Answers
9514 1404 393
Eexplanation:
16. Suppose the roots are α and kα. Then we can write the equation as ...
a(x -α)(x -kα) = 0
ax² -ax(α +kα) +akα² = 0
Comparing to the original equation, we can equate coefficients to get ...
b = -aα(1+k)c = akα²Solving the first for α gives ...
α = -b/(a(1+k)
Substituting into the second, we have ...
c = ak(-b/(a(1+k)))²
Multiplying by a(1+k)², we get ...
(1+k)²ac = kb²
Using k=2 gives ...
9ac = 2b² . . . . . as required
__
17. Using the previous result with k=1 (equal roots), we have ...
(1+k)²ac = kb²
4ac = b² . . . . . for k=1
______
Additional comment
We observed that the problems were similar, but had different factors relating the roots. So, we elected to solve the general case, then fill in the specific values for the two problems.
Related Questions
what is the slope of the line that passes through the points (7, -5) and (10, -7.5)?
A:
[tex] \frac{5}{6} [/tex]
B:
[tex] \frac{6}{5} [/tex]
C:
[tex] - \frac{5}{6} [/tex]
D:
[tex] - \frac{6}{5} [/tex]
Answers
Answer:
C. [tex]-\frac{5}{6}[/tex]
Step-by-step explanation:
just use the equation [tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex] So our first point (7,-5) will be [tex]x_1=7,y_1=-5[/tex]and our second point (10, -7.5) will be [tex]x_2=10,y_2=-7.5[/tex] Then substitute[tex]slope=\frac{(-7.5)-(-5)}{(10)-(7)}=\frac{-2.5}{3}=-\frac{5}{6}[/tex]NEED HELP! just with the 1st 2
Answers
factor completely.
6x^2- 150
A) 6(x-5)^2
B) 6(x-5) (x+5)
C) (3x+2) (2x-75)
D) 6(x+5)^2
E) (2x-15) (3x+10)
Answers
Answer:
B) 6(x-5) (x+5)
Step-by-step explanation:
Common factor.
6 ( ^2 − 25)
Use the sum-product pattern.
6 ( ^2+5−5−25).
Common factor from the two pairs.
6((+5)−5(+5)).
Rewrite in factored form.
6 ( − 5 ) ( + 5).
solve the proportion : 3/8/1=x/8
Answers
Answer: 3
8
1
=
x
8
Also its in a fraction that's why i put it that way.
Step-by-step explanation:
3
8
1
=
x
8
Step 1: Cross-multiply.
3
8
1
=
x
8
(
3
8
)*(8)=x*(1)
3=x
Step 2: Flip the equation.
x=3
Answer:
x=3
what would be the slope intercept form?
Answers
Answer:
[tex]y=\frac{7}{2} - 4[/tex]
Step-by-step explanation:
y = mx + b
Where M is the slope and b is the Y-intercept
Explanation: the slope intercept formula is y=mx+b. The slope is m so it’s 7/2 and the y intercept is -4 so you plug it in.
Is this function linear or nonlinear?
y=2x2−4
10 POINTS
Answers
Answer:
I think it's nonlinear
Which is an equation of the line with a slope of 1/4 and a
y-intercept of - 2?
Answers
Answer:
y = 1/4x - 2
Step-by-step explanation:
I hope this helps :)
Answer:
y = 1/4x - 2
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Slope m = 1/4
y-intercept b = -2
Step 2: Plug into formula
y = 1/4x - 2
Please help if you know trig, will give brainliest! Thank you!
Answers
Answer:
sin^2(a) I believe. Delete my response if needed.
Step-by-step explanation:
tan²(α) (2 cos²(α) + sin²(α) - 1)
Recall that sin²(α) + cos²(α) = 1 for all α. Then sin²(α) - 1 = -cos²(α) :
tan²(α) (2 cos²(α) - cos²(α))
tan²(α) cos²(α)
Rewrite tan(α) = sin(α) / cos(α) :
(sin(α) / cos(α))² cos²(α)
(sin²(α) / cos²(α)) cos²(α)
Cancel the factors of cos²(α) :
sin²(α)
A computer technician charges customers $75 per hour.
Let h represent the number of hours the technician works.
o f(h) = 75 + h
o f(h) = 75 + h
Of(h) = 75h
Of(h) = 75 - h
Answers
Answer:
C. f(h)=75h
Step-by-step explanation:
That is the answer, hope it helps!
