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.
Triangle ABC has coordinates A(1, 1); B(2, 5); C(5, 1). What would be the coordinates of A'B'C' if you translated ABC left 2 and up 5 units? (Hint: x-values go left and right; y-values go up and down) *
A'(-1, 6) B'(0, 10) C'(3, 6)
A'(3, -4) B'(4, 0) C'(7, -4)
Answer:
A'(-1, 6) B'(0, 10) C'(3, 6)
Answer:
I would say it's the first one
What does it mean for a line to have an undefined slope?
Answer:
it means it is a vertices line and the x coordinates never change
Step-by-step explanation:
What is the solution set for -4x - 10 ≤ 2?
x ≤ -3
x ≥ -3
x ≤ 2
x ≥ 2
The relationship between two numbers is described below, where x represents the first number and y represents the second number.
The square of the first number is equal to the sum of the second number and 16. The difference of 4 times the second number and 1 is equal to
the first number multiplied by 7.
Select the equations that form the system that models this situation. Then, select the solution(s) of the system.
X=y+16
4y-1=7
Solve on both sides
4y=8
Y=8/2
Y=4
X= (4)+16
X=20
What is the surface area of a cylinder with a radius of 6 cm and a height of 3 cm?
A.108cm
B.72cm
C.54cm
D.36 cm?
Step-by-step explanation:
2πr^2h
2*22/7*6*6*3
2*22/7*36*3
2*22/7*108
someone please help!! 60 points!!
Answer:
It C am sure it correct....
Answer:
I think the answer would be C.
calculate the perimeter of this figure to the nearest tenth
Answer:
40.9
Step-by-step explanation:
Perimeter = 8 + 10 + 10 + 4 + 8.9
=> 20 + 4 + 8.9 + 8
=> 32 + 8.9
=> 40.9
This is already in the nearest tenth, so the answer = 40.9
If my answer helped, kindly mark me as the brainliest!!
Thank You!!
ANSWER ASAP FOR 35 POINTS!!
A pool has a diameter of 12 feet and a height of 2 feet. If each cubic foot holds 7.48 gallons of water, about how many gallons of water can the pool hold? Use 3.14 for pi.
A) 6764 gallons
B) 2255 gallons
C) 1691 gallons
D) 564 gallons
Answer:
cc
Step-by-step explanation:
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-
which equation represents the line that passes through points (5, 4) and (-5, 0)
The equation should be [tex]y = 2\div 5x + 2[/tex]
Given that,
The points are (5, 4) and (-5, 0)Based on the above information, the calculation is as follows:
here we need to find the slope.
[tex]= (y_2-y_1)\div (x_2-x_1)\\\\= (0-4)\div (-5-5) \\\\= -4\div -10 \\\\= 2\div 5\\\\Y = 2\div 5x + b[/tex]
Now
Put in one point
[tex]4 = 2\div 5(5) + b, b = 2[/tex]
So,
[tex]y = 2\div 5x + 2[/tex]
Learn more: https://brainly.com/question/1301963?referrer=searchResults
pls help i'll give branliest
Answer:
50
Step-by-step explanation:
good luck!!
Answer:
50
Step-by-step explanation:
hope its correct..............
help please I will give brainiest
The tens digit of a two-digit number is 1 less than 3 times the units digit. If the digits are reversed, the new number is 45 less than the original number. Find the number
Answer:
32 is the
number
Step-by-step explanation:
Expand the function f(x)=(3x+2)^4 with the binomial theorem, not factored
Step-by-step explanation:
Enter a problem...
Algebra Examples
Popular Problems
Algebra
Expand using the Binomial Theorem (3x+2)^4
(3x+2)4(3x+2)4
Use the binomial expansion theorem to find each term. The binomial theorem states (a+b)n=n∑k=0nCk⋅(an−kbk)(a+b)n=∑k=0nnCk⋅(an-kbk).
4∑k=04!(4−k)!k!⋅(3x)4−k⋅(2)k∑k=044!(4-k)!k!⋅(3x)4-k⋅(2)k
Expand the summation.
4!(4−0)!0!⋅(3x)4−0⋅(2)0+4!(4−1)!1!⋅(3x)4−1⋅(2)+4!(4−2)!2!⋅(3x)4−2⋅(2)2+4!(4−3)!3!⋅(3x)4−3⋅(2)3+4!(4−4)!4!⋅(3x)4−4⋅(2)44!(4-0)!0!⋅(3x)4-0⋅(2)0+4!(4-1)!1!⋅(3x)4-1⋅(2)+4!(4-2)!2!⋅(3x)4-2⋅(2)2+4!(4-3)!3!⋅(3x)4-3⋅(2)3+4!(4-4)!4!⋅(3x)4-4⋅(2)4
Simplify the exponents for each term of the expansion.
1⋅(3x)4⋅(2)0+4
Hope this helps!
