[tex]{\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]
Let [tex]\alpha[/tex] and [tex]\beta[/tex] be the two zeroes of P(x) = [tex]\sf {a}^{2} + bx + c[/tex]
• A polynomial is always equal to it's factors, also the constant "k" is not equal to zero
[tex] \tt \sf {a}^{2} + bx + c = k(x - \alpha )(x - \beta )[/tex]
• Using distributive property
[tex]\tt \sf {a}^{2} + bx + c = k \bigg( {x}^{2} - \beta x - \alpha x + \alpha \beta \bigg)[/tex]
[tex]\tt \sf {a}^{2} + bx + c = k {x}^{2} -k (\beta x )- k(\alpha x )+k( \alpha \beta )[/tex]
• Taking common
[tex]\tt \sf {a}^{2} + bx + c = k {x}^{2} -kx (\beta + \alpha)+k( \alpha \beta ) - - (1)[/tex]
• Equating coefficients of like terms
[tex] \sf \: a = k - - (2)[/tex]
[tex] \sf b = - k( \alpha + \beta ) - - (3)[/tex]
[tex] \sf c = k \alpha \beta - - (4)[/tex]
★ From 3
[tex] \sf b = - k( \alpha + \beta ) - - (3)[/tex]
★ From 2 we have a = k so we have -
[tex] \sf b = - a( \alpha + \beta ) [/tex]
[tex]\sf - \dfrac{b}{a} = ( \alpha + \beta ) [/tex]
[tex]\sf \therefore \boxed {{ \red{( \alpha + \beta ) = - \dfrac{b}{a} } }}[/tex]
• Sum of zeros = [tex]- \dfrac{b}{a}[/tex]
★ From 4
[tex] \sf c = k \alpha \beta - - (4)[/tex]
★ From 2 we have a = k so we have -
[tex] \sf c = a \: \alpha \: \beta[/tex]
[tex]\sf \dfrac{c}{a} = \alpha \beta[/tex]
[tex]\sf \therefore \boxed {{ \red{( \alpha \beta ) = \dfrac{c}{a} } }}[/tex]
• Product of zeros = [tex] \dfrac{c}{a}[/tex]
Also,
★ From 1
[tex]\tt \sf {a}^{2} + bx + c = k {x}^{2} -kx (\beta + \alpha)+k( \alpha \beta ) - - (1)[/tex]
[tex]\tt \sf {a}^{2} + bx + c = k \bigg( {x}^{2} -x ( \alpha + \beta ) + ( \alpha \beta \bigg) [/tex]
• Now just put S instead of sum of zeroes and P instead of product of zeroes
[tex] \tt \sf {a}^{2} + bx + c = k \bigg( {x}^{2} -x ( S ) + ( P \bigg) [/tex]
[tex]\tt \sf{a}^{2} + bx + c = \boxed{ \red{ \sf \tt k \bigg( {x}^{2} - Sx + ( P \bigg ) }}[/tex]
[tex]\rule{280pt}{2pt}[/tex]
What is the correct answer for the problem 3.12 x 4.0
Hi Brielle the correct answer to your question is 3.12 x 4.0 = 12.48
12.48
Your answer should be 12.48 I hope that helps you
Kaitlin brought 21 pounds of sugar for $10 how many dollars did she pay per pound of sugar
A 10-foot ladder placed on level ground leans against the side of a house. The ladder reaches a point that is 9.2 feet up on the side of the house. ( Answer options A and B and show your work). Will Mark Brainliest if answered correctly. ( Do Not Repost Someone Else's Answers That's Already On Brainly And Any Other Websites Or You'll Be Reported). If you can't help please do not leave a response thank you.
So
Let's see
sinA=Perpendicular/HypotenusesinA=9.2/10sinA=0.92A=sin^{-1}(0.92)A=66.9°#B
So
We need base
cosA=Base/Hypotenusecos75=B/10B=10cos75B=2.58ftAnswer:
a) 67°
b) 2.6 ft
Step-by-step explanation:
Part (a)This problem can be modeled as a right triangle (see attachment 1), where the wall and the ground are the legs, and the ladder is the hypotenuse. Therefore, we can use the sine trig ratio to find the angle.
Trig Ratio
[tex]\sf \sin(\theta)=\dfrac{O}{H}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleH is the hypotenuse (the side opposite the right angle)Given:
[tex]\theta[/tex] = xO = wall = 9.2H = ladder = 10Substituting the given values into the ratio and solving for x:
[tex]\implies \sf \sin(x)=\dfrac{9.2}{10}[/tex]
[tex]\implies \sf x=\sin^{-1}\left(\dfrac{9.2}{10}\right)[/tex]
[tex]\implies \sf x=67^{\circ}\:(nearest\:degree)[/tex]
Part (b)(see attachment 2)
Let y be the distance the foot of the ladder and the foot of the building
We can find y by using the cos trig ratio:
[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]
where:
[tex]\theta[/tex] is the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Given:
[tex]\theta[/tex] = 75°A = grounds = yH = ladder = 10Substituting the given values into the ratio and solving for x:
[tex]\implies \sf \cos(75^{\circ})=\dfrac{y}{10}[/tex]
[tex]\implies \sf y=10\cos(75^{\circ})[/tex]
[tex]\implies \sf y=2.6\:ft\:(nearest\:tenth)[/tex]
The wholesale price for a shirt is $7.50. A certain department store marks up the wholesale price by 80%. Find the price of the shirt in the
department store.
