Step-by-step explanation:
Let the given ratio be pk : qk .
So , here the quadratic equation is lx² + nx + n = 0. With respect to Standard form ax² + bx + c = 0.
We have ,
a = lb = nc = n→ Sum of roots = -b/a = -n/l = qk + pk
→ Product of roots = c/a = n/l = k²pq .
[tex]=> \dfrac{n}{l} = \dfrac{k^2}{pq} \\\\=> k^2 =\dfrac{n}{pql} [/tex]
And here pk and qk is a root of the quadratic equation ,
[tex]=> lx^2 + nx + n = 0 \\\\=> l(pk)^2 + n(pk) + n = 0\\\\=> lp^2k^2+npk + n = 0 \\\\=> lp^2\bigg( \dfrac{n}{pql} \bigg) + np\bigg(\sqrt{\dfrac{n}{pql}} \bigg) + n = 0 \\\\ => n\bigg\{\dfrac{p}{q}+\sqrt{\dfrac{np}{lq}}+1\bigg\} = 0 \\\\=> \dfrac{p}{q}+\sqrt{\dfrac{np}{lq}}+1 =0\\\\=>\sqrt{\dfrac{p}{q}} \bigg( \dfrac{q}{p}+\sqrt{\dfrac{np}{lq}}+1\bigg) = 0 \\\\=> \sqrt{\dfrac{p}{q}}+ \sqrt{\dfrac{q}{p}}+ \sqrt{\dfrac{n}{l}}=0 \\\\\boxed{\red{\bf\longmapsto \sqrt{\dfrac{p}{q}}+ \sqrt{\dfrac{q}{p}} = - \sqrt{\dfrac{n}{l}}}} [/tex]
What is the point-slope form of a line with slope -3 that contains the point
(10, -1)?
Answer:
y - (-1) = -3(x-10)
y+1= -3x+30
y= -3x+30-1
y= -3x+29
WILL GIVE BRAINLEST PLZZ HELP MEEE
Answer:
2
Step-by-step explanation:
(x,y)
Is 2.3 + (-2.4) positive number
Answer:
2.3 + (-2.4) = -.1
Step-by-step explanation:
adding a negative like this is the same 2.3 - 2.4 and subtracting 2.4 from 2.3.
Give the domain and range of a standard square root function.
Answer:
I think the answer is the second option, x >= 0, y>=0
Step-by-step explanation:
I searched it up and the results said that this was the answer.
what are all of the ratios that are equivalent to 1/2
Answer:
there are infinte number of ratios that are equivaent to 1/2
Step-by-step explanation:
2/4, 3/6, 4/8, 5/10, 6/12 ...
Answer:
2/4, 3/6, 4/8, 5/10, 6/12
Step-by-step explanation:
Just multiply the denominator and numerator!!
For example:
1/2 =2/4
1x2=2
2x2=4
Which expression is equal to 5+6+7+8+9?
show that (0.8a+0.4b)^2=(0.8a-0.4b)^2+1.28ab
please help me solve this asap
Step-by-step explanation:
first
(0.8a+0.4b)^2= (0.8a+0.4b) *(0.8a+0.4b)
=
0.64 a^2 + 0.32 ab +0.32ab + 0.16 b^2=
0.64 a^2 + 0.64ab + 0.16 b^2
second
(0.8a-0.4b)^2+1.28ab
= 0.64 a^2 - 0.64ab +0.16 b^2 + 1.28ab
= 0.64 a^2 + 0.64ab + 0.16 b^2
since the first (left parameters ) equals the second(right side parameters)
approved✓✓
The two data sets below show the approximate number of gallons of gasoline Josie and Olivia put into their cars the last 10 times they filled their gas tanks. A dot plot titled josie's Gasoline (gallons). The number line goes from 8 to 12. There are 2 dots above 8, 2 above 9, 6 above 10, and 0 above 11 and 12. A dot plot titled Olivia's Gasoline (gallons). The number line goes from 8 to 12. There are 0 dots above 8 and 9, 6 above 10, 3 above 11, and 1 above 12. Which measure of variability would most accurately compare the two data sets and why?
Answer:
c
Step-by-step explanation:
i got it right on edg 2020
Answer:
c
Step-by-step explanation:
5/4+5/4=_ × 1/4 plz help me
Answer:
10/4
Step-by-step explanation:
the substitution method.
y = -4x + 15
-4x + 7y = 9
Answer: {y,x} = {3,3}
Step-by-step explanation:
1] y=-4x+15
[2] -4x+7y=9
Equations Simplified or Rearranged :
[1] y + 4x = 15
[2] 7y - 4x = 9
Graphic Representation of the Equations :
4x + y = 15 -4x + 7y = 9
Solve by Substitution :
// Solve equation [1] for the variable y
[1] y = -4x + 15
// Plug this in for variable y in equation [2]
[2] 7•(-4x+15) - 4x = 9
[2] - 32x = -96
// Solve equation [2] for the variable x
[2] 32x = 96
[2] x = 3
// By now we know this much :
y = -4x+15
x = 3
// Use the x value to solve for y
y = -4(3)+15 = 3
Solution :
{y,x} = {3,3}
Helpppppp meeee please and thank you
Answer:
Yes, by SAS
Step-by-step explanation:
for the figure shown below, find the value of the variable and the measure of the angles.
x is
measure angle P
measure angle Q
measure angle R
Answer:
All triangles has a total angle of 180. So x+38+2x+18+x=180
Solve for x: 4x+56=180 so 4x=124, x=31
shoprite has various brands of laundry detergent. which brand has the lowest price per ounce?
