We are provided with a quadratic equation , and we have to find it's roots , but let's recall some things
The Standard Form of a quadratic equation is ax² + bx + c = 0 If D > 0 , then the equation have two real and distinct roots/zeroes . If D = 0 , then the equation have two equal roots/zeroes .If D < 0 , then the equation have two imaginary roots/zeroes or you can say that no real rootsWhere , D is the Discriminant whose value is b²- 4ac and the roots of the equation are given by a very famous formula called The Quadratic Formula , which is as follows ;
[tex]{\quad {\boxed{\pmb{\bf x = \dfrac{-b \pm \sqrt{D}}{2a}}}}}[/tex]
Now , coming back on the question ;
We are provided with the equation x² + 6x = -18 , so on comparing this equation with the standard form of quadratic equation , we have , a = 1 , b = 6 and c = 18 . Now calculating the Discriminant ;
[tex]{: \implies \quad \sf D=(6)^{2}-4\times 1 \times 18}[/tex]
[tex]{: \implies \quad \sf D=36-72}[/tex]
[tex]{: \implies \quad \sf D=-18}[/tex]
As , D < 0 , so two imaginary roots exist . Now by quadratic formula ;
[tex]{: \implies \quad \sf x=\dfrac{-6 \pm \sqrt{-36}}{2\times 1}}[/tex]
[tex]{: \implies \quad \sf x=\dfrac{-6 \pm \sqrt{\underline{6\times 6}\times -1}}{2}}[/tex]
[tex]{: \implies \quad \sf x=\dfrac{-6 \pm 6\sqrt{-1}}{2}}[/tex]
[tex]{: \implies \quad \sf x=\dfrac{-6 \pm 6\iota}{2} \quad \{\because \sqrt{-1}=\iota\}}[/tex]
[tex]{: \implies \quad \sf x=\dfrac{2(-3\pm 3\iota)}{2}}[/tex]
[tex]{\quad \qquad \boxed{\bf \therefore \: x=-3 \pm 3\iota}}[/tex]
Question 4
Simplify the expression by combining like terms
Expression: -8yº - 9y +13y - 11y
Like Terms:
Simplified Expression:
I
Answer:
-8y° -7y
Step-by-step explanation:
Like terms:
13y-11y-9y= -7y
-8y°= -8y°
Simplified Expression:
-8y°-7y
please only answer if you know the correct answer and answer all question please please please please please
Answer:
Part A: B) 3
Part B: $40
4. -1
7. 5x + 6y
8. Part A: y = 20x
8. Part B: $300
9. e > 12000 pounds
Step-by-step explanation:
Part A: x = 5t + 5
20 = 5t +5
15 = 5t
t = 3
Part B: x = 5t + 5
x = 5(7) + 5
x = 35 +5
x = 40
4. 24 - 5^2
24 - (5*5)
24 - 25 = -1
7. 2x + 4y + 5 + 2y - 5 + 3x
2x + 3x = 5x
4y + 2y = 6y
5 + (-5) = 0
5x + 6y
8. Part A:
Total = y
Lawns = x
Amount = $20
so y = 20x
8. Part B:
y = 20x
y = 20(15)
y = 300
9. The elephant weighs more than 12000 pounds
Elephant = e
More than = >
Pounds = 12000
e > 12000 pounds
Find the surface area.
5 cm
14 cm
9 cm
3 cm
Answer:C. 2/3 cm/s
Step-by-step explanation:
A motorcycle drives 130 miles in 2 hours 36 minutes. Calculate the average speed.
Answer:
Average speed is like .83miles per minute and roughly 50 per hour
Step-by-step explanation:
Help again please. Its still late.
Answer:
The answer is c.
Step-by-step explanation:
Find the length of BC.
Answer:
12
Step-by-step explanation:
If the perimeter is 58,
take 17(2) for booth sides.
Which you will get 34.
58-34=24
Now you know that the remainder is the two vertical sides.
24/2=12
BC=12
What is the nth term of the sequence 2,5,10,17,28.. ?
n² + 1 = 2 5 10 17 26. So the nth term of the sequence is n²+1.
Terry has a box of craft beads.
• 11 are green
• 27 are yellow
• 24 are blue
• 38 are red
What percent of the beads are red?
Answer:
38% of the beads are red
A TV is originally priced at $350. There is a coupon for 40% off. After the 7% sales tax, what is the price you would pay for the tv
Answer: $234.5
Step-by-step explanation: when you get a 40% off that means you would pay 60% but then you have to play 7% so you have to pay 67% of 350 wich is 234.5
Answer:
$149.8
Step-by-step explanation:
40% of 350 is 140
7% of 140 is 9.8
Helppp im not very good at math so can you guys help me
Answer:
Answer is D. 75 cm2
Step-by-step explanation:
The closest estimate to 70.2 is 75 cm2
Hopefully this helps
find the area of a circle with radius, r = 5.81m. Give your answer rounded to 2 DP.
A≈106.05m²
hope that help
Answer:
A=πr×r
π=3.142, r=5.81
A=3.142×5.81×5.81
A=106.0906~106.09
Pls help me I’ll give out brainliest please dont answer if you don’t know
Step-by-step explanation:
x=-10 is ur answer try it!
Answer:
2x=-20 or simplified version x=-10
Step-by-step explanation:
-8+3x=12+5x
-3x. -3x
-8 = 12+2x
-12=-12+2x
-20=2x
x=-10
A glassblower can produce several sets of simple glasses in about 3 hours. When the glassblower works with
an apprentice, the job takes about 2 hours. Write an equation that can be used to find the amount of time t, in
hours, it would take for the apprentice to make the same number of sets of glasses when working alone.
Using the together rate, it is found that it would take the apprentice 6 hours to make the same number of sets of glasses when working alone.
What is the together rate?The together rate is the sum of each separate rate.
In this problem, the rates are:
Glassblower: 1/3.Apprentice: 1/x.Together: 1/2.Hence, applying the equation for the together rate:
[tex]\frac{1}{2} = \frac{1}{x} + \frac{1}{3}[/tex]
[tex]\frac{x + 3}{3x} = \frac{1}{2}[/tex]
[tex]2x + 6 = 3x[/tex]
[tex]x = 6[/tex]
It would take the apprentice 6 hours to make the same number of sets of glasses when working alone.
To learn more about the together rate, you can take a look at https://brainly.com/question/25159431
The ages of three brothers are consecutive integers. The sum of their ages is 63. Find their ages.
Can someone plz help me with this??
Answer:
it's the second choice (3=3)
Answer:
y = - x + 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 3) and (x₂, y₂ ) = (3, 1)
m = [tex]\frac{1-3}{3-1}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1 , then
y = - x + c ← is the partial equation
To find c substitute (1, 3 ) into the partial equation
3 = - 1 + c ⇒ c = 3 + 1 = 4
y = - x + 4 ← equation of line
Caleb cut a rope into 4 pieces. The lengths of the pieces of rope are 5 2/8 inches, 7 7/8 inches, 4 1/8 inches, and 3 3/8 inches. Which choice is the closest estimate of the length of the original rope
Answer:
the actual answer is 20.625 and since there aren't any choices I'll give u my estimated answer: 20
Step-by-step explanation:
I got my estimated answer by rounding each length of rope down or up according to if it was less than 4/8 or higher. example: rounded 7 7/8 to 8
hope this helps <3
Determine the y intercept I don’t know how please help
Answer:
(0, -2)
Step-by-step explanation:
Since line is intersecting y axis at point (0, - 2)
Hence, y-intercept = (0, - 2)
There is 5 yellow 3 red 4 green 2 blue and 2 white what is the probability of picking white then green
Answer:
2 (I think)
Step-by-step explanation:
4-2=2
Answer:
1/30
Step-by-step explanation:
the probability of picking white is 2/16 simplified to 1/8
the probability of picking a green would equal to 4/15
notice that it is not 4/16, because you already picked out one of the colours, and you are not replacing it, so if you take it out, then there is 15 left to pick from.
you would then multiply
1/8 x 4/15
= 4/120
simplified to
1/30
Please Help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
26:26
Step-by-step explanation:
I hope I've helped :)
for ssc
1: a man walks 7km in 2 hours and 2 km in 1 hour in the same direction.what is the man's avarage speed for the whole joumey?
salamat po kong sino makaka sagot
Answer:
Average speed is 3 kilometers an hour
please help me! i'll mark you brainliest
20 points, (maths)
Answer:
5/6 of the time or 50 minutes
Step-by-step explanation:
Select the table that represents a linear function. (Graph them if necessary.)
Ο Α. | xo
1 2 3
y 11 8 5 2
B. x 0
X 0 1 2 3
y 0258
C. X 0
1 2 3
y 10974
O D. X 0 1 2 3
y 8 6 6175
HELP !!!!!
Answer: D
Step-by-step explanation:
Scrbkfvjtfcbjt hffcjtfbnid. Jrcvnfccb
Answer:
yeah i know the secret codeto Sy evvceryvcx evtrtyev ivyreviqvvt. qut
Step-by-step explanation:
PLEASE MARK BRAINLIEST!!!!!!!!!!!!!!!!!!!!please help!!!!! thank you
Answer:
b
Step-by-step explanation:
Q1 - Finding simple interest
Find the simple interest on a loan of:
£7500 borrowed for 6 years at a
rate of 12% p.a.
interest = £
Answer:
£ 5400
Step-by-step explanation:
P = £ 7500
r = 12% = 0.12
t = 6 years
Simple Interest = P*r*t
= 7500 * 0.12 * 6
= £ 5400
hi hi hi hi hi help help help help
Answer:
rate
Step-by-step explanation:
r(t)=d
r=d/t
r=miles/hour=mph
r=12
Answer: I THINK it’s d
Step-by-step explanation:
2(6+2x-1) pleas help fast
Answer:
4x+10
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
2(6+2x-1) = 8. Mark me Brainliest.
how do I change 2y = 3x + 8 into slope-intercept form?
A tree casts a shadow 31 feet long when the angle of
elevation of the sun is 58º. Find the height of the tree.
Answer:
x=24.2198542
ROUND IF NEEDED
Step-by-step explanation:
We are trying to find the height of the tree or the vertical side
We are given
The angle of elevation or the angle at the ground ,38The horizontal length, 31.Since we have a side that is adjacent to that angle and we are trying find backside that us opposite of that angle
we are going to use tangent
[tex] \tan(x) = \frac{opp}{adj} [/tex]
plug 38 in for x or theta, x for opp side and 31 for adjacent side
[tex] \tan(38) = \frac{x}{31} [/tex]
Multiply 31 by both sides to find x
x=24.2198542
ROUND IF NEEDED.
Someone PLEASE HELP
Let C = 2.32 N + 34180 represent the cost, C, of raising a child to 18 years of age, on an income, N.
If the cost is $120,000, what is the income?
$37,382
$36,991
$36,521
$35,856
QUESTION 49 I NEED HELP ASAP
Answer:
$36991
Step-by-step explanation:
C = 2.32N + 34180
120000 = 2.32N + 34180
85820 = 2.32N
N = 85820/2.32
N = 36991
Answer: $36991