Answers
[tex](2n+1)^2=4n^2+4n+1[/tex] therefore, the first blank is 1.
[tex]4n^2+4n+1=2(2n^2+2n)+1[/tex] therefore, the two other blanks are both 2.
The number in the proof ''The square of the sum of two consecutive integers is odd'' is 2 and 2.
To prove that, The square of the sum of two consecutive integers is odd.
The expression to prove is,
Let us assume that two consecutive integers are n and (n + 1).
Hence, the expression is written as,
[n + (n + 1)]² = (2n + 1)²
= (2n)² + 2 × 2n × 1 + 1²
= 4n² + 4n + 1
= 2 (2n² + 2n) + 1
= odd
Therefore, the number in the blanks are 2 and 2.
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Related Questions
what is the sum of the interior angles of a regular hexagon
Answers
Answer:
see below
Step-by-step explanation:
The sum of the interior angles of any polygon can be found with the formula 180(n - 2) where n = number of sides. In this case, n = 6 so the answer is 180(6 - 2) = 180 * 4 = 720°.
Answer:
The sum of the interior angles of a regular hexagon is 720°
Step-by-step explanation:
As we know that the sum of interior angle is 180(n-2). So the number of sides of hexagon is 6. Now, 180(6-2)=180*4=720°
What is 12.5% of 72
Answers
Answer:
[tex]\boxed{9}[/tex]
Step-by-step explanation:
[tex]\sf of \ refers \ to \ multiplication.[/tex]
[tex]12.5\% \times 72[/tex]
[tex]\frac{12.5}{100} \times 72[/tex]
[tex]\sf Multiply.[/tex]
[tex]\frac{900}{100} =9[/tex]
help please, got a little lost in everything
Answers
Answer:
375 mm cubed
Step-by-step explanation:
The volume would stay the same because the same number of the same pennies are being used.
If the question was asking for the surface area, then the answer would be different.
Hope that helped!!! k
Answer: 375 mm cubed
Reduce 5/15 to its lowest terms
Answers
Answer:
The answer is 1/3
Answer:
1/3
Step-by-step explanation:
The factors of 5 are 1,5;
* The factors of 15 are 1,3,5,15.
We can see that the GCD is 5 because it is the largest number by which 5 y 15 can be divided without leaving any residue.
To reduce this fraction, simply divide the numerator and denominator by 5 (the GCF).
So, 5 /15
= 5÷5 /15÷5
= 1 /3
1.Solve by factorization method: x+1/x=11 1/11 2.Comment on the nature of roots for 4x^2-5=2(〖x+1)〗^2-7 plz, help...
Answers
Answer:
The equation
[tex]4\,x^2-5=2\,(x+1)^2-7[/tex]
can be solved by first expanding all indicated operations, and later when the constant terms disappear, by factoring out 2x , leaving the equation as a product of two factors equal zero, from which it is easy to extract the roots. See below.
Step-by-step explanation:
When solving for x in the following expression, and using factoring to apply at the end the zero product theorem:
[tex]4\,x^2-5=2\,(x+1)^2-7\\4\,x^2-5=2\,(x^2+2x+1)-7\\4\,x^2-5=2\,x^2+4\,x+2-7\\4\,x^2-5=2\.x^2+4\,x-5\\4\,x^2=2\,x^2+4\,x\\4\,x^2-2\,x^2-4\,x=0\\2\,x^2-4\,x=0\\2\,x\,(x-2)=0[/tex]
We observe that for the last product, to get a zero, x has to be zero (making the first factor zero), or x has to be "2" making the binomial factor zero.
Which expression represents the prime factorization of 243?
Answers
Answer:
[tex]\boxed{3^5}[/tex]
Step-by-step explanation:
Hey there!
Look at the image below↓
By looking at the image we can tell the PR expression is [tex]3^5[/tex].
Hope this helps :)
Answer:
Below in bold.
Step-by-step explanation:
Dividing by primes:
3 ) 243
3 ) 81
3 ) 27
3) 9
3.
So the prime factors of 243 are 3 * 3 * 3 * 3 * 3 or 3^5.
divide the sum of -5,-10 and -9 by the product of 2 and -3
Answers
Answer: 1/4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
=(-5)+(-10)+(-9)/2*(-3)
=-5-10-9/-6
=-24/-6
=4 ans.....
What’s is the greatest common factor of 100x^2 - 250xy + 75x
Answers
Answer:
The greatest common factor of the expression is 25x
Step-by-step explanation:
Here, we are interested in giving the greatest common factor of the expression.
We can do this by factorization till we have no common factors left.
the expression is;
100x^2 -250xy + 75x
we start with the common factor x;
x(100x -250y + 75)
The next thing to do here is to find the greatest common factor of 100,250 and 75.
The greatest common factor here is 25.
Thus, we have;
25x(4x -10y + 3)
There is no more factor to get from the terms in the bracket. This simply means that the terms in the bracket are no longer factorizable
So the greatest common factor we have is 25x
simplify 3/7
into a whole number
Answers
Answer:
You can't because it's not a "full fraction" like 7/7. The best you can do is turn that into a decimal like 0.43
Step-by-step explanation:
For the function f(x) = 3(x − 1)2 + 2, identify the vertex, domain, and range.
Answers
Answer:
Ok, our function is:
f(x) = 3*(x - 1)^2 + 2.
First, domain:
We should assume that the domain is all the set of real numbers, and then we see if for some value we have a problem.
In this case we do not see any problem (we can not have a zero in the denominator, and there is no function that has problems with some values of x)
Then the domain is the set of all real numers.
Vertex:
Let's expand our function:
f(x) = 3*x^2 - 3*2*x + 1 + 2
f(x) = 3*x^2 -6*x + 2
The vertex of a quadratic function:
a*x^2 + b*x + c is at:
x = -b/2a
here we have:
a = 3 and b = -6
x = 6/2*3 = 6/6 = 1.
And the value of y at that point is:
f(1) = 3*(1 - 1)^2 + 2 = 2
Then the vertex is at: (1, 2)
Range:
The range is the set of all the possible values of y.
Ok, we can see that the leading coefficient is positive, this means that the arms of our quadratic function will go up.
Then the minimal value of our quadratic function is the value at the vertex, y = 2.
This means that the range can be written as:
R = y ≥ 2
So the range is the set of all real numbers that are larger or equal than 2.
in a 10 team league, each teams play every other team exactly twice. find the total number of games played in the league
Answers
Addition can be defined as the process of adding two numbers. The total number of games played in the league is 90.
What is Addition?Addition can be defined as the process of adding two numbers such that the result is the combined value of the two numbers.
Given that in a 10-team league, each team play every other team exactly twice. Therefore, the total number of games that will be played by the first team is 18, similarly, the number of games that will be played by the second team is 16.
Therefore, as mentioned above the series will continue with a common difference of -2 and will continue till 0. Thus, the total number of games played in the league is,
Total number of games = 18 + 16 + 14 + 12 + 10 + 8 + 6 + 4 + 2 = 90
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A rectangular sheet of steel is being cut so that the length is four times the width the perimeter of the sheet must be less than 100 inches . Which inequality can be used to find all possible lengths,l.of the steel sheet
Answers
Answer:
w>10
length = 40
Step-by-step explanation:
Let
Width=w
Length=4w
Perimeter is less than 100 inches
Perimeter of a rectangle= 2( Length + width)
100 < 2(4w+w)
100 < 8w+2w
100 < 10w
w > 10
Length =4w
=4 × 10
=40 inches
Answer:
5/2l <100
Step-by-step explanation:
PLATO
All the edges of a cube have the same length. Tony claims that the formula SA = 6s, where s is the length of
each side of the cube, can be used to calculate the surface area of a cube.
a. Draw the net of a cube to determine if Tony's formula is correct.
b. Why does this formula work for cubes?
Frances believes this formula can be applied to calculate the surface area of any rectangular prism. Is
she correct? Why or why not?
d. Using the dimensions of Length, Width and Height, create a formula that could be used to calculate the
surface area of any rectangular prism, and prove your formula by calculating the surface area of a
rectangular prism with dimensions L = 5m, W = 6m and H=8m.
Answers
Answer:
Here's what I get
Step-by-step explanation:
a. Net of a cube
Fig. 1 is the net of a cube
b. Does the formula work?
Tony's formula works if you ignore dimensions.
There are six squares in the net of a cube.
If each side has a unit length s, the total area of the cube is 6s.
c. Will the formula work for any rectangular prism?
No, because a rectangular prism has sides of three different lengths — l, w, and h — as in Fig. 2.
d. Area of a rectangular prism
A rectangular prism has six faces.
A top (T) and a bottom (b) — A = 2×l×w
A left (L) and a right (R) — A = 2×l×h
A front (F) and a back (B) — A = 2×w×h
Total area = 2lw + 2lh + 2wh
If l = 5 m, w = 6 m and h = 8 m,
[tex]\begin{array}{rl}A &=& \text{2$\times$ 5 m $\times$ 6 m + 2$\times$ 5 m $\times$ 8 m + 2 $\times$ 6 m $\times$ 8 m}\\&=& \text{60 m}^{2} + \text{80 m}^{2} + \text{96 m}^{2}\\&=& \textbf{236 m}^{2}\\\end{array}[/tex]
Please answer now question
Answers
Answer:
1664 yd²Step-by-step explanation:
P = 2•(¹/₂•24•16) + 2•(20•20) + 24•20 = 384 + 800 + 480 = 1664 yd²
Suppose that the cost of renting a snowmobile is $37.50 for 5 hours.
a. If c represents the cost and ݄ represents the hours, which variable is the dependent variable?
b. What would be the cost of renting 2 snowmobiles for 5 hours? please and thanks ( i"ll give brainiest )
Answers
b) 2($37.50) = $75
Therefore it would cost $75 to rent 2 snowmobiles for 5 hours.
how do you find the area of an open cylinder... what is the Formula?? please help
Answers
Answer:
Cylinder has a formula
π×r²×h
so of it is open
π×r²×h - π×r²
Answer:
pls give brainiest
Step-by-step explanation:
A=2πr×h(r+h)
I answered all my work correctly but I don’t understand this one.
Answers
Q (0-2), (-1-1)
= (-2,-2)
D (-2-2), (2-1)
= (-4, 1)
V (2-2), (4-1)
= (0,3)
J (3-2), (0-1)
= (1,-1)
You can also draw it on a graph and then translate all coordinates 2 units left and 1 down to see the end results.
Which polynomial is a factor of both expressions? x – 8 x + 7 x – 2 (x – 2)2
Answers
Answer:
C. x-2
Step-by-step explanation:
edge
Answer: the 3rd the answer c
x-2
Step-by-step explanation:
Variance 0.7775
Find the standard deviation (hint: the standard deviation is the square root of the variance)
Answers
Answer:
0.88175960442
Step-by-step explanation:
The square root of 0.7775 is 0.88175960442
The value of standard deviation will be;
⇒ 0.8803
What is mean by square root of a number?
A square root of a number is a value that multiplied by itself gives the same number.
Given that;
The value of Variance = 0.7775
Now,
Since, The standard deviation is the square root of the variance.
Hence, We can formulate;
The value of standard deviation = √0.7775
= 0.8803
Thus, The value of standard deviation will be;
⇒ 0.8803
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A fish jumps out of the water at a speed of 12 feet per second. The height y (in feet) of the fish above the surface of the water is represented by the equation y=-16x^2+12x, where x is the time (in seconds) since the jump began. The fish reaches its highest point above the surface of the water after 0.375 seconds. How far above the surface is the fish at this time?
Answers
Answer:
The fish is 2.25 ft above the surface at 0.375 seconds
Step-by-step explanation:
Given:
y=-16x^2+12x
x=0.375 seconds
Substitute x=0.375 into the equation
y=-16x^2+12x
= -16(0.375)^2 +12(0.375
= -16(0.140625) + 4.5
= -2.25 + 4.5
= 2.25
y=2.25 ft
The fish is 2.25 ft above the surface at 0.375 seconds
URGENT PLZ HELP THANK YOU!
Answers
Answer:
[tex](-5)^{11}[/tex]
Step-by-step explanation:
We can use the exponent rules. If we have [tex]\frac{a^b}{a^c}[/tex], then it will simplify to [tex]a^{b-c}[/tex].
b is 5, c is -6, and a is -5 so:
[tex]-5^{5-(-6)}\\-5^{11}[/tex]
Hope this helped!
Jack is building a square garden. Each side length measures 777 meters. Jack multiplies 7\times77×77, times, 7 to find the amount of space in his garden is equal to 494949 square meters. Which measurement does 494949 square meters represent?
Answers
Answer:
49 square meters represent area of the square garden
Step-by-step explanation:
Each side length=7 meters
He multiplied 7 × 7 times to find the amount of space
=49 square meters
Jack is trying to measure the area of his square garden
Area of the square garden = length^2
=Length × length
Recall,
Length=7 meters
Area of the square garden= 7 meters × 7 meters
=49 square meters
Find f(x) and g(x) so the function can be expressed as y = f(g(x)). (1 point) [tex]y=\frac{7}{x^{2} } +10[/tex]
Answers
Answer:
The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.
Step-by-step explanation:
Let suppose that [tex]g(x) = \frac{1}{x^{2}}[/tex], then [tex]f(g(x))[/tex] is:
[tex]f(g(x)) = 7\cdot \left(\frac{1}{x^{2}} \right) + 10[/tex]
[tex]f(g(x)) = 7\cdot g(x) + 10[/tex]
Thus,
[tex]f(x) = 7\cdot x + 10[/tex]
The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.
Which phrase best describes the relationship indicates by the scatter plotting?
Answers
Answer: negative correlation
Step-by-step explanation: If you look at the points in this graph here, I would say that those points are very close to a perfect line.
Notice that the slope of the line is negative.
This means it will be a negative correlation.
So the line is a very good estimate of the points.
a cone with base radius 7 cm has a volume of 308 cm cube find the vertical height of the cone take π 22/7
pls now
Answers
Answer:
h=6.003 cm
Step-by-step explanation:
[tex] \frac{1}{3} \pi {r}^{2} h \: \: is \: the \: volume \: of \: cone[/tex]
1/3×22/7×7×7×h=308
h=308/51.3
Answer:
h = 6 cm
Step-by-step explanation:
r = 7 cm
Volume of cone = 308 cm³
[tex]\frac{1}{3}\pi r^{2}h=308\\\\\\\frac{1}{3}*\frac{22}{7}*7*7*h=308\\\\\\h=\frac{308*3*7}{22*7*7}\\\\\\h=2*3[/tex]
h = 6 cm
Name a real world context to describe the sums of rational numbers.
Answers
Step-by-step explanation:
when you are cooking you need to measure fractions of ingredients
5/14, 7/10, 5/6, 11/15, 19/2
Answers
Answer:
5/14 = 0.36
7/10 = 0.7
5/6 = 0.83
11/15 = 0.73
19/21 = 0.9
(round to the tenth)
so the answer is;
5/14, 7/10, 11/15, 5/6, 19/21
Step-by-step explanation:
Hope it helps!
A, B, C, D, E, F, ... 2, 3, 5, 7, 11, 13, ... what number is the letter Z replaced with?
Answers
Answer:
Z=101
Step-by-step explanation:
A=2
B=3
C=5
D=7
E=11
F=13
From the above illustration, it can be deduced that A to Z represent prime numbers in ascending order.
Prime numbers are natural numbers that are greater than 1 and are only divisible by 1 and itself.
Therefore,
G=17
H=19
I=23
J=29
K=31
L=37
M=41
N=43
O=47
P=53
Q=59
R=61
S=67
T=71
U=73
V=79
W=83
X=89
Y=97
Z=101
What is the difference between sin^-1 and sin?
Answers
Answer:
Step-by-step explanation:
sin of angle x is the trig ratio sine of x.
sin-1 x is the angle whose sine is x.
sin-1 x can also be written as arcsin x.
help8b2 • 2b3 a) 16b-2 ,b) 16b6 ,c) 16b-4 ,d) 16b5
Answers
Answer:
16b^5
Step-by-step explanation:
8b^2×2b^3
= 16b^2+3
= 16b^5
Answer:
D)16b5
Step-by-step explanation:
8b2×2b3
= 16b2+3
= 16b5