Answer:81x^4+216x^3+216x^2+96x+16
Step-by-step explanation:cause yussss
Pllzzzz help it’s an exam !!!! A side of the triangle below has been extended to form an exterior angle of 125 . Find the value of x
Answer:35
Step-by-step explanation:
take 180 and subtract those numbers and u get ur answer
The correct answer in the box. Linear function g is shown in the graph.
Write the slope-intercept form of the equation representing this function.
Answer:
this is right on the test
Step-by-step explanation:
Answer:
The correct answer is
g(x)=2x+1
Step-by-step explanation:
I got it right on the Edmentum test.
Simplify:
3-2i
-11-8i
Answer:
1i and -19i
Step-by-step explanation:
3-2=1, therefor: 1i
-11-8=-19, therefor: -19i
Which equation represents the function graphed on the coordinate plane?
g(x)=|x+4|-2
g(x)=|x-4|-2
g(x)=|x-2|-4
g(x)=|x-2|+4
please help me this is due in a couple of minutes!!!!!! please help me.
Answer: A g (x)= [x+4]-2
Step-by-step explanation:
Donna wants to calculate the height of a tree. She finds the length of the tree's shadow is 25 meters and the angle of elevation from the ground to the top of the tree is 30°. Find the height of the tree to the nearest whole number.
Answer:55
Step-by-step explanation:
5(x+3)-5
simplify this.
Answer:
5x+10
Step-by-step explanation:
Distribute:
=(5)(x)+(5)(3)+−5
=5x+15+−5
Combine Like Terms:
=5x+15+−5
=(5x)+(15+−5)
=5x+10
By which rule are these triangles congruent?
A) AAS
B) ASA
C) SAS
D) SSS
Answer:
A) AAS
Step-by-step explanation:
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
Pencils were ordered in boxes containing 6 pencils each. The grade level has 100 students. If the teachers want to start the year with 4 pencils per student, how many boxes do they need to buy before the school year starts?
Answer:
67
Step-by-step explanation:
(4*100)/6
=400/6
=66.67
Round to get 67
which of the following equations represents the graph?
A. y = 3/4x - 3
B. y = 3/4x + 4
C. y = 4/3x - 3
D. y = 4/3x + 4
Answer:
D) 4/3 x + 4
Step-by-step explanation:
The y-intercept is at point (0, 4) and the x--intercept is at point (-3, 0).
The equation for every straight line is y = mx + b. y is y, m is the slope, x is x, and b is the y value in the y-intercept
Now we will use the formula for slope, which is rise/run or more understandable , the change in y/change in x.
y2 - y1/x2 -x1
0 - 4/-3 - 0
-4/-3 = 4/3
Remember when I said the y-intercept was (0, 4) and b was the value of the y in the y-intercept? 4 is the value of y in the y-intercept.
The answer is 4/3x + 4.
what is 2/3x + 1/4x= 6 ??????
Answer:
x=72/11
Step-by-step explanation:
PLEASE HELP
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why AHIJE AKLM?
Check all that apply.
А. НА
B. ASA
C. AAS
D. LL
E. HL
F. LA
Answer:
Option A and Option C
Step-by-step explanation:
Given:
IJ ≅ LM
∠J ≅ ∠M
To Prove:
ΔHIJ ≅ ΔKLM
Statements Reasons
1). IJ ≅ LM 1). Given
2). ∠J = m∠M 2). Given
3). ΔHIJ ≅ ΔKLM 3). By HA property Or AAS property of
congruence
Therefore, Option A and Option C are the correct options.
If , which equation describes the graphed function? A. y = f(-x) − 3 B. y = -f(x) + 3 C. y = -f(x) – 3 D. y = f(-x) + 3
Answer:
y=-f(x)-3
Step-by-step explanation:
when f is negative it is reflected over the x-axis and -3 means to translate 3 units down
y = -f(x) – 3 describes the graphed function.
When f is negative it is reflected over the x-axis.
-3 means to translate 3 units down.
How do you identify a function?By using inspecting the inputs (x-coordinates) and outputs (y-coordinates), you could decide whether or no longer the relation is a function. Keep in mind, that this is a feature each input has only one output.
What are examples of graph functions?Function Graphs.Linear. Quadratic. Cubic. Square Root. Cube Root. Absolute Value. Reciprocal.Learn more about graph functions here: https://brainly.com/question/4025726
#SPJ2
Does anyone know how to do this I’ve been trying for hours and I can’t find anything to help me?
Answer:
Honestly dude try your hardest u got this i belive in u ask your mom or dad or big brother or big sister if your seeing this right now im trying to help if if u love your mom u would do the same.
Step-by-step explanation:
The ratio of boys to girls in Coach Sheppard's class is 3 to 5. There are 20 girls in the
class.
What is the total number of students in Coach Sheppard's class?
Answer:
32 Students
Step-by-step explanation:
3/5 = 12/20
This means you add the boys and girls to get 32.
select the equation that represents the function given in the table below:
Please help!
Answer:
im to lazy to do an equation
Step-by-step explanation:
