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belka [17]
3 years ago
11

If the 10th of the 10 consecutive numbers is 10, what is their sum?

Mathematics
1 answer:
liq [111]3 years ago
7 0
Represent these consecutive numbers (assuming that they are all integers):

x
x+1
x+2
x+3
x+4
x+5
and so on
x+8
x+9 is the tenth number.  x+9 = 10, so x = 9.

Think of it this way:  there are 10 consecutive numbers, and the last one is 10.

Working backwards, we get the sequence 10, 9, ... 3, 2, 1.

The sum of such an arith sequence is equal to the count of the numbers times the average of the first and last terms:

sum here = 10(1+10)/2 = 5(11) = 55          (answer)
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Figure ABCD is a parallelogram. What is the value of n?
Zigmanuir [339]

Answer

Find out the what is the value of n.

To prove

By using the parallelogram property .

In parallelogram opposite angels are congruent .

As shown in the figure .

∠B = ∠ D

As given

∠B = (2n + 32)°

∠D = (4n - 2)°

(2n + 32) =  (4n - 2)

solving the above

4n -2n = 32 +2

2n = 34

n = \frac{34}{2}

n = 17

Therefore the value of n is 17 .


5 0
3 years ago
Read 2 more answers
A rectangle has a length that is three feet more than twice it’s width. If the area of the rectangle is 90 square feet, then alg
Mkey [24]

Answer:

Length=27feet\\Width=12 feet

Step-by-step explanation:

Let, the length of the rectangle be 'L'

and, width of the rectangle be 'W'

length=2*Width+3

L=(2W+3) feet\\\\

Area of the rectangle= 90 square feet

Area of a rectangle = Length*Width

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Using Factorization Method to solve quadratic equation:

2W^2-12W+15W-90=0

Taking common from the equation:

2W(W-12)+15(W-12)=90\\\\(W-12)(2W+15)=0\\\\W-12=0\\\\W=12 feet

OR

2W+15=0\\\\2W=-15\\\\W=-7.5 feet

The Width cannot be negative, therefore Width(W)=12 feet

Length=2*Width+3\\\\=(12*2)+3\\\\=24+3\\\\=27 feet

Length=27feet\\Width=12 feet

3 0
3 years ago
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8 0
3 years ago
What is the solution to the equation below?
Ghella [55]

Answer:

x= 4

Step-by-step explanation:

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\sqrt{2x} = 2\sqrt{x-2}          

(\sqrt{2x}  )^{2}  = (2\sqrt{x-2})^2      [ square both sides ]

2x = 4(x-2)  

2x=4x-8

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6 0
2 years ago
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What is the perimeter of rhombus STAR
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Answer:

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Step-by-step explanation:

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