Answer:
1) Perfect square, 2) Perfect square, 3) Not a perfect square, 4) Perfect square, 5) Perfect square, 6) Not a perfect square, 7) Perfect square, 8) Not a perfect square, 9) Not a perfect square, 10) Not a perfect square.
Step-by-step explanation:
From Algebra we must remember that a trinomial is a perfect square if and only if:
[tex](a+b)^{2} = a^{2}+2\cdot a\cdot b + b^{2}[/tex], [tex]\forall \,a,b\in\mathbb{R}[/tex] (Eq. 1)
Now we proceed to prove each trinomial:
1) [tex]a^{2}+2\cdot a +1[/tex]:
If [tex]a^2 =a^2[/tex] and [tex]b^{2} = 1[/tex], then [tex]a = \pm a[/tex] and [tex]b =\pm 1[/tex]. Therefore, [tex]2\cdot a\cdot b = 2\cdot (\pm a)\cdot (\pm 1) = \pm 2\cdot a[/tex]. In a nutshell, we conclude that this polynomial is a perfect square.
2) [tex]4+4\cdot a +a^{2}[/tex]
If [tex]a^{2} = 4[/tex] and [tex]b^{2} = a^{2}[/tex], then [tex]a = \pm 2[/tex] and [tex]b = \pm a[/tex]. Therefore, [tex]2\cdot a \cdot b = 2\cdot (\pm 2)\cdot (\pm a) = \pm 4\cdot a[/tex]. In a nutshell, we conclude that this polynomial is a perfect square.
3) [tex]a^{2}-3\cdot a +9[/tex]
If [tex]a^{2} = a^{2}[/tex] and [tex]b^{2} = 9[/tex], then [tex]a = \pm a[/tex] and [tex]b = \pm 3[/tex]. Therefore, [tex]2\cdot a \cdot b = 2\cdot (\pm a)\cdot (\pm 3) = \pm 6\cdot a[/tex]. In a nutshell, we conclude that this polynomial is not a perfect square.
4) [tex]4\cdot a^{2}+24\cdot a + 36[/tex]
If [tex]a^{2} = 4\cdot a^{2}[/tex] and [tex]b^{2} = 36[/tex], then [tex]a = \pm 2\cdot a[/tex] and [tex]b = \pm 6[/tex]. Therefore, [tex]2\cdot a \cdot b = 2\cdot (\pm 2\cdot a)\cdot (\pm 6) = 24\cdot a[/tex]. In a nutshell, we conclude that this polynomial is a perfect square.
5) [tex]a^{4}-10\cdot a +25[/tex]
If [tex]a^{2} = a^{4}[/tex] and [tex]b^{2} = 25[/tex], then [tex]a = \pm a^{2}[/tex] and [tex]b = \pm 5[/tex]. Therefore, [tex]2\cdot a \cdot b = 2\cdot (\pm a^{2})\cdot (\pm 5) = \pm 10\cdot a^{2}[/tex]. In a nutshell, we conclude that this polynomial is a perfect square.
6) [tex]25\cdot a^{2}+20\cdot a + 9[/tex]
If [tex]a^{2} = 25\cdot a^{2}[/tex] and [tex]b = 9[/tex], then [tex]a = \pm 5\cdot a[/tex] and [tex]b = \pm 3[/tex]. Therefore, [tex]2\cdot a \cdot b = 2\cdot (\pm 5\cdot a)\cdot (\pm 3) = \pm 30\cdot a[/tex]. In a nutshell, we conclude that this polynomial is not a perfect square.
7) [tex]a^{2}\cdot b^{2}-14\cdot a \cdot b + 49[/tex]
If [tex]a^{2} = a^{2}\cdot b^{2}[/tex] and [tex]b^{2} = 49[/tex], then [tex]a = \pm a\cdot b[/tex] and [tex]b = \pm 7[/tex]. Therefore, [tex]2\cdot a\cdot b = 2\cdot (\pm a\cdot b)\cdot (\pm 7) = \pm 14\cdot a \cdot b[/tex]. In a nutshell, we conclude that this polynomial is a perfect square.
