Answer:
refer to workings
Step-by-step explanation:
Perimeter=15+15+8+8=46cm
Area=15×8=120cm²
prove that 1³+2³+....n³=n²(n+1)²/4. principle of mathematics induction
[tex]\sf 1^3+2^3\dots n^3=\dfrac{n^2(n+1)^2}{2}[/tex]
[tex]\\ \sf\longmapsto 1^3+2^3+\dots n^3=\left(\dfrac{n(n+1)}{2}\right)^2[/tex]
Solution:-Let
[tex]\\ \sf\longmapsto P(n)=1^3+2^3\dots n^3=\left(\dfrac{n(n+1)}{2}\right)^2[/tex]
For n=1
[tex]\\ \sf\longmapsto P(1)=\left(\dfrac{1(1+1)}{2}\right)^2[/tex]
[tex]\\ \sf\longmapsto P(1)=\left(\dfrac{1(2)}{2}\right)^2[/tex]
[tex]\\ \sf\longmapsto P(1)=\left(\dfrac{2}{2}\right)^2[/tex]
[tex]\\ \sf\longmapsto P(1)=(1)^2[/tex]
[tex]\\ \bf\longmapsto P(1)=1=1^3[/tex]
Let k be any positive integer.
[tex]\\ \sf\longmapsto P(k)= 1^3+2^3\dots k^3=\left(\dfrac{k(k+1)}{2}\right)^2[/tex]
We have to prove that p(k+1) is true.
consider
[tex]\sf 1^3+2^3\dots k^3+(k+1)^3[/tex]
[tex]\\ \sf\longmapsto \left(\dfrac{k(k+1)}{2}\right)^2+(k+1)^3[/tex]
[tex]\\ \sf\longmapsto \dfrac{k^2(k+1)^2}{4}+(k+1)^3[/tex]
[tex]\\ \sf\longmapsto \dfrac{k^2(k+1)^2+4(k+1)^3}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{k+1)^2\left\{k^2+4k+4\right\}}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{(k+1)^2(k+2)^2}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{(k+1)^2(k+1+1)^2}{4}[/tex]
[tex]\\ \sf\longmapsto \left(\dfrac{(k+1)(k+1+1)}{2}\right)^2[/tex]
[tex]\\ \sf\longmapsto (1^3+2^3+3^3\dots k^3)+(k+1)^3[/tex]
Thus P(k+1) is true whenever P(k) is true.
Hence by the Principal of mathematical induction statement P(n) is true for [tex]\bf n\epsilon N.[/tex]
Note:-
We can solve without simplifying the Question .I did it for clear steps and understanding .
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Answer:
Step-by-step explanation:
[tex]1^3=1=\dfrac{1^2*(1+1)^2}{4} =\dfrac{4}{4} =1\\\\\\\displaystyle \sum_{i=1}^{n+1}\ i^3=(\sum_{i=1}^{n}\ i^3) + (n+1)^3\\\\\\=\dfrac{n^2*(n+1)^2}{4} +(n+1)^3\\\\\\=(n+1)^2*(\frac{n^2}{4} +n+1)\\\\\\=(n+1)^2*\dfrac{n^2+4n+4}{4} \\\\\\=\dfrac{(n+1)^2*(n+2)^2}{4}[/tex]
what is
{Review} 8 x 9 = *
This is a required question
4. {Review} 12 x 4 = *
5. {Review} 7 x 8 = *
6. {Review} 6 x 3 = *
7. {Review} 9 x 5 = *
8. {Review} 6 x 8 = *
9. {Review} 27 ÷ 3 = *
10. {Review} 36 ÷ 6 = *
11. {Review} 132 ÷ 12 = *
12. {Review} 110 ÷ 11 = *
13. {Review} 28 ÷ 4 = *
14. {Review} 35 ÷ 7 = *
15. {Review} 937 + 593 = *
This is a required question
16. {Review} 9,004 - 3,526 = *
17. {Review} 36 x 7 = *
18. {Review} 48 ÷ 4 = *
19. {4.NBT.A.1} __________ x 10 = 300 *
20. {4.NBT.A.1} 3,000 x 10 = __________ *
21. {4.NBT.A.1} Which numbers make this equation true? __________ x 10 =__________ *
300,000 ; 30,000
30,000 ; 300,000
30,000 ; 30,000
22. {4.NBT.A.3} Round 5,389 to the nearest 10. *
23. {4.NBT.A.3} Round 124,389 to the nearest 1,000. *
