Answers
Answer:
p = [tex]\frac{12}{7}[/tex]
Step-by-step explanation:
let the root be α then the other root is 3α
The sum of the roots of a quadratic equation is
α + 3α = - [tex]\frac{b}{a}[/tex] = - [tex]\frac{-8}{7}[/tex] = [tex]\frac{8}{7}[/tex]
Thus 4α = [tex]\frac{8}{7}[/tex] ( divide both sides by 4 )
α = [tex]\frac{2}{7}[/tex]
The product of the roots of a quadratic equation are
α × 3α = [tex]\frac{c}{a}[/tex] = [tex]\frac{p}{7}[/tex], that is
3α² = [tex]\frac{p}{7}[/tex] ← substitute value of α
3 × ([tex]\frac{2}{7}[/tex] )² = [tex]\frac{p}{7}[/tex]
3 × [tex]\frac{4}{49}[/tex] = [tex]\frac{p}{7}[/tex]
[tex]\frac{12}{49}[/tex] = [tex]\frac{p}{7}[/tex] ( cross- multiply )
49p = 84 ( divide both sides by 49 )
p = [tex]\frac{84}{49}[/tex] = [tex]\frac{12}{7}[/tex]
Related Questions
U-substitutions only work for specific kinds of expressions. Below, you are asked to choose a value of n for which u-substitutions will be a useful integration technique. Then, you are to compute the antiderivative with that specific n. (E.g., if n = 5 makes u-subs work, then solve the integral with a 5 in place of n).
(a) [ zºeke*+1 "'de
(b) /co cos(1/2) dr
(c) / r+n dr 22 + 8x - 4
Answers
Answer:
Step-by-step explanation:
(a) [tex]\int x^n e^{5x^4+1} \ dx[/tex]
Suppose [tex]5x^4 + 1 = f[/tex]
by differentiation;
[tex]\implies \ 20 x^3 dx = df --- (1)[/tex]
Suppose n = 3
Then, the integral
[tex]I = \int x^ 3 e^{5x^4 + 1} \ dx[/tex]
[tex]= \int e^f \ \dfrac{df}{20}[/tex]
[tex]= \dfrac{1}{20} \int e^f \ dt[/tex]
[tex]= \dfrac{1}{20} e^f + C[/tex]
recall that [tex]f = 5x^4 + 1[/tex]
Then;
[tex]\mathbf{ I = \dfrac{1}{20}e^{5x^4+1}+C}[/tex]
(b) [tex]\int \dfrac{cos (\dfrac{1}{x^3})}{x^n } \ dx[/tex]
suppose; [tex]\dfrac{1}{x^3} = f[/tex]
[tex]x^3 = f[/tex]
[tex]\implies -3x^{-4} \ dx = df[/tex]
[tex]\implies \dfrac{1}{x^4} \ dx =-\dfrac{1}{3} df[/tex]
If n = u, then the integration is:
[tex]I = \int \dfrac{1}{x^4} \ cos (\dfrac{1}{x^4}) \ dx[/tex]
[tex]= \int -\dfrac{1}{3} \ cos \ f \ df[/tex]
[tex]= -\dfrac{1}{3} \int \ cos \ f \ df[/tex]
[tex]= -\dfrac{1}{3} \ sin \ f + C[/tex]
Since; [tex]x^3 = f[/tex]
Then;
[tex]\mathbf {I = -\dfrac{1}{3} \ sin \ \Big( \dfrac{1}{x^3}\Big) + C}[/tex]
(c) [tex]\int \dfrac{x+n}{x^2 + 8x -4} \ dx[/tex]
Suppose [tex]x^2 + 8x - 4 = f[/tex]
Then, by differentiation of both sides
[tex](2x + 8) \ dx = df[/tex]
[tex](x + 4) \ dx = \dfrac{1}{2} \ df[/tex]
Suppose n = 4 in integration, then:
[tex]I = \int \dfrac{(x + 4) }{x^2 +8x -4} \ dx[/tex]
By substitution;
[tex]I = \int \dfrac{1}{2}\dfrac{1}{f} \ df[/tex]
[tex]= \dfrac{1}{2} \ \ { In |f|} + C[/tex]
[tex]\mathbf{= \dfrac{1}{2} \ \ { In |x^2+8x -4|} + C}[/tex]
The suitable substitutions of n are 3,4,4 respectively.
