Root x= 3 of multiplicity 2, it means we can factor it with : (x-3)²
Root x = 1, of multiplicity 1, it means we can factor this polynomial with : (x-1)
Root x = -3, of multiplicity 2, it means we can factor this polynomial with : (x+3)²
Finally we get this expression : (x-3)²(x+3)²(x-1)
This expression is a polynomial of degree 5 but what is the y intercept of it ?
Basically, we need to replace x by zero and the value of the expression will be the y intercept :
let x = 0
then ,
(0-3)²(0+3)²(0-1) = 9*9*(-1) = -81 #-162
We need an y intercept of value = -162
Thus we simply need to multiply by 2, and finally f(x) = 2(x-3)²(x+3)²(x-1)
satisfies all the required condition
Good Luck
The points K(5,-5)(5,−5), L(9,-5)(9,−5), and M(7,3)(7,3) form a triangle. Plot the points then click the "Graph Triangle" button.
3. A savings account is started with an initial deposit of $500. The account earns 1.5% interest compounded annually. (a) Write an equation to represent the amount of money in the account as a function of time in years. (b) Find the amount of time it takes for the account balance to reach $800. Show your work. Answer:
Answer:
31.334... years
Step-by-step explanation:
Initial value = $500
r = 1.5%
t = ?
A = (500)[tex]e^{.015*t}[/tex]
I was unsure if the question was asking to express the equations in terms of t =, but i did those steps anyway just in case.
A/500 = [tex]e^{.015*t}[/tex]
ln A/500 = ln[tex]e^{.015*t}[/tex]
ln A/500 = .015*t
ln(A/500)/.015 = t
t = ln(A/500)/.015
To find the amount of time it takes for the account balance to reach $800, we plug in $800 for A in the equation that solves for t.
t= ln(800/500)/.015 = 31.334...(rounded) years
We also could have solved by plugging in $800 into the original equation and then solving for t, but i found it to be easier to find the equation for t prior to solving. Hope this helps!
Find the value of x given that the area of the triangle is 8 ft2.
(x + 1) ft
(3x - 7) ft
Answer:
Step-by-step explanation:
Joel wants to buy a new tablet computer from a store having a 20% off sale on all tablets. The tablet he wants has an original cost of $190. He also wants to make sure he has enough money to pay the 5% sales tax. How much will Joel pay for the tablet?
Answer:
161.5 $
Step-by-step explanation:
the cost of table after the discount = 100% - 20% = 80%
the cost of table after the discount = Original cost × 80%
=(190)(0.8)
=152 $
the cost of table after the discount plus the tax = (the cost of table after the discount) + (Original cost × 5%)
=152+(190)(0.05)
=152+9.5
=161.5 $
So... The total amount will Joel pay for the tablet = 161.5 $
How many time can 3/8 go into 12?
Answer:
32
Step-by-step explanation:
This is a division problem.
12 divided by 3/8.
12 ÷ 3/8 = 12/1 × 8/3 = (12 × 8)/(1 × 3) = 4 × 8 = 32
Answer: 32
Find the area of the shape shown below.
2 2 2 2 6
Answer:
12 units squared
Step-by-step explanation:
This requires a 3-step solution.
1. The triangle on the left:
To get an area for a triangle, you do: base times height divided by 2.
You get 4/2, which is 2 units squared for the first triangle.
2. The square:
Pretty easy, it is 2 x 2 which is 4.
3. The last triangle:
Same thing as the first triangle, 2 x 6 divided by 2.
You get 12/2 which is 6.
To get the final area: You add them up.
2 + 4 + 6, which is 12.
One pint of milk is about 560 ml. Rosa has 3.5 pints of milk. How many litres of milk does rosa have?
Help pls
261,256,251,...
Find the 50th term.
Find the 50th term.
Answer:
16
Step-by-step explanation:
261 - 256 - 251
-5 by step
to 50th term there is 49 -5's from 261.
261 + 49.(-5) = 261 - 245 = 16
Answer:
16
Step-by-step explanation:
The sequence appears to be an arithmetic sequence. To find the 50th term we should create a general formula for the sequence.
General formula of an arithmetic sequence: [tex]a_n=a_1+(n-1)d[/tex]
where An = nth term, a1 = first term , n = number of terms and d = common difference.
The first term is 261 so a1 = 261
The common difference appears to be -5
( 256 - 261 = -5 ) and ( 251 - 256 = -5 )
so d = -5
We want to find the 50th term so n = 50
We then plug all of this in to get the 50th terms
Formula : [tex]a_n=a_1+(n-1)d[/tex]
a1 = 261 , n = 50 and d = -5
[tex]a_n=261 + (50-1)-5[/tex]
subtract 1 from 50
[tex]a_n=261+(49)(-5)[/tex]
multiply 49 and -5
[tex]a_n=261-245[/tex]
subtract 245 from 261
[tex]a_n=16[/tex]
The 50th term is 16
Ray had $50. he bought two shirts that cost $19 each. how much money did Ray have after buying the shirts? Alex's answer to the word problem is $29. Is Alex's answer reasonable? explain.
Answer: No, it's not
Step-by-step explanation:
19*2=38
50-38 = 12
Alex awnsered 29 which is $17.00 off.
Cameron wants to buy a camera for $259. He has $50 and plans to save $20 each week. How many weeks will it take to save enough money to buy the camera? (not including
sales tax)
Answer:
About 11 Weeks
Step-by-step explanation:
I found out by multiplying 11 by 20 and got 220. Then, adding 50 is 270, which is just over 259. It's not ten because 200 is just underneath his goal.
Help!!!!!!please help i will fail
Answer:
WHAT is to solve their is notting
Step-by-step explanation:
Write an equation in slop intercept form with a given slope. Slope: 5/6, y-intercept: 8
y=5/6x+8
...............
100 points brainlyest if right
Answer:
I don't know the question
Step-by-step explanation:
I would love to help tho
Answer:
you never put the question up for us to answer it
Step-by-step explanation:
Suppose a quadratic equation has the form x^2 + x + c = 0. Show that the constant c must be less than 1/4 in order for the equation to have two real solutions.
Answer:
see explanation
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 )
Then for the equation to have 2 real roots , the discriminant must be greater than zero , that is
b² - 4ac > 0
x² + x + c = 0 ← is in standard form
with a = 1, b = 1, c = c , then
b² - 4ac > 0
1² - (4 × 1 × c) > 0
1 - 4c > 0 ( subtract 1 from both sides )
- 4c > - 1
Divide both sides by - 4, reversing the inequality as a result of dividing by a negative quantity.
c < [tex]\frac{1}{4}[/tex]
Select the graph of the equation y + x + 3 = 0.
Answer:
the fourth image
Step-by-step explanation:
y + x + 3 = 0
y = -x - 3
meaning slope = -1
and y-intercept is -3
answer: image attached
because they all look similar, it is the one that moves exactly one block per unit
givien the function 6x+6y=5 rearrange the equation so that x is the independant varible
Answer:
so 6x = -6y + 5
divide by 6
x = 5
Step-by-step explanation:
Find all solutions of cos()=−1/2 on the interval [−
Answer:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10!!
Step-by-step explanation:
Help please and thank you
Answer:
Perimeter of trapezoid ABCD is 22.8
Step-by-step explanation:
6 + 6 + 8.2 + 2.6 = 22.8
I hope this helps!
What is the quotient ?
7 with a power of -6 over 7 with a power of 2
Answer: [tex]\frac{1}{7^8}[/tex] or [tex]\frac{1}{5764801}[/tex]
Step-by-step explanation:
First, since the two roots (7) are the same, you subtract the exponents, which gives you -6 - 2 to get -8, giving you [tex]7^{-8}[/tex]
Next, you change [tex]7^{-8}[/tex] to [tex]\frac{1}{7^8}[/tex] or [tex]\frac{1}{5764801}[/tex]
I hope that helps :)
Guys help me on this one please…
Answer: 6. 35 hours
7. 741 Miles
8. 1.5 or 1.54
Step-by-step explanation:
6. 142.20/6=23.7
829.50/23.7=35
7. 117/3=39
39x19=741
8.19/12.35=1.538
6. What is the value of the underlined digits?
504,405,623
Math
Answer:
Which one is underlined?
Step-by-step explanation:
the frist 5 is in the 100 millionth place
the frist 0 is in the 10 millionth place
the frist 4 is in the 1 millionth place
the second 4 is in the 100 thousand place
the second 0 is in the 10 thousand place
the second 5 is in the 1 thousand place
the 6 is in the 100s place
the 2 is in the 10s place
and the 3 is in the 1s place
A pencil at a stationery store costs $1, and a pen costs $1.50. Shawn spent $12 at the store. He bought a total of 9 items. Which system of equations can be used to find the number of pencils (x) and pens (y) he bought? (5 points)
1.5x + y = 12
x = 9y
x + 1.5y = 12
x + y = 9
x + 9y = 12
x = 1.5y
9x + y = 12
x = 1.5y
Answer:
9 = x + y
1x + 1.5y = 12
Step-by-step explanation:
9 (number of items) = x (number of pencils) + y (number of pens)
1x (cost of x number of pencils) + 1.5y (cost of y number of pen s)= 12 (total cost)
Select all equations that do NOT have a solution.
A 8x + 4x = 0
B 6x + 2 = 4x + 2 + 2x
C 4x – 8x – 3 = 6 – 4x
D 5x + 1 = 1 – 5x
E 12x – 3 – 5x = 9 + 7x – 6
Answer:
C and E are the answers:)
Step-by-step explanation:
Hope this helps!
Answer- C,D, and E
If you plug in any number for those proplems you will get a different number a each side
PLEASE HELP!! ASAP THANKS
I'll put this as random but you can answer it...
ill give yall 10 points if yall do it!
Answer: 4 gallons = 15 liters, 8 liters = 2 gallons, 12.5 liters = 3 gallons, and 6 gallons = 23 liters.
Answer:
yea no
Step-by-step explanation:
i really don't know sorry tho
what is the value of 7
7 can be written as :-
7 + 0 = 7
7 - 0 = 7
7 × 1 = 7
7 ÷ 1 = 7
7¹ = 7
_____
Hope it helps ⚜
Maya solved 1/4 of a crossword puzzle before dinner and a part of it after dinner. If Maya solved 3/4 of the crossword in all, what fraction of the puzzle did she solve after dinner?
Choose the equation that matches the word problem.
Answer:2/4
Step-by-step explanation: you would just subtract 3/4 by 1/4 to get 2/4
what is a fraction between 2/3 and 4/7
Answer:
3/5
Step-by-step explanation:
it is between 2/3 and 4/7
Consider this diagram of quadrilateral ABCD, which is not drawn to scale.
Answers: Choice B and Choice D.
[tex]\angle ABE \cong \angle CDE[/tex] and [tex]\overline{AE} \cong \overline{CE}[/tex]
=====================================================
Explanation:
The tickmarks tell us which segments are congruent to one another. The segments with single tickmarks show that AE and CE are the same length. So this is why [tex]\overline{AE} \cong \overline{CE}[/tex]
---------------
The two triangles AEB and CED can be proven congruent through the use of the SAS theorem. From there, use CPCTC to conclude that the corresponding angles ABE and CDE are the same measure i.e. [tex]\angle ABE \cong \angle CDE[/tex]. They are alternate interior angles which helps lead to side AB being parallel to CD.
Answer:
B & D or <ABE=<CDE, AE=CE
Step-by-step explanation:
I got it right on khan
Help help help help math math math
