Step-by-step explanation:
Solution :-Given quadratic equation is
px²-6qx-(9p-10q) = 0
On comparing with the standard quadratic equation ax²+bx+c = 0
a = p
b = -6q
c = -(9p-10q) = -9p+10q
Given roots of the equation = 2 Ⴛ - 3 and
2 Ⴛ - 3 and 2β – 3
We know that
Sum of the roots = -b/a
=> 2 Ⴛ - 3 + 2β – 3 = -(-6q)/p
=> 2 Ⴛ + 2β - 6 = 6q/p
=> 2 Ⴛ + 2β = (6q/p)-6
=> 2 Ⴛ + 2β = (6q-6p)/p
=> 2(Ⴛ + β) = (6q-6p)/p
=> Ⴛ + β = (6q-6p)/(2p)
=> Ⴛ + β = 2(3q-3p)/(2p)
=> Ⴛ + β = (3q-3p)/p ---------(1)
Product of the roots = c/a
=> (2 Ⴛ - 3 )( 2β – 3) = (-9p+10q)/p
=> 4Ⴛ β-6Ⴛ - 6β+9 = (-9p+10q)/p
=> 4Ⴛ β-6(Ⴛ +β)+9 = (-9p+10q)/p
=> 4Ⴛ β-6[(3q-3p)/p]+9 = (-9p+10q)/p
=> 4Ⴛ β-6[(3q-3p)/p] =[ (-9p+10q)/p]-9
=> 4Ⴛ β-6[(3q-3p)/p] = (-9p+10q-9p)/p
=> 4Ⴛ β-6[(3q-3p)/p] = (-18p+10q)/p
=> 4Ⴛ β =[(-18p+10q)/p]+6[(3q-3p)/p]
=> 4Ⴛ β =[(-18p+10q)/p]+[(18q-18p)/p]
=> 4Ⴛ β =[(-18p+10q)+18q-18p)]/p
=> 4Ⴛ β = (-36p+28q)/p
=> 4Ⴛ β = 4(-9p+7q)/p
=> Ⴛ β = 4(-9p+7q)/4p
=> Ⴛ β = (-9p+7q)/p
=> Ⴛ β = (7q-9p)/p ----------(2)
We know that
The quadratic equation whose roots are Ⴛ and β is x²-(Ⴛ+ β)x +Ⴛ β = 0
=> x²- [ (3q-3p)/p]x + [ (7q-9p)/p] = 0
=> [px²-(3q-3p)x+(7q-9p)]/p = 0
=> [px²-(3q-3p)x+(7q-9p)] = 0×p
=> px²-(3q-3p)x+(7q-9p) = 0
Answer :-The required quadratic equation is
px²-(3q-3p)x+(7q-9p) = 0
Used Formulae:-The standard quadratic equation is ax²+bx+c = 0The quadratic equation whose roots are Ⴛ and β is x²-(Ⴛ+ β)x +Ⴛ β = 0Sum of the roots = -b/aProduct of the roots = c/aThe robotics club has created 10 racing robots for the end of year science fair. each robot has the same chance of winning the race. what are the chances that robot a and robot b finish in the top three spots, but robot c is not in the top three?
Answer: [tex]\frac{7}{120}[/tex]
Step-by-step explanation:
Find side b if side a = 8.5 inches and side c = 15 inches.
inches
c
b
a
а
Type the correct answer, then press Enter. Use the
calculator if necessary. Round to the nearest
hundredth if the answer is uneven.
what is the area of the small square?
Answer:
4
Step-by-step explanation:
Since it is a square all sides are the same. For the first one 5 x 5 eqals 25. For the second one since it has a 2 on one side we multiply 2 x 2 to get 4.
What is the mode of the data represented in this line plot?
Answer:
8
Step-by-step explanation:
Mode is the number that repeats itself the most in data, because 8 contains the most X's, it is the mode
i know i got the first half right, i’m not sure what i need to do for the second half. please help
Answer/Step-by-step explanation below:
[tex]2 - x < 7[/tex]
[tex]- x + 2 < 7[/tex]
[tex]-x + 2 -2 < 7 - 2[/tex]
[tex]-x < 5[/tex]
[tex]\frac{x}{-1 } < \frac{5}{-1}[/tex]
[tex]x > - 5[/tex]
Kavinsky
sinθ/cosθtanθ=1
how is this identity true?
Answer:
This is actually not an identity.
Zoey goes out to lunch. The bill, before tax and tip, was $9.45. A sales tax of 3% was added on. Zoey tipped 15% on the amount after the sales tax was added. What was the total cost of the meal, plus tax and tip? Round to the nearest cent.
Answer:
$11.34
Step-by-step explanation:
I think you meant tenth where you said “nearest cent”, so it’s $11.30.
Answer:
$11.34
Step-by-step explanation:
i hope u get this right.
Which student spends the most time at the beach?
Describe the data you would expect someone to collect from this question?
Answer:
someone would probably collect the amount of students go to the beach and how they spend their time at the beach.
(05.02) Find the measure of angle x in the figure below:
55
45
80
55
100
Answer: x = 70
Step-by-step explanation:
Sum of angles in a triangle is 180
55 + 45 + y = 180
110 + y = 180
(110 - 110) + y = (180 - 110)
y = 70
Vertical angles are congruent so y = x
x = 70
If Tshepo and his friends take N6 from Bloemfontein which town are they going to pass on their way to East London?
The town of Komani and Maletswai will be passed by Tshepo and his friends if they take N6 from Bloemfontein to East London.
Where is the N6?The location is a national route in South Africa that connects the East London with Bloemfontein the via route of Komani and Maletswai.
The Komani is a town in the middle of the Eastern Cape Province of South Africa while the Maletswai is also a town in central South Africa on the banks of the Orange River, Eastern Cape Province of SA.
Therefore, the town of Komani and Maletswai will be passed by Tshepo and his friends if they take N6 from Bloemfontein to East London.
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What is 1x1 divided by 3
Answer:
The answer to this one is 0.3333
Answer:
0.3333
Step-by-step explanation:
I need help with this question please
Answer:
85 cm
Step-by-step explanation:
the strut forms a right triangle with the end of the pole.
let the ends of the strut be x from the top of the pole . then
using Pythagoras' identity with 2 legs x and hypotenuse 1.2
x² + x² = 1.2²
2x² = 1.44 ( divide both sides by 2 )
x² = 0.72 ( take square root of both sides )
x = [tex]\sqrt{0.72}[/tex] ≈ 0.85 m ( to 2 dec. places )
the ends are 0.85 m = 85 cm from the top of the pole
What is the surface area of the square pyramid
Answer:
[tex]33 {ft}^{2} [/tex]
Step-by-step explanation:
SA = 4(Area of ) + Area of ⬜
= 4(bh/2) + l*b
[tex]4(3 {ft}\times 4ft) \div 2 + (3ft \times 3ft)[/tex]
[tex]4 \times (12 {ft}^{2}) \div 2 + 9 {ft}^{2} [/tex]
[tex]24 {ft}^{2} + 9{ft}^{2} [/tex]
[tex]33 {ft}^{2} [/tex]
Can someone explain it to me or tell me how to do it please
Answer:
area is 24m^2
Step-by-step explanation:
base=6
height=4
Formula : base* height
6*4=24
Answer:
1/2 b*h
1/2 * 6* 4
=12
Step-by-step explanation:
For a triangle formula is half multiply by the base and times the hight and get the answer
Find the area of each parallelogram below.
Answer:
area of first
parallelogram
= 25x8
=200m^2
area of second
parallelogram
12x7
=84f^2
Step-by-step explanation:
I hope it's helpful for you
A copy machine prints 10 copies per 1/5 minute. At what rate, in copies per minute, does the copy machine print?
Answer:
50 copies/minute
Step-by-step explanation:
10 copies = [tex]\frac{1}{5} minute[/tex]
So to find the number of copies per minute, multiply the equation by 5:
50 copies = 1 minute
Answer:
50 per minute
Step-by-step explanation:
We are given the information that the copy machines prints 10 per 1/5 minute. In order to find the rate per one minute, we can multiply both values by 5. This is because 1/5 x 5 = 1, since we multiply by 5x the given time, the machine will produce 5x the amount of copies in that amount of time.
10x5 = 50
Therefore the machines prints 50 copies per minute.
Hope this helped!
In an obstacle course, participants climb to the top of a tower and use a zip line to travel across a mud pit. The zip line extends from the top of a tower to a point on the ground 48.2 feet away from the base of the tower. The angle of elevation of the zip line is 33°. Estimate the length of the zip line to the nearest tenth of a foot.
Using relations in a right triangle, it is found that the length of the zip line is of 40.4 feet.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.This situation can be modeled by a right triangle, in which the extension of the zip line of 48.2 feet is the hypotenuse and the length is the adjacent side to the angle of 33º, hence:
[tex]\cos{33^\circ} = \frac{l}{48.2}[/tex]
l = 48.2 x cos(33º)
l = 40.4.
The length of the zip line is of 40.4 feet.
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is this the right answer?...
Answer:
quadrant II
Step-by-step explanation:
Kindly refer to the attatched image to see where each quadrant lies.
If we look at the positioning of "A" and the attatched image we can say that "A" lies in quadrant II
Select ALL the sets that are the three side lengths of right triangles.
Answer:
c and d, b
Step-by-step explanation:
a - 49+64 = 113 so not a rt triangle
b - 16+100 = 116 again not rt triangle but 84+16 = 100 which is a rt triangle
c - 8+121 = 129 rt triangle
d - 1+3 = 4 rt triangle
Answer:
C and D
Step-by-step explanation:
Taylor's box of crackers states that 4 cookies contain 62 grams of carbohydrate. if taylor eats 7 crackers, how many grams of carbohydrates did she eat? solve using proportion
Answer: 108.5 grams of carbohydrates
Step-by-step explanation:
4 crackers=62 grams of carbs
62/4=15.5 per crackers
15.5 x 7=108.5 grams or carbs
Each of the letters in the word MATHEMATICS are written on separate index cards. The cards are then placed in a hat. What is the probability of randomly drawing an index card with a vowel on it from the hat? Write you answer as a fraction. Example a/b
Total number of pieces of paper = 11
Number of pieces with a vowel = 4
Probability of picking a vowel = 4/11 (answer)
What value of w would make the equation true
Step-by-step explanation:
[tex] \frac{12w + 8}{6} = \frac{8w - 16}{3 } \\ 36w + 24 = 48w - 96 \\ 36w - 48w = - 96 - 24 \\ - 12w = - 120 \\ w = 10[/tex]
How do I solve/ set up equation? Will give brainliest pls help
Answer:
See below ~
Step-by-step explanation:
Finding x
2x - 28 = x/23/2x = 283x = 56x = 56/3 = 18.66666667The exact side length of the small square is 18.66666667 cm and the exact side length of the big square is 37.3333334 cm.The approximate side length of the small square is 18.7 cm and the approximate side length of the big square is 37.3 cm.I just need the graph coordinates
Answer:
Step-by-step explanation:
(0,2), (2,3), (4,4), (6,5), (8,6), (10,7) are the coordinates.
25+(-14)-18 ____ 25+(-14) -(-18) (Fill the blank with > or <)
Answer:
<
Step-by-step explanation:
25+(-14)-18 ---> 25-32=-7
25+(-14)-(-18) ---> 43-14=29
Which expressions are equivalent to -6+4q+(-6q)−6+4q+(−6q)minus, 6, plus, 4, q, plus, left parenthesis, minus, 6, q, right parenthesis ?
Choose all answers that apply:
(Choice A)
-6(q+1)-4q−6(q+1)−4qminus, 6, left parenthesis, q, plus, 1, right parenthesis, minus, 4, q
(Choice B)
2(q-3)2(q−3)2, left parenthesis, q, minus, 3, right parenthesis
(Choice C)
None of the above
The expressions equivalent to -6 + 4q + (-6q) is C. None of the above
Which expressions are equivalentThe expression -6 + 4q + (-6q) can be simplified to -2q - 6,
Evaluating the given options, we have
Option (b); 2(q - 3) = 2q - 6
Option (c): -6(q + 1) - 4q = -10q - 6
Therefore, None of the above expressions are equivalent
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Subtracting Fractions with an unlike Denominator?
5/8 - 2/32 =
Subtrahend: 2/32
[tex]\implies \dfrac{2}{32} \implies \dfrac{1 \times 2}{16 \times 2} \implies \underlin\dfrac{1}{16}[/tex]
2) Determine the LCM of the denominators.The LCM of the denominators in the subtraction problem (5/8 - 2/32) can be determined by writing the multiples of 16 (Simplified denominator) and 8.
Writing the multiples of the denominators (16 and 8):
Multiples of 16 ⇔ 16, 32, 48, 64, 80...Multiples of 8 ⇔ 8, 16, 24, 32, 40...Since we can see that 16 is a common multiple and is has the least value in both multiples, 16 is the common multiple of 8 and 16.
3) Solving the subtraction problem.Multiply such number to the denominators such that the denominators are equivalent to the LCM. Keep in mind that the number we multiply in the denominator must be multiplied to the numerator.
[tex]\implies \dfrac{5}{8} - \dfrac{1}{16}[/tex]
[tex]\implies \dfrac{5 \times x}{8 \times x} - \dfrac{1}{16} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [8x = \text{LCM}][/tex]
[tex]\implies \dfrac{5 \times 2}{8 \times 2} - \dfrac{1}{16} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [8 \times x = \text{LCM} \implies 8 \times x = 16 \implies x = 2][/tex]
[tex]\implies \dfrac{10}{16} - \dfrac{1}{16}[/tex]
[tex]\implies \dfrac{10}{16} - \dfrac{x}{16x} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [16x = \text{LCM}][/tex]
[tex]\implies \dfrac{10}{16} - \dfrac{1 \times 1}{16 \times 1} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [16 \times x = \text{LCM} \implies 16 \times x = 16 \implies x = 1][/tex]
[tex]\implies \dfrac{10}{16} - \dfrac{1}{16}[/tex]
Finally, let's subtract the fractions as the fractions have like denominators.
[tex]\implies \dfrac{9}{16}[/tex]
Therefore, the simplified fraction is 9/16.
Notes:Parts of a subtraction problem:
Subtrahend: The number, variable, or expression being subtracted from the minuend of the expression. Minuend: The starting value of the expression. Difference: The solution to a subtraction problem.Learn more about subtracting unlike fractions:
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Find four numbers that are evenly divisible by both 2 and 9
Answer:
18
36
72
144
Step-by-step explanation:
For numbers to be divisible by 2 they must end in an even number
For numbers to be divisible by 9 the sum of the digits must be divisible by 9
Giving brainlyest to the person with the correct answer :)
Answer:
13.44 meters ahead
Step-by-step explanation:
phil distance = 6.59 m/s *12 sec meters
Mary dist = 5.47 *12 meters
difference :
6.59 *12 - 5.47 *12 = 13.44 meters
someone please help me what is (m - 5) divided by 4 where 5 = 17