What is integration?The process of finding integrals is called integration.
a)[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]
Suppose
[tex]5x^4+1 =t\\20x^3 dx =dt[/tex]
So, we need n=3 for easy integration.
[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]
[tex]I = \frac{1}{20} \int\limits {e^{t} } \, dt[/tex]
[tex]I=\frac{e^{t} }{20}[/tex]
[tex]I = e^{5x^{4}+1 }/20 +c[/tex]
b)Similarly for [tex]f(x) = \int\limits\frac{cos(\frac{1}{x^3} )}{x^n} \, dx[/tex]
n=4 is needed for easy integration.
I = [tex]\frac{-1}{3} sin(\frac{1}{x^3} ) +c[/tex]
c)For [tex]f(x) = \int\limits \frac{x+n}{x^{2} +8x-4} \, dx[/tex]
n=4 is needed for easy integration.
[tex]I = \frac{1}{2} log(x^{2} +8x-4)[/tex]
Hence, the suitable substitutions of n are 3,4,4 respectively.
To get more about integration visit:
https://brainly.com/question/2633548
I will give a brainlist if someone could answer this problem with a explanation:)
Answers
Answer:
Step-by-step explanation:
The two base angles in each triangle are equal. (The triangle is isoceles and the property used is angles opposite equal sides are equal).
Now the tricky part. The peak angles are also equal. That's because both peak angles are made equal by Peak angle + 2*base angle = 180
Peak angle = 180 - 2*base angle
Therefore the triangles are congruent by SAS.
I suppose you could get them equal by taking one of the base angles (all 4 are equal to each other) and the peak angles and claim equality by ASA, but it seems a little bit tortuous to me.
Write an expression to represent each problem. Then, draw a model to solve.
1.
How many fourths are in 3 fourths?
Answers
Their are 3 fourths in 3/4. Kinda a trick question that seems too simple but it correct.
39) Solve the inequality: 4(x+5)≤116
A. x≤−51
B. x≤−40
C. x≤24
D. x≥24
Answers
Answer:
x≤24
Step-by-step explanation:
4(x+5)≤116
x+5≤29
x≤29-5
x≤24
How many distinct ways can all the letters on "Geometry" be arranged to form a new "Word"?
Answers
I need help please if you can
Answers
Answer:
i really dont know
Step-by-step explanation:
i just dont
Solve the equation.
7(1 – 8x) – 6 = 169
Answers
Answer:
x=-3
Step-by-step explanation:
rearrange terms
distribute
subtract the numbers
subtract 1 from both sides of the equation
simplify
Answer:
Step-by-step explanation:
Here you go mate
Step 1
7(1-8x)-6=169 Equation/Question
Step 2
7(1-8x)-6=169 Simplify
-56x+1=169
Step 3
-56x+1=169 Subtract 1
-56x=168
Step 4
-56x=168 Divide both sides
Answer
x=-3
Pls help I don’t know what to do and it’s due today
Answers
Answer:
it's easier if you use the scan & solve. that brainly provided for you
Step-by-step explanation:
Ryan's garden=1.3 yards wides
We know that,
1 yard=0.914 meters
so,
1.3 yards=0.914×1.3=1.1882=1.9
So,
Ryan's garden is 1.9 meters wide.
The econ motel charges $260 for four nights at this rate how much would seven nights cost
Answers
Answer:
$455 for seven nights
Step-by-step explanation:
260/4= 65
65 is the cost for 1 night
65*7=455
Answer:
$455
Step-by-step explanation:
260 divided by 4 will give you how much for one night so then multiply that answer by 7 and you have your answer.
Consider following situation, which involves two options. Determine which option is less expensive. Are there unstated factors that might affect your decision?
You currently drive 325 miles per week in a car that gets 14 miles per gallon of gas. You are considering buying a new fuel-efficient car for S16,000 (after trade-in on your current car that gets 47 miles per gallon
premiums for the new and old car are $1000 and $600 per year, respectively. You anticipate spending $1500 per year on repairs for the old car and having no repairs on the new car. Assume gas costs $3.50 pen
ive-year period, is it less expensive to keep your old car or buy the new car?
a five-year period, the cost of the old car iss) and the cost of the new car issThus, over a five-year period, it is less expensive to
and to the nearest dollar as needed
Answers
9514 1404 393
Answer:
it is less expensive to purchase a new car
Step-by-step explanation:
The expected cost of gas, insurance, and repairs for the old car are ...
Total miles in 5 years = (325 mi/wk)(52 wk/yr)(5 yr) = 84,500 mi
Old car
Gas cost in 5 years = (84,500 mi)/(14 mi/gal)($3.50/gal) = $21,125
Insurance cost in 5 years = (5 yr)($600/yr) = $3,000
Repair cost in 5 years = ($1500/yr)(5 yr) = $7,500
Total operating cost in 5 years = $21125 +3000 +7500 = $31,625
__
New Car
Gas cost in 5 years = (84,500 mi)/(47 mi/gal)($3.50/gal) ≈ $6,293
Insurance cost in 5 years = (5 yr)($1000/yr) = $5,000
Repair cost in 5 years = (0)(5 yr) = 0
Total operating cost in 5 years = $6293 +5000 = 11,293
__
Difference in operating costs is $31,625 -11,293 = $20,332.
It is less expensive to purchase a new car for any price less than $20,300. If the new car costs only $16,000, it is the less-expensive option.
Purchase of a new car is the least-expensive option.
__
Additional comments
The cost of financing, annual license fees, and resale value of the new car may also come into play. In addition, the relative non-economic values of consumption of new materials, adding old materials to the scrap heap, and environmental pollution may figure in the decision. While the car dealer may pay for maintenance costs of a new car, it seems likely that at least one set of tires will be required in 5 years (85000 miles). (Assuming wheel alignment is not an issue for tire wear, that cost may balance out for the two cars.)
How many different 3-digit numbers can be made using the digits 6, 7, and 8 if no digit is reapeated? One digit is repeated?
Answers
Answer:
You can make infinite 3-digit number using the digits 6,7 and 8. Hope it helps :)
True or false
$24 fir 6 ft of chain represents a rate of $4 per foot of chain
Answers
Answer:
I think its true but im not sure
Step-by-step explanation:
Brian has reduced his cholesterol level by 14% after his last check up. If his original level was 180, what is his approximate cholesterol level now?
Answers
Answer:
154.8 is you answer
Step-by-step explanation:
Use substitution to determine which system is represented by the graph.
Answers
Answer:
2x + 4y = 28
-2y = x + 28
Step-by-step explanation:
Looking at the graph, we can see that the lines do not intersect. Therefore, they do not have a shared solution. We need to find the system of equations that does not have a solution.
1) Let's try to solve the third system given (counting from the top). To solve with the substitution method, we need to isolate one variable in one of the equations. I chose to isolate y in -2y = x + 28:
[tex]-2y = x + 28\\y = \frac{-1}{2}x -14[/tex]
2) Now that we've isolated the y in that equation, substitute what y equals in that equation for the y in the other equation. So, substitute [tex]\frac{-1}{2}x-14[/tex] for y in 2x + 4y = 28 and simplify:
[tex]2x + 4(\frac{-1}{2}x - 14) = 28\\2x - 2x- 64 = 28\\-64 = 28[/tex]
In a normal situation, the x's would not cancel out, and we would be able to isolate x to get the x-value of the solution. However, in this case, they have, and we ended up with a false statement, as -64 does not equal 28. Whenever this happens, it means the system does not have a solution. Therefore, the third option would represent the system in the graph.
