Hi. I need help with these questions.
See image for question.
Answer 20 and 21
Answers
Answer:
20. The vertex is (2/3, 14/3) | p = 3, q = -2/3 and r = 14/321. 20x² + 2x - 3 = 0Step-by-step explanation:
20.
Giveny = 3x² - 4x + 6To findThe least value of the y and the corresponding value of xConstants p, q and r such that 3x² - 4x + 6 = p(x + q)² + rSolutionThe given is the parabola with positive a coefficient, so it opens up and the minimum point its vertex.
The vertex has x = -b/2a and corresponding y- coordinate is found below:
x = - (- 4)/2*3 = 2/3, and y = 3(2/3)² - 4(2/3) + 6 = 4/3 - 8/3 + 6 = 14/3So the vertex is (2/3, 14/3)The vertex form of the line has the equation:
y = a(x - h)² + k, where (h, k) is the vertexPlugging in the values:
y = 3(x - 2/3)² + 14/3Comparing with p(x + q)² + r, to find out that:
p = 3, q = -2/3 and r = 14/3=====================================
21.
(i) α and β are the roots of: ax² + bx + c = 0
Show that:
α + β = -b/a and αβ = c/aSolutionKnowing the roots, put the equation as:
(x - α)(x - β) = 0x² - αx - βx + αβ = 0x² - (α+β)x + αβ = 0Comparing this with the standard form:
ax² + bx + c = 0Divide by a to make the constants of x² same:
x² + b/ax + c/a = 0Now comparing the constants:
- (α+β) = b/a ⇒ α+β = - b/aαβ = c/a--------------------------------------------
(ii)
Givenα and β are the roots of: 3x² - x - 5 = 0To Find The equation with roots 1/2α and 1/2βSolutionThe sum and the product of the roots:
α + β = -b/a = 1/3αβ = c/a = -5/3The equation is:
(x - 1/2α)(x - 1/2β) = 0x² - (1/2α + 1/2β)x + 1/(2α)(2β) = 0x² - (α + β)/(2αβ)x + 1/4αβ = 0x² - (1/3)/(2(-5/3))x + 1/(4(-5/3)) = 0x² + 1/10x - 3/20 = 020x² + 2x - 3 = 0Related Questions
y 5x=2
What are the coordinates
Answers
Answer:move -5x to the right becomes 5x
Y=5X+2
When x =1 5(1)+2= 7 for Y
When X=2 5(2)+2= 12 for Y
When X =-1 5[-1)+2/ -3
Coordinates (1,7).(2,12)(-1,-3)
Step-by-step explanation:
PLEASE
The simple interest formula is I=Prt, where I is the interest, P is the principal, r is the interest rate, and t is the time.
What is the interest rate if the principal is $25,000, the interest is $10,875, and the time is 15 years?
Answers
Answer:
$40781250
Step-by-step explanation:
Okay so the formula for simple interest is: I = P x T x R divided by 100
25000 x 10875 x 15 = 4078125000 / 100 = $40781250
If you have the multiple choice answers:
A. $160
B. $200
C. $1600
D. $16,000
the answer is C. $1600
here's why:
The principal is $10,000, the interest rate is 2%, and the time is 8 years.
I = Prt
= $10,000 · 2% ⋅ 8
= 10,000 ⋅ 0.02 ⋅ 8
= 1600
So, the interest earned is $1600.
Evaluate the limit 8n^2+5n+2/3+2n
Answers
Answer:
8n^2+7n+2/3
Step-by-step explanation:
combine like terms
5n+2n=7n
Answer: D on edg
Step-by-step explanation:
is 1 ÷2 the same as 1/2?
Answers
Answer:
Step-by-step explanation:
yes it is
Answer:
yes----------------------
Simplify (2x^2 y^3)(4x^3 y^4) I put 69 Points
Answers
Answer: 16x^4y^12
Step-by-step explanation:
don’t forget about the exponent 4.
can u pls find the slope intercept form pls?
Answers
Answer:
y = - 7/5x + 18/5
Slope: - 7/5
y - intercept: (0, 18/5)
Hope this helps!!
Silvia opens a $500 simple interest checking account with a rate of 8%.After 6 months what is the interest rate on her account?
Answers
Casey orders 3 pizzas and 2 orders of breadsticks for a total of $29.50. Rachel orders 2 pizzas and 3 orders of breadsticks for a total of $23. How much would it cost to order 5 pizzas and 6 orders of breadsticks?
