Answer:
All answers EXCEPT answer C. are perfect square trinomials.
Step-by-step explanation:
A perfect square trinomial is polynomial that satisfies the following condition:
[tex](a+b)^{2} = a^{2}+2\cdot a \cdot b + b^{2}[/tex], [tex]\forall\,a,b\in\mathbb{R}[/tex]
Let prove if each option observe this:
a) [tex]4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2}[/tex]
1) [tex]4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2}[/tex] Given
2) [tex](2\cdot x)^{2}+ 2\cdot (2\cdot x)\cdot (3\cdot y)+(3\cdot y)^{2}[/tex] Definition of power/Distributive, associative and commutative properties.
3) [tex]a = 2\cdot x[/tex], [tex]b = 3\cdot y[/tex] Definition of perfect square trinomial/Result.
b) [tex]9\cdot a^{2}-36\cdot a + 36[/tex]
1) [tex]9\cdot a^{2}-36\cdot a + 36[/tex] Given.
2) [tex](3\cdot a)^{2}-2\cdot (3\cdot a)\cdot 6 + 6^{2}[/tex] Definition of power/Distributive, associative and commutative properties.
3) [tex]a = 3\cdot a[/tex], [tex]b = 6[/tex] Definition of perfect square trinomial/Result.
c) [tex]x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2}[/tex]
1) [tex]x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2}[/tex] Given
2) [tex]x\cdot y\cdot (1-4\cdot x+4\cdot x)[/tex] Distributive property.
3) [tex]x\cdot y \cdot 1[/tex] Existence of the additive inverse/Modulative property.
4) [tex]x\cdot y[/tex] Modulative property/Result.
d) [tex]a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}[/tex]
1) [tex]a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}[/tex] Given
2) [tex](a\cdot b)^{2}+2\cdot (a\cdot b)\cdot (2\cdot a^{2})+(2\cdot a^{2})[/tex] Definition of power/Distributive, associative and commutative properties.
3) [tex]a = a\cdot b[/tex], [tex]b = 2\cdot a^{2}[/tex] Definition of perfect square trinomial.
All answers EXCEPT answer C. are perfect square trinomials.
The perimeter of a rectangle is 100 ft , if the wife is 20 ft what is the value of the length?
Answer:
30
Step-by-step explanation:
since the width is 20, there are 2 sides, so multiply by 2 and it's 40. Subtract 40 from 100 and you get 60. 60 is both lengths combined, so divide by 2 and you have 30 as your length. :)
the fraction below represents two factions of the same whole. How much of the 5/6 is in the 1/3?
A.2/5
B.1/2
C.5/9
D.6/9
Which of the following is an informal proof of the given conjecture? Conjecture: All squares are similar
Answer:
the last one, i just got 100%
Step-by-step explanation:
Option 4 : Square A has side lengths a₁ =3, a₂= 3 and Square B has side lengths b₁=6,b₂=6 Then show that the ratio of corresponding side length is equal: a₁ /a₂=b₁/b₂, 3/3=6/ 6 is the informal proof of the given conjecture.
What is informal proof?Informal proofs are used to proof a theorem in different methods of proving theorems and steps of the proof are not formally framed.
Mostly by taking a particular example a theorem is proved.
All square are similar.
This statement is true
∴ Option 1 is false
Option 2 is formal proof as sides of squares A and B are taken as variables x and y therefore this proof can be used for any pair of two squares
Option 3. is wrong proof as the two sides of square A and B are taken unequal but square has all four sides equal.
Option 4 is correct proof but it is not a formal one as a particular example is taken to proof with statement
Therefore option 4 is the correct option that show the informal proof of the given statement.
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Plaase help me ...................
Which problem would be best solved by dividing decimals?
Answer:C
Step-by-step explanation:
I would like someone to help please, find the reciprocal of 10 1/2
Answer:
2/11
Step-by-step explanation:
10 1/2 is the same as 11/2. The reciprocal of 11/2 is 2/11
How do you do b,c,d?
Step-by-step explanation:
(b) x is at 2 twice, and -2 twice.
y is at 2 three times, and -2 three times.
The graph that fits is I.
(c) x is at 2 twice, and -2 twice.
y is at 2 once, and is never negative.
The graph that fits is IV.
(d) x is at 2 and stays there for a period of time.
y is at -2 and stays there for a period of time.
The graph that fits is II.
Suppose it takes John 18 minutes to run 3 miles. How long would it take him to run 7 kilometers? round to the nearest minute
Answer: 26 Minutes
Step-by-step explanation:
3 mi * 1.609 km/1 mi = 4.82 km
4.82 km/ 18 minutes = 7 km/ x minutes
4.82x=18*7
x=126/4.82
x=26.14 ~ 26 Minutes
One mile contains 1 mile = 1.690KM.
According to the if we convert 7km into miles 4.3496 miles. Thus the correct answer for the question is 26 minutes
Explanation:
That its taken the when john runs 18 minutes for 3 miles that is km4.82 than if we consider 1.34 miles is required to be covered more when subtract the value 4.3496-3.0000-1.34miles it should be 13is half of it multiply by 2 minutes more is required to cover the left distance is carried by Dividing 18by 1.34 and multiplying by 2
Thus we conclude that above answer to the Question is correct
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Zoe bought 1.5 pounds of apples for $3.50 per pound. She wanted to find the total cost using partial products.
Answer:
She spent $5.25
Step-by-step explanation:
The total cost of the apples is $5.25 if Zoe bought 1.5 pounds of apples for $3.50 per pound.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Zoe bought 1.5 pounds of apples for $3.50 per pound.
Let x be the total cost of the product:
x = 3.50x1.5
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
x = $5.25
Thus, the total cost of the apples is $5.25 if Zoe bought 1.5 pounds of apples for $3.50 per pound.
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Find the value that makes the equation
2d + 4 = 12 true.
Answer:d=12
Step-by-step explanation:
Select the correct expressions.
Which expressions are equivalent to 3x + 2(x - 1) - 4?
3x + 2x - 2 - 4
5x6
3(x-4)
3(x + 2) - 6
6(x - 1)
Solve for x.
8x=4x−32
A)x = 8
B)x = 4
C) x=−4
D) x=−8
Answer:
x=-8
Step-by-step explanation:
i took the quiz
Answerd
Step-by-step explanation:
Match each unit rate to its ratio. PLEASE HELP
Answer:
1½ gallons per minute3 gallons per minute ⅔ gallon per minute 9 gallons per minuteStep-by-step explanation:
You have to divide both numbers.
What is the greatest common factor of 12,18,26
Rewrite 1/4 barrel over 2/3 of an hour as a unit rate
A.2 2/3
B. 1/6 barrel/hour
C. 6 barrels/hour
D. 3/8 barrel/hour
Answer:
d
Step-by-step explanation:
Help help help me on this math
Answer:
x=2
Step-by-step explanation:
4x-9=-1
+9 = +9
4x=9+(-1)
4x=8
divided by 2
x=2
Hope this helps :)
Truckco manufactures two types of trucks: 1 and 2. Each truck must go through the painting shop and assembly shop. If the painting shop were completely devoted to painting Type 1 trucks, then 800 per day could be painted; if the painting shop were completely devoted to painting Type 2 trucks, then 700 per day could be painted. If the assembly shop were completely devoted to assembling truck 1 engines, then 1,500 per day could be assembled; if the assembly shop were completely devoted to assembling truck 2 engines, then 1,200 per day could be assembled. Each Type 1 truck contributes $300 to profit; each Type 2 truck contributes $500. formulate an LP that will maximize Truckco’s profit.
Answer:
Step-by-step explanation:
Let y represent type 2 truck and x represent type 1 truck. The painting can be represented by the inequality:
[tex]\frac{x}{800}+\frac{y}{700}\leq 1[/tex] (1)
The assembling can be represented by the inequality:
[tex]\frac{x}{1500}+\frac{y}{1200} \leq 1[/tex] (2)
Also, x, y ≥ 0
The objective function is given as:
max z = 300x + 500y
Plotting 1 and 2 using online geogebra
From the graph, the optimal value is at (0,700). Hence:
max z = 300(0) + 500(700) = $350000
For each line, determine whether the slope is positive, negative, zero, or undefined.
Line 1
Line 2
Line 3
Line 4
O Positive
Negative
O Zero
O Undefined
O Positive
O Negative
O Zero
O Undefined
O Positive
O Negative
O Zero
O Undefined
O Positive
O Negative
O Zero
O Undefined
Answer:
1. Negative
2. Undefined
3. Positive
4. Zero
Step-by-step explanation:
just took notes on subject and know answer. 100% sure its right
The slope of a line is determined by its steepness.
The formula for calculating slope is expressed as;
[tex]\frac{\triangle y}{\triangle x} = \frac{y_2-y_1}{x_2-x_1}[/tex]
For the first graph, we can assume the coordinates (-1, 0) and (0, -2), the [tex]\frac{\triangle y}{\triangle x} = \frac{-2-0_1}{0-(-1)}\\\frac{\triangle y}{\triangle x} = \frac{-2}{1}\\\frac{\triangle y}{\triangle x} = -2\\\\[/tex]
Since the slope is -2 which is a negative value, hence the slope of LlNE 1 is negative
For the vertical line, since the line is parallel to the y axis and the change in the x-value is zero, hence the slope of LINE 2 will be UNDEFINED
For the THIRD graph, we can assume the coordinates (2, 0) and (0, -2), the [tex]\frac{\triangle y}{\triangle x} = \frac{-2-0}{0-2}\\\frac{\triangle y}{\triangle x} = \frac{-2}{-2}\\\frac{\triangle y}{\triangle x} = 1\\\\[/tex]
Since the slope is 1 which is a negative value, hence the slope of LlNE 3 is positive
For the horizontal line (fourth graph), since the line is parallel to the x-axis and the change in the y-value is zero, hence the slope of LINE 4 will be ZERO
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Someone help me please
Answer:
x=6.4
Step-by-step explanation:
4^2+5^2=x^2
x=6.40
Shureka Washburn has scores of 81, 67, 79, and 43 on her algebra tests. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 71 or higher, given that the final exam counts as two tests.
Answer:
72+67+82+79=300
300/4=75
300+81+81=462
462/6=77
Step-by-step explanation:
find the coordinate of the midpoint of the segment with the given endpoints -7 and 8
Answer:
The coordinate of the midpoint is 1/2
Step-by-step explanation:
Midpoint
The midpoint of a segment defined in a one-dimension system is
[tex]\displaystyle \bar x=\frac{x_1+x_2}{2}[/tex]
Where x1 and x2 are the coordinates of the points.
The given segment has endpoints x1=-7 and x2=8, thus:
[tex]\displaystyle \bar x=\frac{-7+8}{2}[/tex]
[tex]\displaystyle \bar x=\frac{1}{2}[/tex]
The coordinate of the midpoint is 1/2
simplify the expression. write your answer in scientific notation
(9.6x10^3) x (6.7x10^2)
-3 1/5+(-6 1/2) please help quickly
Answer:
Exact Form:
-97/10
Decimal Form:
−9.7
Mixed Number Form:
-9 7/10
Answer:
i think that it is -9 7/10
Step-by-step explanation:
-3 1/5+(-6 1/2. 3+6=9 1/5+1/2=7/10. and that would make the final answer -9 7/10
It is known that Ray AP bisects angle CAT. If m<CAT = 5x+17 and m<PAT = 3x-4, then determine the value of x.
Answer:
x = 25
Step-by-step explanation:
It is given that, ray Ray AP bisects angle CAT. It means,
[tex]\angle CAT=\angle CAP+\angle PAT[/tex]
Also, [tex]\angle CAP = \angle PAT[/tex]
It gives, [tex]\angle CAT=2\angle PAT[/tex]
ATQ,
[tex]\angle CAT = 5x+17 \ \text{and}\ \text{PAT}=3x-4[/tex]
So,
[tex]5x+17=2(3x-4)\\\\5x+17=6x-8[/tex]
Taking like terms together,
[tex]5x-6x=-8-17\\\\-x=-25\\\\x=25[/tex]
So, the value of x is 25.
Find the area of polygon PQRS.
A. 7 units squared
B. 12 units squared
C. 17 units squared
D. 22 units squared
Answer:
12 unit squared....................
What is the distance between the points (15, -18) and (-6, -18) in the coordinate plane?
Answer:
the distance will be 21 whatever feet and so on. :)
hope this helps
A rectangle has an area of 6x ^ 2 + 7x - 3 square units. Which of the following could represent the perimeter of the rectangle in terms of ?
Which scenario could represent the expression −100÷5?
A baker evenly places 100 cookies among 5 sheet pans. How many cookies does the baker place on each sheet pan?
A baker evenly places 100 cookies among 5 sheet pans. How many cookies does the baker place on each sheet pan?
A group of 5 friends decide to split a debt of $100 evenly among each other. How much does each friend owe?
A group of 5 friends decide to split a debt of $ 100 evenly among each other. How much does each friend owe?
A person eats 5 cups of popped popcorn for a total of 100 calories. How many calories are in each cup of popped popcorn?
A person eats 5 cups of popped popcorn for a total of 100 calories. How many calories are in each cup of popped popcorn?
A principal evenly splits 100 students into 5 teams for a field day. How many students are on each team?
A principal evenly splits 100 students into 5 teams for a field day. How many students are on each team?
Answer:
_20
Step-by-step explanation:
that is my answer I just use calculator and I get that answer
round each number to the nearest ten 74.362 28.45 13.09
Answer:
74, 30, 13
Step-by-step explanation:
Answer: 74, 28 and 13
Step-by-step explanation:
Consider the tables.
Which table shows input and output values that
represent a quadratic function?
Table A
x
fx)
-10
8
-8
4
-6
0
4
4
2
48
O Table A
O Table B
Table B
X
fx)
46
--10
-1,002
8
-514
4
-66
-218
Table C
O Table D
-2
410
Table C
-10
1,002
8
802
46
602
4
402
12
202
fix)
Table D
X
f(x)
-10
-112
-8
--76
-6
1148
4
28
2
16
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Answer:
i think its a
Step-by-step explanation:
The ratio of the change in the y and x values, in the table gives the slope
graph of the linear function.
Correct response:
The slope of the linear function is -6
What is slope?The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. So the change in y coordinate with respect to the change in x coordinate can be written as, dx/dy.
here, we have,
Method used for finding the slope
From the given table, we have;
The first difference of the y-values = 2 - 8 = -6 = Constant
The rate of change of the x-values = 1 = Constant
Therefore;
The function is a linear function;
The slope, m, is given by the formula;
m = y2 - y1/x2-x1
Taking a pair of points as follows;
(0, -4) = (x₁, y₁)
(2, -16) = (x₂, y₂)
We have;
m = -6
The slope of the linear function, m = -6
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Complete question:
The table represents a linear function.
What is the slope of the function?
0-6
O 4
х
-2
-1
0
1
2
у
8
2
-4
-10
-16
04
O 6
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