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3 years ago

Am I correct please let me know I need to know if wrong what is the correct answer ?? ASAP please

Mathematics

1 answer:

Oxana [17]3 years ago

7 0

Vertical asymptotes are vertical dotted line

that is x=2

horizontal asymptotes are horizontal dotted line

that is y=1

so,

option-C.......Answer

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If y varies directly with x, and y= 10 when x = 4, find y when x = 10.

mixer [17]

Answer:

Step-by-step explanation:

6 0

2 years ago

How many terms of the arithmetic sequence {1,22,43,64,85,…} will give a sum of 2332? Show all steps including the formulas used

MA_775_DIABLO [31]

There's a slight problem with your question, but we'll get to that...

Consecutive terms of the sequence are separated by a fixed difference of 21 (22 = 1 + 21, 43 = 22 + 21, 64 = 43 + 21, and so on), so the n-th term of the sequence, a (n), is given recursively by

• a (1) = 1

• a (n) = a (n - 1) + 21 … … … for n > 1

We can find the explicit rule for the sequence by iterative substitution:

a (2) = a (1) + 21

a (3) = a (2) + 21 = (a (1) + 21) + 21 = a (1) + 2×21

a (4) = a (3) + 21 = (a (1) + 2×21) + 21 = a (1) + 3×21

and so on, with the general pattern

a (n) = a (1) + 21 (n - 1) = 21n - 20

Now, we're told that the sum of some number N of terms in this sequence is 2332. In other words, the N-th partial sum of the sequence is

a (1) + a (2) + a (3) + … + a (N - 1) + a (N) = 2332

or more compactly,

$\displaystyle\sum_{n=1}^N a(n) = 2332$

It's important to note that N must be some positive integer.

Replace a (n) by the explicit rule:

$\displaystyle\sum_{n=1}^N (21n-20) = 2332$

Expand the sum on the left as

$\displaystyle 21 \sum_{n=1}^N n-20\sum_{n=1}^N1 = 2332$

and recall the formulas,

$\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n$

$\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2$

So the sum of the first N terms of a (n) is such that

21 × N (N + 1)/2 - 20N = 2332

Solve for N :

21 (N ² + N) - 40N = 4664

21 N ² - 19 N - 4664 = 0

Now for the problem I mentioned at the start: this polynomial has no rational roots, and instead

N = (19 ± √392,137)/42 ≈ -14.45 or 15.36

so there is no positive integer N for which the first N terms of the sum add up to 2332.

4 0

2 years ago

Please help me with number 7

Wittaler [7]

"twelve decreased by twice a number" ---> 12 - 2x

"8 times the sum of number and 4" ---> 8(x + 4)

12 - 2x = 8(x + 4)

12 - 2x = 8x + 32 (distributive property)

12 = 10x + 32 (add 2x to both sides)

-20 = 10x (subtract 32 from both sides)

x = -2 (divide both sides by 10)

That's answer.

4 0

3 years ago

A lotion is made from an oil blend costing $1.50 per ounce and glycerin costing $1.00 per ounce. Four ounces of lotion costs $5.

vovikov84 [41]

Answer:

A=(4-g) 1.5

Step-by-step explanation:

Let g be the amount of glycerin in the lotion. We know that there are 4 ounces total of lotion; this means that there are 4-g ounces of the oil blend.

The oil blend costs $1.50 per ounce; this gives us the expression (4-g)1.5 for the oil blend.

8 0

3 years ago

Read 2 more answers

Solve for b. 4b-3b+7= 10

Morgarella [4.7K]

b = 3

Step-by-step explanation:

$4b - 3b + 7 = 10$