Answers
Answer:
$54.50
Step-by-step explanation:
3 pizzas + 2 breadsticks = $29.50
2 pizzas + 3 breadsticks = $23
5 pizzas + 6 breadsticks = $x
multipy first equation by 3 and second by -2
9 pizzas + 6 breadsticks = $88.50
-4 pizzas -6 breadsticks = $-46
add the equations up, 9-4 pizzas + 6-6 breadsticks = $88.50-46
5 pizzas = $42.50 , divide by 5 both sides
1 pizza = $8.50
Substitute the price of a pizza, 2 pizzas + 3 breadsticks = $23
2*8.50 + 3breadstiks = $23
17 + 3 breadsticks = $23 subtract 17 from both sides so
3 breadsticks = $23 -$17 divide by 3
1 breadstick = 6/3= $2
$5*8.50 for pizzas + $6*2 for breadsticks = $54.50
Jordan's activity tracker showed that when she walked for 12 minutes she took 804 steps. Karen's activity tracker showed that she walked 2,100 steps in 32 minutes. Who was walking at a faster rate?
Answers
Given:
Jordan's walked for 12 minutes she took 804 steps.
Karen's walked 2,100 steps in 32 minutes.
To find:
Who was walking at a faster rate?
Solution:
We need to find the unit rate of Jordan and Karen.
[tex]\text{Unit rate}=\dfrac{\text{Total steps}}{\text{Total time}}[/tex]
Unit rate of Jordan,
[tex]\text{Unit rate}=\dfrac{804}{12}[/tex]
[tex]\text{Unit rate}=67[/tex]
Unit rate of Karen,
[tex]\text{Unit rate}=\dfrac{2100}{32}[/tex]
[tex]\text{Unit rate}=65.625[/tex]
Clearly, 67 > 65.625.
Since, unit rate of Jordan is greater, therefore she walked faster.
Solve for x and y
Plz I need help it’s for geometry
Answers
Answer:
Angle x = 21
Angle y = 146
A car  travel 63 miles in 30 minutes if the car travels constant how many hours does the car travel in 50 minutes
Answers
Answer:105 miles
Step-by-step explanation
63/30= m/50
multiply 63x50
multiply 30x m
now you have
30m = 3150
so you divide
30m/30 and 3150/30
m=105
Answer:105 miles
Step-by-step explanation:
If a number is divisible by 3, then its odd
Answers
Answer:
and? obviously bc 3 isnt a even number so then the answer wont be even
What is an equilateral triangle?
a.
a triangle with equal sides and angles
c.
a sacred triangle used in Islamic art
b.
a triangle whose angles equal 360
d.
none of the above
Answers
Answer:
A
Step-by-step explanation:
Answer:
A. a triangle with equal sides and angles
What is the answer?
-1.2x=12
Answers
775757874875875345634634563456
Triangle ABC is similar to Triangle DEF. What is the scale factor from DEF (25 points)
to ABC?
Answers
Answer:
3/2 or 1.5 (A)
Step-by-step explanation:
9 divided by 6 is 1.5
15 divided by 10 is 1.5
12 divided by 8 is 1.5
Answer:
3/2 or 1.5 (A)
Step-by-step explanation:
You need at least 30 cubic feet of sand to fill a sand box. Each bag contains 2.5 cubic feet of sand. What is the minimum number of bags you need to buy?
Answers
Answer:
12 bags of sand
Step-by-step explanation:
The minimum number of sand to fill the sandbox = 30 cubic feet
The volume or quantity of sand per bag is = 2.5 cubic feet
The minimum number of bags needed to fill the sandbox = 30 / 2.5 = 12 bags
Can every parallelogram be changed into a rectangle
with equal area? Explain.
Answers
Answer:
Every parallelogram can be made into a rectangle, which is why we use the same formula to find the area of a parallelogram and a rectangle.
Step-by-step explanation:
Because the parallelogram and rectangle are composed of the same parts, they necessarily have the same area.
George has 525 songs on his mobile device and downloads 3 new songs a week. represent the total number of songs he has after w weeks.
