Answers
Problem 1
I'm assuming your teacher means "list all the possible rational roots".
If so, then we use the rational root theorem. This is the idea where we'll divide the factors of the last term over the factors of the first coefficient.
Factors of 5: 1, 5Factors of 3: 1, 3If we divide said factors in the order mentioned, then we get this list of possible positive rational roots:
1/1, 1/3, 5/1, 5/3
That list simplifies to
1, 1/3, 5, 5/3
That takes care of the positive possible rational roots. We double the list to incorporate the negative possible rational roots as well
-1, -1/3, -5, -5/3
Answer: 1, -1, 1/3, -1/3, 5, -5, 5/3, -5/3Note: We can rewrite that list in bold into [tex]\pm 1, \pm\frac{1}{3}, \pm 5, \pm \frac{5}{3}[/tex] to shorten it.
============================================================
Problem 2
We'll follow the same idea as the previous problem
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 4: 1, 2, 4
To keep track of everything, I made a spreadsheet table. Refer to the diagram below. The factors of 36 are laid across the top while the factors of 4 are along the left side. Each inner cell represents dividing the headers.
For example, 36/4 = 9 is in the bottom right corner. The first table is before the fractions are reduced, and the second table after the fractions are reduced.
As the second table shows, we have a few repeats. The unique items here are:
1,2,3,4,6,9,12,18,36,1/2,3/2,9/2,1/4,3/4,9/4
We'll then mirror this set to include negative values as well to write the full list of all possible rational roots.
Answer: 1,2,3,4,6,9,12,18,36,1/2,3/2,9/2,1/4,3/4,9/4-1,-2,-3,-4,-6,-9,-12,-18,-36,-1/2,-3/2,-9/2,-1/4,-3/4,-9/4============================================================
Problem 3
Factors of 15: 1, 3, 5, 15Factors of 5: 1, 5Divide the factors of 15 over the factors of 5 to get
1/1, 1/5, 3/1, 3/5, 5/1, 5/5, 15/1, 15/5
That list reduces to
1, 1/5, 3, 3/5, 5, 1, 15, 3
we can then toss out the duplicates to get
1, 3, 5, 15, 1/5, 3/5
Don't forget to include the negative values as well
Answer: 1, 3, 5, 15, 1/5, 3/5-1, -3, -5, -15, -1/5, -3/5============================================================
Problem 4
The steps will be effectively the same as before. You can write out the factors like done in problem 3, or make a table like done in problem 2. I'll skip the steps shown here unless you need me to go over them.
Answer: 1, 3, 9, 1/2, 3/2, 9/2-1, -3, -9, -1/2, -3/2, -9/2============================================================
Problem 5
There's not really much new here, except for the fact that the first term has coefficient of 1. This is a special case where all we have to do is list the factors of the last term -40 to generate all the roots we need. This is because each time we're dividing over +1 or -1 which doesn't really change the overall result (except for the sign part).
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Don't forget the negative values as well
Answer:1, 2, 4, 5, 8, 10, 20, 40-1, -2, -4, -5, -8, -10, -20, -40
Related Questions
Marie bought 6 pounds of apples for $0.87 per pound and
paid for them with a $10 bill. How much did she get back
in change?
Answers
Answer:
5.22
Step-by-step explanation:
rjskstks5oslyatkao5sylslgsltsirsotzktzo
Answer:
$4.78
Step-by-step explanation:
6 x 0.87 = 5.22
10.00 - 5.22 = 4.78
Maire got $4.78 back
in change
How many solutions does this system have?
y = 5x + 6
y – 5x = 7
A. no solutions
B. 1 solution
C. 2 solutions
D. infinitely many solutions
Answers
Answer:
No Solutions
Step-by-step explanation:
The two lines never intersect
Answer:
A
Step-by-step explanation:
y = 5x + 6 → (1)
y - 5x = 7 ( add 5x to both sides )
y = 5x + 7 → (2)
Substitute y = 5x + 7 into (1)
5x + 7 = 5x + 6 ( subtract 7 from both sides )
5x = 5x - 1 ( subtract 5x from both sides )
0 = - 1 ← is False
This indicates the system has no solution
The sum of the first n terms of a sequence is Sn = n(n + 1)(n + 2).
