Answer:
[tex]c^2 = 9dp[/tex]
Step-by-step explanation:
Given
[tex]dx^2 + cx + p = 0[/tex]
Let the roots be [tex]\alpha[/tex] and [tex]\beta[/tex]
So:
[tex]\alpha = 2\beta[/tex]
Required
Determine the relationship between d, c and p
[tex]dx^2 + cx + p = 0[/tex]
Divide through by d
[tex]\frac{dx^2}{d} + \frac{cx}{d} + \frac{p}{d} = 0[/tex]
[tex]x^2 + \frac{c}{d}x + \frac{p}{d} = 0[/tex]
A quadratic equation has the form:
[tex]x^2 - (\alpha + \beta)x + \alpha \beta = 0[/tex]
So:
[tex]x^2 - (2\beta+ \beta)x + \beta*\beta = 0[/tex]
[tex]x^2 - (3\beta)x + \beta^2 = 0[/tex]
So, we have:
[tex]\frac{c}{d} = -3\beta[/tex] -- (1)
and
[tex]\frac{p}{d} = \beta^2[/tex] -- (2)
Make [tex]\beta[/tex] the subject in (1)
[tex]\frac{c}{d} = -3\beta[/tex]
[tex]\beta = -\frac{c}{3d}[/tex]
Substitute [tex]\beta = -\frac{c}{3d}[/tex] in (2)
[tex]\frac{p}{d} = (-\frac{c}{3d})^2[/tex]
[tex]\frac{p}{d} = \frac{c^2}{9d^2}[/tex]
Multiply both sides by d
[tex]d * \frac{p}{d} = \frac{c^2}{9d^2}*d[/tex]
[tex]p = \frac{c^2}{9d}[/tex]
Cross Multiply
[tex]9dp = c^2[/tex]
or
[tex]c^2 = 9dp[/tex]
Hence, the relationship between d, c and p is: [tex]c^2 = 9dp[/tex]
Please anyone help anyway you can
Need some help working these out
Answers:
Problem 1) 40 degreesProblem 2) 84 degreesProblem 3) 110 degrees===============================================
Explanation:
For these questions, we'll use the inscribed angle theorem. This says that the inscribed angle is half the measure of the arc it cuts off. An inscribed angle is one where the vertex of the angle lies on the circle, as problem 1 indicates.
For problem 1, the arc measure is 80 degrees, so half that is 40. This is the measure of the unknown inscribed angle.
Problem 2 will have us work in reverse to double the inscribed angle 42 to get 84.
-------------------
For problem 3, we need to determine angle DEP. But first, we'll need Thales Theorem which is a special case of the inscribed angle theorem. This theorem states that if you have a semicircle, then any inscribed angle will always be 90 degrees. This is a handy way to form 90 degree angles if all you have is a compass and straightedge.
This all means that angle DEF is a right angle and 90 degrees.
So,
(angle DEP) + (angle PEF) = angle DEF
(angle DEP) + (35) = 90
angle DEP = 90 - 35
angle DEP = 55
The inscribed angle DEP cuts off the arc we want to find. Using the inscribed angle theorem, we double 55 to get 110 which is the measure of minor arc FD.
Evaluate 2x when x = 4
COULD SOMEONE HELPP
Is 3,9,19,33,51.. a linear or non-linear sequence?
Jai shree ram. sjkaoaoauwyyw7272okebsbskpszbahzijzgzgz
Answer:
non-linear
Step-by-step explanation:
dosnt go up by the same amount each time
Choose the method of pay that would result in the most earnings for one month on sales of 73,620
Answer:
Step-by-step explanation:
For option A: Earning = 0.06 x $73,620 = $4,417.20
For option B: Earning = $3,000 + 0.02 x $73,620 = $3,000 + $1,472.40 = $4,472.40
For option C: Earning = 0.04 x $50,000 + 0.09 x ($73,620 - $50,000) = $2,000 + 0.09 x $23,620 = $2,000 + $2,125.80 = $4,125.80
For option D: Earning = 0.05 x $35,000 + 0.07 x $(73,620 - 35,000) = $1,750 + 0.07 x $38,620 = $1,750 + $2,703.4 = $4,453.40
Therefore, the method that yields the most earning is monthly salary of $3,000 plus 2% commission on all sales .
Answer:
b.
Monthly salary of $3,000 plus 2% commission on all sales.
Step-by-step explanation:
edge 2021
please help.[tex]\frac{4}{x+2} +\frac{8}{x+5} -\frac{8}{x+3} -\frac{4}{x+6}[/tex]
What is the solution to the equation −4(2y − 4) − 4y = 4? (put number answer only)
Answer:
y=1
Step-by-step explanation:
Let's solve your equation step by step.
Step 1: Simplify both sides of the equation.
−4(2y−4)−4y=4
(−4)(2y)+(−4)(−4)+−4y=4(Distribute)
−8y+16+−4y=4
(−8y+−4y)+(16)=4(Combine Like Terms)
−12y+16=4
−12y+16=4
Step 2: Subtract 16 from both sides.
−12y+16−16=4−16
−12y=−12
Step 3: Divide both sides by -12.
y=1
Becky roller skated 4/6 of a mile on Wednesday and 2/8 of a mile on Friday. How far did Becky roller skate in all?
