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.
please help me please
Answer:
42
Step-by-step explanation:
4x + 2 = 1/2 (4x + 44) Be careful how you do this. I have multiplied both sides by 2
2(4x + 2) = 4x + 44 Remove the brackets (distributive)
8x + 4 = 4x + 44 Subtract 4x from both sides
8x-4x + 4 = 44
4x + 4 = 44 Subtract 4 from both sides
4x + 4-4 = 44-4
4x = 40 Divide by 4
4x/4 = 40/4
x = 10
The mid line is 4x + 2
The mid line is 4*10 + 2
The mid line is 40 + 2
The mid line is 42
The base is 4x + 44
The base is 4*10 + 44
The base is 40 + 44 = 84 which is twice the midline. I did this just to show it is twice as big as the midline.
what is 30% as a fraction in simplest form.
Answer:
3/10
Step-by-step explanation:
3/10
In simplest form, 30% as a fraction is 3/10. We know that 30% = 30/100
A scale drawing of a rectangular flag is 12 inches long and 8 inches wide. If the scale is 1 inch: 2.4 feet, what is the length and width of the actual flag?
Answer: length = 28.80 feet
Width = 19.20 feet
Step-by-step explanation:
Scale used = 1 inch:2.4 feet
Length or scale drawing = 12 inches
Width of scale drawing = 8 inches
Length of actual flag = (12 × 2.4 feet) = 28.80 feet
Width of actual flag = (8 × 2.4 feet) = 19.20 feet.
Answer:Answer: length = 28.80 feet
Width = 19.20 feet
Step-by-step explanation
Scale used = 1 inch:2.4 feet
Length or scale drawing = 12 inches
Width of scale drawing = 8 inches
Length of actual flag = (12 × 2.4 feet) = 28.80 feet
Width of actual flag = (8 × 2.4 feet) = 19.20 feet.
Write an expression
You charge $10.50 per hour to babysit and you spent $15 on
candy.
Answer:
10.50x + 15 = y
Step-by-step explanation:
x = amount of hours spent babysitting.
y = total amount of money.
PLEASE HELP ASAP
Which criteria can be used to prove triangles are congruent? Select all that apply.
A.) ASA
B.) AAS
C.) SAS
D.) SSA
E.) HL
Answer:
A, B, C, and E
Step-by-step explanation:
SSA doesn't work because this leaves room for two possible answers in some situations.
The other postulate, HL (hypotenuse-leg) works for right triangles; it's basically a short cut for SSS postulate because if the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg on another, the other side also has to be congruent.
The criteria can be used to prove triangles are congruent: ASA, AAS, SAS and HL.
What is Congruence in Triangles?If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.
Two triangles are said to be congruent if they are of the same size and same shape.
Necessarily, not all the six corresponding elements of both the triangles must be found to determine that they are congruent.
Based on studies and experiments, there are 5 conditions for two triangles to be congruent.
They are SSS, SAS, ASA, AAS, and RHS congruence properties.
The postulate, known as HL (hypotenuse-leg), is applicable to right triangles.
As if a right triangle's hypotenuse and leg are congruent with those of another, then the other side must likewise be congruent.
Learn more about congruence of triangles here:
https://brainly.com/question/20521780
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The gas tank in sampson car has a capacity of 19.1 gallons . on a Tripp to see his cousin , Sampson begins with 12.8 gallons if gas in the tank he stops after driving for 2 hours and fills the tank to capacity with 14.4 gallons. When sampson arrives at his cousins house he has 3.7 gallons of gas left. How much gas , did sampson use on his trip
Answer:
23.5 gallons
Step-by-step explanation:
The gas tank in Daniel's car has a capacity of 19.1 gallons.
On a trip to see his best friend Daniel begins with 12.8 gallons of gas in the tank.
He stops after driving for 2 hours and fills the tank to capacity with 14.4 gallons.
When Daniel arrives at his friend's house, he has 3.7 gallons of gas left.
Total amount of gas filled was (12.8 + 14.4) = 27.2 gallons.
The amount of gas remaining after the trip was 3.7 gallons
The amount of gas, in gallons, used by Daniel on his trip was 27.2 - 3.7 = 23.5 gallons
Answer:
fat nuts
Step-by-step explanation:
i forgor
1. Andrew went to FYE to buy music for the band. He spent a total of $112 on 14 music purchases. one Music CDs were on sale for $10 and cassettes were on sale for $3. How much did Andrew pay for each music CD and each cassette tape? Enter your one-sentence interpretation in the space below.
Answer:
Total Money spent on Music CDs = 10 [tex]\times[/tex] 10 = $100
Total Money spent on Cassette tapes = 4 [tex]\times[/tex] 3 = $12
Step-by-step explanation:
Given that:
Total money spent = $112
Number of music purchases = 14
Cost of one Music CD = $10
Cost of one cassette = $3
To find:
How much money was paid for each music CD and each cassette.
Solution:
Let the number of Music CDs purchased = [tex]x[/tex]
Money spent on Music CDs = [tex]\$10\times x[/tex]
Then the number of cassette tapes purchased = [tex]14-x[/tex]
Money spent on cassette tapes = [tex]\$3\times (14-x)[/tex]
As per the question statement:
[tex]10x+3(14-x)=112\\\Rightarrow 10x+42-3x=112\\\Rightarrow 7x=112-42\\\Rightarrow 7x=70\\\Rightarrow x =10[/tex]
Therefore, number of Music CDs purchased = 10
Total Money spent on Music CDs = 10 [tex]\times[/tex] 10 = $100
And number of cassette tapes purchased = 14 - 10 = 4
Total Money spent on Cassette tapes = 4 [tex]\times[/tex] 3 = $12
three more than the quotient of a number and 7 is at most 92. Find the number
Answer:
The number is 623.
Step-by-step explanation:
[tex]\frac{x}{7}+3 =92\\\frac{x}{7} =89\\x=623[/tex]
You are running a fuel economy study. One of the cars you find is blue. It can travel 44 1/2 gallons of gasoline. Another car is red. It can travel 25 3/5 on 4/5 gallons of gasoline. What is the unit rate for miles per gallon for each car? Which car could travel the greater distance on 1 gallon of gasoline?
Question:
You are running a fuel economy study. One of the cars you find is blue. It can travel [tex]44\frac{1}{2}[/tex] miles on [tex]1\frac{1}{4}[/tex] gallons of gasoline.
Another car is red. It can travel [tex]25\frac{3}{5}[/tex] on [tex]\frac{4}{5}[/tex] gallon of gasoline.
What is the unit rate for miles per gallon for each car?
Which car could travel the greater distance on 1 gallon of gasoline?
Answer:
(a)
[tex]Rate = 35\frac{3}{5}\ miles\ per\ gallon[/tex]
[tex]Rate = 32\ miles\ per\ gallon[/tex]
(b)
The blue car will travel faster
Step-by-step explanation:
Given
Blue Car:
[tex]Distance = 44\frac{1}{2}\ miles[/tex]
[tex]Gasoline = 1\frac{1}{4}\ gallons[/tex]
Red Car
[tex]Distance = 25\frac{3}{5}\ miles[/tex]
[tex]Gasoline = \frac{4}{5}\ gallons[/tex]
Solving (a):
This is solved by dividing the distance travelled by the amount of gasoline.
i.e.