The given graph shows the simultaneous relationship of equations 2x + 4y = 28 and -2y = x + 28. Option C is correct.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
From the graph, the two lines represents the simultaneous relationship,
Where,
The slope of the both lines is,
m = -1/2
And y-intercept of both lines is,
C₁ = 7 and C₂ = - 14
Now,
equations of the lines are,
y = -x/2 + 7 and y = -x/2 - 14
x + 2y = 14 and x + 2y = -28
or
2x + 4y = 28 - - - - - -(1) and -2y = x + 28 - - - - - - -(2)
Now,
From equation 2 substitute y in equation 1
2x + 4[-x - 28]/2= 28
2x - 2x - 56 = 28
-56 = 28
So the lines are parallel and has no solution.
Thus, the given graph shows the simultaneous relationship of equations 2x + 4y = 28 and -2y = x + 28. Option C is correct.
Learn more about simultaneous equations here:
https://brainly.com/question/16763389
#SPJ2
This question has 2 parts.
Part A: Matt has 2/3 yard of fishing line. He uses 3/8 of the line to make fishing knots. How much fishing line does he use to make fishing knots?
Part B: Kara says Matt uses 25/24 of the line to make knots. Explain Kara’s error and tell how to use an equation to find the amount of line Matt uses.
Answers
Answer:
um well i can do part A
Step-by-step explanation:
its 6/24 which equals 1/4 yards
Start with 2. Add 6 to each term to get the following term. What is the 6th term of the sequence?
Answers
Answer:
32
Step-by-step explanation:
We can either add all the terms.
2+6=8
2,8
8+6=14
2,8,14
14+6=20
2,8,14,20
20+6=6
2,8,14,20,26
26+6=32
2,8,14,20,26,32
The Sixth term is 32
or We can multiply 6 times 5 (30) and add 2, which would give us 32.
The reasoning behind this is that we are adding six five times (so six times five) and we are also adding the first term (2).
PLEASE HELP PLEASE 100 POINTS PLUS BRAINLIEST
(I had the answer already but it deleted and now I can’t find it)
Answers
Step-by-step explanation:
Area of Sector
= θ/360° * πr² (degrees) or 0.5r²θ (radians)
Question 11:
(88°)/360° * π(19)² = 277.23ft².Question 12:
(260°)/360° * π(11)² = 274.54mi².Question 13:
0.5(6.2)²(7π/12) = 35.22km².Question 14:
0.5(7.1)²(5π/3) = 131.97cm².Question 15:
(215°)/360° * π(4.5)² = 37.99yd².Question 16:
0.5(21.4)²(13π/18) = 519.54m².here is the answers!
Area of Sector
= θ/360° * πr² (degrees) or 0.5r²θ (radians)
Question 11:
(88°)/360° * π(19)² = 277.23ft².
Question 12:
(260°)/360° * π(11)² = 274.54mi².
Question 13:
0.5(6.2)²(7π/12) = 35.22km².
Question 14:
0.5(7.1)²(5π/3) = 131.97cm².
Question 15:
(215°)/360° * π(4.5)² = 37.99yd².
Question 16:
0.5(21.4)²(13π/18) = 519.54m².
Find all real zeros of the function y= -5x - 7.
Answers
A TV that usually sells for $171.38 is on sale for 15% off. If sales tax on the TV is 9%, what is the price of the TV, including tax?
Answers
Answer:
171.38 - 15% plus tax= 171.23
Hope this helped!
Part2
Please help I’ll make u brainly
Answers
Answer:
someone game me that same question but sadly i wasn't able to get the answer sorry for the inconvience
Step-by-step explanation:
Answer:
3. 2nd degree. Leading term:
[tex] {3x}^{2} [/tex]
Leading coefficient: 3x
Part 1:
[tex] {2x}^{2} + 11x + 15[/tex]
Part 2:
[tex] {3x}^{2} - x - 2[/tex]
Part 3:
[tex] - {x}^{2} + 12x + 17[/tex]
(Part 3 should be correct, double check it, I think it cancels out the minuses in the part 2 equation?)
P.S. I forgot to solve the equations on this and the first page, don't forget that and I can leave another answer for those if you need!
Will mark brainliest!!!Solve for each variable
Answers
Answer:
n=5, m = 4
Step-by-step explanation:
It is a parallelogram so m+8 = 3m and 2n-1 = 9
A convex polygon has 6 sides what is the sum of its interior angles 1980°.
Answers
Step-by-step explanation:
Sum of interior angles in a polygon
= 180°(n - 2), where n is the number of sides.
Hence a convex polygon with 6 sides
=> 180°(6 - 2) = 720°.
HELP ASAP
What is the area of the shaded region?
(2571 - 48) cm
O (2517 - 30) cm
(2517 - 24) cm
(257-12) cm
Answers
Answer:
Step-by-step explanation:
We are given a circle with a partially shaded region. First, we need to determine the area of the whole circle. To do this, we need the measurement of the radius of the circle:
Use the Pythagorean theorem to solve for the other leg of the right triangle inside the circle:
5^2 = 3^2 + x^2
x = 4
The radius is 4 + 1 cm = 5 cm
So the area of the circle is A = pi*r^2
A = 3.14 * (5)^2
A = 25pi cm^2
To solve for the area of the shaded region:
Ashaded = Acircle - Atriangles
we need to solve for the area of the triangles:
A = 1/2 *b*h
A = 1/2 *6 * 5
A = 15 cm^2
Atriangles = 2 * 15
Atriangles = 30 cm^2
Ashaded = 25pi - 30
Amy purchased a brand–new mountain bike, which she's riding through the winding trails. The bike's displacement is given by
s(t) = t3 − 2t2 + 3. What is the bike's acceleration after three minutes?
Answers
Answer:
a = 14 m/min²
Step-by-step explanation:
The displacement of bike is given by :
[tex]s(t)=t^3-2t^2+3[/tex]
Velocity, [tex]v=\dfrac{ds(t)}{dt}[/tex]
Finding velocity of the bike.
[tex]v=\dfrac{d}{dt}(t^3-2t^2+3)\\\\=3t^2-4t[/tex]
Acceleration, [tex]a=\dfrac{dv(t)}{dt}[/tex]
[tex]a=\dfrac{d}{dt}(3t^2-4t)\\\\=6t-4[/tex]
At t = 3 minutes,
a = 6(3) - 4
= 18-4
= 14 m/min²
So, the bike's acceleration after 3 minutes is 14 m/min².
Marcos owns and operates a shuttle service that runs every hour and transports customers between their hotels and the city's downtown area. Let X represent the number of customers on a randomly chosen trip.
Based on previous data, here is the probability distribution of X along with summary statistics:
X = # of customers 0 1 2 3
P(X) 0.10 0.20 0.30 0.40
Mean: μx = 2
Standard deviation: σx = 1
Suppose that each trip costs Marcos $1 in fuel regardless of how many customers he has, and each customer on a trip pays him $10. Let Y represent Marcos' net gain from a randomly chosen trip. What are the mean and standard deviation of Y?
Answers
Answer:
Mean y = 19 ; SD y = 10
Step-by-step explanation:
Given that:
No of customers : __ 0 ____ 1 _____ 2 ___ 3
P(x) : ___________0.10 __ 0.20 __0.30 _0.40
Fuel cost =$1 (constant)
Amount paid per customer =$10
Number of customers = x
σx = 1 ; μx = 2
σ^2 = 1^2 = 1
Mean of Y
μy = E(Y)
= E(10x - 1)
= 10(Ex) - 1
E(x) = 2
= 10(2) - 1
= 20 - 1
= 19
σY = SD(y)
SD(10x - 1)
10*SD(x) - 1
SD(x) = 1
10(1) - 0
Note : SD of a constant = 0
10 - 0
= 10
The mean of Y is 19 and the standard deviation of Y is 10 and this can be determined by using the given data.
Given :
Marcos owns and operates a shuttle service that runs every hour and transports customers between their hotels and the city's downtown area. Let X represent the number of customers on a randomly chosen trip.Standard deviation: σx = 1 Suppose that each trip costs Marcos $1 in fuel regardless of how many customers he has, and each customer on a trip pays him $10. Let Y represent Marcos' net gain from a randomly chosen trip.The mean of Y can be calculated as given below:
[tex]\rm \mu(Y)=E(Y)[/tex]
[tex]\rm \mu(Y)=E(10x - 1)[/tex]
[tex]\rm \mu(Y) = 10E(x) - 1[/tex]
According to the given data, the value of E(x) is 2. Substitute the value of E(x) in the above expression.
[tex]\rm \mu(Y) = 10(2) - 1[/tex]
[tex]\rm \mu(Y) = 19[/tex]
Now, the standard deviation of Y can be calculated as:
[tex]\rm \sigma_Y=SD(Y)[/tex]
[tex]\rm \sigma_Y=SD(10x-1)[/tex]
[tex]\rm \sigma_Y=10SD(x)-SD(1)[/tex]
The value of SD for a constant is zero.
[tex]\rm \sigma_Y=10(1)-0[/tex]
[tex]\rm \sigma_Y = 10[/tex]
For more information, refer to the link given below:
https://brainly.com/question/12402189
Find two consecutive whole numbers that 34 lies between.
Answers
Answer:
34 lies in between 5 and 6
5^2=25, 6^2=36, so sqrt(34) lies between 5 and 6
Answer this question
(Factors of 36)
1,36
_,_
_,_
4,9
_,_
*please answer asap!*
Answers
Answer:
1,36 2,18 3,12 4,9 and 6,6
Step-by-step explanation:
If you multiply them, they equal 36
Suppose potato chips cost 22.5 cents per ounce. What would a bag of chips cost if it contained 12 oz? Round your answer to the nearest cent, if necessary
Answers
Answer:
the anser is 22.10
Step-by-step explanation:
you have to round to the nearest ten. here is a tip 4 or down round down 5 or up round up now you are good to go! and also to find me if you need help
Which is the hidden question in this problem?
Jason bought 6 season tickets to the theatre. Each ticket cost $120.
A season parking pass cost $30. How much did Jason spend for the tickets and the parking pass?
A Will the tickets cost more than $1,500?
B. How much more is the cost of the tickets than the cost of the parking pass?
How much do six season tickets cost?
D
How much will two parking passes cost?
Answers
Answer
how much more is the cost of tickets than the cost of parking pass
Step-by-step explanation:\
i think, sorry if im wrong but its kinda hard to understand what you typed.
Answer:
A: No the tickets won't cost more than $1500.
B: 90 more dollars.
6 season tickets cost $720
D: 2 parking tickets will cost $60
.12 divided by 7.15 please put step by step thank you
Answers
Answer:
59.58333
Step-by-step explanation:
715/12
write in long division format ( which u did )
divide 71 by 12 to get 5
multiply 71 by 12 = 5
subtract 60 by 71
bring down the next number
115/12 =9
multiply 12 by 9
subtract 180 by 115
add a decimal on the top and bring down zero
divide 70 by 12 = 5
multiply 5 by 12
subtract 60 - 70
bring down a zero
divide 100 by 12 = 8
multiply 12 by 8
subtract 96 by 100
bring down zero
divide 40 by 12 = 3
anddd u get the point
sorry it took so long