Answer:
it is the first one f(h)=75+h
24. Michael leaves his house at 0837 and travels by motorcycle to the railway station, which is 27 km from his
house.
(i) If he arrives at the station 36 minutes later, find the average speed at which he travels in km/h.
(ii) If the train, which is due at 0942, is 11 minutes late, how long will he have to wait?
Answers
Answer:
i) 45km/hr
ii)29 min
Step-by-step explanation:
average speed = distanced travelled / time elapsed
It took 36min and need to convert to hr
36min x [tex]\frac{hours}{60 min}[/tex] = [tex]\frac{36 hr}{60 min}[/tex] = [tex]\frac{9 }{15 }[/tex] hours
distanced travelled is 27 km;
average speed = 27km / (9/15hr) = 45 km/hr
Add 36min to 0837 becomes 0913, the train will arrive at 0942 and the wait will be the difference of 0942 - 0913 = 29 min
what is the square root of 81 by the difference between the product of -1 and -3 and the square root of 4
Answers
Answer:
3
Step-by-step explanation:
The expression is [tex]\sqrt{81} -(-1*-3*\sqrt{4})[/tex] Type the expression into a calculator.
01:29:01 Nikhil gets paid a 5 percent commission on every pair of shoes that he sells. He earned $1.00 on the last pair of shoes that he sold. The expression that can be used to represent x, the price of the shoes, is 0.05 x = 1 What was the price of the shoes?
Answers
Answer:
the price of the shoes is $20
Step-by-step explanation:
According to the question, The computation of the price of the shoes is shown below:
Data provided in the question
0.05x = 1
Based on the above information
We now solve for x
x = 1 ÷ 0.05
It can be written as
= 100 ÷ 5
= $20
hence, the price of the shoes is $20
Find the value of x
Answers
Answer:
65
Step-by-step explanation:
remember a TRIANGLE always have a 180 degrees total angle,
so 45+70=115
180-115=65
A rocket ship travels at 2.0×104 miles per hour. If a satellite is 2.5×105 miles from Earth, how long will it take the rocket to make the trip from Earth to the satellite? (Hint: Divide the distance to the satellite by the speed.) Write your answer in scientific notation.
Answers
Answer:
20104 and 25105
Step-by-step explanation:
Which identity is the result of using the pythagorean theorem to show that a triangle with side lengths x^2 - 1, 2x, and x^2 + 1 is a right triangle?
A. (x^2 - 1)^2 + (2x)^2 = -(x^2 + 1)^2
B. -(x^2 -1)^2 + (2x)^2 = (x^2 +1)^2
C. (x^2-1)^2 + (2x)^2 = (x^2 +1)^2
D. (x^2 - 1)^2 - (2x)^2 = (x^2 + 1)^2
Answers
9514 1404 393
Answer:
C. (x^2-1)^2 + (2x)^2 = (x^2 +1)^2
Step-by-step explanation:
Inexplicably, three of the four answer choices have minus signs in them. Those are all incorrect. The appropriate choice is ...
C. (x^2-1)^2 + (2x)^2 = (x^2 +1)^2
__
Expanded, this is ...
x^4 -2x^2 +1 +4x^2 = x^4 +2x^2 +1 . . . . the desired identity
Answer:
C. (x^2-1)^2 + (2x)^2 = (x^2 +1)^2
Step-by-step explanation:
The battery life for Bruhier's cell phone is longer when he has fewer apps running. When only one app is running, the battery will last for
16 hours. When four apps are running, the battery will only last for 4 hours.
This situation represents
variation.
The constant of variation, k, is equal to
If eight apps are running, Bruhler's battery will last for 4 hours
Answers
Answer:
inverse, 16, 4
Step-by-step explanation:
The constant of variation when eight apps are running, battery lasts for 4 hours is 32.
What is Inverse Variation?When a variable varies inversely with the other variable, i.e. on increasing one variable the other decreases is called Inverse Variation.
The battery life varies inversely with the number of apps running
The battery life is denoted by b
and the number of apps is denoted by a
then
[tex]\rm b\; \alpha \; (1/a)\\\\b = k /a[/tex]
here k is the proportionality constant
The battery lasts for 16 hours when the apps opened is 1
The battery lasts for 4 hours when the apps opened is 4
16 = k
The constant of variation when eight apps are running, battery will last for 4 hours
[tex]\rm 4 = k /8[/tex]
k = 32
To know more about Inverse Variation
https://brainly.com/question/11592410
#SPJ2
The triangles in the picture are congruent by which method
Answers
Answer:
ASA
Step-by-step explanation:
Anyone????? That can help me answer these
Answers
Answer:
5. 3050ft³ (rounded to 3 s.f.)
6. 4190ft³(rounded to 3 s.f.)
7. 4600ft³(rounded to 3 s.f.)
Formulas (For easier reference):
Volume of a cone: pi×r²×[tex]\frac{h}{3}[/tex]
Volume of cylinder: pi×r²×h
Volume of a sphere: [tex]\frac{4}{3}[/tex]×pi×r³
Volume of a hemisphere: [tex]\frac{2}{3}[/tex]×pi×r³
Step-by-step explanation:
You can just apply the formulas to the question:
5. Volume of cone = pi×9²×[tex]\frac{(16-10)}{3}[/tex]
= 162pi
Volume of cylinder = pi×9²×10
= 810pi
Volume of figure = 162pi+810pi
= 972pi
= 3050ft³ (rounded to 3 s.f.)
6. Volume of sphere = [tex]\frac{4}{3}[/tex]×pi×10³
= 1333[tex]\frac{1}{3}[/tex]pi
= 4190ft³(rounded to 3 s.f.)
7. Volume of hemisphere = [tex]\frac{2}{3}[/tex]×pi×(26÷2)³
= 1464[tex]\frac{2}{3}[/tex]pi
= 4600ft³(rounded to 3 s.f.)
The local farm market sell peppers at five for $2.25
Answers
Answer:
Wait what is the question?
(x + 26)
(3x)
X=
Helpppp
Answers
Answer:
x = 13
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesGeometry
Vertical AnglesStep-by-step explanation:
Step 1: Set up equation
3x = x + 26
Step 2: Solve for x
Subtract x on both sides: 2x = 26Divide 2 on both sides: x = 13How many kilograms equal 22 pounds? [1 pound = 0.454 kilogram
Answers
Answer: 9.97903k = 21.99999528
10k = 22.0462p
Step-by-step explanation:
Answer:
B 9.988
LOLOLOLOL
4y – 9 = -63
Someone, please help me find the steps of this equation!!
HELP ME PLEASE!!!
Answers
Answer:
The answer is y=-13.5
Step-by-step explanation:
4y-9=-63
add 9 from both sides because it's negative
4y=-54
divide both sides by 4 to isolate the variable
y=-13.5
Answer:
4y-9=-63
add 9 from both sides because it's negative
4y=-54
divide both sides by 4 to isolate the variable
y=-13.5
Can someone help me I don’t understand this
Answers
Use pythagorean theorem to get EG. If you have EG, you also have all the sides of the equilateral triangle.
On a number line, which fraction would is to the right of
1/2
A)
2/12
B)
1/3
C)
10/20
D)
16/25
Answers
Answer:
B
Step-by-step explanation:
Edge 2020
Answer:d
Step-by-step explanation:
I got it right 100%
Select the equation of a line in slope-intercept form that passes through (-2, 2) and is perpendicular to the graph of y=1/2 x-3.
O A y=-2x + 2
O B. y=-2x - 2
O C. y=x-2
O D.y= 3x+2
Answers
Answer:
B
Step-by-step explanation:
Topic: Coordinate Geometry
If you would like to venture further, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!
Heres my question! pls help if u can
Answers
Answer:
18 tiles
Step-by-step explanation:
Area of a floor is 12 × 15 = (12 × 12) × (15 × 12) = 324 inch²
Area of tile is 18 inch²
324 ÷ 18 = 18 tiles
through: (1, -1), parallel to y=x+1
Answers
An arts academy requires there to be 3 teachers for every 75 students and 4 tutors for every 48 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 108 students?
Answers
Answer:
A. or B.
Step-by-step explanation:
I
a potato chip company packages chest by stacking them into a tall cylindrical K which units are most appropriate for measuring the thickness of an individual chip
Answers
Answer:
MIllimeters
Step-by-step explanation:
Its simple who measures this in inches or centimeters, or meters or anything else
Benjamin bought a 5-pound bag of flour for $7.95. What is the unit price per ounce of flour? (1 pound = 16 ounces)
Answers
Answer:
7.95 divided by 5 times 16 so 7.95 divided by 80= so about 10 cents
Step-by-step explanation: