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]
jenna has 24 dimes and quarters in her purse. in total the coins are worth $3.60. How many of each coin does she have?
Answer:
Jenna has 24 Dimes and 6 Quarters
Step-by-step explanation:
Hopefully this helps
HELP PLEASE!!! i do not understand
Answer:
a)-3>-7
b)3>-4 The symbol was preserved.
c)-6<8 The symbol was reversed.
Step-by-step explanation:
Hope this helps! :)
What is the value of y?
03
04
05
06
Answer:
03
Step-by-step explanation:
Subtract 4, divide by 2, then get 3
The value of y from the figure is 3.
What is Rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°).
A rectangle has equal and parallel opposite sides.
A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.
We have a figure of rectangle whose length = 10 + 2x or 18
and width = 10 or 2y+ 4
As, we know the opposite sides of rectangle are equal.
So, 10+ 2x = 18
2x = 8
x= 4
and, 10 = 2y+ 4
2y= 6
y= 3
So, the value of y is 3.
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HELP AND I WILL GIVE BRAINLIEST
Answer:
Step-by-step explanation:
HELP PLEASE FOR BRAINLIEST
in a circle of radius 17cm calculate the length of a chord which is 8cm from the centre
Answer:
The length of the chord is 30cm
Step-by-step explanation:
Given
[tex]r = 17cm[/tex]
[tex]d = 8cm[/tex]
Required
Calculate the chord length (L)
This is calculated as:
[tex]L = 2 * \sqrt{(r^2 -d^2)[/tex]
So:
[tex]L = 2 * \sqrt{(17^2 - 8^2)[/tex]
[tex]L = 2 * \sqrt{225[/tex]
[tex]L = 2 * 15[/tex]
[tex]L = 30cm[/tex]
Find the surface area of the figure below:
Answer:
216 is the surface area
Step-by-step explanation:
48+48+48+48+12+12
Milo wants to roll epoxy on his garage floor. In order to do this he needs to know the area of his rectangular-shaped garage. The measurements are 20+ (radical) 3 feet by 20+ (radical) 3 feet.
What is the area of his garage floor?
(Remember, the formula for the area of a rectangle is A = lw.)
Please help. I've been stuck on this problem. :)
Answer:
A
Step-by-step explanation:
i got it right on edge
The area of his garage floor Milo wants to roll epoxy is 403 + 40√3 ft².
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
Given, Milo wants to roll epoxy on his garage floor.
The measurements are 20 + √3 feet by 20 + √3 feet.
Therefore, The area of his garage floor is,
= (20 + √3)×(20 + √3) ft².
= 400 + 20√3 + 20√3 + √3×√3 ft².
= 400 + 40√3 + 3 ft².
= 403 + 40√3 ft².
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The distance y (in miles) that Train A travels in x hours is represented by the equation y=68x . The graph shows the distance that Train B travels. (0, 0) and (1, 64).
Answer:
For train A, the distance traveled as a function of time in hours is written as:
y = 68*x
For train B, we know that it's equation passes through the points (0, 0) and (1, 64)
Remember that:
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Then the slope for the equation of train B is:
a = (64 - 0)/(1 - 0) = 64
Then equation of train B is something like:
y = 64*x + b
Now, we know that it passes through the point (0, 0), this means that when x = 0, we also have y = 0, then if we replace these two values in the equation we get:
0 = 64*0 + b
0 = 0 +b
then b = 0
This means that the equation for train B is:
y = 64*x
Where again, y is the distance in miles and x is the time in hours.
If we look at both equations, we can see that train A has a larger slope, which means that for each unit of time, train A travels a larger distance, then we can conclude that train A is faster than train B.
1. Find the next three in the sequence. 2,7,12,17
2. find the formula for the nth term.
Please show the working
Answer:
the next three terms are 2,7,12,17,22,27,32
have a nice day
Answer:
n + 5
Step-by-step explanation:
n+5
2,7,12,17,22,27,32
Simplified the expression write your answer as a power
Answer:
2^8/3^8
Step-by-step explanation:
When multiplying powers with the same base, add the number in the exponent. For example, if you were multiplying 2^4 and 2^3, you would add 3 and 4 (3+4=7), and write your answer as 2^7. In this case, the bases being multiplied are both 2/3, so you can add 2 and 6 for a sum of 8 and put 8 as the exponent: (2/3)^8. The fully simplified expression is 2^8/3^8 because the exponent applies to both the numerator and the denominator.
its a lot but i hope this will help!! please lmk if i made a mistake
Answer:
256/6561
Step-by-step explanation:
Line AOB is a straight line.
Answer:
2nd, third and fifth options are the correct answers.
Step-by-step explanation:
Hope it helps you in your learning process.
simplify -(2x-3)+7-4x
-6x + 10 is the answer!!!!
QUESTION ATTACHED (on inverse proportion)
Answer:
this is the answer :) good luck
Answer: This is not my work! Don't report me!
Step-by-step explanation:
I don't really understand this but I found a similar question that was answered and that answer is expert verified. I hope its correct and it helps you!
During the 2020 NBA Season, Jimmy Butler played in the Championship Game against the Los Angeles Lakers. The total points scored by Jimmy Butler for the Conference Semifinals, Conference Finals, and Championship games are listed below. 12, 35, 22, 40, 25, 23, 22, 17, 24, 17, 14, 20, 17, 17, 30, 13, 40 What is the first quartile of the data set?
Answer:17
Step-by-step explanation:
Number them in order from lowest to highest and find the median it will help with finding the Q1
I give free brainlest :D
Answer:
Yes plz!
Step-by-step explanation:
Answer:
yeah sure i'll take some
Step-by-step explanation:
Tonya drives for 5 hours at 55 mph. How far does she go?
Is the domain of {-2, 1, 2, 3} and range of {2, 3} a function?
mb 4
Step-by-step explanation:
pweieieiwiwordiowleieieiqhqhe
reposting again
i will give brainliest to best answer
Answer:
the answer is c plz trust
Step-by-step explanation:
What is the value of x in the equation 3x − 5 = x + 7?
Answer:
6
Step-by-step explanation:
For each pair of pants, Pedro has 2 shirts. Which models show this relationship? Check all that apply.
Step-by-step explanation:
Given - For each pair of pants, Pedro has 2 shirts.
To find - Which models show this relationship?
Proof -
Let Pedro has total number of pair of pants = x
Now,
As given
For 1 pair of pants , Pedro has total number of shirts = 2
⇒For x pair of pants , total number of shirts = 2x
So, Total number of clothes Pedro has = x + 2x = 3x
Answer:it’s A and D
Hope this helped
What would the cross sections be of a triangular prism cut diagonally NOT through the base?
A circle
B ellipse
C rectangle
D square
E trapezoid
F triangle
Answer:it might be (F)
Step-by-step explanation:
Tell me if I’m right or wrong
Mr. Green baked 24 cookies. 5 sixths of the cookies were oatmeal. How many oatmeal cookies did Mr. Green bake?
Answer:
20
Step-by-step explanation:
there r 24 cookies
5/6 of 24 is 20 because 24/6 is 4 and 4*5 is 20
Answer:
20 oatmeal cookies
Step-by-step explanation:
If it is 6ths then divide 24 by 6 which is 4 and multiply 5 by 4 which is 20
If the complement of an angle is 79 degree , then the angle will be of .............measures
Answer:
11°
Step-by-step explanation:
90°-79°
=11°
Hope it helps
25 Points!!. $1.60 for 8 oz, (cheese)
What’s the unit price?
Find the missing length of the right triangle below
Answer:
C = 13
Step-by-step explanation: According to the pythagorean theorem, which states A² + B² = C². This means that in this equation 5²+12²=x². When we solve this we get 169=x². Since 169 is the perfect square of 13 therefore the answer is 13.
What is the measure of m
ned help asap will give brainly
Answer:
angle 5 and 8 are not vertical angles because they dont cross with another live diaglaly
Step-by-step explanation:
Answer:
Corresponding Angles: the angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.
Alternate Interior: The term alternate interior angles is often used when two lines are cut by a third line, a transversal .
Vertical Angle: each of the pairs of opposite angles made by two intersecting lines.
Step-by-step explanation:
The equation of the line l passing through (0, 3) and perpendicular to d: 5x + 3y = 0 is l: 5y − bx = c. What is the value of c?
9514 1404 393
Answer:
15
Step-by-step explanation:
The value of c can be found by using the given point values in the equation for the line.
5y -bx = c
5(3) -b(0) = c . . . . . fill in x and y
15 = c
Simplify the expression.
t+2+6t
Answer:
2t + 8
Step-by-step explanation:
add the like terms.