8) [tex]a^{2}-2\cdot a -1[/tex]
If [tex]a^{2} = a^{2}[/tex] and [tex]b^{2} = -1[/tex], then [tex]a = \pm a[/tex] and [tex]b = \pm i[/tex]. Therefore, [tex]2\cdot a \cdot b = \pm 2\cdot a \cdot i[/tex]. In a nutshell, we conclude that this polynomial is not a perfect square.
9) [tex]16\cdot a^{2} + 24\cdot a +36[/tex]
If [tex]a^{2} = 16\cdot a^{2}[/tex] and [tex]b^{2} = \pm 36[/tex], then [tex]a = \pm 4\cdot a[/tex] and [tex]b = \pm 6[/tex]. Therefore, [tex]2\cdot a \cdot b = 2\cdot (\pm 4\cdot a)\cdot (\pm 6) = \pm 48\cdot a[/tex]. In a nutshell, we conclude that this polynomial is not a perfect square.
10) [tex]10+6\cdot a +a^{2}[/tex]
If [tex]a^{2} = 10[/tex] and [tex]b^{2} = a^{2}[/tex], then [tex]a = \pm\sqrt{10}[/tex] and [tex]b = \pm a[/tex]. Therefore, [tex]2\cdot a \cdot b = \pm 2\cdot \sqrt{10}\cdot a[/tex]. In a nutshell, we conclude that this polynomial is not a perfect square.
The units digit of a two-digit number is four more than the tens digit. If the number is doubled, it will be one more than the reversed number. Find the number. (Number: 32 Reversed number: 23)
Answer:
37
Step-by-step explanation:
2-digit number: 10x + y
y = x + 4
20x + 2y = 10y + x + 1
8y = 19x - 1
8x + 32 = 19x - 1
11x = 33
x = 3
Number: 37
Answer:
Answer:
37
Step-by-step explanation:
2-digit number: 10x + y
y = x + 4
20x + 2y = 10y + x + 1
8y = 19x - 1
8x + 32 = 19x - 1
11x = 33
x = 3
Number: 37
IF YOU HAVE ANSWER PLEASE ANSWER
The math teacher said, "Please ___ each expression on the board. Show your work so that I can see how you found the value."
its ether evaluate, operation or commutative
please help me with this
Step-by-step explanation:
-4 = x - y ...1
4 = -x + y ...2
...1 + ...2
-4+4 = x-y +(-x+y)
0 = 0
and I don't know next lol
will mark brain list if answered correct) On this number line, zero represents sea level. Plot the following points based on the description provided.
• 1.5 above sea level
• absolute value of –4.5
• –2
• opposite of 4
• absolute value of 1
• 2.5 below sea level
• greatest common factor of 8 and 12
• –(–3)
• -3 1/2
• opposite of –5
Answer:
The points would be:
1.5
4.5
-2
-4
1
-2.5
4
3
-3.5
5
Step-by-step explanation:
MY REAPORT CARD IS COMING SOON AND I HAVE ALL F'S my mom snitches and would tell everyone like she did last time so before my mom get's it should I
A. run away from home
B. Break her phone
C. blackmail her, when she DOES get it
♡ The Question ♡
-MY REAPORT CARD IS COMING SOON AND I HAVE ALL F'S my mom snitches and would tell everyone like she did last time so before my mom get's it should I
A. run away from home
B. Break her phone
C. blackmail her, when she DOES get it
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Answer ♡
- None of the Above!
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Explanation/Step-By-Step ♡
- A would not be a very good idea, running away from home can get you in trouble either from your parents/family/guardians, or police/fire department, that would most likely upset your mother more and could cause some issues. B wouldn't be good because soon enough she will most likely find out, breaking somebody's phone can be a bad idea too, if they're in danger they won't be able to call anybody or ask for any help. Including something important could be saved there, not to mention phones are very expensive and it could be devastating.
C isn't much of a better idea either, blackmailing somebody isn't something to be proud of and if anything, is very risky. Blackmailing is demanding money from somebody in return for not revealing compromising info about the person you're threatening. This may only be reputation ruining, but not to mention if the police/fire department find out you're threatening somebody for money you could most likely get arrested.
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ Tips ♡
-I would recommend going for more of a simple plan, waking up early, getting ready, and to begin your schoolwork and start studying more! This can be helpful for your education/knowledge, including creating a safe place for everybody around you and to avoid being in any tight situation or any danger/discipline. If you ever need more help, feel free to always submit any questions onto Brainly so people can answer your questions and help improve your grades!