[tex]Rate = Distance/Gasoline[/tex]
Blue Car:
[tex]Rate = 44\frac{1}{2} / 1\frac{1}{4}[/tex]
[tex]Rate = \frac{89}{2} / \frac{5}{4}[/tex]
[tex]Rate = \frac{89}{2} * \frac{4}{5}[/tex]
[tex]Rate = \frac{89}{1} * \frac{2}{5}[/tex]
[tex]Rate = \frac{89 * 2}{1 * 5}[/tex]
[tex]Rate = \frac{178}{5}[/tex]
[tex]Rate = 35\frac{3}{5}\ miles\ per\ gallon[/tex]
Red Car:
[tex]Rate = 25\frac{3}{5}/\frac{4}{5}[/tex]
[tex]Rate = \frac{128}{5}/\frac{4}{5}[/tex]
[tex]Rate = \frac{128}{5} * \frac{5}{4}[/tex]
[tex]Rate = \frac{128 * 5}{5 * 4}[/tex]
[tex]Rate = \frac{128}{4}[/tex]
[tex]Rate = 32\ miles\ per\ gallon[/tex]
(b)
In (a), we have:
[tex]Rate = 35\frac{3}{5}\ miles\ per\ gallon[/tex] --- Blue Car
[tex]Rate = 32\ miles\ per\ gallon[/tex] --- Red Car
By comparison:
The rate of the blue car is greater than that of the red
Hence, the blue car will travel faster
Notebooks cost $1.39 each. What are the possible numbers of notebooks that can be purchased with $10
Answer:
7
Step-by-step explanation:
HOPE THIS HELPS
PLZ MARK BRAINLIEST
Answer:
7 notebooks
Step-by-step explanation:
The total for the nine will be 9.73 I’d you get 8 notebooks it will be 11.12 with us too much.
what is the measure of ABC?
Answer:
ABC = 55°
Step-by-step explanation:
Angle A plus Angle C equals Angles B.
Add them together then subtract from 180°.
Please help! ! ! ! !
help!!
3x+6x+14=41
Solving Multi-Step Equations by Combining Like Terms
Answer:
x = 3
Step-by-step explanation:
Given
3x + 6x + 14 = 41, that is
9x + 14 = 41 ( subtract 14 from both sides )
9x = 27 ( divide both sides by 9 )
x = 3
Answer:
x=3
Step-by-step explanation:
3x+6x+14=41
9x + 14 = 41
- 14 = - 14
9x = 27
x=3
The atomic number of an element B is 17. The number of electrons in its ion B will be:
(a) 17 (b) 18. (c) 19. (d) 20.
answer with explanation
Answer:
18
Step-by-step explanation:
don't step answer. Because I am lol
help me how do I solve 2(m+3) =22
Answer:
m = 8
22/2 = 11
11 - 3 = 8
m = 8
PLEASE HELP 30 POINTS...PLEASE HELP PLEASE
Answer:
u haven't attached anything
but if u need any help ask the question again or put it in the comments
ur welcome
Answer:
free points
Step-by-step explanation:
Only number 12 plz I’ll give brainliest(ASAP)
Answer:
120 m/h
120 m/(3600 seconds)
(1/3)m/s
15 * (1/3) = 5
He travels 5 miles in 15 seconds
Step-by-step explanation:
Use the Distributive Property to expand the expression you obtained in part B.
The expression is 2(100 − x).
Answer:
The expression 2(100 − x) expands to 200 − 2x.
Step-by-step explanation:
2(100) − 2(x).
Multiply within each term:
200 − 2x.
Answer:
2(100 − x)
Distribute the 2:
2(100) − 2(x).
Multiply within each term:
200 − 2x.
The expression 2(100 − x) expands to 200 − 2x.
Step-by-step explanation:
Mark me brainliest please?
Solve the equation using square roots.
2(x + 1)2 - 7 = 25
solution: x=
x=7
I'm sorry if I'm wrong
The product of 3 x is less than 9
please help
I need it right now
thank you
Answer: Okay, I can't answer 1. and 2. because I don't know who Iris is, an the team/students
Send a pic of the teams
Step-by-step explanation:
This table represents a linear function. Find the missing values to complete the table.
Answer:
(2,5) and (7,12.5)
Step-by-step explanation:
Solve for change in y over change in x using the points (3,13/2) and (6,11). You can then get the equation y=1.5x+2. Then plug in the values you are given from the missing points using the equation. Hope this helped! If it did, please mark the brainliest.
For the following right triangle, find the side length x. Round your answer to the nearest hundredth.
