Answer:
-2
Step-by-step explanation:
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A rectangle has sides measuring (4x + 5) units and (3x + 10) units.
Part A: What is the expression that represents the area of the rectangle? Show your work. (4 points)
Part B: What are the degree and classification of the expression obtained in Part A? (3 points)
Part C: How does Part A demonstrate the closure property for polynomials? (3 points)
Part A
Like with any other rectangle, we multiply the length and width to get the area
This applies even when we have algebraic expressions like this (recall that x is simply a placeholder for a number).
So,
area = length*width
area = (4x+5)*(3x+10)
area = w(3x+10) ..... replace (4x+5) with the variable w
area = 3xw + 10w ..... distribute
area = 3x(4x+5)+10(4x+5) .... plug in w = 4x+5
area = 3x*4x+3x*5 + 10*4x+10*5 .... distribute again
area = 12x^2+15x + 40x+50
area = 12x^2+55x+50
Answer: 12x^2+55x+50
=======================================================
Part B
The degree of any single variable polynomial is the largest exponent. In this case, the largest exponent is 2. This 2nd degree polynomial is considered a quadratic. Because we have three terms, this quadratic polynomial is also a trinomial. So there are many ways to describe the result of part A. Possibly the quickest way to describe it is to say "quadratic trinomial" to say all that has been mentioned in this paragraph.
Answers:
Degree = 2Classification = quadratic trinomial=======================================================
Part C
The concept of closure is the idea of taking two objects of the same type, applying some operation to them, and getting an output object of the same type.
Admittedly that last paragraph is a bit vague so I'll go over a few examples.
If we take any two integers and add them up, then we get another integer. This shows integers are closed under addition.We can also multiply any two whole numbers to get some other whole number. This is another example of closure.A non-example would be dividing whole numbers. Something like 10/2 = 5 is a whole number but 10/3 = 3.33 is not. This shows that integers are not closed under division. We don't always get a whole number output.
With polynomials, multiplying any two of them will result in some other polynomial. It's basically using the two examples in the bullet points and building upon them. That's the short version of why polynomials are closed under multiplication.
For this particular problem, (4x+5), (3x+10), and 12x^2+55x+50 are all polynomials.
-----------
In terms of notation,
polynomialA * polynomialB = polynomialC
This notation hopefully shows that multiplying any two polynomials leads to another polynomial.
Refer to this previous problem I answered
https://brainly.com/question/24065851
Specifically, the top of part C talking about a coin machine should hopefully help if any of the concepts here don't make sense. If neither this current page nor the link helps, then let me know and I'll try to rephrase things another way.
A set of integers each is greater than 40 and less than 46. List the members.
Answer:
{41 , 42 , 43 , 44 , 45}
Answer:
Set (x) = {41, 42, 43, 44, 45}
Step-by-step explanation:
Given statement,
→ A set of integers each is greater than 40 and less than 46.
Now the set will be,
→ 40 < x < 46
Then the members of the set are,
→ 40 < x < 46
→ 40 < 41 < 46
→ 40 < 42 < 46
→ 40 < 43 < 46
→ 40 < 44 < 46
→ 40 < 45 < 46
The list of required integers are,
→ 41, 42, 43, 44, 45
→ {41, 42, 43, 44, 45}
Hence, this is the correct answer.
Sandra buys three more apples than Lebo bought. Lebo has seven apples left after he has sold 17 apples . If Sandra only sells eight apples , how many does she have left
Answer:
sandra had 19 apples left
Step-by-step explanation:
17+7=24
that means that sandra had 27 apples because she had 3 more apples
27-8=19
im confused on the bottom circle answer its a bit weird it reads "a. (use algebra) Use the diagram at the right. What algebraic expression represents GK?
b. if GK = 30, what are GH and JK?"
Step-by-step explanation:
well you need to add the right expressions for the shorter lines so that there is no overlap. otherwise GK would be too long.
so, how can we combine the 3 red lines to get exactly GK ?
we cannot just add 2 of these lines. the results would always be either too long or too short.
but we see "2x + 3" overlaps a bit with "4x - 3". and hey, the third line "x" is just the length of the overlap of the other 2 lines.
so, we can add the first 2 lines, IF we reduce first one of them by the overlap length.
I picked the second line.
so, we have
2x + 3 - x + 4x - 3 = GK
5x = GK
so, "5x" is the algebraic expression representing GK.
now, if GK = 30, then we know
5x = 30
x = 6
GH = 2x + 3 - x (again, we need to shorten that line by the overlap length to count only to H)
= 2×6 + 3 - 6 = 6 + 3 = 9
JK = GK - GJ = 30 - (2x + 3) (here we need the full line, as we are dealing with J)
= 30 - 2×6 - 3 = 15
What does -(-3) equal?
It does equal to +3
explanation = -(-3) = -1×(-3) = +3
When you multiply two negative numbers it turns out positive
Can someone please tell me what 23=x+14 is? Thanks
Answer:
9=x
Step-by-step explanation:
23=x+14
23 - 14=x
9=x
Answer:
x=9
Step-by-step explanation:
23=x+14
x+14=23
x =23-14
x=9
9+(-2)+11+(-8)=
Help?
Answer:
10
Step-by-step explanation:
9+(-2)+11+(-8)=10
firstly 9+-2=7 then 7+11=18 and finally 18+-8 =10
Answer:
10
Step-by-step explanation:
Dado un rectángulo ∎ABCD de lados de longitud x y y con área 15 cm2, sea AC una de sus diagonales de longitud d, esprese la longitud d en función de la longitud x.
La longitud de las diagonales del rectángulo con área de 15 centímetros cuadrados se describe con [tex]d = \frac{\sqrt{x^{2}+225}}{x}[/tex].
El área de rectángulo que mediante la ecuación de área estándar, mientras sus diagonales pueden ser descritas mediante el teorema de Pitágoras, los cuales se describen a continuación:
Área
[tex]A = x\cdot y[/tex] (1)
Diagonal
[tex]d = \sqrt{x^{2}+y^{2}}[/tex] (2)
Donde:
[tex]A[/tex] - Área del rectángulo, en centímetros cuadrados.[tex]d[/tex] - Diagonal del rectángulo, en centímetros.[tex]x, y[/tex] - Lados del rectángulo, en centímetros.Despejamos [tex]y[/tex] en (1):
[tex]y = \frac{A}{x}[/tex]
Luego, aplicamos la fórmula a (2) para eliminar la variable:
[tex]d = \sqrt{x^{2}+\frac{A^{2}}{x^{2}} }[/tex]
Simplificamos la expresión resultante: ([tex]A = 15\,cm^{2}[/tex]):
[tex]d = \frac{\sqrt{x^{2}+A^{2}}}{x}[/tex]
[tex]d = \frac{\sqrt{x^{2}+225}}{x}[/tex]
La longitud de las diagonales del rectángulo con área de 15 centímetros cuadrados se describe con [tex]d = \frac{\sqrt{x^{2}+225}}{x}[/tex].
Invitamos a leer esta pregunta sobre rectángulos: https://brainly.com/question/17143193
Help Please need answer in 10 minutes
Answer:
Answers
Step-by-step explanation:
If 24 litres of water are poured into an empty tank, then 3/4 of the tank is filled. How many litres does a tank hold?
What is the greatest common factor of 42 and 64
Use the data from the table on the right to fill the stem and leaf plot
High Temperatures
During February
City A - 28
City B - 54
City C - 34
City D - 50
City E - 34
Key – 1|5 = 15
Answer:
city d
Step-by-step explanation:
50
Choose the best description for the real number 35
Answer:
A) Irrational, because it is not a terminating or repeating decimal.
Step-by-step explanation:
Every time a square root results in a decimal, it will always never end, and never repeat. The square root of 35 qualifies for both of these qualities, therefore, making the answer (A). Hope this helps!
please help i’m failing algebra and it’s only the 3rd week
HELP MEE PLEASEEE #11 A) and B) pleaseeee
Answer:
The paper is not clear :(
Step-by-step explanation:
1. After a workout class, Lenia's heart rate
decreases at a rate of 17 beats per minute for
6 minutes. How much did Lenia's heart rate
decrease in the 6-minute period?
Answer:
102
Step-by-step explanation:
17 beats * 6 minutes = 102
Select the point that satisfies y<_x2 - 4x + 2.
A, 5,5
B. 4,4
C. 2,2
D. 1,1
Answer:
A 5,5
Step-by-step explanation:
5 <_ 25 - 20 +2
5 <_ 7
hope this helps
7
9
20
3
9
A number is removed from this list and the median and range do not change
Write down this number.
Hope it a right answer for you
Answer:
Removing the number 7 wont change the median nor the range
What is the value of the 20th term in this sequence? f(n)=6n−18
The value of the 20th term in this sequence will be 102
Since we are given f(n)=6n−18.
In this case, we have been given n to be 20. Therefore, f(n)=6n−18 will then be written as:
f(n)=6n−18
f(20) = 6(20) - 18
f(20) = 120 - 18
f(20) = 102
In conclusion, value of the 20th term in this sequence will be 102
Read related link on:
https://brainly.com/question/12246947
Answer:
102
Step-by-step explanation:
thats the answer ....
A recipe calls for 2 1/2 cups of flour. If I already added 3/4 of a cup of flour, how much more flour would I need to add?
Answer:
6 1/2 - 2 3/4 = 3 3/4
6.5 - 2.75= 3.75
James walked at a constant rate for 3 hours as shown in the graph. Jaycee walked 14.5 miles in 3 hours at a constant rate. Who walked farther, and how much farther?
Answer:
Jaycee walked [tex]2.5[/tex] miles farther.
Step-by-step explanation:
Given
Jaycee walked 14.5 miles in 3 hours at a constant rate.
Step 1 of 1
From given graph [tex]$(1,4)$[/tex], [tex]$(2,8)$[/tex] is a two points.
Then the equation of the line are [tex]$y=4 x$[/tex]
This imply at [tex]$x=3[/tex] ;
[tex]y=12$[/tex]
Therefore, James walked [tex]12[/tex]miles in [tex]3[/tex] hours.
Jaycee walked [tex]$14.5$[/tex] miles in [tex]3[/tex] hours.
Jaycee walked farther and that is [tex]$(14.5-12)$[/tex]mile
[tex]=2.5[/tex]miles
Learn more about miles, refer :
https://brainly.com/question/8956751
plz help me only 4 b
Answer:
[tex] \frac{ \sqrt{2} }{4} [/tex]
Step-by-step explanation:
attached
Solve for x.
x/5= 20
0.25
4
100
10
Answer:
100
Step-by-step explanation:
x ÷ 5 = 20
multiply both sides with 5
x = 100
Answer: 100
HOPE THIS HELPS
Last year’s match at Wimbledon between John Isner and Nicolas Mahut, which lasted 11 hours and 5 minutes, set a record for the longest match in tennis history. The fifth set of the match lasted 8 hours and 11 minutes. Approximately what fraction of the whole match was taken up by the fifth set?
Using proportions, it is found that approximately 74% of the whole match was taken up by the fifth set.
What is a proportion?A proportion is a fraction of total amount, and is given by the number of desired outcomes divided by the number of total outcomes.In this problem:
To build the fraction, we find the times in minutes.The fifth set took 8 hours and 11 minutes, that is, 8 x 60 + 11 = 491 minutes.In total, the match lasted 11 hours and 5 minutes, that is, 11 x 60 + 6 = 665 minutes.Hence:
[tex]p = \frac{491}{665} \approx 0.74[/tex]
Approximately 74% of the whole match was taken up by the fifth set.
You can learn more about proportions at https://brainly.com/question/24372153
Helpppppppppppppppppppp
Answer:
[tex]3 {x}^{2} y - {y}^{2} [/tex]
[tex]y(3 {x}^{2} - y)[/tex]
is the answer
Answer:
[tex]3x {}^{2}y - y {}^{2} \\ 3x {}^{2} - \frac{y {}^{2} }{y} \\ 3x {}^{2} - y[/tex]
Step-by-step explanation:
please mark me brainliest pleasecomplete the table for the given rule
PLEASE HELP QUICK
Answer:
16, 8, 36
Step-by-step explanation:
To solve for x for the first answer, multiply 4 by y
[tex]y = \frac{x}{4} \\\\y (4) = x\\\\x = 4(4)\\ x= 16[/tex]
To solve for x for the second answer, multiply 2 by y
[tex]y = \frac{x}{4} \\\\y (4) = x\\\\x = 2(4)\\ x= 8[/tex]
To solve for x for the third answer, multiply 9 by y
[tex]y = \frac{x}{4} \\\\y (4) = x\\\\x = 9(4)\\ x= 36[/tex]
Find the distance between the two points rounding to the nearest tenth! PLEASE HELP ASAP!!! :
what is the anwser to this on the number line 7 - 6y > 19
Answer:
y < -2
Step-by-step explanation:
7 - 6y > 19
Subtract 7 from each side
7-7 - 6y > 19-7
-6y > 12
Divide each side by -6. remembering to flip the inequality
-6y/-6 < 12/-6
y < -2
What is the decimal equivalent of 8/3?
A. 2.6
B. 0.375
C. 8.3
D. 26
Answer:
A
Step-by-step explanation:
8/3 basically means 8 divided by 3. ( 8 ÷3)
Therefore 8÷3 = 2.667
helpppp 2x-1>5 and 3x-5<19
Answer:
3 < x < 8
Step-by-step explanation:
Solve each part separately
2x - 1 > 5 ( add 1 to both sides )
2x > 6 ( divide both sides by 2 )
x > 3 , that is
3 < x
and
3x - 5 < 19 ( add 5 to both sides )
3x < 24 ( divide both sides by 3 )
x < 8
Then putting the two together
3 < x < 8