24. {4.NBT.A.3} Round 2,748,091 to the nearest 100,000. *
25. {4.NBT.A.2} Fill in the blank. 73,458 is ______ 233,101 *
greater than
less than
equal to
26. {4.NBT.A.2} Fill in the blank. 57,388 is ______ 75,388 *
greater than
less than
equal to
27. {4.NBT.A.2} Fill in the blank. 1,432,748 is ______ 1,432,478 *
greater than
less than
equal to
28. {4.NBT.A.2} Write the number three hundred forty-two thousand, five hundred seven in expanded form. *
300,000 + 40,000 + 2,000 + 500 + 7
300,000 + 4,000 + 200+ 500 + 7
30,000 + 4,000 + 2,000 + 500 + 7
29. {4.NBT.A.2} Write the number three hundred forty-two thousand, five hundred seven in standard form. *
Answer:
8 x 9 = 72
4. 48
5. 56
6. 18
7. 45
8. 48
9. 9
10. 6
11. 11
12. 10
13. 7
14. 5
15. 1530
16. 5478
17. 252
18. 8
19. 30
20. 30,000
21. 30,000; 300,000
22. 5,390
23. 124,000
24. 2,700,000
25. less than
26. less than
27. greater than
28. 300,000 + 40,000 + 2,000 + 500 + 7
29. 342,507
Step-by-step explanation:
For the rounding numbers, if the hundredth or tenth place is not 5 or more the number does not change.
Write 7 hundred as a decimal
Answer:
Step-by-step explanation:
7/100 as a decimal is 0.07.
Answer:
7.00
Step-by-step explanation:
To get a decimal, you move the decimal point to the left twice. If you move the decimal point two times to the left on 700, you would get 7.00.
Let x = 0.99999....Do you think that x < 1 or x = 1?
Answer:
x<1
Step-by-step explanation:
why? because is still 0....
Britney bought 2 apples, 5 bananas, and 8 oranges at the grocery store.
Which is the ratio of apples to bananas written as a decimal?
Answer:
2 apples: 5 bananas: 8 oranges
Final answer: 1 apple: 2,5 bananas ( divide by 2 )
Answer:
D.0.8
Step-by-step explanation:
The ratio in mathematics indicates how many times one number contain another. To find this ratio you must make a division of both. numbers. For example the ratio X to Y is X/Y.
As there are 4 apples to 5 bananas, the ratio of apples to bananas is:
4/5=0.8
F(x) = (x-2)(x + 1)
X+1
Which statements describe the end behavior of the graph of the function shown? Check all that apply.
As x,
y1.
As x,y".
As x,y -—-.
As x,y 1.
As x,y.
As x + y -0.
Answer:
the second and the last one
Step-by-step explanation:
answer was revealed on edg after i took quiz
The option (2) As x → ∞, y → ∞, and option (6) As x → –∞, y → –∞ are correct if the function f(x) = (x - 2)(x + 2)/(x + 1).
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function shown in the picture.
f(x) = (x - 2)(x + 2)/(x + 1)
The above function is a fractional function:
The denominator of the function cannot be zero:
x + 1 ≠ 0
x ≠ -1
From the graph of a function:
If x → ∞, y → ∞
If x → –∞, y → –∞
Thus, the option (2) As x → ∞, y → ∞, and option (6) As x → –∞, y → –∞ are correct if the function f(x) = (x - 2)(x + 2)/(x + 1).