Round your answer to the nearest cent, as necessary.
Answer:
$13.50.
Step-by-step explanation:
80% = 0.80 as a decimal fraction.
The marked up price
= 7.50 + 0.80 * 7.50
= $13.50.
so the new price will just be 7.5 plus 80% of 7.5
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{80\% of 7.50}}{\left( \cfrac{80}{100} \right)7.50}\implies 6\hspace{5em}\underset{selling~price}{\stackrel{7.50~~ + ~~6}{13.50}}[/tex]
What is the solution of the equation 3x + 5 + 2x - 12
Answer:
7/5
Step-by-step explanation:
3x + 5 + 2x - 12 = 0
5x - 7 = 0
5x = 7
x = 7/5
During the last year the value of your house decreased by 20%. If the value of your house is $265000 what was the value of your house last year? Round your answer to the nearest cent if necessary
Answer:
53000
Step-by-step explanation:
“for each expression find value that could be added as a constant term to make each expression a perfect square” these are two separate questions please help
Step-by-step explanation:
here you go hopefully it helps
Enter the answer to the problem below, using the correct number of significant figures.
30.01 + 5.55 + 80.761
Answer:
116.32100
Step-by-step explanation:
How to find surface area of prisms
Answer:
Step-by-step explanation:
The formula for the surface area of a prism is obtained by taking the sum of (twice the base area) and (the lateral surface area of the prism). The surface area of a prism is given as S = (2 × Base Area) + (Base perimeter × height) where "S" is the surface area of the prism.
(x + 7) + (y + 4)2 = 16
Center:
Radius:
Answer:
Center: (-7, -4)
radius = 4
Explanation:
Equation: (x + 7)² + (y + 4)² = 16Circle formula:
(x - h)² + (y - k)² = r²(h, k) denotes the center of the circle, "r is radius"
Rewrite the following equation in standard form:
(x - (-7))² + (y - (-4))² = 4²From this identify:
h = -7, k = -4, radius = 4General equation
(x-h)²+(y-k)²=r²
So
(x+7)²+(y+4)²=16(x+7)²+(y+4)²=4²Center=(-7,-4)
Radius=4
Elodia borrowed $30,000 from her aunt to start a delivery business. Her
aunt charged her an annual simple interest rate of 4%. After 7 years,
Elodia repaid her aunt in one payment, with interest. What was the total
amount Elodia paid her aunt?
A $211,200
B $114,000
C $30,001
D $38,400
Answer:
The answer is D she paid 38,400
Step-by-step explanation:
30,000 + 8400 = 38,400
PLEASE Find the value of x?
Answer:
Step-by-step explanation:
11 + 5 = big hipo = 16
16 / x = x / 5
x*x = 16*5
x² = 80
x = [tex]\sqrt{80}[/tex] (do this lame calculus)
x = 4[tex]\sqrt{5}[/tex]
y² = (4[tex]\sqrt{5}[/tex])² - 5²
y² = (4[tex]\sqrt{5}[/tex]) * (4[tex]\sqrt{5}[/tex]) - 25
y² = 16 + 4[tex]\sqrt{5}[/tex] + 4[tex]\sqrt{5}[/tex] + [tex]\sqrt{25}[/tex] - 25
y² = 16 + 8[tex]\sqrt{5}[/tex] + 5 - 25
y² = 16 + 8[tex]\sqrt{5}[/tex] - 20
y² = - 4 + 8[tex]\sqrt{5}[/tex]...
I give up..
Robert and Casey added the following values shown below. Who solved correctly+
Casey is correct and he will get the correct solution.
We have given that,
ROBERT CASEY
5 1/8+ 2 1/3 = 7 1/2 -4 1/2+ 6 3/4= 2 1/4
Robert's 5 1/8 + 2 1/3 = 7 1/2 is wrong because if 5+2 = 7, I would have to change the denominator of both fractions so they are both the same.
What is the equation?A statement that the values of two mathematical expressions are equal.
The denominator would have to be 24.
That would make the fractions 3/24 and 8/24.
If you added them together, it would not be able to simplify to 1/2.
Casey is correct.
-4 1/2 + 6 3/4 = 2 1/4 is correct
because 4 - 6 = 2.
In order to make the fractions have the same denominator, you would have to multiply -1/2 by 2 on both numerator and denominator which would equal -2/4.
Now add -2/4 and 1/4 and you get 1/4.
To learn more about the equation visit:
https://brainly.com/question/1214333
#SPJ1
Jenna’s car can travel 15 miles on 300 gallons of gas. How far can it travel on 18 gallons of gas?
Answer:
the answer is 36 gallon
Step-by-step explanation:
Kay is making bead necklaces. She has 80 red beads and 64 blue beads. What is the greatest number of identical necklaces she can make if Kay wants to use all of the beads?