2. Both the populations of the Candy Kingdom and the Fire Kingdom are in decline; their populations
since 2010 are given by the functions below:
Cit) 1000 - 500
F(t) = 2500 - 1000
Will their populations ever be equal? If so, when will that happen and what will that population be?
Otherwise, briefly explain why their populations will never be equal.
Answer:2. Both the populations of the Candy Kingdom and the Fire Kingdom are in decline; their populations
since 2010 are given by the functions below:
Cit) 1000 - 500
F(t) = 2500 - 1000
Will their populations ever be equal? If so, when will that happen and what will that population be?
Otherwise, briefly explain why their populations will never be equal.
Step-by-step explanation:
a. A bag contains 7 b l u e marbles, 10 g r e e n marbles, and 5 r e d marbles. If a marble is drawn from the bag, replaced, and another marble is drawn, what is the probability of drawing first a b l u e marble and then a r e d marble
7 + 10 + 5 = 22 total marbles.
Picking a blue one first would be 7 blue/22 total = 7/22
Picking a red one would be 5 red / 22 total = 5/22
Picking blue first and then red = 7/22 x 5/22 = 35/484
Find the opposite of each integer. 0=
Answer:
The opposite of 0 is 0
Which of the following is equal to 7 1/4
Answer:
D. [tex]\sqrt[4]{7}[/tex]
Step-by-step explanation:
Answer:
d.
Step-by-step explanation:
The demand for tickets to an amusement park is given by p = 70 - 0.2q, where p is the price of a ticket in dollars and q is the number of people attending at that price.
a. What price generates an attendance of 3,000 people? What is the total revenue at that price? What is the total revenue if the price is $20?
b. Write the revenue function as a function of attendance, q, at the amusement park.
c. What attendance maximizes revenue?
d. What price should be charged to maximize revenue?
e. What is the maximum revenue? Can we determine the corresponding profit?
Answer:
Step-by-step explanation:
From the information given:
p = 70 - 0.02q
when:
q = 3000
p = 70 - 0.02 (3000)
p = 70 - 60
p = 10 dollars
The total revenue = price × number of people
= 10 × 3000
= 30000 dollars
If the price is $20
20 = 70 - 0.02q
0.02q = 70 - 20
0.02q = 50
q = 50/0.02
q = 2500
∴
If price is $20, The total revenue = 20 × 2500
= 50000 dollars
b)
The revenue function R = price × attendance
R = p × q
R = (70 - 0.02q)q
R = 70q - 0.02q²
c)
R(q) = 70q - 0.02q²
Taking the differential of the value on the right hand side.
R'(q) = 70 × (1) - 0.02 × (2q)
R'(q) = 70 - 0.04q
If we set R'(q) = 0
70 - 0.04q = 0
70 = 0.04q
q = 70/0.04
q = 1750 (critical point)
R"(q) = 0 - 0.04 × 1
R"(q) = -0.04
R"(1750) = -0.04 < 0
∴
R is maximum when q = 1750
d)
At q = 1750
p = 70 - 0.02(q)
p = 70 - 0.02(1750)
p = 70 - 35
p = 35 dollars
e)
R(q) = 70q - 0.02q² because R is max at q = 1750
R(1750) = 70 × 1750 - 0.02 × (1750)²
R_(max) = 122500 - 61250
R_(max) = 61250 dollars
Given that the actual price is 20 dollars when the price is changed to 35 dollars, we have a maximum revenue of:
Suppose:
p = 20 and q = 2500 (from a)
Then;
R = p × q
R = 20 × 2500
R = 50000 dollars
If R = 35, then q = 1750
R_{max} = 35 × 1750
R_{max} = 61250 dollars
∴
Profit = R_{max} - R
Profit = 61250 - 50000
Profit = 11250 dollars
James went to the store to return a defective $45 tape recorder for a refund. At the same time, he bought some batteries for $3 per package. If he received $33 dollars of his refund, how many packages of batteries did he buy?
Answer:
4
Step-by-step explanation:
he should have gotten 45 back
but he only got 33
so the DIFFERENCE is how much he got in batteries, how many packs? well 45−33 = 12 12÷3=4
James bought 4 packages of batteries if James went to the store to return a defective $45 tape recorder for a refund. At the same time, he bought some batteries for $3 per package.