What is the 4th term of the sequence?
O 48
O 120
O 60
O 396
Answers
Answer:
60
Step-by-step explanation:
S₄ = 4(4+1)(4+2) = 120
S₃ = 3(3+1)(3+2) = 60
4th term = 120-60=60
Maya is saving money to buy a game. So far she has saved $6, which is two-thirds of the total cost of the game. How much does the game cost?
Answers
Answer:
9 dollars
Step-by-step explanation:
Since 6 is 2/3 of the total price, and half of 6 is 3, add three to 6 and you get 9.
Answer:
9 dollars
Step-by-step explanation:
if 6 dollors==>2/3from the game totall price
1 complete game how much
6÷2/3=9dollars
14 A formula for determining the finite sum, S, of an arithmetic sequence of numbers is
S=n/2(a+b)
where n is the number of terms, a is the first term, and b is the last term.
Express b in terms of a, S, and n.
Answers
Answer:
b = 2S/n - a.
Step-by-step explanation:
S=n/2(a + b)
a + b = S / n/2
a + b = 2S/n
b = 2S/n - a.
If the formula for determining the sum of the given arithmetic sequence is S = n/2(a + b), then 'b' can be expressed as b = [(2S/n) - a].
What is an arithmetic sequence ?An arithmetic sequence is a sequence where the difference between any to consecutive terms are always equal.
Here, a and b are the first and the last terms respectively and n is the number of terms.
Therefore, the sum of the arithmetic sequence is:
S = n/2(a + b)
⇒ 2S/n = (a + b)
⇒ b = (2S/n) - a
Learn more about an arithmetic sequence here: https://brainly.com/question/25715593
#Tag #SPJ2
What is the slope-intercept equation
for the following line?
Answers
Answer:
y = - x + 1
Step-by-step explanation:
Slope = 2/-2 = -1
y-intercept: 1
y = -x + 1
Answer:
y = -x + 1
Step-by-step explanation:
Given the points (2, -1) and (0, 1):
Let (x1, y1) = (2, -1)
(x2, y2) = (0, 1)
Substitute these values into the slope formula:
m = (y2 - y1)/(x2 - x1)
m = [1 - (-1)] /(0 - 2)
m = (1 + 1)/ -2
m = 2/-2 = -1
Therefore, the slope, m = -1.
Next, the y-intercept is the y-coordinate of the point (0, b) where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0.
The ordered pair, (0, 1) represents the y-intercept. Its y-coordinate is the value of b = 1.
Therefore, the linear equation of the graph in slope-intercept form is:
y = -x + 1
What is the slope of the line that passes through the points (8, -4) and (6, 2) ? Write your answer in simplest form.
Answers
Answer:
m=-3
Step-by-step explanation:
I just used the slope formula. Hope this helps! Also, I'm certain this is correct.
Remember what we know about vertical angles and solve for x.
Then tell me the measure of Angle A.
(show your work)
Answers
Answer:
m<a is 32º
Step-by-step explanation:
4x-8=2x+12
+8 +8
4x=2x+20
-2x -2x
2x=20
÷2
x=10
4x-8
4(10)-8
40-8
32
gradient from 2 - 1/2y = 0
Answers
Given :
2 - 1/2y = 0To find :-
The gradient form .Solution :-
The gradient form/ slope intercept form
y = mx + c ,On converting ,
2 - 1/2y = 0 1/2y = 2 y = 2*2y = 4y = 0x + 48/n = 1/3
help plssss
Answers
Answer:
24
Step-by-step explanation:
Answer:
n=1/24
Step-by-step explanation:
8/n=1/3
n=1/3÷8
=1/3×1/8
=1/24
(1/3) to the power of 3
Plz
Answers
Answer:
1/27
have a lovely day <3
Answer:
[tex]\frac{1}{27}[/tex]
Step-by-step explanation:
[tex]\frac{1}{3} ^3[/tex]
[tex]\frac{1}{3}[/tex] × [tex]\frac{1}{3}[/tex] × [tex]\frac{1}{3}[/tex]
[tex]\frac{1}{27}[/tex]
Show that (√7+i√3/√7-i√3 + √7-i√3/√7+i√3) is real
Answers
Answer:
Step-by-step explanation:
Step-by-step explanation:
[tex]\large\underline{\sf{Solution-}}[/tex]
Consider,
[tex]\rm \longmapsto\:\dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } [/tex]
On taking LCM, we get
[tex]\rm \: = \: \dfrac{ {( \sqrt{7} + i \sqrt{3})}^{2} + {( \sqrt{7} - i \sqrt{3})}^{2} }{( \sqrt{7} + i \sqrt{3})( \sqrt{7} - i \sqrt{3})} [/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}}} \\ [/tex]
and
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}} \\ [/tex]
So, using these Identities, we get
[tex]\rm \: = \: \dfrac{2\bigg[ {( \sqrt{7})}^{2} + {(i \sqrt{3}) }^{2} \bigg]}{ {( \sqrt{7}) }^{2} - {(i \sqrt{3})}^{2} } [/tex]
[tex]\rm \: = \: \dfrac{2(7 + 3 {i}^{2})}{7 - {3i}^{2} } [/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {i}^{2} = - 1}}} \\ [/tex]
So, using this, we get
[tex]\rm \: = \: \dfrac{2(7 - 3)}{7 + 3} [/tex]
[tex]\rm \: = \: \dfrac{2 \times 4}{10} [/tex]
[tex]\rm \: = \: \dfrac{4}{5} [/tex]
Hence,
[tex] \red{\rm\implies \:\boxed{\sf{ \dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } \: is \: purely \: real}}}[/tex]
Pls help me:
1) 3/5 ÷ 3=
2 )2÷ 2/5=
Answers
1) 0.2
2) 5
Check the image below
The table shows the shipping fee options for two online marketplaces.
Online Market Shipping Fees
Deals Flat fee of $12
Sell Ur Stuff 11% of selling price
If you sell a smart phone online for $115, how much will you pay if you use the online market with the lesser fee?
Answers
Since 11% of $115 is $12.65, it is convenient to pay the flat fee of $12.
If you sell a smart phone online for $115, to determine how much you will pay if you use the online market with the lesser fee, the following calculation must be performed:
115 x 0.11 = X 12.65 = X
Thus, since 11% of $115 is $12.65, it is convenient to pay the flat fee of $12.
Learn more in https://brainly.com/question/25206811
Please help first person to answer correctly with no links get 50 points and marked as brainliest no links please
Answers
Answer:
C, first I'm not sure if it's correct, but hear me out.
Step-by-step explanation:
If we already know that B=34 we need to find out the rest.
B=50 (Estimated)
D=45 (Estimated)
34+50+45
34+50=84+45=129, 129 estimated=130, and since their is no answer choice but C it should be C, I could be very wrong though.
What is the end of your proof? (What are you proving?)
Answers
Answer
with
Step-by-step explanation:
Statement Reasons
1.∠1 ≅ 4 Given
2.∠1 = ∠2 Being Vertically opposite angles.
3.∠4 = ∠3 Being Vertically opposite angles.
4.∠2 = 3 From Statement no 2 & 3, Transitive property.
5.∠2 ≅ 3 From Statement 4
Proved.
what is the perimeter of 10cm length and 8cm width of a rectangle ?
Answers
Answer:
36 cm
Step-by-step explanation:
rectangle perimeter = sum of all the side
10+8+10+8=36 cm
Answer:
Step-by-step explanation:
Perimeter =2(10+8)=36 cm.
The linear system is graphed. Is it an independent or dependent system?
-2x+3y=5
-4x+6y=10
GRAPH IN PICTURE:
A. neither
B. Dependent
C. Independent
Answers
A. Neither
Thanks me later
40 POINTS!
Please answer for
m∠1 AND m∠2
Answer choices for m∠1:
50, 110, 70, 90
Answer choices for m∠2:
70, 110, 40, 140
Answers
Answer:
70°, 140°, 50°
Step-by-step explanation:
110° and the angle inside the triangle are adjacent angles and sum to 180°, so
angle inside triangle = 180° - 110° = 70°
The triangle on the left is isosceles ( 2 congruent sides ) then base angles are congruent
∠ 1 = angle inside triangle = 70°
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ 2 is an exterior angle of the triangle on the left, so
∠ 2 = 70° + 70° = 140°
∠ 2 is also an exterior angle of the triangle on the right, so
∠ 3 + 90° = 140° ( subtract 90° from both sides )
∠ 3 = 50°
Solve 5x + 2 = 22
Solve 2x-5=7
Solve 2x+5=12
Answers
Answer:
x = 4
x = 6
x = 7/2
Step-by-step explanation:
Solve 5x + 2 = 22:
5x+2-2=22-2 (subtract 2 from both sides)
5x=20
x=4
Solve 2x-5=7
2x-5+5=7+5 (add 5 to both sides)
2x=12
x=6
Solve 2x+5=12
2x+5-5=12-5 (subtract 5 from both sides)
2x=7
x= 7/2
=> 5x + 2 = 22
=> 5x = 22 – 2
=> 5x = 20
=> x = 20/5
=> x = 4
Solve 2x-5=7=> 2x - 5 = 7
=> 2x = 7+5
=> 2x = 12
=> x = 12/2
=> x = 6
Solve 2x+5=12=> 2x + 5 = 12
=> 2x = 12-5
=> 2x = 7
=> x = 7/2
Can you pls help me??
Answers
Answer:
[tex] \sqrt{10} [/tex]
Step-by-step explanation:
use
a^2 +b^2=c^2
c² = a² + b²
c² = 3² + 1²
c² = 9 + 1
c² = 10
c = √10
Help with trigonometry
Use pythagorean theorem to find the length of x
Answers
Answer:
x =√969
Step-by-step explanation:
AC²=AB²+BC². (Formula)
(35)²=(16)²+BC²
1225-256=BC²
969=BC²
BC=√969
Just add a random answer
Answers
Fill in the blank statement to make it true. -3 x _ =12
Answers
Azim wants to order school spirit t-shirts for the fundraising club. Company R charges a $70 screen setup fee plus $11.25 per t-shirt. Company S charges a $35 screen setup fee plus $14.75 per t-shirt. What equation can determine the number of t-shirts, x, that need to be ordered for the total cost of Company R to equal the total cost of Company S?
Answers
Answer:
10 t shirts
Step-by-step explanation:
70 + 11.25x = 35 + 14.75x
35 + 11.25x = 14.75x
35 = 3.5x
10 = x
Rise over run please ??
Answers
Answer:
1 / 1
Step-by-step explanation:
Your line has a 1 to 1 ratio of rise over run.
Find the missing side of each triangle. Leave your answer in simplest radical form.
(Please show ur work)
Answers
Answer:
X = [tex]\sqrt{21}[/tex] or 4.5825756...
Step-by-step explanation:
[tex]A^{2} + B^{2} = C^{2}[/tex]
[tex]10^{2} + x^{2} = 11^{2}[/tex]
[tex]x^{2} = 11^{2} - 10^{2}[/tex]
[tex]x^{2} =121-100[/tex]
[tex]x^{2} =21[/tex]
x = [tex]\sqrt{21}[/tex]
Hope this helps!
___________
[tex] \: [/tex]
[tex]\boxed{ \rm{answer \: by \: { \boxed{ \rm{☆HayabusaBrainly}}}}}[/tex]
Step by step :x² = (11)² - (10)²
x² = 121 - 100
x² = 21
x = 4,6✔
Which describes how to find the solution to 3p < 14?
Answers
Answer:
p < 14/3
Step-by-step explanation:
Answer:
a.divide both sides with 3
Step-by-step explanation:
- How are the functions y = x and y = x + 4 related? How are their graphs related?
Answers
Answer:
Either horizontal translation 4 units to the left or vertical translation UP 4 units
Step-by-step explanation:
Will mark as brainiest (Must show work)
Answers
Answer:
m∠CAB = 40°
Step-by-step explanation:
DAC = 99
DAB = 59
B is inside DAC, and so is DAB. So CAB must add to 59 to get to 99, nothing over that because it's inside DAC.
So 99 - 59 = 40
CAB must be 40°
That's all I can say for now. Hope this helps and a thank won't hurt! :)