13
11
Answer:
use a2+b2=c2 so
Step-by-step explanation:
11(squared)+b(squared)=13(squared)
=121+b2=169
-121. -121
b2= 48
square root 48
Side B= 6.928
and then just round 6.928
hope this helped
Using the Pythagorean Theorem, it is found that the side length is of x = 6.93.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
In this problem, we have that:
[tex]h = 13, l_1 = 11, l_2 = x[/tex]
Hence, applying the Theorem:
[tex]h^2 = l_1^2 + l_2^2[/tex]
[tex]13^2 = 11^2 + x^2[/tex]
[tex]x^2 = 169 - 121[/tex]
[tex]x = \sqrt{48}[/tex]
x = 6.93.
More can be learned about the Pythagorean Theorem at https://brainly.com/question/26396675
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Using the graph, find the
1. Domain
2. Range
3. Is it a function? Why or why not?
9514 1404 393
Answer:
domain: {-5, -4, 2, 5}range: {-6, 1, 3, 4, 5}no: fails the vertical line testStep-by-step explanation:
The domain is the list of x-values of the points on the graph. It is ...
{-5, -4, 2, 5}
The range is the list of y-values of the points on the graph. It is ...
{-6, 1, 3, 4, 5}
__
Two of the points, (2, 1) and (2, 4), have the same x-value. When a single input has multiple outputs, the relation is not a function.
If you were to draw a vertical line at x=2, it would intersect the relation in more than one place. Thus, we say the relation "fails the vertical line test." A vertical line will never intersect the graph of a function in more than one place.
HELPPPP! ILL GIVE YOU BRAINLIEST!
Answer:Can you put the question?? Thank You
Step-by-step explanation:
Answer:
what can i help with?
Step-by-step explanation:
A streetlight that is 10 feet tall casts a 2.5-foot-long shadow. A nearby flagpole casts a 9-foot-long shadow. What is the height of the flagpole?
Answer:
The height of the flagpole is 36 feet
Step-by-step explanation:
The given parameters are;
The height of the street light = 10 feet
The shadow cast by the streetlight = 2.5 feet
The shadow cast by the flagpole = 9 foot
The height of the flagpole is given as follows;
The height of the street light/(The shadow cast by the streetlight) = (The height of the flagpole)/(The shadow cast by the flagpole)
∴ The height of the flagpole = (The shadow cast by the flagpole) × (The height of the street light)/(The shadow cast by the streetlight)
By substituting the values, we get;
The height of the flagpole = 9 ft. × 10 ft./2.5 ft. = 36 feet
The height of the flagpole = 36 feet.
A sporting goods store has 4 catchers mitts, 28 baseball gloves , 52 bats and 96 baseball in stock. What is the ratio of baseballs to baseball gloves
96:28
96 baseballs to 28 baseball gloves
Mandy makes beaded bracelets and sells them for $5 each. If she sells the bracelets for 250% of the cost of her materials, how much does each bracelet cost to make?
Each bracelet costs $
to make.
Answer:
Each bracelet cost $2 to make.
Step-by-step explanation:
I did the assignment.
Answer:
$2
Step-by-step explanation:
(Brainliest plz) if im right
HELP! WILL MARK BRAINLIEST, PAST DUE!!!
Answer:
1/2 and - 1/2
Step-by-step explanation:
umm ok so for slope you do m = y2-y1/ x2-x1 which can probably be any point since they havent specified so we will do
A) L (-8,8) and (0,4)M
m= 4-8/0-8
=-4/-8
= 1/2
B ) now for b its asking for the certain points of
n and p
(4,2) N and (8,0) P
m= y2-y1/x2-x1 = 0-2/8-4= -2/4 = - 1/2 for ur slope
these should be right.
What is 254−−√+524−−√ in simplified radical form?
Enter your answer in the box.
Answer:
Step-by-step explanation:
2√54+5√24
2 * sqrt(9*6) + 5*sqrt(4*6)
2*sqrt(9) *sqrt(6) + 5*sqrt(4) * sqrt(6)
2*3 sqrt(6) + 5*2 sqrt(6)
6sqrt(6)+10sqrt(6)
16sqrt(6)
Answer:
16sqrt(6)
Step-by-step explanation:
