The value of n/p is 8.
What is quadratic equation?
A quadratic equation in algebra is any equation that can be written in standard form as where x is an unknown and where a, b, and c denote known numbers, where a ≠ 0.
Let, for x^2 + mx + n = 0
⇒ x = 2α or 2β
From the given condition,
for x^2 + mx + n = 0 ⇒ x = α or x = β
Then,
2(α + β) = -m ..(1)
4αβ = n ..(2)
and α + β = -p ..(3)
αβ = m ..(4)
From equation (1) and (3),
-m/2 = -p
⇒ p = m/2
and from equation (2) and (4),
n/4 = m
⇒ n = 4m
Therefore,
n/p = 4m / (m/2) = 4 x 2 = 8
Hence, n/p = 8.
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Which equation represents the line that is perpendicular to y = 4 5 x + 23 and passes through (-40,20)? A. y = - 5 4 x − 15 B. y = - 5 4 x − 30 C. y = 4 5 x + 52 D. y = 4 5 x − 56
The equation of the required perpendicular line is y = (-5/4)x - 30.
We are given an equation. The equation is linear in nature. The equation represents a straight line. The equation of the given straight line is y = (4/5)x + 23. We need to find the equation of the straight line that is perpendicular to the given line and passes through the point that has coordinates (-40, 20).
The slope of the given line is 45. Let the slope of the required perpendicular line be represented by the variable "m". The slope of the perpendicular line must be the negative reciprocal of the slope of the given line.
m = -1/(4/5)
m = -5/4
The equation of the required line is of the form y = mx + c.
y = (-5/4)x + c
We know that this line passes the point (-40, 20).
20 = (-5/4)(-40) + c
20 = 50 + c
c = -30
Hence, the equation of the required line is y = (-5/4)x - 30.
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Fill in the table using this function rule.
y=-5x+1
X
-2
0
2
4
y
0
0
0
0
Start over
S
Answer:
x y
-2 -9
0 1
2 -9
4 -19
explanation:
you simply replace the x with the figure given in the x table or columns or rows
Answer:
so -2024y0000 division is s
For each equation, find y when x = -6. Then find x when y = 20.
y = 6x +8 solve for y and x
y = 2/3x solve for y and x
y = -x + 5 solve for y and x
y = 6.5x + 7 solve for y and x
x=14/3 and y=-28 when x = -6. and y = 20 for equation y = 6x +8
x=30 and y=-4 for when x = -6. and y = 20 for equation y = 2/3x
x=-15 and y=11, when x = -6. and y = 20 for equation y = -x + 5
x=2 and y=-2 , when x = -6. and y = 20 for equation y = 6.5x + 7
What is Equation?Two or more expressions with an Equal sign is called as Equation.
For equation y = 6x +8
When x=-6
y=6(-6)+8=-36+8=-28
when y =20
20=6x+8
28=6x
x=28/6=14/3
x=14/3 and y=-28 when x = -6. and y = 20 for equation y = 6x +8
For equation y = 2/3x
When x=-6, y=2/3(-6)=-4
y=20, 20=2/3x
60=2x
x=30
x=30 and y=-4 for when x = -6. and y = 20 for equation y = 2/3x
For equation y = -x + 5
When x=-6, y=6+5=11
When y=20,
20=-x+5
15=-x
x=-15
x=-15 and y=11, when x = -6. and y = 20 for equation y = -x + 5
For equation y = 6.5x + 7
When x=-6
y=6.5(-6)+7
y=-39+7=-2
When y=20
20=6.5x+7
13=6.5x
2=x
x=2 and y=-2 , when x = -6. and y = 20 for equation y = 6.5x + 7
Hence,
x=14/3 and y=-28 when x = -6. and y = 20 for equation y = 6x +8
x=30 and y=-4 for when x = -6. and y = 20 for equation y = 2/3x
x=-15 and y=11, when x = -6. and y = 20 for equation y = -x + 5
x=2 and y=-2 , when x = -6. and y = 20 for equation y = 6.5x + 7
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A train passes through a 360 m long tunnel completely in 24 seconds. It passes through another tunnel 216 m long completely in 16 seconds at the same average speed. Find the length of the train.
The average speed of the train is 18m/sec and the length of the train is 72 m.
let x represent the length of the train.
and 'S' be the speed of the train.
Given, that the train passes through 360 m long tunnel completely in 24 sec.
⇒ 360+x/24 = s
⇒ 24s = 360+x ...eq(1)
And also given that it passes through another tunnel 216 m long completely in 16 sec.
⇒ 216+x/24 = s
⇒ 16s = 216 + x .... eq(2)
⇒ subtract eq(1) from eq(2)
⇒ 24s = 360 + x
16s = 216 + x
8s = 144
s = 18 m/sec
length of the train: 24s = 360+x
24(18) = 360+x
432 = 360+x
x = 432-360
x = 72m
Hence the length of the train is 72 m.
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Membership in the Volunteers Club increased by 15% from last year. If the number of members last year was m, complete a simplified expression to represent the number of members this year. Enter your answer in the box.
m
The simplified expression to represent the number of members this year is 1.15m
What is an expression?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
From the information, the membership in the volunteers Club increased by 15% from last year. If the number of members last year was m.
The number of members will be:
= Old members+ Increase in members
= m + (15% × m)
= m + 0.15m
= 1.15m
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The car makes one complete rotation about its circuit
every 36 minutes, at a fairly constant rate. Through how
many degrees would the car, which starts from its original
position, drives by the circuit from 8:00 AM to 3:00 PM,
on the same day.
8 AM to 3 PM is 7 hours = 420 mins
Find how many rotations:
420 / 36 = 11.66666 rotations
Using ratio
1 rotation : 360 degrees
11.66666 : x degrees
x = 11.66666 / 1 * 360 = 4200 degrees
through (-3,-1) perp to y=-1/2x=5
PLease ANSWER HURRY
The equation of line passing through the point (-3, -1) and is perpendicular to the line y = -x/2 - 5 is y = 2x + 5
What are perpendicular lines?perpendicular lines are defined as two lines that meet or intersect each other at right angles (90°).
In such lines the product of their gradients is -1.
if y = -x/2 - 5
then comparing the equation with y = mx + c
it means slope(m) = -1/2
so the slope(p) of the second line perpendicular to the above line will be
p x m = -1
p = -1/m
p = -1 ÷ -1/2
p = 2
so if x = -3, y = -1 and substituting these values into the equation of line , y = mx + c becomes
-1 = 2 x (-3) + c
-1 = -6 + c
collect like terms
c= 6 - 1
c = 5
Equation of the second line becomes,
y = 2x + 5
In conclusion, the equation of the lines passing through point(-3, -1) is y = 2x + 5
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You invet $892 at the end of each year in an invetment with annual rate of return 6%. How much will the invetment be worth after 15 year?
You invest $892 at the end of each year in an investment with annual rate of return 6%. Then the investment worth after 15 year will be 14182.8 dollar
we know that
SI = prt
where
SI= simple interest
A= amount
P= principal
r= rate
t= number of year
according to the question
SI= 892* 0.06*1
= 53.52
A = 892+53.52
= 945.52
after 15 years amount will be
A= 945.52*15
= 14182.8
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an airplane is travelling down a runway at a speed of 66 feet per second, when it begins to slow down. the airplane decelerates at a constant rate of 6 feet per square second. how many feet does the airplane travel before it stops? (do not include units in your answer.
With deceleration of 6 ft/s² and initial speed of 66 ft/s, the airplane will stop after travelling 363 ft.
Use the equation of motion:
v² = u² + 2 · a · s
Where:
v = final velocity
a = acceleration
u = initial velocity
s = distance
Deceleration is a negative acceleration.
Parameters given from the problem:
u = 66 ft/s
a = - 6 ft/s²
v = 0 since the airplane stops.
Plug these parameters into the formula:
v² = u² + 2 · a · s
0 = 66² + 2 · (-6)· s
s = 66² / 12
s = 363 ft.
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Kirk has just moved to Vindale and wants to check out some nearby restaurants. Starting from home, he drives 15 kilometers west, 45 kilometers east, and 75 kilometers west. Which direction must Kirk go to get back to his home?