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.
We have:
James went to the store to return a defective $45 tape recorder for a refund. At the same time, he bought some batteries for $3 per package
Let he buy x number of packages of batteries.
The cost of packages of batteries = 3x
The linear equation one variable can be framed:
33 + 3x = 45
3x = 45 - 33
3x = 12
x = 4
Thus, James bought 4 packages of batteries if James went to the store to return a defective $45 tape recorder for a refund. At the same time, he bought some batteries for $3 per package.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ5
Can someone help me
Answer:
1) The distance between points is: [tex]\sqrt{290}[/tex]
Option B is correct option.
2) The distance between points is: [tex]\sqrt{10}[/tex]
Option A is correct option.
Step-by-step explanation:
Find the distance between points
Question 1
(8,-5),(-3,8)
The formula used is: [tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have [tex]x_1=8, y_1=-5,x_2=-3,y_2=8[/tex]
Putting values and finding distance
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(-3-8)^2+(8-(-5))^2}\\Distance=\sqrt{(-11)^2+(8+5)^2}\\Distance=\sqrt{(-11)^2+(13)^2}\\Distance=\sqrt{121+169}\\Distance=\sqrt{290}[/tex]
So, the distance between points is: [tex]\sqrt{290}[/tex]
Option B is correct option.
Question 2
(-1,6),(-4,-7)
The formula used is: [tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have [tex]x_1=-1, y_1=6,x_2=-4,y_2=-7[/tex]
Putting values and finding distance
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(-4-(-1))^2+(-7+6)^2}\\Distance=\sqrt{(-4+1)^2+(-1)^2}\\Distance=\sqrt{(-3)^2+(-1)^2}\\Distance=\sqrt{9+1}\\Distance=\sqrt{10}[/tex]
So, the distance between points is: [tex]\sqrt{10}[/tex]
Option A is correct option.
Three out of eight students wore white shoes what percent of students did wore white shoes
Answer:
37.5 percent wore white shoes
Step-by-step explanation:
hurry plz Im running out of time
what is 753 and 251 round to hundredth
15 points
Answer:I am pretty sure its 800
Step-by-step explanation:
Answer:
753 rounds to 753 because it is already rounded. 251 stays the same to because it cant round any further. I hope I have helped :)
What is 52114 divided by 47
Answer:
1108.808511
Step-by-step explanation:
Answer:11108.80
Step-by-step explanation:
What is this? I don't know and I'm struggling bad please help
Answer:
steeper
Step-by-step explanation:
y = mx + c where m is the slope and c is the y-intercept.
The slope has been changed from 2 to 4. The higher the slope, the steeper it is. Thus, the slope is steeper now.
Answer:
i'm not sure sorry
Step-by-step explanation:
Evaluate the expression: (–2)2 + (–4)2 + (18 – 23).
A. –19
B. 19
C. –17
D. 3
Answer:
c
Step-by-step explanation:
(–2)2 + (–4)2 + (18 – 23) = -4-8-5= -17
Find the acute angle between the lines. 5x ? y = 2, 6x + y = 6
Answer:
Acute angle Ф = 20.77° (Approx)
Step-by-step explanation:
Given:
5x - y = 2
6x + y = 6
Find:
Acute angle
Computation:
5x - y = 2
6x + y = 6
So,
y = 5x - 2.....eq1
y = -6x + 6......eq2
Slop line y = mx + c
On comparison
m1 = 5 , m2 = -6
So,
TanФ = I(m1-m2)/(1+m1m2)I
TanФ = I(5+6)/(1-30)I
TanФ = 11/29
Ф = 20.77° (Approx)
Acute angle Ф = 20.77° (Approx)
The neighbor sold 16 cake pops for $1.75 each. How much money did the neighbor collect?
Answer:
$28
Step-by-step explanation:
$1.75 x 16 = $28
Answer: 10.05
Step-by-step explanation:
Alexandra spends 1/3 of her daysleeping and 3/8 of her day at work. What fraction of Alexandra’s day is occupied by sleep or work?
Answer:
17/24
Step-by-step explanation:
Change the denominators to match
8/24 + 9/24 = 17/24
What is this? Please answer with an explanation
F(x)=2x^3-2x+1 relativeminimum
Step-by-step explanation:
F(x) = 2x³ - 3x + 1.
d/dx [2x³ - 3x + 1] = 6x² - 3.
Firstly, we wish to find the stationary points of F(x).
When 6x² - 3 = 0, x = -0.707 or x = 0.707.
Now we use Second Derivative test:
d/dx [6x² - 3] = 12x.
Since 12(-0.707) < 0, x = -0.707 is a relative maximum point.
Since 12(0.707) > 0, x = 0.707 is a relative minimum point.
Hence x = 0.707. To find the exact point you can substitute the value of x back into the equation 2x³ - 3x +1.