Learn more about the function here:
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add 8+5
think of a number path start at 8 add 2 to make 10
Answer:
- Each sum which is larger than 10 can be found by first making a 10. For example, to find 8 + 5, we can write. \begin{align} 8+5 &= 8 + (2+3) \\ &= (8+2) + 3 \\ &= 10 + 3 \\ &= 13
Step-by-step explanation:
Adding 9 to another single digit number can also be done by first making a 10. For example.
- Hope this helped ^^
A recipe calls for 3 cups of pecans for every 5 cups of walnuts. How many cups of pecans should be added to 8 cups of walnuts?
Answer:
4.8
Step-by-step explanation:
3:5
3/5 : 1
8(3/5):1(8)
4.8:8
(25x3) + (10x3) is my question i dont know the answer
Answer:
75+30=105....................
<3 help mi i’m down bad
Sol Levin sold 22 pairs of shoes each day.
Monday through Wednesday, 28 pairs on Thursday,
and 31 on Friday. How many shoes must he sell on
Saturday to average 29 pairs sold for the 6 days
he worked during the week?
Answer:
Sol Levin needs to sell 49 pairs shoes on Saturday.
Step-by-step explanation:
29 x 6 = 174
(22 x 3) + 28 + 31 + x = 174
66 + 28 + 31 + x = 174
94 + 31 + x = 174
125 + x = 174
(125 - 125) + x = (174 - 125)
x = 49
In the coordinate plane, plot AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯ given by the points A(−4, 5), B(−4, 8), C(2, −3), D(2, 0)
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The x-coordinate is the same in each pair of points, so the line segment will be a vertical line segment 3 units long.
Whats the answer for this question
Answer:
m+5
Step-by-step explanation:
4m+5-3m
1m+5
Which expression can be used to find the slope of a line containing the points (–3, 2) and (7, –1)?
A. (Image 092552)
B. (Image 092607)
C. (Image 092618
D. (Image 092630)
Answer:
C. (Image 092618
Step-by-step explanation:
[tex]slope = \frac{y_{2} - y_{1} }{x _{2} - x_{1} } [/tex]
y1 is 2
y2 is -1
x1 is -3
x2 is 7
substitute:
[tex]slope = \frac{ - 1 - 2}{7 - ( - 3)} [/tex]
I need to know the answer to the two question
Answer:
Question 1:
78 - 5 - 7
Question 2:
[tex] - \frac{1}{6} [/tex]
In a football game, what is the probability that one team will tie and lose?
Answer:
1/3
Step-by-step explanation:
In a group 40% like football ,70% like cricket and 30% like both games
Answer:
40%
Step-by-step explanation:
40+30+70=140
180-140= 40
Here is a circle, centre O, and the tangent to the circle at the point (-3, 4) on the circle. У P (-3, 4) X -5 O Oา Find an equation of the tangent at the point P. Give your answer in the form y = ax + b where a and b are both fractions with denominator 4.
Answer:
[tex]y=\frac{3}{4}x+\frac{25}{4}[/tex]
Step-by-step explanation:
when a line is tangent to a circle, it is perpendicular to the line from the center of the circle to the intersection of the line and the circle. so first we are going to find the slope of the line in the circle.
to find the slope use the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{4-0}{-3-0}=\frac{4}{-3}=-\frac{4}{3}[/tex] so the slope is -4/3
the slope of the line perpendicular to this is the opposite reciprocal: 3/4 so now we have y= 3/4 x +b, to find b plug in the point (-3,4) to get 4=-9/4 +b, b=25/4 the equation is y=3/4 x +25/4
What is the solution to the equation below? Round your answer to two decimal places.
4e^2x + 16 = 36
A. X = 3.22
B. x = 0.80
C. x = 1.61
D. x = 1.39
9514 1404 393
Answer:
B. x = 0.80
Step-by-step explanation:
We suspect you want the solution to the exponential equation ...