Kirk will drive 15 kilometer east to get back to his home
How to determine the amount Kirk has to drive to get homeThe problem will be solved using basic addition operator and subtraction
Let the given information be represented as follows
he drives 15 kilometers west = 15 W
45 kilometers east = 45 E
75 kilometers west = 75 W
Kirk will drive East to get home = ?
since the distances are all in the horizontal direction we add up the west directions and subtract the east direction
15 W + 75 W = 45 E + ?
90 W = 45 E + ?
? = 90 - 45
? = 45 E
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Finding Angle Measures When Parallel Lines Are Cut By a Transversal
Answer and Explanation:
m∠1 = 43° because opposite angles are congruent
m∠2 = 137° because ∠2 and 43° are supplementary, so m∠2 + 43° = 180°
m∠3 = 137° because opposite angles are congruent, so m∠3 = m∠2
m∠5 = 43° because alternate angles are congruent
m∠6 = 137° because ∠5 and ∠6 are supplementary, so 43° + m∠6 = 180°
m∠7 = 137° because alternate exterior angles are congruent, so m∠7 = m∠2
m∠8 = 43° because alternate exterior angles are congruent, so m∠8 = m∠1
Answer:
angle 1: 43
angle 2: 137
Step-by-step explanation:
Lets find angle 1 first :)
Since oposite diagonal angles are the same, this will make angle 1 43 degrees :)
Now lets find angle 2!
Since 1 was 43 degrees, and a flat line is 180 degrees we must subtract!
Lets do that now!
180 - 43 = 137
Angle 2 will be 137 degrees!
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Your rate of pay is 9.45 per hour if you workers 5 hours for 3 days and 7 hours for 2 days what is your gross pay before deductions
Answer: 274.05 dollars
Step-by-step explanation:
9.45 x 5 x 3 = 141.75
9.45 x 7 x 2 = 132.3
141.75 + 132.3 = 274.05
Brainliest by any chance?
The distance of a golf ball from the hole can be represented by the right side of a parabola with vertex (−1, 8). The ball reaches the hole 1 second after it is hit. What is the equation of the parabola, in vertex form, that represents the ball's distance, y, from the hole, x seconds after the ball is hit?.
The equation of the parabola, in vertex form, that represents the ball's distance, y, from the hole, x seconds after the ball is hit is
y = (-2m/s^2)t^2 + (-2m/s)t + 6m
Define quadratic equation.ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given,
Assume for the moment that the hole is located at y = 0m, where x represents the time variable.
We are aware of:
The vertices are (-1s, 8m).
x in seconds and y in meters, I presume
The ball enters the hole at time x = 1s, hence we also have the following point:
(1s, 0m).
The vertex of the quadratic equation y = ax2 + bx + c is located at:
x = -b/2a,
Next, we have:
-1 = -b/2a.
Next, we have equations for trees:
8m = a(-1s)2, b(-1s), and c
0m = (a(1s)2) + (b(1s)2) + (c)
-1s = -b/2a.
The third equation should have one variable isolated first, and then it should be substituted in one of the other two:
1s2a = b.
Therefore, we can change b to bi 1s2a in the first two equations.
8m = 1s×2a×1s - a×1s2a1s + c
0m = 1s×2a×1s + a×1s×2a + c
We can combine the two equations to get:
8m is equal to a(1s2 - 2s2) + c, or a×1s2 - c.
0m is equal to a(1s2 + 2s2) + c, or a×3s2 + c.
We may quickly remove c from the second equation and then substitute it in the first equation:
c = -a3s^2
The initial equation is now:
8m is equal to -a×1s2 - a×3s2 - a×4s2.
a = 8m/-4s^2 = -2m/s^2.
We can now determine the values of c and b using a.
c = -(-(-2m/s2)*3s2)*3s2 = 6m.
B is equal to 1s*2a = 1s*(-2m/s2) = -2m/s.
The equation is then:
y = (-2m/s^2)t^2 + (-2m/s)t + 6m
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Which graph shows the solution to the system of linear inequalities?
y < 2x – 5
y > –3x + 1
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the right of the line is shaded. The second dashed line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the right of the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the right of the line is shaded. The second solid line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the right of the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the left of the line is shaded. The second dashed line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the left of the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the left of the line is shaded. The second solid line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the left of the line is shaded.
The graph of the system of inequalities can be seen in the image at the end.
How to get the graph of the system of inequalities?
