5 in as x in g(x) 5 - 2 = 3. Now put the 3 as x into f(x) and solve. 4(3) + 3 = 15
2. g(f(-6)) 4(-6) + 3 = -21. -21 - 2 = -23
3. (f(f(7)) 4(7) + 3 = 31, 31(7) + 3 = 220
4. g(f(x)) 4(x-2) + 3 = 4x - 8 + 3 = 4x - 5
When a function is substituted into another function it is known as a composite function.
Given the following functions:
f(x) = 4x + 3
g(x) = x - 2
Determine [tex]f(g(x)) \ and \ g(f(x))[/tex]
[tex]f(g(x)) = f(x-2)\\ f(x-2) = 4(x-2)+3\\ f(x-2)=4x-8+3\\ f(x-2) = 4x - 5\\ f(g(x)) = 4x - 4 [/tex]
1) Determine the value of [tex]f(g(5))[/tex]
[tex]f(g(5))=4(5) - 4\\ f(g(5))=20-4\\ f(g(5))=16[/tex]
2) For the function [tex]g(f(-6))[/tex]
[tex]g(f(-6))=4(-6) + 1\\ g(f(-6))=-24+1\\ g(f(-6))=-23[/tex]
3) For the value [tex]f(f(7)), [/tex]we need to determine [tex] f(f(x))[/tex]
[tex]f(f(x)) = f(4x+3)\\ f(f(x))= 4(4x+3)+3\\ f(f(x))=16x+12+3\\ f(f(x))=16x+15\\ f(f(7)) = 16(7) + 15\\ f(f(7)) = 127[/tex]
4) For the function [tex]g(f(x));[/tex]
[tex]g(f(x))=(4x+3)-2\\ g(f(x))=4x+3-2\\ g(f(x))=4x+1[/tex]
learn more on composite functions here: https://brainly.com/question/10687170
can someone help me with this asap, please and thank you (pic attached) *math*
Answers
Step-by-step explanation:
the "x-2" makes it shift by 2 to the right (functional values are created at x that "should have happened" at 2 x units before, so the whole graph moves to the right).
the 0.4 factor compresses it by the factor 0.4
the "-" at the beginning just "flips" (reflects) it to the other side of the x-axis.
what is 7/8 x 4 ? ( 7/8 is a fraction)
Answers
Answer:
7/2 or 3 1/2
Step-by-step explanation:
7/8*4/1=28/8
Simplify= 7/2 or as a mixed fraction = 3 1/2
Hope this helps
Can I have the brainliest if I am right?
I need help putting these together in the correct place
Answers
Answer:
whats do you mean by that whats the question ❓
determine if the two triangles are congruent.If they are state how you know
Answers
Answer:
1. yes, both triangles sides are congruent
2. yes, they have congruent sides and they have a congruent angle
3. yes, congruent sides and angle
4. yes, 2 congruent angles
5. no, only one congruent angle not enough proof
6. yes, 2 congruent angles
7. no, only one congruent angle not enough proof
8. no, only one congruent side
The lunch choices last Friday were mushroom or pepperoni pizza. The cafeteria made 40
pizzas in all, 40% of which were mushroom pizzas. How many mushroom pizzas did the
cafeteria make?
Answers
Answer
16 mushroom pizzas
(6x²+2x-1)-(8x²-x-5)
Answers
Answer:
-2x^2 + 3x + 4
Hope this helps. :D
Step-by-step explanation:
Pls give brainliest.
The regular price of a ladder is $250. If a customer uses the coupon, what percent will the customer save?