4e^(2x) +16 = 36
e^(2x) +4 = 9 . . . . . . . . . . . divide by 4 (because we can)
e^(2x) = 5 . . . . . . . . . . . . . . subtract 4
2x = ln(5) . . . . . . . . . . . . . . . take natural logs
x = ln(5)/2 ≈ 0.804719 . . . . .divide by the coefficient of x
x ≈ 0.80
(2x-5)3 =Alguien sabe cual es el resultado de esta operación
Answer:
6x - 15
Step-by-step explanation:
(2x - 5)3
3(2x) - 3(5)
6x - 15
Candice recorded outdoor temperatures as -5°C, 2°C and 1°C. Which of the following correctly compares the three temperatures?
Answer:
2°C
Step-by-step explanation:
outdoor temperature
Explore
Drag the digits 0 to 9 to the boxes to create an original
rectangle and a scaled copy.
2
9
0
8
Answer:
I don’t understand this
Step-by-step explanation:
what is 15 times 7/5 compared to 15 equal?
Answer:
I do not know
Step-by-step explanation:
Answer all questions olve the following logarithmic ec 2 log10 x + log103 = log10 75
[tex]2 log_{10}x + log_{10}(3) = log_{10}(75) [/tex]
Step-by-step explanation:
We can rewrite the left-hand side as
[tex]2\log{x} + \log{3} = \log{3x^2}[/tex]
Here, we used the following properties of logarithms:
[tex]\log{x^a} = a\log{x}[/tex]
[tex]\log{ab} = \log{a} + \log{b}[/tex]
We can then write
[tex] \log{3x^2} = \log{75} \Rightarrow 3x^2 = 75[/tex]
or
[tex]x = 5[/tex]
Subtract. Write your answer in simplest form.
5/- 10/5
Answer:
-1/10
Step-by-step explanation:
(5/(-10))/5 = -(5/10)/5 = 1/10
(Hopefully this helped you out!)
please help Dave drives to work. While driving the car over nine days, he observes his daily average speed and lists it in the table below. Day Average Speed (MPH) 1 45 2 62 3 44 4 70 5 59 6 66 7 54 8 63 9 67 The median speed at which Dave drove to work was __________. 63 miles per hour 59 miles per hour 62 miles per hour 58.89 miles per hour
The median speed at which Dave drove to work was 62 miles per hour.
To find the median speed at which Dave drove to work, we need to arrange the average speeds in ascending order and determine the middle value.
Sorting the average speeds in ascending order:
44, 45, 54, 59, 62, 63, 66, 67, 70
Since we have nine values, the median will be the middle value when the data is arranged in ascending order. In this case, the fifth value, which is 62, represents the median speed at which Dave drove to work.
Dave drove to work at a median speed of 62 miles per hour as a result.
for such more question on median
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Describe a sequence of translations, rotations, and reflections that takes Polygon P to Polygon Q.
Step-by-step explanation:
hope it is helpful for you
2. A doctor treated 2000 patients over a period of time. If he worked for 5 hours a day and spent 15 minutes on each patient how many days did the doctor spend to treat all patients?
Answer:
The answer is 6000 days.
Solve the equation. 14 = a – 8
Answer:
[tex]14 = a - 8 \\ \\ - a = - 8 - 14 \\ \\ - a = - 22 \\ \\ a = 22[/tex]
Jimmy's dog weighed 60 pounds 4 months ago. Since then his weight has increased by 6% How much does Jimmy's dog weigh now
Answer: 3.6
Step-by-step explanation:
Answer:
63.6 pounds
Step-by-step explanation:
Jimmy's dog's weight was 60 pounds 4 months ago and now it is weighing 6% heavier.
So 6% of 60 is
[tex]\frac{x}{60} *100=6[/tex]
x=360/100
x=3.6
So Jimmy's dog weighs 60+3.6=63.6 pounds
what are the coefficients of the equation y=x^2+5x+6
Answer:
1, 5
Step-by-step explanation:
a numerical or constant quantity placed before and the variable in an algebraic expression (e.g. 4 in 4x y).
Answer: 1 and 5
Step-by-step explanation: