Answers
Answer:
The values of k that make the given equation having imaginary roots are:
k < -18, or (-∞,-18).
Step-by-step explanation:
Nature of the Roots of a Quadratic Equation
The standard representation of a quadratic equation is:
[tex]ax^2+bx+c=0[/tex]
where a,b, and c are constants.
Solving with the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
The expression:
[tex]d=b^2-4ac[/tex]
Is called the discriminant. The discriminant determines the nature of the roots of a quadratic equation as follows:
If d=0, there is only one real root.
if d>0, there are two different real roots
if d<0, there are two different imaginary (complex) roots
We are given the equation:
[tex]-2x^2+12x+k=0[/tex]
Comparing with the standard quadratic equation, we have:
a=-2, b=12, c=k
Calculating the discriminant:
[tex]d=12^2-4(-2)k[/tex]
[tex]d=144+8k[/tex]
If the equation has imaginary roots, then d<0, thus:
144 + 8k < 0
Subtracting 144:
8k < -144
Dividing by 8:
k < -18
The values of k that make the given equation having imaginary roots are: k < -18, or (-∞,-18).
Related Questions
what additional information is needed that the following triangle are congruent by SSS
Answers
Answer:
Side ACwith DF
Step-by-step explanation:
need to be taught how to do this, thanks
Answers
Answer:
x = 36.27
Step-by-step explanation:
By using the steps to find sin θ backwards, we can find x, the hypotenuse.
sin θ = [tex]\frac{opposite}{hypotenuse}[/tex] or side [tex]\frac{a}{c}[/tex] (as seen in my example picture).
We already know the value for sin (α), which is 32° because its given. The opposite side (a) is 20 and the hypotenuse side (c) is x which are both also given.
So the equation now looks like:
sin 32° = [tex]\frac{20}{x}[/tex]
Don't solve for the sin 32 yet! First, we have to isolate the variable.
To get rid of the x in the denominator you have to multiply both sides by x:
( sin 32 ) · x = ( [tex]\frac{20}{x}[/tex] ) · x
( sin 32 ) x = 20
Then, you have to divide both sides by sin 32 to get x by itself:
(( sin 32 ) x ) ÷ ( sin 32 ) = 20 ÷ ( sin 32 )
x = 20 ÷ ( sin 32 )
Lastly, you have to use a calculator to find 20 ÷ ( sin 32 ), and it should give you 36.2695543766.
The question asks you to round to 2 decimal places so:
x = 36.27
A jacket was on sale for 20% off its original price of $60. Now, it is on sale for an additional 10% off its previous sale price. Determine whether each statement is true or false. True False The jacket is now 40% off its original price. The jacket now costs $48.00. The jacket is now 72% of its original price. The jacket now costs $43.20.
Answers
Answer:
Step-by-step explanation:
Step one:
given
original price= $60
discount =20% of 60
discount = 20/100*60
discount = 0.2*60
discount = $12
selling price= 60-12= $48
Added price= 10% off $48
Added price= 10/100 *48
Added price= 0.1 *48
Added price= $4.8
new price= 4.8-48=$43.2
the new price of the jacket is $43.2
1. The jacket is now 40% off its original price
40/100*60=$24-----False
2. The jacket now costs $48.00-----False
3. The jacket is now 72% of its original price= 72/100*60=$43.2----True
4. The jacket now costs $43.20------True
HURRY I NEED HELP QUICK!!!!!!!
Which equation represents the graph shown?y =
y = x - 35
y = x + 35
y = 35 x
y = x/35 (fraction)
Answers
Answer:
y = 35xStep-by-step explanation:
If you notice, point 4 on the x-axis (horizontal) coincides with 140 on the y-axis.
If you multiply x * 35 = 140
x is four.
Please need helppppp
Answers
Answer:
90 degrees
Step-by-step explanation:
Hope this helps with your answer
please help! it’s a true or false question plssss!
Answers
Answer:
True
Step-by-step explanation:
Mr. Win owns a toy store. He wants to display 12 new motion toys in the store window. Each toy uses 3 batteries. If N represents the total number of batteries he needs, which sentence is correct?
Answers
Answer: See explanation
Step-by-step explanation:
You didn't state the sentences but let me help out based on the information given.
Number of new motion toys = 12
Number of batteries used by each toy = 3
Since N represents the total number of batteries he need, the value of N will be:
= Number of toys × Number of batteries used by each toy
= 12 × 3
= 36
That means N equals 36.
what is the reciprocal of 4, 5/2, and 1/2
Answers
Answer:
1/4 2/5 2/1
Step-by-step explanation:
repcpical means you flip them upside down
Answer:
[tex]\frac{1}{4}[/tex], [tex]\frac{2}{5}[/tex], [tex]and[/tex] [tex]\frac{2}{1}[/tex]
Step-by-step explanation:
Remember, to find the reciprocal of a fraction, you just have to switch the 2 numbers into the opposite place.
Q1: [tex]\frac{4}{1}[/tex] ⇒ [tex]\frac{1}{4}[/tex]
Q2: [tex]\frac{5}{2}[/tex] ⇒ [tex]\frac{2}{5}[/tex]
Q3: [tex]\frac{1}{2}[/tex] ⇒ [tex]\frac{2}{1}[/tex]
Hope this helps! <3
-13/20 - 7/5 = what
Answers
Answer:
Step-by-step explanation:
-13/20 - 7/5= -41/20 or -2 1/20 or -2.05
Simplify the expression.
20(p + 2) + 16(-3 - p)
Answers
X-X=
write the solution too.
Answers
Answer:
0
Step-by-step explanation:
X-X
=0
if anils hieght was 150cm and amans height was 100cm then the ratio of their heights would be
Answers
Answer:
3/2 or 150%
Step-by-step explanation:
150:100 = 150/100 = 15/10 = 3/2
In other words, 150%
does anyone know what 3.2 ÷ 0 ???
Answers
Answer:
Infinity
Step-by-step explanation:
Look it up, its how it works. 0 can go into 3.2 infinity times.
What is the rate of change for -8x-4y=10-2x+6y
Answers
Answer:
X7
Step-by-step explanation:kk
Jenna collected data on how many CDs her friends owned and how many hours per week they listened to music. Her data is shown in the table.
CDs Owned
15/15/8/18/11
Hours Listened 7 8 5 10 9
Which scatter plot correctly represents this data?
ОА
Ос.
new
CDS Ow
12 16
CDs Owned
Ов.
OD.
CDs Owned
CDs Owned
Answers
Answer:
im pretty sure it would be d
Step-by-step explanation:
Answer:
It is D
Step-by-step explanation:
got it right on the test
What is an equation of the line with slope 6 and y-intercept -4 in slope-intercept form?
Answers
Answer: y = 6x-4
Step-by-step explanation:
The formula for slope-intercept is y=mx+b so all you have to do is plug in the slope which is m and plug in the y intercept which would be b
Plz don’t take s these points if u don’t know how to do these math I just need help I wanna pull up my grade :(
Answers
Answer: For The first Picture I think the Surface area is 234in^2
For the second picture 72in^2
For the third picture 102in^2
Step-by-step explanation:
Answer:
234
192
102
Step-by-step explanation:
Which equation can be used to represent the statement? Half of a number minus seven is one and five-tenths. One-half + x = 1.5 One-half x minus 1.5 = 7 StartFraction x over 2 EndFraction minus 7 = 1.5 7 minus StartFraction x over 2 EndFraction = 1.5
Answers
Given:
Statement is "Half of a number minus seven is one and five-tenths."
To find:
The equation for the given statement.
Solution:
Let the unknown number be x.
Half of a number : [tex]\dfrac{x}{2}[/tex]
Half of a number minus seven : [tex]\dfrac{x}{2}-7[/tex]
One and five-tenths : [tex]1\dfrac{5}{10}=1.5[/tex]
Half of a number minus seven is one and five-tenths:
[tex]\dfrac{x}{2}-7=1.5[/tex]
The required equation for the given statement is [tex]\dfrac{x}{2}-7=1.5[/tex].
Therefore, the correct option is C.
Answer:
its c
Step-by-step explanation:
Find the slope between these two points:
(-5,3) and (4,6)
Answers
Answer:
1/3
Step-by-step explanation:
Stephon went to the Griffin Fair with $25.50. He bought a hot dog and a drink for $4.25, and he wanted to spend the rest of his money on ride tickets which cost $1.25 each. What is the maximum number of ride tickets that he can buy?
Answers
17
Step-by-step explanation:
$25.50-$4.25=$21.5 [ 21.5 is the mony he has left after he bought the food]
$21.25÷$1.25=17 [we will divide the rest of his mony with the cost of 1 ticket so we can get how many tickets he can buy]
A firecracker is fired straight up into the air out of a window of a building. Its height, in meters, is given by h = − 5 t 2 + 30 t + 20 , where t is the time, in seconds, the fircracker has been in the air.
Answers
Answer:
See explanation
Step-by-step explanation:
Given that the equation for the firecracker is h = − 5 t^2 + 30 t + 20
It is impossible to solve this question unless the height (h) in meters is supplied. If the height was supplied, we could set up the quadratic equation and solve it yielding two values for the time. The values of t obtained is the time in seconds required for the firecracker to reach the given height h.
You can apply these tips and solve the question seamlessly.
7x-5=2x SOLVE THE PROBLEM
Answers
Answer:
x = -17.5
Step-by-step explanation:
7x-5= -35
-35/2 = -17.5
Answer: The answer is x=1.
Step-by-step explanation: To solve this problem you’ll need to isolate the variable by dividing each side by factors that don't contain the variable.
What percent of the model is shaded? What is the equivalent ratio? What is the equivalent decimal? What is the equivalent fraction?
Answers
Answer:
73 73/100 0.73 73/100
Step-by-step explanation:
hope this helps
73% of the model is shaded, 146/200 is the equivalent ratio.0.73 is the equivalent decimal and 146/200 is the equivalent fraction
What is Fraction?A fraction represents a part of a whole.
Given,
A grid model with 100 squares. 73 squares are shaded.
We need to find percent of the model is shaded
As there are 100 grids with 73 shaded.
73% of the model is shaded
Now let us find equivalent ratio of 73/100
Multiply numerator and denominator 2
73/100×2/2
146/200
146/200 is the equivalent ratio.
73/100=0.73 is the equivalent decimal.
146/200 is the equivalent fraction.
Hence,73% of the model is shaded, 146/200 is the equivalent ratio.0.73 is the equivalent decimal and 146/200 is the equivalent fraction.
To learn more on Fractions click:
https://brainly.com/question/10354322
#SPJ2
Which graphs show continuous data?
Select each correct answer.
A line graph with Outdoor Temperature on the horizontal axis and Heating Cost on the vertical axis with a single line decreasing from left to right
A line graph with Outdoor Temperature on the horizontal axis and Heating Cost on the vertical axis with a single line decreasing steeply from left to right
A line graph with Outdoor Temperature on the horizontal axis and Heating Cost on the vertical axis with a single line starting from a high Heating Cost point decreasing from left to right
A graph with Outdoor Temperature on the horizontal axis and Heating Cost on the vertical axis with six points decreasing in a steep linear formation from left to right
Answers
Answer:
A B and D
Step-by-step explanation:
Answer:
Ok, ok, I see what's happening here
You're face to face with greatness, and it's strange
You don't even know how you feel
It's adorable
Well, it's nice to see that humans never change
Open your eyes, let's begin
Yes, it's really me, it's Maui
Breathe it in
I know it's a lot
The hair, the bod
When you're staring at a demi-god
What can I say except, "You're welcome"
For the tides, the sun, the sky
Hey, it's okay, it's okay
You're welcome
I'm just an ordinary demi-guy
Hey
What has two thumbs and pulled up the sky
When you were waddling yea high?
This guy
When the nights got cold
Who stole you fire from down below?
You're lookin' at him, yo
Oh, also I lassoed the sun
You're welcome
To stretch your days and bring you fun
Also I harnessed the breeze
You're welcome
To fill your sails and shake your trees
So what can I say except you're welcome
For the islands I pulled from the sea
There's no need to pray, it's okay
You're welcome
Ha, I guess it's just my way of being me
You're welcome
You're welcome
Well, come to think of it
Kid, honestly I could go on and on
I could explain every natural phenomenon
The tide, the grass, the ground
Oh, that was Maui just messing around
I killed an eel
I buried its guts
Sprouted a tree, now you got coconuts
What's the lesson?
What is the take-away?
Don't mess with Maui when he's on a break-away
And the tapestry here on my skin
Is a map of the victories I win
Look where I've been
I make everything happen
Look at that mean mini-Maui just tickety-tappin'
(Ha ha ha ha ha ha, hey)
Well, anyway let me say, "You're welcome" (you're welcome)
For the wonderful world you know
Hey, it's okay, it's okay, you're welcome (you're welcome)
Well, come to think of it, I gotta go (hey)
Hey, it's your day to say, "You're welcome" (you're welcome)
'Cause I'm gonna need that boat
I'm sailing away, away, you're welcome (you're welcome)
'Cause Maui can do anything but float
You're welcome
(You're welcome)
You're welcome
And thank you
Which expression is equivalent to x-4?
Answers
Answer:
c) [tex](1/x)^{4}[/tex]
Step-by-step explanation:
[tex](1/x)^{4}[/tex] = [tex]1^{4} /x^{4}[/tex]
=> 1 /[tex]x^{4}[/tex]
=> [tex]x^{-4}[/tex]
If my answer helped, kindly marl me as the brainleist!!
Answer:
Choice C. X^-2 + x^-2
Step-by-step explanation:
When u have exponents u either add them or subtract them.
Here u just do -2 + -2 which gives u an exponent of x^-4.
What percent of 50 is 15?
A. 4%
B. 25%
C. 30%
D. 15%
Answers
30% is the answer........
Answer:
Option C 30%
Step-by-step explanation:
let x%of 50 is 15
X/100×50=15
50x/100=15
X/2=15
X=30
So option C. (30%) is correct
In the diagram, PT is parallel to QR. What is the measure of angle PQR in degrees?
Answers
Answer:
116 degrees
Step-by-step explanation:
Help with this one question please
Answers
Answer:
x [tex]\leq[/tex] 6
Place a 0 in the center of your line. Mark 6 units to the right and fill in a circle at the number 6. Then draw an arrow starting at the number 6 to the left. This should all be done on the line aka your graph.
Step-by-step explanation:
Expand
2x + 6 [tex]\leq[/tex] 18
Solve for x
2x [tex]\leq[/tex] 12
x [tex]\leq[/tex] 6
Everything is shown below (the answer and step-by-step explanation):
What is the slope of the line through (-7, -8) and (0,4)
Answers
Help me you guys
ILYG
Answers
Answer:
7
Step-by-step explanation:
The answer is 7
Answer:
It's 7
Hope this helped!