The nature of the roots of the quadratic equation 4[tex]x^{2}[/tex] - 8x + 9 =0 are imaginary.
given equation:
4[tex]x^{2}[/tex] - 8x + 9 =0
now we need to find the nature of the quadratic equation
nature of roots :
Case I: [tex]b^{2}[/tex] – 4ac > 0
When a, b, and c are real numbers, a ≠ 0 and the discriminant is positive, then the roots α and β of the quadratic equation ax2 +bx+ c = 0 are real and unequal.
Case II: [tex]b^{2}[/tex]– 4ac = 0
When a, b, and c are real numbers, a ≠ 0 and the discriminant is zero, then the roots α and β of the quadratic equation ax2+ bx + c = 0 are real and equal.
Case III: [tex]b^{2}[/tex]– 4ac < 0
When a, b, and c are real numbers, a ≠ 0 and the discriminant is negative, then the roots α and β of the quadratic equation ax2 + bx + c = 0 are unequal and not real. In this case, we say that the roots are imaginary.
Case IV: [tex]b^{2}[/tex] – 4ac > 0 and perfect square
When a, b, and c are real numbers, a ≠ 0 and the discriminant is positive and perfect square, then the roots α and β of the quadratic equation ax2 + bx + c = 0 are real, rational and unequal.
for the above given equation:
a = 4
b = -8
c = 9
=[tex]b^{2}[/tex] - 4ac
= [tex](-8)^{2}[/tex] - 4(4)(9)
= (56) -144
= -88< 0
the roots are imaginary
The nature of the roots of the quadratic equation 4[tex]x^{2}[/tex] - 8x + 9 =0 are imaginary
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Root5 /2 root5 -1
can be written in the form
a+rootb /c
where a, b and c are integers.
Find the values of a, b and c when the resulting fraction
is written in its simplest form.
Answer:
10, 5, 19
Step-by-step explanation:
Recall that
[tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex]
So we can multiply the fraction by
[tex] \frac{2 \sqrt{5} + 1 }{2 \sqrt{5} + 1 } [/tex]
And get
[tex] \frac{ \sqrt{5} }{2 \sqrt{5} - 1} \times \frac{2 \sqrt{5} + 1 }{2 \sqrt{5} + 1 } = \frac{10 + \sqrt{5} }{20 - 1} = \frac{10 + \sqrt{5} }{19} [/tex]
What’s the diameter of a circle that had a radius of 4cm
Answer:
8
Step-by-step explanation:
Answer is =8cm
Step-by-step explanation:
d=2r=2·4=8cm
PLEASE HELP! this is a 4 part problem but here is the last part :)!!!
Calculate the area of the shaded area !!
EZ FREE POINTS!!
Answer:
20 sq units
Step-by-step explanation:
Answer:
20 sq units
Hope it helps :)
What value of x will make the equation below true?
14−(x+7)=3
what is the same as 8/9?
Answer:
8×1/9
Step-by-step explanation:
It is same as 8/9 because 8×1=8
Use the quadratic formula to find both solutions to the quadratic equation
given below.
3x2 - 5x + 1 = 0
ILL MAKE YOU BRAINLEST JUST HELP
Answer:
i only know one answer which is d
Step-by-step explanation:
Answer:
Step-by-step explanation:
i think b and d
A scale drawing of a dance floor is shown. What is the area of the actual dance floor? 22 cmon the top and bottom and 14 cm on the sides 5 cm equals 8 feet
Answer:
The area of the dance floor will be 788.48ft²
Step-by-step explanation:
Since 5cm represents 8ft, it means
1cm represents 8/5ft.
The scale length is 22cm, therefore the actual length would be
22 x 8/5ft = 35.2ft
The scale breadth is 14cm, therefore the actual breadth would be
14 x 8/5ft = 22.4ft
The area of the dance floor will be
(35.2ft)(22.4ft) = 788.48ft²
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Find the measure of the sixth interior angle of a hexagon if the measure
of the other five interior angles are 80°, 90°, 130°, 130°, and 150°. (Show
all work)
Answer:
140°
Step-by-step explanation:
The sum of interior angles of a n-agon is (n - 2) * 180°
a hexagon should have the sum of angles equal to
4 * 180° = 720°
Now we know that the other five angles have total measure
80° + 90° + 130° + 130° + 150° = 580°
So the sixth one has to be:
720° - 580° = 140°
Answer:140°
Step-by-step explanation: required equation : 180*(n-2)
since it is a hexagon, the sum of all interior angles=180*(6-2)
=180*4 =720°
now the measure of 6th angle=720 -(80+90+130+130+150)
= 720 -580
= 140
Help me solve this pls!!
5+ 8 x-3=
Find the surface area of a square pyramid with side length 6 yd and slant height 6 yd.
Answer:36
Step-by-step explanation:
.
Find the perimeter of a room with a length of 28 ft. and a width of 19 ft.
Answer:
98 ft
Step-by-step explanation:
28x2 + 19x2
=98
Answer:
Is the room a rectangle size? If so:
28 + 28 = 56
19 + 19 = 38
56 + 38 = 94 ft.
Opposite sides are parallel and equal:
therefore whenever there is two given lengths make sure to multiply them two times then add them together if only its a rectangle.
if its a square make sure to multiply the given length 4 times.
Steve reaches into a bag with 5 marbles 3 yellow marbles and 2 green marbles and randomly selects one the he puts the marble back and sam reaches into the same bag and randomly selects a marble is this independent or dependent
Answer:
Independent
Step-by-step explanation:
The reliance of an event on the outcine of another event gives rise to a dependent event. For any two or more event, whereby the outcome of event A has no effect on the possible outcome of event B, then such scenario is termed as being Independent. In the scenario described above, the outcome oof Sam's pick does not depend on the outcine of Steve's pick. This is because, once Steve makes his selection, the marble is returned into the box before Sam makes his own selection.Therefore, no matter the color of marble picked by Steven, it will have no bearing on the outcome of Sam's pick.
Can someone help me with this one too please
Answer:
1) f - 2
2) 45 + b
3) s - 82
4) 52c
5) t/5
Answer:
1) f-2
2) 45+b
3) s-82
4)52c
5)t/5
What's the common difference of the sequence -5, -2, 1, 4, 7, ...?
A) d= -5
B) d= 2
C) d=-3
D) d= 3
Answer:
The answer is D) d=3!!!!!
What is the length of AB⎯⎯⎯⎯⎯? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth. cm A horizontally-aligned scalene triangle A B C. Side A C is labeled as 18 centimeters. Side B C is labeled as 12 centimeters. Angle C is labeled as 79 degrees.
Answer:
AB = 19.6 cm
Step-by-step explanation:
Let AB be represented by c. Applying the cosine rule, we have;
[tex]c^{2}[/tex] = [tex]a ^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos C
= [tex]12^{2}[/tex] + [tex]18^{2}[/tex] - 2(12 x 18) Cos [tex]79^{o}[/tex]
= 144 + 324 -432(0.19081)
= 468 - 82.4299
[tex]c^{2}[/tex] = 385.5701
c = [tex]\sqrt{385.5701}[/tex]
c = 19.6359
The side AB of the given triangle is 19.6 centimetres.
Answer:
19.6
Step-by-step explanation:
took the quiz. Shows correct
Ashleys Shoe Store buys shoes for $35 and then sells them for
$85.
What is the percent of increase on the price of the shoes?
Round to the nearest whole number
Given: BD bisects AE, A = E
Prove: ABC EDC
(No links)
Answer:
All sides are equal better explenation bellow
Step-by-step explanation:
It's a mirror flip of a ABC triangle
Yet you can say AB Is = to DE
And since most likely it's a 60° triangle all the angles are 60°
All triangles have 180°
Which means AB =BC
BC= AC
BC =CD
DE= CD
CE=DE
Which means all the sides are equal
2/14 as a decimal (please explain)
Answer:
Hi! The answer to your question is 0.142857. (Convert the fraction to a decimal by dividing the numerator by the denominator)
Step-by-step explanation:
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Hope this helps!!
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Find the measure of the angle indicated
72⁰
HOPE IT HELPS YOU THANK YOU ☺
Answer:
37 degree
Step-by-step explanation:
RQS is suspened by arcRS
RQS=1/2(RS)
RQS=1/2(74)
RQS=37
i need help with this
Answer:
<FNM = 73
Step-by-step explanation:
we are given
GNF = 60
MNL = 47
60+47=107
107-180=73
A student incorrectly says the volume of the regular hexagonal prism, to the nearest cubic centimeter, is 1,619 cm3. What is the correct volume? What error did the student most likely make?
The volume of the regular hexagonal prism is ___ cm3.
Answer:
17.5
Step-by-step explanation:
Troy and two of his friends help troy's dad do yard work. After his dad paid $35 for gas, the boys made 128. How much did each child make?
khan academy - 6th grade advanced
Answer:
its b
Step-by-step explanation:
find the measure of each interior angle of a regular polygon with the following number of sides 10
Answer:
36 will be the measure.
Hope it helps!!!
Step-by-step explanation:
What fraction describes the probability for two coins being tossed at the same time to both land on heads?
3/4
1/4
1/2
Answer: 1/4
Step-by-step explanation:
A coin has two outcomes which are either the head or the tail. When a coin is tossed, the probability of getting a head is 1/2 and likewise for a tail.
Therefore, the probability for two coins being tossed at the same time to both land on heads will be:
= 1/2 × 1/2
= 1/4
Answer:
1/4
Step-by-step explanation:
You buy a used car for $12,000. The value of y of the car decreases by 15% each year. Find the value of the car in: a. 1 Year
Step-by-step explanation:
12 000 × 15/100
= $1 800
value of the car = 12 000 - 1 800
= $ 10 200
Brian invests £990 into his bank account. He receives 2.6% per year simple interest. How much will Brian have after 3 years? Give your answer to the nearest penny where appropriate.
Answer:
£1067.22
Step-by-step explanation:
A = P(1 + rt)
A = £990(1 + 0.026*3)
A = £1067.22
Mark brainliest if this helped!
Mark brainliest if this helped!
describe the correlation in the scatterplot below
The first bubble options are positive linear, positive linear with one outlier, negative linear, negative linear with one outlier, nonlinear ,and no.
the second bubble options are decrease , increase, show no pattern and follow a linear pattern
Answer:
'no' and 'show no pattern'
Step-by-step explanation:
with scatter plots like these, there is no exact information at all, what so ever
Answer:
linear positive/ follow a linear pattern
Step-by-step explanation: