Find the value of k , if one of the two roots of the equation : x2 + k X – 98 = 0 is double
the additive inverse of the other.
«+
C
Given:
[tex]x^2+kx-98=0[/tex]
One of the two roots of the given equation is double the additive inverse of the other.
To find:
The value of k.
Solution:
Let two roots of the given equation are [tex]\alpha[/tex] and [tex]\beta[/tex].
According to the question,
[tex]\beta=2(-\alpha)[/tex] (Additive inverse of [tex]\alpha[/tex] is [tex]-\alpha[/tex])
[tex]\beta=-2\alpha[/tex]
If [tex]\alpha[/tex] and [tex]\beta[/tex] are roots of the quadratic equation [tex]ax^2+bx+c=0,[/tex] then
[tex]\alpha+\beta=-\dfrac{b}{a}[/tex]
[tex]\alpha\beta=\dfrac{c}{a}[/tex]
We have,
[tex]x^2+kx-98=0[/tex]
Here, a =1, b=k and c=-98.
[tex]\alpha+\beta=-\dfrac{k}{1}[/tex]
[tex]\alpha-2\alpha=-k[/tex] [tex][\because \beta=-2\alpha][/tex]
[tex]-\alpha=-k[/tex]
[tex]\alpha=k[/tex] ...(i)
Now,
[tex]\alpha\beta=\dfrac{c}{a}[/tex]
[tex]\alpha(-2\alpha)=\dfrac{-98}{1}[/tex] [tex][\because \beta=-2\alpha][/tex]
[tex]-2\alpha^2=-98[/tex]
Divide both sides by -2.
[tex]\alpha^2=49[/tex]
Taking square root on both sides.
[tex]\alpha=\pm \sqrt{49}[/tex]
[tex]\alpha=\pm 7[/tex]
Using (i), we get
[tex]k=\pm 7[/tex]
Therefore, the value of k is either -1 or 1.
Need this for my final... PLEASE. HELP
Answer:
I will answer it but what is the question?
Step-by-step explanation:
A gym membership charges a one-time application fee of $15, plus $32 each month. Which of the following equations could represent the total cost, y, for x number of months?
A.y = 32x + 15
B.y = 15x + 32
C.y = 47x
D.15y = 32x
Answer:
The answer is A. y =32x + 15
Step-by-step explanation:
The reason behind this is the rate. The amount of money each month is the slope (m). The additional fee would be the b.
Jada has 25% of her goal of $80 saved up for her trip. How much money does Jada have saved?
$20
36
$40
$35
$36.00
Answer:
$20
Step-by-step explanation:
trust me
Answer:
I believe $20 since 25% is 1/4 of 100% so 80/4 is 20 sorry if im wrong <3
select all the lines that have a slope of 5/2
Answer:
the answer is e i think.
Step-by-step explanation:
PLZZ HELPP IM FAILLING THIS CLASS
Answer:
Hope this helps!!! :)
Step-by-step explanation:
#1: if there is buy 1 get 1 free, then buy 6 get 3 free. so 2.8 times 3 = $8.4
#2: 4 for $3. break it up to 1 for $0.75. now 0.75 times 6 = $4.5
#3: the second one. $4.5 < $8.4
#4: 45 times 12 = $54
Pam buys 6 of these kits and has a total of 144 cookies and icing
packets. The equation shown represents
this situation.
6(x + 12) = 144
What does the variable x represent in Pam's equation?
>
A the number of cookies in one kit
B) the number of cookies in all 6 kits
the number of icing packets in all 6 kits
D the number of icing packets in one kit
Answer:
A
Step-by-step explanation:
Cane buys candy in bulk and sells it at a 25% markup. If c represents the original cost of the candy, which expression represents the markup price
Answer:
C. 1.25cStep-by-step explanation:
Options are: A. 25c B. 0.75c C. 1.25c D. 1.25c - 1.25---------------------
Original price = c
Markup = 25%
Markup price is:
c + 25% =c + 0.25c = 1.25cCorrect option is C
Plz help me with this
Answer:
The first choice
Step-by-step explanation:
It says that its decreasing so the slope is negative.
It also starts of with 565 so that's the y intercept
everything is above
Answer:
Option B
Step-by-step explanation:
8 - 2x < 18
Subtract 8 from both sides;
-2x < 10
Divide both sides by -2
x > -5
Answer:
X > -5
it would be B.
open circle on -5 and the arrow point on the right. Because x can be any number greater than -5.
Step-by-step explanation:
8 - 2x < 18
- 2x < 18 - 8
-2x < 10
x > 10/-2
x > -5
1/3^3= 1/27 I will need this answer soon as possible plz
Reduce by cancelling the common factors.
(13)x−1=27 Convert the exponential equation to a logarithmic equation using the logarithm base (13) of the right side (27) equals the exponent (x−1)log13(27)=x−1
Li bought his dog Spot a huge bone that is 15 inches long. Spot chews 4 inches off the bone every day. What is the new length of the bone after 3 days?
Answer:
3 inches
Step-by-step explanation:
If the dog chews off 4 inches every day, you first have to multiply the inches by the number of days, which in this case is 3 x 4, which equals 12. In 3 days, he chewed off 12 of the original 15 inches, leaving only 3 inches left.
A parallelogram is transformed according to the rule (x,y) → (x, y). Which is another way to state the
transformation?
Ro, 90°
Ro, 180°
Ro, 270°
Ro, 360°
Answer:
Ro, 360°
Step-by-step explanation:
Given
(x,y) transformed to (x,y)
Required
Determine the transformation
We have the following observations
Before transformation, the coordinates are: (x,y)
After transformation, the coordinates are: (x,y)
In other words, the coordinates before and after the transformation are the same.
This implies that there is a 360 degrees rotation.
Simply put, when there are no changes in the pre and post transformation of a point, line or shape, then the transformation is 360 degrees
The parallelogram transformed according to the rule (x,y) → (x, y), in other words can be stated as 360 degrees rotation (Ro, 360°).
360 degrees rotation
For 360 degrees rotation, the coordinates before and after the transformation will be the same.
According to this rule, the transformation of (x,y) gives (x, y)
Thus, the parallelogram transformed according to the rule (x,y) → (x, y), in other words can be stated as 360 degrees rotation (Ro, 360°).
Learn more about 360 degrees rotation here: https://brainly.com/question/98217
Which word phrase could represent 4÷m?
Abe was taking his 8-year-old brother to an amusement park. The cost of Abe's ticket was $32.75, and tickets for children age 12 and under was of that price. How much did Abe have to pay to get himself and his little brother into the park?
Answer:
$65.50
Step-by-step explanation:
Cost of Abe's ticket = $32.75
Tickets for children age 12 and under was of that price.
This means Abe's brother also paid $32.75 for tickets
Cost of Abe's brother tickets = $32.75
How much did Abe have to pay to get himself and his little brother into the park?
Total cost of the tickets = $32.75 + $32.75
= $65.50
OR
Total cost of the tickets = $32.75 × 2
= $65.50
3/4 square feet in 1/4 hour
Answer:
ill assume you're asking the answer for 1 hour
Step-by-step explanation:
multiply each side by 4. then, 12/4(3)=1
so 3 square feet and hour
(0,0)
M is the midpoint of CD. If the midpoint M
is (-3, 5) and C is (2,3), then what are the
coordinates of D?
O
(-1/2,4)
(-8,7)
o
(-4,1)
Answer:
The answer is (3-,5) watch is C cause if you do that but in math form it's the same
Write the verbal phrase as a algebraic expression
8 less than a number
Help me this hard it is due to day plzzzz
Answer:
line a
Step-by-step explanation:
because its going higher than line b and when it reaches 10 hours it he wil be way beyond his daugter
Answer: line a
Step-by-step explanation:
line a becuse the walking is going strigt ahead and it quicker too
An item had an original price of $5.00. It had a percent markup of 45%. What was the value of the markup?
Answer:
markup price = $2.25
Step-by-step explanation:
markup = 45% of $5
markup = 45/100 x 5
markup = $2.25
selling price = $5 + $2.25
selling price = $ 7.25
Answer:
$2.25
Step-by-step explanation:
edgems 2020-2021
-4(16+5)
Giving Brainlist out
Answer:
16
Step-by-step explanation:
-4(16+5)
5+16=20
20 sub -4 = 16
Write the equation of the line that passes through (-3,9) and is parallel to y = -2x + 5
Answer:
y = -2x +3
Step-by-step explanation:
Parallel lines always have the same slope
To insert the point, use the slope intercept formula: y =mx+b
insert y (9)
insert x (-3)
insert the slope -2
9 = (-2)(-3) + b
9 = 6+b
subtract 6 from both sides
3 = b
I give Brainlliest! 15 pionts!
Write the decimal as a percent.
0.768 =
Answer:
76.8%
Step-by-step explanation:
All you have to do is multiply the decimal by 100.
Answer:
76.8%
Step-by-step explanation:
I just did a thing and got the answer -v-
You are going to work out the problem 25.7 divided by 0.05. When you rewrite the problem what does dividend become?
Please answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!
Answer:
For every 2 boys in class, there is 1 girl in class
Step-by-step explanation:
Write an absolute value inequality for the graph
Step-by-step explanation:
sooooo hard
wysjamajaklansjsmz.zu
I'll be friend
What is the equation of the line through (4, -3) and (0, -2)?
A. y = 4x + 2
B. y=-4x - 2
C. y = -12- 2
D .y= 4x + 2
Brainliest to whoever is correct!
The correct product for the problem below.
[tex](- \frac{8}{5}) (\frac{2}{3}) (-4)[/tex]
A) -64/15
B) 64/15
C) 16/60
D) -16/60
E) 64/60
Answer:
[tex]\huge\boxed{\sf \frac{64}{15} }[/tex]
Step-by-step explanation:
[tex]\sf (-\frac{8}{5} )(\frac{2}{3})(-4)\\\\= \frac{(-8)(2)(-4)}{5*3} \\\\= \frac{64}{15} \\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807The jazz band is selling tickets to raise money for new music stands.
They already had some money in their account when they started
selling tickets at $5.00 each. After selling 3 tickets, the band had a
total of $50 in their account.
Let x = the number of tickets sold, and let y = the total
amount of money in the jazz band's account.
Write an equation in point-slope form.
Answer: y - $50 = $5*(x - 3)
Step-by-step explanation:
We know that each ticket is sold at $5.00
The band initially had an amount of money M.
We know that after selling 3 tickets, the band had $50
We can write this as:
M + 3*$5.00 = $50
M + $15 = $50
M = $50 - $15 = $35
We want to write the equation for the account in the point-slope form.
We know that the slope will be equal to the cost of a single ticket, and we already have the point:
x = 3
y = $50
Then we can write:
y - $50 = $5*(x - 3)
This is the equation we wanted to find.
Help me please.
Trevors mark on a math test was 10/15
Anne’s mark was 15/20
Trevor said each of us got 5 wrong so our marks are equal
Agree or disagree with this statement