Here we have the following system of inequalities:
y < 2x - 5
y > -3x + 1
So first we need to graph the two lines:
y = 2x - 5
y = -3x + 1
With dashed lines (because the symbols < and > are used).
And then we shade all the region below the line:
y = 2x - 5
And we shade the region above the line:
y = -3x + 1
So we will get the graph below:
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Can I get some help please?
Answer:
66
Step-by-step explanation:
The angle 108 is equal to the angle 42 plus the vertical angle to x
108-42 = 66 this is the measurement for the vertical angle to x. Vertical angles are congruent so angle x is 66
Given the ordered pair (-5, 4), name the coordinates after a rotation of 90° counter-clockwise.
Answer:
(-5,-4)
as 90 degree rotation counter clockwise would land in the third quaderant where both x and y are negative
60 POINTS FOR FULL CORRECT ANSWER!!!!! I NEED IT NOW!!!!!
Whose sequence proves trapezoid PQRS is similar to trapezoid KLMN? Why?
THE ACTIVITY IS : Unit Activity: Transformations
The equation of a line is y = -3x – 2. What are the slope and the y-intercept of the line?
A.
slope = -3 and y-intercept = 2
B.
slope = 3 and y-intercept = -2
C.
slope = 3 and y-intercept = 2
D.
slope = -3 and y-intercept = -2
Answer:
D
Step-by-step explanation:
The slope if before the x so in this case it's -3.
The y-intercept is at the end so it's -2.
Answer:
D. slope = -3 and y-intercept = -2
Step-by-step explanation:
Slope Intercept Form:
y - y₁ = m(x - x₁) (original version)y = mx + b (simplified version)The variables:
m ⇒ represents slopeb ⇒ represents the y-intercepty = -3x -2
m = -3b = -2
Select the choice that represents the two-variable equation after it has been solved for y in terms of x.
3(y + 2) - 4x = 0
Answer:
Step-by-step explanation:
3y+6-4x=0
3y-4x=0-6
3y-4x=-6
y-4x=6/3
y-4x=2
y-x=2/4
y-x=0.5
Which is in between 120º F and 130º F?
Answer:
121-129 F is in between
Step-by-step explanation:
(−100) ÷ {200 − (14 − (−16) ) × 5} + 10 =
Answer: 8
Step-by-step explanation:
= (-100) ÷ (200 - (14 + 16) x 5) + 10
= (-100) ÷ (200 - 30 x 5) + 10
= (-100) ÷ (200 - 150) +10
= (-100) ÷ 50 + 10
= -2 + 10
=8
Answer: 8
Step-by-step explanation: Remember BIDMAS, order of operations (brackets, indices, division, multiplication, addition, subtraction), since we have multiple brackets inside one another we'll start with the most inner brackets and then work from there.
14-(-16) = 30
30 x 5 = 150
200 - 150 = 50
(-100) ÷ 50 = -2
-2 + 10 = 8
What is the answer
The question is what is the equation of line a and then b
Which graph shows y= 1/2 [x]?
The third graphical representation is that of the function y = 1/2[x] .
The given function is y = 1/2[x] .
This is called the box function or the greatest integer function.
So for the equation of the line y = 1/2 x the graph passes through origin and through the points (2,1) , (4,2) and many more.
Now for the greatest integer function will take all the values of x greater than 1 up to 2 and round it off to 2.
so the points on the graph will be.
(2,1) , (3,1.5) , (4,2)....
This is clearly seen in the third option.
The integer function that returns an integer closest to the given real number is the largest integer function. also referred to as the step function. The greatest integer function rounds the input to the nearest integer. As a result, the equation to get the greatest integer is rather simple. It has the sign x, where x can represent any value.
The letter "x" denotes the biggest integer function for each real function. Real values are rounded to the nearest integer that is smaller than the input value by the function. Another term for this function is the floor function.
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Can anyone please help meee!!
Answer:
equilateral acute
Step-by-step explanation:
equilateral-- all the sides have the same length
acute-- all the angles are below 90 degree
Answer:
Step-by-step explanation:
You'r answer should be an equilateral acute.
help please and thankyou
The ratio that can be used to find x is sin 21 = x/22.
What are the trigonometric ratios?The trigonometric ratios are the ratios that we can use to obtain the sides and the angles that are in a right angled triangle. The term right angled triangle has to do with a triangle that has one of its angles as 90 degrees.
