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sladkih [1.3K]
3 years ago
5

A pencil and ruler cost $1.50 together. The ruler costs $1.00 more than the pencil. How much does the pencil cost.

Mathematics
2 answers:
Anastasy [175]3 years ago
8 0
The pencil costs 50c
Nina [5.8K]3 years ago
5 0
The pencil costs 50 p and the ruler costs £1
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98 = x + 55 what is it????
strojnjashka [21]

Answer:

x = 43

Step-by-step explanation:

x = 98 - 55

<u>x = 43</u>

3 0
3 years ago
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What is the sum of the first 51 consecutive odd positive integers?
Angelina_Jolie [31]
We call:

a_{n} as the set of <span>the first 51 consecutive odd positive integers, so:

</span>a_{n} = \{1, 3, 5, 7, 9...\}

Where:
a_{1} = 1
a_{2} = 3
a_{3} = 5
a_{4} = 7
a_{5} = 9
<span>and so on.

In mathematics, a sequence of numbers, such that the difference between two consecutive terms is constant, is called Arithmetic Progression, so:

3-1 = 2
5-3 = 2
7-5 = 2
9-7 = 2 and so on.

Then, the common difference is 2, thus:

</span>a_{n} = \{ a_{1} , a_{1} + d, a_{1} + d + d,..., a_{1} + (n-2)d+d\}
<span>
Then:

</span>a_{n} = a_{1} + (n-1)d
<span>
So, we need to find the sum of the members of the finite series, which is called arithmetic series:

There is a formula for arithmetic series, namely:

</span>S_{k} = ( \frac{a_{1} +  a_{k}}{2}  ).k
<span>
Therefore, we need to find:
</span>a_{k} =  a_{51}  

Given that a_{1} = 1, then:

a_{n} = a_{1} + (n-1)d = 1 + (n-1)(2) = 2n-1

Thus:
a_{k} = a_{51} = 2(51)-1 = 101

Lastly:

S_{51} = ( \frac{1 + 101}{2} ).51 = 2601 

4 0
3 years ago
PLS HELP ME AND SHOW WORK.
Alex17521 [72]

Answer:

4 = (x  + 7 {)}^{2}  + (y  -  3 {)}^{2}

Step-by-step explanation:

equation of a circle

{r}^{2}  = (x -  {h} )^{2}  + (y -  {k)}^{2}

we know the center is (-7, 3)

the radius is 2

we replace (h,k) with the center coordinates

and input the radius

{2}^{2}  = (x -( - 7)) ^{2}  + (y  -  3)^{2}

simplify to this:

4 = (x  + 7 {)}^{2}  + (y  -  3 {)}^{2}

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3 years ago
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Alexandra [31]

Answer:

x=2x,3x,5x

Step-by-step explanation:

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2 years ago
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Gre4nikov [31]

Answer:1.5g

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