Answer:
32
Step-by-step explanation:
80/2 = 40
64/2 = 32
so she can make about 32
Graph a line representing the proportional relationship with slope 3 containing the point (2, 6).
To graph the line, plot two points on the line.
Answer:
(1, 3) and (0, 0)
Step-by-step explanation:
y = mx + b
m is the slope which is 3 (given)
b is the y intercept
(x, y) → (2, 6)
6 = 3(2) + b
6 = 6 + b
b = 0
so the equation is y = 3x
one point:
y = 3(1)
y = 3 when x = 1
(1, 3)
y = 3(0)
y = 0 when x = 0
(0, 0)
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
x = 11
Step-by-step explanation:
All the sides of a rhombus are equal, so you can set the equations equal to one another.
2x + 46 = 7x - 9
Subtract 2x from both sides
46 = 5x - 9
Add 9 to both sides
55 = 5x
Divide both sides by 5
x = 11
Mark my answer as the brainliest if it helped you out!
A pack of red pens can be divided into equal shares among 3, 5, 6 and 9 teachers with no pen left over?
Answer:
90 red pens
Step-by-step explanation:
we need to find the least common multiple of the numbers 3 , 5 , 6 , 9
6 = 2 × 3
9 = 3²
then
LCM(3,5,6,9) = 2×5×3² = 2×5×9 = 90
The number 90 can be divided into 3 ,5 ,6 ,9 with no remainder
Therefore the pack must have 90 pens or a multiple of 90
For example 180 , 270 ...
The soccer team played 7 games and scored the following number goals in each game: 2, 1, 3, 5, 3, 1, 4. What was the median number of goals the team scored for the seven games? goals
Answer:
3
Step-by-step explanation:
first put them in order
1 1 2 3 3 4 5
then cancel them down go from the front to the back so go like
1 then 5 then 1 again then 4 and etc
u would then end up with the last two numbers which is 3 and 3. if u had numbers like 5 and 7 u would have to find the number in the middle of which would be 6. in the case the two numbers you are left with is 3 and 3 since there both the same the answer would be 3
hope this helped :)
There are white, blue, and red boats in a marina. Two-thirds of the boats in the marina are white,
5
8
of the remaining boats are blue, and the rest are red. If there are 6 red boats, how many boats are in the marina?
find the absolute value of the complex number 4+4i
Answer:
4√2
Step-by-step explanation:
complex no, z=√(a2+b2)
where, a=4 and b=4
z=√(4*4+4*4)
z=√(16+16)=√(32)
z=4√2
Find the measure of the missing angles.
Answer:
Below in bold.
Step-by-step explanation:
m< b = 180 - 36
= 144 degrees (adjacent angles.)
m < c = 144 degrees (opposite angles)
Help help me help help please help help me help help please help help me help help please help help me help help please help
Answer:
Question 7:
Answer: f(2) = 4
Question 8: 3 + x
How do I do step by step
Answer:
1.1
Step-by-step explanation:
Write out a long division problem! Since you can't have a decimal in the divisor, multiply both numbers by 10. This will leave you with 39.6÷36. Now all you have to do is follow the steps and end up with an answer of 1.1
In the diagram ABC = AFGD. Complete each statement.
Answer:
Rotate the second triangle, so the 30° angles line up with each other (C and D). Then you should be able to fill in the corresponding sides.
AB ≅ FG
AC ≅ FD
∠B ≅ ∠G
∠A ≅ ∠F
AC = 60
m∠F = 60°
Hope this helps.
Polygon abcde is congruent It polygon tvsrk
Answer: The answer is (A) ∠T.
Step-by-step explanation: Given that the polygon ABCDE is congruent to the polygon TVSRK. We are to find the corresponding angle of ∠EAB.
In the two polygons, the corresponding vertices are
A ⇒ T
B ⇒ V
C ⇒ S
D ⇒ R
E ⇒ K.
Therefore, ∠EAB, which is ∠A will correspond to ∠T.
Thus, the correct option is (A) ∠T.
?/1
message
At the store in Michigan, a box of cookies is priced at $8.50. When Zach goes to the store he has a coupon for 30% off the box of cookies. In Michigan, there is a 4% sales tax. How much did Zach have to pay for the book?
Answer:
$5.72
Step-by-step explanation:
What is the answer to this question: 100 + 100?
Answer:
200
Step-by-step explanate
100+100 = 200
used a calculator
Pls ingore all of the questions below, but help me with the attached image
What is the only number that has the same number of letters as it's meaning? ...
What number doesn't have its own Roman numeral? ...
What is the only even prime number? ...
What is the smallest perfect number? ...
What is our current numerical system based on? ...
Is Pi a rational or irrational number?
Answer:
v=50
u=80
Step-by-step explanation:
RT=RS
v=50
u=180-50-50=80
HELP PLEASE HELP PLEASE
Answer:
D 1/4
Step-by-step explanation:
Your question is a problem in reading comprehension. It tells you its own answer.
x is always 1/4
