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OLga [1]
3 years ago
11

Find the sum of integers from 33 to 47:

Mathematics
2 answers:
ICE Princess25 [194]3 years ago
8 0

Answer:

Step-by-step explanation:There are formulas to work this out, but you can also suss out an answer by a liberal application of critical thinking.

Okay, you want to add 51 + 52 + 53 + … + 99 + 100, right? (The … represents all the numbers in between, in case you were wondering.)

Well, that’s a total of 50 numbers. And if you know anything about addition, you know that it doesn’t matter what order you add them.

So you could also say 51 + 100 + 52 + 99 + 53 + 98 + … and so on.

Let’s see what happens. 51 + 100 = 151. So far so good.

Then, 52 + 99 also equals 151. And 53 + 98 also equals 151. Since there are 50 numbers, that’s 25 pairs that are going to add up to 151.

151 + 151 + 151 + 151 + … (21 more instances of 151).

So we can simplify our workload a bit. Instead of adding up all the numbers by hand, we can just multiply 151 by 25.

151 x 25 = 3775

From that, we can work out a generic formula that will allow you to add any sequence of numbers…without actually adding.

Let a be the first number in the sequence, and let n be the last number in the sequence. The number of numbers is (n - a) + 1. (You have to add 1, because if you just subtract, it’s like you’re losing the lowest number in the sequence).

So…you get the sum by adding the first and last number in the sequence, and then multiplying that result by half of the total number of numbers.

(a+n)((n−a)+12)  

an−a2+a+n2−an+n2  

−a2+a+n2+n2  

−a(a−1)+n(n+1)2  

Let’s check to see if it works!

−51(51–1)+100(100+1)2  

−51(50)+100(101)2  

−2550+10,1002  

75502  

3775  

Note that if the starting number were 1, the formula would simplify to  n(n+1)2

defon3 years ago
4 0

Answer:

600

Step-by-step explanation:

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What is the first step in simplifying the following expression: 2 + 3(4 + 5×2) − 8 + 3^2
ch4aika [34]

Answer:

5 x 2 inside the parenthesis

Step-by-step explanation:

We need an order of operations to ensure we always arrive at the correct answer. It gives us a consistent way to work with numbers. We use the mnemonic device like PEMDAS to remember the correct order.

P-parenthesis

E-exponents

M-multiplication

D-division

A-add

S-subtract.

We apply them left to right doing inner operations before outer operations.

There fore our first step is in the parenthesis and multiplication because it is the inner most operations. 5 x 2 inside the parenthesis.

4 0
3 years ago
A home is to be built on a 56 foot 9 inch wide lot. The house is 5 feet 5 inches from the side of the lot and is 34 feet 10 inch
daser333 [38]
<span>Total lot - house -other side
=(56 ft 9 in) - (34 ft 10 in) - (5 ft 5 in)
=(55 ft 21 in) - (34 ft 10 in) - (5 ft 5 in)
=16 ft 6 in
Convert to inches: </span>16 ft x 12 in/ft)+ 6 in= Total in inches<span>192 in + 6 in= Total in inches
198 in= Total in inches 
Check: One side + house + other side = Lot width
(5 ft 5 in)+(34 ft 10 in)+(16 ft 6 in)=Lot width
56 ft 9 in=Lot width, which equals the given.</span>
8 0
2 years ago
If tan theta =3, find the value of tan theta + tan (theta+pi) + tan (theta +2pi)
sweet-ann [11.9K]

Answer:

tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 9

Step-by-step explanation:

Given

tan\theta = 3

Required

Find

tan\theta + tan(\theta + \pi) + tan(\theta+2\pi)

Calculate tan(\theta + \pi) \ and\ tan(\theta+2\pi)

Using tan rule

tan(\theta + \pi)  = \frac{tan\theta + tan\pi}{1 - tan\theta tan\pi}

So:

tan(\theta + \pi)  = \frac{tan\theta + 0}{1 - tan\theta *0}

tan(\theta + \pi)  = \frac{tan\theta}{1 }

tan(\theta + \pi)  = \tan\theta

tan(\theta+2\pi)

tan(\theta + 2\pi)  = \frac{tan\theta + tan2\pi}{1 - tan\theta tan2\pi}

tan(\theta + 2\pi)  = \frac{tan\theta + 0}{1 - tan\theta *0}

tan(\theta + 2\pi)  = \tan\theta'

'So:

tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = tan\theta +tan\theta +tan\theta

tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 3+3+3

tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 9

4 0
2 years ago
Solve the quadratic equation.<br> 2x2 + 35 = 17x
atroni [7]
Get it to equal 0

minus 17x from both sides

2x²-17x+35=0

tricky part
get something like
(2x-a)(x-b)
we know the signs  are negative since the middle term is negative and last term is positive

so a and b are either 1 and 35 or 5 and 7

(2x-1)(x-35), nope
(2x-35)(x-1) nope
(2x-5)(x-7), nope
(2x-7)(x-5), yep

(2x-7)(x-5)=0
set to zero
2x-7=0
2x=7
x=7/2

x-5=0
x=5


x=7/2 and 5
8 0
2 years ago
The table shows the price for different numbers of chocolate boxes: Number of Chocolate Boxes Price (in dollars) 2 10 3 15 4 20
galina1969 [7]
To know if they are proportional check to see if there is a number common to the relationship between the y and x to all the numbers:
10/2=5
15/3=5
20/4=5
25/5=5
There is a relationship of 5 and the 5 is multiplied to the x=boxes.

Yes, because the price is 5 times the number of boxes
8 0
3 years ago
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