Courtney walked from her house to the beach at a constant speed of 444 kilometers per hour, and then walked from the beach to the park at a constant speed of 555 kilometers per hour. The entire walk took 222 hours and the total distance Courtney walked was 888 kilometers.
Answer:
I suppose that each number is repeated 3 times, the actual question is:
Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour, and then walked from the beach to the park at a constant speed of 5 kilometers per hour. The entire walk took 2 hours and the total distance Courtney walked was 8 kilometers.
Now, remember the relation:
Distance = Speed*Time
Let's define:
D1 = distance between Courtney's house and the beach.
D2 = distance between the beach and the park.
T1 = time that it took the first walk.
T2 = time that it took the second walk.
We know that the total distance Courtney walked is 8km, then:
D1 + D2 = 8km.
And we also know that the entire walk took 2 hours, then:
T1 + T2 = 2h.
We also have the equations:
D1 = 4km/h*T1
D2 = 5km/h*T2.
Then we have a system of equations:
D1 + D2 = 8km
T1 + T2 = 2h
D1 = 4km/h*T1
D2 = 5km/h*T2.
To solve this, first let's replace equations 3 and 4 in the first equation:
4km/h*T1 + 5km/h*T2 = 8km
Now we have only two equations left:
4km/h*T1 + 5km/h*T2 = 8km
T1 + T2 = 2h
Now we can isolate one of the variables in the second equation and then replace it in the first equation, i will isolate T1:
T1 = 2h - T2.
Replacing this in the first equation gives:
4km/h*(2h - T2) + 5km/h*T2 = 8km
Now let's solve this for T2.
8km - 4km/h*T2 + 5km/h*T2 = 8km
8km + 1km/h*T2 = 8km
1km/h*T2 = 0
from this, we have T2 = 0
This would mean that T1 = 2h.
Then:
D1 = 4km/h*2h = 8km.
T2 = 0
D2 = 5km/h*0 = 0.
This happens because the numbers in the problem were not well thought.
You can see that when she spends the 2 hours walking at the smaller speed, she already reaches the total distance, then if she walked any amount of time at the larger speed, the total distance would be more than 8km.
There was 4/5 of a cake sitting on the counter. Daryl ate 1/3 of the left over cake. How much cake was left over after he ate?
Answer:
0.46 is the left over 23/50 is the fraction
The table shows data collected to represent the functional relationship between the number of hours an auto factory is open and the number of cars produced. A 2-column table with 5 rows. Column 1 is labeled x with Hours, x with entries 3, 5, 7, 9, 11. Column 2 is labeled Cars, y with entries 75, 125, 175, 225, 275. What is the domain of the function represented by the table? all real numbers x greater-than-or-equal-to 0 {3, 5, 7, 9, 11} {75, 125, 175, 225, 275}
Answer:its 3,5,7,9,11
Step-by-step explanation:i m pretty sure it's this one because I got it from briainly
Answer:
b
Step-by-step explanation:
i took the test and this was right
5star answer don't u think????
can i please get some help
Answer: number 5 is A number 6 is B
Step-by-step explanation:
Please answer the blanks and I will mark you brainlist if you answer it and show it why
Answer:
2 dollars
72 dollars
Step-by-step explanation:
im not completely sure
Answer:
Arianna paid $2.75 for each photo coaster. If she purchased three dozen photo coasters, how much did she spend? $99.00
Step-by-step explanation:
A submarine is traveling level at ¯75 feet below the surface of the sea. The Captain gives orders to dive the submarine to a depth three times their current level. What is the new cruising level?
Answer:
264 {feet}
below sea level
Step-by-step explanation:
Ascending means moving towards the surface.
So the submarine is 340 feet below sea level.
The submarine ascends 76 feet.
∴
340 − 76 =
264 below sea level.
Step-by-step explanation:
Tantasic charges a reservation fee of 20$ and $1 per minute in a tanning bed. Bettersun charges no reservation fee but charges 2$ per minute. How many minutes will the price be the same
Answer:
The indifference point is 20 minutes
Step-by-step explanation:
Giving the following information:
Tantasic:
Reservation fee of 20$ and $1 per minute
Bettersun:
2$ per minute.
First, we need to structure both total cost formulas:
Tantasic= 20 + 1x
Bettersun= 2x
x= number of minutes
Now, we equal both formulas and isolate x:
20 + 1x = 2x
20 = 1x
20= x
The indifference point is 20 minutes
WILL GIVE BRAINLIEST !!!
Find the equation of the line. Use the exact numbers.
Equation: y = __x + __
Answer:
Step-by-step explanation:
y=2/3x+4. 4 is the y intercept. 2/3 is the slope. y=mx+b where m is the slope and b is the y intercept
(work)(study) + (work)(practice) + (work)(perseverance)
9514 1404 393
Answer:
(work)(study + practice + perseverance)
Step-by-step explanation:
(work) is the common factor in the three products. It can be factored out:
(work)(study + practice + perseverance)
There are screws, nuts and bolts in a tool box. The ratio of the number of
Screws to the number of nuts to the number of boits is 2:3:7. The
difference between the number of nuts and the number of bolts is 112.
Find the number of each item
Answer:
Step-by-step explanation:
56:84:196 would be the answer
hello quick question because i am dumb and dont know how to explain things just need some clarification
how do you tell if a domain is continuous or discrete on a table not a graph •~•
Step-by-step explanation:
gegsbdqneyqillzfjmtucznYEmdnfhhthtej62wrr334tyyytyyttffgfrwgeyeyiqlstl7o4a1
9514 1404 393
Answer:
The domain is always discrete when it is found from a table.
Step-by-step explanation:
A table necessarily lists a finite number of discrete points. The domain, as found from a table, is always discrete.
__
If the table is said to be a representation of a continuous function, then the domain of that continuous function will be continuous.
Your question seems to have to do with a table alone, not a table and an equation, or a table and a graph. A table (of points) alone cannot express a continuous domain.
__
Additional comments
One can conceive of tables that would have continuous domains, as, for example, a table with entries ...
(x, y) = (0 ≤ x < 3, 3x+2), (3 ≤ x < 6, 4x-1), ...
Such a table is not a list of points, but is a piecewise function definition. We presume this is not what you're concerned with.
The trail starts at P(−7, 6) and goes to Q(4, 6). It goes from Q to R(4, −6) and then to S(6, −6). What is the total length (in units) of the biking trail?
We know, distance between two points A( p,q) and B(r,s) is given by :
[tex]AB=\sqrt{(p-r)^2+(q-s)^2}[/tex]
So, distance between P an Q is :
[tex]PQ=\sqrt{(-7-4)^2+(6-6)^2}\\\\PQ=11\ units[/tex]
Distance between Q and R is :
[tex]QR=\sqrt{(4-4)^2+(6-(-6))^2}\\\\QR=12\ units[/tex]
Distance between R and S is :
[tex]RS=\sqrt{(4-6)^2+(-6-(-6))^2}\\\\RS=\sqrt{4}\\\\RS = 2\ units[/tex]
Therefore, total distance is 11 + 12 + 2 = 25 units.
Hence, this is the required solution.
boris's super metal detector not only helped him win the science fair but also helped him find $6.20 in nickels and dimes yesterday morning. If boris found 14 more dimes than nickels, how many nickels did he find
Answer:
32 Nickels
Step-by-step explanation:
Given
Coins: Nickels (N) and Dimes (D)
$0.05 = 1 nickel and $0.10 = 1 dime
So, the amount implies:
[tex]0.05N + 0.10D = 6.20[/tex]
The number of coin implies:
[tex]D = 14 + N[/tex]
Required
Determine the number of nickels found
Substitute 14 + N for D in [tex]0.05N + 0.10D = 6.20[/tex]
[tex]0.05N + 0.10(14 + N) = 6.20[/tex]
[tex]0.05N + 1.4 + 0.10N = 6.20[/tex]
Collect Like Terms
[tex]0.05N + 0.10N = 6.20 - 1.4[/tex]
[tex]0.15N = 4.8[/tex]
Solve for N
[tex]N = 4.8/0.15[/tex]
[tex]N = 32[/tex]
Hence, he found 32 nickels
A twelve-hour clock is set at the correct time on the afternoon of May 17th. Somebody knocked the clock off the wall and now it loses 6 minutes per day. How much time will the clock be behind 3 weeks later?
Answer:
126 minutes (or 2 hours and 6 minutes)
Step-by-step explanation:
7 days in a week times 3 weeks = 21 days
6 minutes a day times 21 days = 126 minutes behind
TIMED TEST WILL GIVE BRAINLIEST
During an algebra class, a teacher asks for examples of non-prime numbers. Jake says 51, Teresa says 41, and Liu says 21. Which student(s) are correct in their response?
Answer:
D. Jake and Liu
Step-by-step explanation:
41 is prime so Teresa is wrong. The other two are not prime.
Use two sets of coordinates to write an equation
to describe the relationship.
Answer/Step-by-step explanation:
An equation that describes the relationship can be written as [tex] y = mx [/tex].
Using the two sets of coordinates, (2, 140) and (4, 280), calculate the slope (m) as shown below:
[tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{280 - 140}{4 - 2} = \frac{140}{2} = 70 [/tex]
Substitute m = 70 into [tex] y = mx [/tex]
The equation would be:
[tex] y = 70x [/tex]
This equation can be interpreted as follows:
The heart's resting rate is 70 beats each minute.
5) Contains (3,-1) and (6,- 13)
Help please
Answer:
The slope of the line is -12/3
Step-by-step explanation:
remember, rise over run
My I have brainliest please? :)
ANSWER PLEASE? I NEED HELP!
Answer:
5x+2=17
x=3
Step-by-step explanation:
Answer:
x=3
Step-by-step explanation:
17-2=15
15/5=3
What is the largest number of three consecutive integers whose sum is 42? O A. 13 B. 17 O C. 15 D. 12
Answer: 13
Step-by-step explanation:
3X + 3 - 3 = 42 - 3
3X = 39
3X/3 = 39/3
X = 13
Which means that the first number is 13, the second number is 13 + 1 and the third number is 13 + 2. Therefore, three consecutive integers that add up to 42 are 13, 14, and 15.
13 + 14 + 15 = 42
We know our answer is correct because 13 + 14 + 15 equals 42 as displayed above.
Solve for x.
−x − 4( 1−x)>1
x −1
x>5/3
x<−1
Answer: x> 5/3
Step-by-step explanation: Let's solve your inequality step-by-step.
−x−4(1−x)>1
Step 1: Simplify both sides of the inequality.
3x−4>1
Step 2: Add 4 to both sides.
3x−4+4>1+4
3x>5
Step 3: Divide both sides by 3.
3x /3 > 5 /3
x> 5 /3
An adult ticket to a school play cost $5 and a student ticket cost $3. $460 dollars was collected and 120 tickets were sold. How many student tickets were sold?
Timmy wants to buy a scooter and the price was $150. When he goes to the store a
second time, he found that the price was marked down by 15%. Then when he gets to the
register the cashier tells him today only he gets an additional 10% off the sales price. What is
the final cost of the scooter including the discounts?
Answer:
112.5
Step-by-step explanation:
total discount: 25%
Answer:
Step-by-step explanation:
150*15% off =22.50 off total 127.50. Then he gets the 10% off 127.50*10%= 12.75 off total cost $114.75
It may look like 25% off at once, but most stores will do the discounts separately so they don't lose too much money.
50 POINTS FOR EACH ANSWER!!! Write the difference of the expressions 17x−13y+8 and 20x+6y and simplify it.
Answer:
-3x-19y+8
Step-by-step explanation:
Answer:
-3x-19y+8
Step-by-step explanation:
thanks for 50 points.
The linear equation y = one-half x + 1 is represented by the graphed line. A second linear equation is represented by the data in the table. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 2, 4. Column 2 is labeled y with entries 7, 6, 5, 4. In which square is the solution located?
The correct answer is the letter D
Answer:
d
Step-by-step explanation:
cuz im a goddddd
Choose the scenario that could be represented by :
A. Five pounds of oats are divided equally among eight horses.
B. Five friends, share eight cookies equally.
C. An eight-hour bus trip is divided into five equal parts.
D. An eight-foot ribbon is cut into five equal pieces.
Answer:
The answer is A
Step-by-step explanation:
I took the test
Answer:
The answer is A
Step-by-step explanation:
I took the test too