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2 years ago

Y - 8 = -10 How do I verify the solution ?

Mathematics

1 answer:

prisoha [69]2 years ago

4 0

Answer:

y = -2

Step-by-step explanation:

SOLUTION :-

Solve the equation.

Add 8 to both sides in order to isolate the equation.

$=> y - 8 + 8 = -10 + 8$

$=> y = -2$

∴ y = -2

VERIFICATION :-

To verify the solution of y , just put the solution (y = -2) in place of y in equation and check whether L.H.S = R.H.S.

L.H.S :-

-2 - 8 = -10

R.H.S. :-

-10 (already given)

⇒L.H.S. = R.H.S. (verified)

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Dont really understand how to do this

bija089 [108]

Answers:

$t_{10} = -22 \ \text{ and } S_{10} = -85$

========================================================

Explanation:

$t_1 = \text{first term} = 5\\t_2 = \text{first term}-3 = t_1 - 3 = 5-3 = 2$

Note we subtract 3 off the previous term (t1) to get the next term (t2). Each new successive term is found this way

$t_3 = t_2 - 3 = 2-3 = -1\\t_4 = t_3 - 3 = -1-3 = -4$

and so on. This process may take a while to reach $t_{10}$

There's a shortcut. The nth term of any arithmetic sequence is

$t_n = t_1+d(n-1)$

We plug in $t_1 = 5 \text{ and } d = -3$ and simplify

$t_n = t_1+d(n-1)\\t_n = 5+(-3)(n-1)\\t_n = 5-3n+3\\t_n = -3n+8$

Then we can plug in various positive whole numbers for n to find the corresponding $t_n$ value. For example, plug in n = 2

$t_n = -3n+8\\t_2 = -3*2+8\\t_2 = -6+8\\t_2 = 2$

which matches with the second term we found earlier. And,

$tn = -3n+8\\t_{10} = -3*10+8\\t_{10} = -30+8\\t_{10} = \boldsymbol{-22} \ \textbf{ is the tenth term}$

---------------------

The notation $S_{10}$ refers to the sum of the first ten terms $t_1, t_2, \ldots, t_9, t_{10}$

We could use either the long way or the shortcut above to find all $t_1$ through $t_{10}$ . Then add those values up. Or we can take this shortcut below.

$Sn = \text{sum of the first n terms of an arithmetic sequence}\\S_n = (n/2)*(t_1+t_n)\\S_{10} = (10/2)*(t_1+t_{10})\\S_{10} = (10/2)*(5-22)\\S_{10} = 5*(-17)\\\boldsymbol{S_{10} = -85}$

The sum of the first ten terms is -85

-----------------------

As a check for $S_{10}$ , here are the first ten terms:

t1 = 5
t2 = 2
t3 = -1
t4 = -4
t5 = -7
t6 = -10
t7 = -13
t8 = -16
t9 = -19
t10 = -22

Then adding said terms gets us...

5 + 2 + (-1) + (-4) + (-7) + (-10) + (-13) + (-16) + (-19) + (-22) = -85

This confirms that $S_{10} = -85$ is correct.

6 0

2 years ago

Calculate 50% of 200

OlgaM077 [116]

Answer:

100

Step-by-step explanation:

hopes this helps

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2 years ago

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Elijah brought a total of 16 pounds of peanuts and cashew nuts and paid $49.50 if peanuts cost $2.75 per pound and cashews nuts

maria [59]

Answer:

The number of pounds of cashew is 11

Step-by-step explanation:

Let P represent the peanut

Let C represent the cashew nut.

From question, we were told that Elijah brought a total of 16 pounds of peanuts and cashew nuts. This can be written as:

P + C = 16 (1)

The total cost = $49.50

Cost per peanut = $2.75

Cost per cashew = $3.25

The above can be represented as:

49.50 = 2.75P + 3.25C. (2)

From equation 1,

P + C = 16

P = 16 — C

Substitute the value of P into equation 2:

49.50 = 2.75P + 3.25C.

49.50 = 2.75(16 — C) + 3.25C

49.50 = 44 — 2.75C + 3.25C

49.50 = 44 + 0.5C

Collect like terms

49.50 — 44 = 0.5C

5.5 = 0.5C

Divide both side by 0.5

C = 5.5/0.5

C = 11

Therefore, the number of pounds of cashew is 11

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Which table shows a decreasing linear relationship?

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Table C since it is decreasing at a constant rate of 5.
55 - 5 = 50
50 - 5 = 45
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