Now;
Given that;
Sin θ = opposite/hypotenuse
opposite = x
hypotenuse = 22
θ = 21 degrees
It now follows that to obtain the side x we have to use;
sin 21 = x/22
Hence, in looking for the side x, we have to use sin 21 = x/22
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A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 1234 and 120 respectively. The standard error of the mean is.
The standard error of the mean is 11.99
Given,
In the question :
No. of observation is 100
The sample mean is = 1234
Standard Deviation is = 120
To find the standard error of the mean.
Noe, According to the question:
No. of observation:
N = [tex](C_{v}[/tex] / ∈[tex])[/tex] ^2
Where,
∈ = allowance % error of mean
[tex]C_{v}[/tex] = coefficient of variation
[tex]C_{v} =[/tex] σ / x bar × 100
σ = standard deviation and x bar = mean
x bar = 1234 , σ = 120 and N = 100
[tex]C_{v} = \frac{120}{1234}[/tex] × 100
[tex]C_{v}[/tex] = 9.72%
N = [tex](C_{v}[/tex] / ∈[tex])[/tex] ^2
100 = (9.72/∈)^2
100∈^2 = (9.72)^2
∈^2 = 0.944784
∈ = 0.972%
The standard error of mean = mean x percentage of absolute mean error
= 1234 x 0.972/100
= 11.99
Hence, The standard error of the mean is 11.99
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12. Jill has 20 coins, consisting of nickels and dimes
totalling $1.40. How many nickels does Jill have?
Hint: Let the number of nickels be n, and the
number of dimes be 20 - n.
The number nickel is 12, and the number dimes are 8 if Jill has 20 coins, consisting of nickels and dimes totaling $1.40.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Jill has 20 coins, consisting of nickels and dimes totaling $1.40.
Let the number of nickels be n, and the number of dimes is 20 - n.
$1 = 10 dimes
$1 = 20 nickels
(1/20)n + (1/10)(20 - n) = 1.40
After solving:
n = 12
The number nickel = 12
The number dimes = 20 - 12 = 8
Thus, the number nickel is 12, and the number dimes are 8 if Jill has 20 coins, consisting of nickels and dimes totalling $1.40.
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Find the angle x using circle theorem
Hey there! I explained and wrote everything on paper since it's hard to type so you can view the pic uploaded! Hope it helps, if you have any doubts, please feel free to ask :)
g a coin is tossed 10 times, recording whether it comes up heads or tails each time it is tossed. how many outcomes involve at least 8 heads?
Using combination formula , total 987 ways or outcomes are possible /involve atleast 8 heads.
We have given that, a coin is tossed 10 times .
total possble outcomes = 2¹⁰ = 1024
here, the chances of occurrence of tail and heads and equal so, this is independent event .
we want to calculate total numbers of possble wats atleast 8 heads occurs .
At least 8 heads means exactly two toss gives Tail as a result.
here we count sequences with exactly 8 heads, and also count sequences with more than three heads. We could compute this by equivalent, by subtracting from 1025 the number of sequences with no head, only one head, and only 2 heads
= 1024 - ⁸C₀ ( + ⁸C₁ + ⁸C₂ )
= 1024 - ( 1+8+28) = 1024 - 37
= 987
Hence , 987 outcomes involve atleast 8 heads.
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PLEASE ANSWER I WILL MARK BRAINLYEST
Factor −6x2 + 18x.
1. 6x(−x + 3)
2. −6x(x + 3)
3. x(6x + 18)
4. 6(−x2 + 18x)
Answer: 6x(-x+3)
Step-by-step explanation:
You can factor out the 6 and x. -6x^2 divided by 6x = -x, and 18x divided by 6x = 3. So the answer is 1. 6x(-x+3)
Answer:
-6x^2+18x
-6x^2-18x
6x^2+18x
-6x^2+108x
Step-by-step explanation:
1.
6x(-x+3)
6x(-x)+6x(3)
-6x^2+18x
2.
-6x(X+3)
-6x(X)+-6x(3)
-6x^2-18x
3.
x(6x+18)
x(6x)+x(18)
6x^2+18x
4.
6(-x^2+18x)
6(-x^2)+6(18x)
-6x^2+108x
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