Answers
Answer:
y= 3w+525
Step-by-step explanation:
Choose the graphs that indicate equations with no solution
Answers
Answer:
The ones that dont touch are 2
Step-by-step explanation:
I’m sure that’s what you need. Hope I could Explain correctly
Mark it as brainlist
please help me on this
Answers
Answer:
x = 3
Step-by-step explanation:
7(2 - x) - 5(x - 1) = -6x + 1 (distribute the 7 and the 5)
14 -7x -5x + 5 = -6x + 1 (collect like terms)
-12x + 19 = -6x + 1 (add 12 on both sides)
19 = 6x + 1 (subtract 1 on both sides)
18 = 6x (divide by 6 on both sides)
3 = x
Hope this helps ya!!
y=5x-17 y=x+3 can someone help me with this? thanks
Answers
Answer:
x=5, y=8
Step-by-step explanation:
we can use subsitution to solve this so:
5x-17=x+3 since they bot equal y (y=y)
4x-17=13 subtract x from both sides
4x=20 add 17 to both sides
x=5
then, plug in x to solve for y (either equation) :
y = x+3
y = (5) + 3
y = 8
If f(x)=-9x-2, find f(7)
Answers
Answer:
x= -1/5
Let me know if you need an explanation :)
Which are skew lines? Check all that apply.
•A and B
•C and B
• B and E
• E and C
• A and E
• A and C
Answers
Answer:
C and B; A and C; E and C;
Step-by-step explanation:
Skew Lines are lines that do not intersect and are not parallel. Skew lines must be in 2 different planes because in 1 plane 2 lines either intersect or are parallel. Assuming that a,b, and e are on the plane in front and c is on the plane in the back we can say that A and B, B and E, and A and E can not be skew lines because they lie on the same plane. This leaves C and B, E and C, and A and C.
Answer:
C and B; E and C; A and C
Step-by-step explanation:
Answer
Kiran buys supplies for the school’s greenhouse. He buys 푓 bags of fertilizer and 푝 packages of soil. He pays $5 for each bag of fertilizer and $2 for each package of soil and spends a total of $90. The equation 5푓 +2푝 = 90 describes this relationship. If Kiran solves the equation for 푝, which equation will result?
Answers
Answer and explanation:
Given that Kiran buys x bags of fertilizer and y packages of soil
He pays $5 for each bag of fertilizer and pays $2 for each package of soil
He spends a total of $90
So his equation is
5x+2y= $90
If we solve the equation for y(packages of soil)
We would have:
2y=$90-5x
y= $90-5x/2
Therefore Kiran's equation to get number of packages of soil is
y=$90-5x/2
PLEASE GUYS HELP ME I WILL GIVE BRAINLIST OR WHATEVER IS CALLED I HAVE AN IMAGE ATTACHED TO
Rosie draws a triangle, ABC.
• AB = 8 cm
• AC = 9 cm
• Angle BAC = 75
a) Draw a sketch of Rosie's triangle.
b) Use your sketch to work out the area of Rosie's triangle.
cm
Answers
Answer:
34.77
Step-by-step explanation:
help pls i need the angles one
Answers
If you answer this I'll mark you the brainest
During a 4-second practice round, one of the Click Bots made only 8 clicks.
Amir claims that the unit rate is 2 clicks per second.
Chloe disagrees. She says it's 0.5 clicks per second.
Who is correct?
Amir or chloe and why ?
Answers
Answer:
Step-by-step explanation:
Answer:
amir is correct
Step-by-step explanation:
amir is correct because 8/4 is 2. Therefore if the button is clicked 2 times each second then the button will be clicked 8 times every 4 seconds
aye can u help me ??
An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $3600 and his stock in Company B was worth $5350. The stock in Company A has increased 19% since last year and the stock in Company B has increased 24%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).
Answers
Answer:
I have the same question let me know if you get the answer
Please quick You purchase a car using a $15,000 loan with a 5% simple interest rate.
(a) Suppose you pay the loan off after 4 years. How much interest do you pay on your loan? Show your work. (10 points)
Answers
Answer:
a) $3000
Step-by-step explanation:
a)
interest = Principal x rate as decimal x time
interest = 15,000 x 0.05 x 4
interest = 3000
You have 10 friends coming to the party, so you need to buy enough packages of cupcakes and brownies for everyone to get at least two. Don't forget yourself!
Answers
Answer:
44 cakesStep-by-step explanation:
Step one:
we are told that there are 10 friends coming,
if you are going to include yourself, a total of 11 persons in the party.
if everyone will have at least 2 of cupcakes and brownies, hence they will get 4 cakes each
Step two:
The total number of cakes you will need to get for everyone is
4*11= 44 cakes
Hence you will need 44 cakes with you inclusive