Answer:
3/4
Step-by-step explanation:
4/6 + 2/8 =
x 8 x6
24/48 + 12/48 = 36/48 = 3/4
(8x + 9) + (15 - 8x)
Find the amount of the principal on a loan at 6% interest for 140 days if the interest was $253.15, using the exact interest method. (Round to the nearest whole dollar amount)
Answer:
$11,000
Step-by-step explanation:
Given that :
Time, t = 140 days = 140/365 = 0.3835years
Interest paid = 253.15
Interest % = 6%
Principal, p =?
Using the relation :
Interest = principal * rate * time
253.15 = p * 0.06 * (140/365)
253.15 = 0.0230136p
P = 253.15 / 0.0230136
P = 11000.017
Hence, the principal amount = $11,000
help ???????????????
Answer:
1. 14 people said 1 hour or more
2. 52 people
3. 13 people said it takes them less than half an hour and 13 people said it takes them more than half a hour. difference is 0
4. the data is taken in pairs of 2 people
Step-by-step explanation:
bottom question
5- 2
10 - 6
15 - 4
20 - 6
25 - 0
30 - 8
35 - 4
40 - 0
45 - 6
50 - 2
55-0
60-8
65-6
Help me plsssssssssssssssss
Answer:
e tenta de novo fazer a questãotenta rever o conteudo onde vc estudou isso
Step-by-step explanation:
John wants to buy a new motorcycle. The tax rate is 9%. How much tax will
he pay if the motorcycle cost is $4500? (i need this quickly, i'm trying to study for my math test tomorrow but i don't even know how to do the math- pls help!)
Answer:
$405.00
Step-by-step explanation:
$4500.00×9%=$405.00
10.
4+y=-3 and x-3y=-18
Use what you know about ratios to describe a rate.
Answer:
down below
Step-by-step explanation:
A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates.
1. True or False: While using the Pythagorean Theorem, if A and B squared
are added and it equals C squared, it is a right triangle.*
*
Answer:
true because its correct
A pizza store sold 36 pepperoni pizzas in a day, which was 24% of their pizza sales.
What was the total number of pizzas sold that day?
Answer:
150 pizzas
Step-by-step explanation
36 pizzas are equivalent to 24% so i divided both sides by 4 which gave me 9 pizzas for 6% . But 6 cannot fully fit into 100 so it will have to be a decimal i did 100 divided by 6 so i would know what i would have to divide both sides by which gave me 50/3 which was 16.66666667 which when i times by 9 by it gave me 150 pizzas
Hope this helps
Determine whether Joe is shorter or taller than the height of the tepee
Answer:
shorter
Step-by-step explanation:
What is the y-intercept, b, of the additive relationship represented by this table?
Enter your answer as an integer in the box.
b =
x y
1 4
3 6
Answer:
3
Step-by-step explanation:
First step: Find the slope, Using the Formula y2 - y1 / x2 - x1 =
6-4=2 3-1=2 then u divde the y/x 2/2=1 So the slope is 1.
Step 2: Use the Slope- Intercept formula, Y=mx+b so 4 = 1(1)+b so 4 = 1 + b
Step 3: subtract 1 on both sides so 4-1=3 1-1=0 so 3 is the Y-Intercept.
if 3 more than 5 times a number is seven more than three times that number, what is the result when the number is added to 10
Answer: 12
Step-by-step explanation:
3 more than 5 times a number = 3+5x
seven more than three times that number = 7+3x
is = "="
Thus,
3 + 5x = 7 + 3x
2x = 4
x = 2
2 + 10 = 12
Hope it helps <3 :)
use the disturbitive property to write an expression that is equivalant to 8(a+4)
Answer:
8a + 32
Step-by-step explanation:
To use the distributive property, multiply 8 x a and multiply 8 x 4
Pat volunteered to bake 80 biscuits for a family reunion breakfast. She plans to bake 8 biscuits in each pan. Which number sentence can be used to find p, the number of pans of biscuits that she will need to bake?
Answer: 10 pans
Step-by-step explanation:
Step 1:
If the number of biscuits needed= 80
Step 2:
And the number of biscuits on each pan= 8
Step 3:
Then the number of pans needed= 80 ÷ 8
Answer: 80 ÷ 8 = 10pans
How many solutions does the system of linear equations have?
y = 34x + 12
y = 43x
Answer:
x=4/3 and y=172/3
Step-by-step explanation:
hope this helps!
solve for r in the parallelogram
The formula for the volume of a cylinder is V=pi*r^2h. The cylinder to the right has an exact volume of 360x cubic meters. Find it's height.
Answer:
12.7342
Step-by-step explanation:
V=360
d=6
r=1/2*d=3
r^2=9
360/pi=114.592
114.592/9=12.7342
What is the apparent solution to this system of equations?
(Write your answer as an ordered pair)
(FIRST TO ANSWER GETS BRAINLIEST)
Answer:
x = (3,3)
Step-by-step explanation:
This is going to be x = (3,3) because this is showing where the x, y stand. The x goes, ∧ and the y goes to the ⇒ SO this is going to be x = (3,3) because the x comes first before the 2!
Choose all of the points that are solutions to the equation y = x ^ 2-3x-4 .
Answer:(0,-4), (1,0), (2,6)
Find the equation of the line shown.
You have 40 minutes to exercise at the gym, and you want to burn 300 calories total using both
machines. The amount of calories burned on each machine is shown in the picture below. How
much time should you spend on each machine?
Machine a burns 8 calories per minute machine b burns 6 calories per minute.
66.6666666667 as a mixed number in simplest form
Answer:
66 67/100
Step-by-step explanation:
Answer:
Mix Number form: 66 2/3
Simplest Form: 6.66
Hope this helps.