Solve Mathematics question, in photo. Please

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Answer 1

Answer: (-2,3) if you just plug in X and y you get both -4 and 12

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A certain type of bacteria doubles every 8 hours. A culture begins with 30 000. Without use of given equation, use the help of your ability to set up a pattern to determine how many bacteria are there after a) 8 hours b) 16 hours c)d days

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Not sure what you mean by "without use of given equation".
At time 0hrs, there is 30 000.
Since it doubles every 8hrs, at time 8hrs there is 60 000 or 30 000 x 2
In another 8hrs, it will double again, so at time 16hrs, it will be 120 000 or 30 000 x 2 x 2
In another 8hrs, double again, so at time 24hrs, it will be 240 000 or 30 000 x 2 x 2 x 2
This is also 30 000 x 8 as 2x2x2=8. I'll come back to this later.

You add an extra x 2 for each 8 hrs. By the end of the 2nd day, it would be
30 000 x2 x2 x2 x2 x2 x2
This is also
30 000 x8 x8
Every day we add an extra x8
We use powers to specify this.
30 000 x 8^d
So after 4 days
30 000 x 8^4 = 30 000 x8 x8 x8 x8
Note that this is NOT the same as 30 000 x 8 x 4

Cameron opens a checking account and a savings account at his local bank. He deposits $10,000 into his checking account and $2,000 into his savings account. He will withdraw $1,200 from his checking account each year. His savings account earns 8% interest each year. In how many years will both accounts have the same balance?

Answers

The correct answer is:
5.9 years.

Explanation:
Let x be the number of years. For the checking account, our expression would be 10000-1200x, since he withdraws $1200 from his account each year, and he begins with $10,000.

The formula for simple interest is:
I=prt
where:
p is the principal, r is the rate and t is the time

using our information, we have
p=2000,
r=8%=8/100=0.08, and
t=x.

This gives us 2000(0.08)(x).
However, we must add the $2000 to this (interest is added on to the principal); this gives us:
2000+2000(0.08)(x).

Setting these two equal, we have:
10000-1200x = 2000+2000(0.08)(x).

Simplifying the right hand side, we have:
10000-1200x=2000+160x.

Add 1200x to both sides:
10000-1200x+1200x=2000+160x+2000x;
10000=2000+1360x.

Subtract 2000 from both sides:
10000-2000=2000+1360x-2000;
8000=1360x.

Divide both sides by 1360:
$(8000)/(1360) = (1360x)/(1360)$ ;
5.9=x.

Let x be the number of needed years.

1. He deposits $10,000 into his checking account and he will withdraw $1,200 from his checking account each year. Then after x years he will have $10,000-$1,200x in his checking account.

2. He deposits $2,000 into his savings account and his savings account earns 8% interest each year, then after x years he will have $\$2,000\cdot (1.08)^x.$

3. Equate these amounts of money:

$10,000-1,200x=2,000\cdot (1.08)^x.$

4. Solve this equation:

divide the equation by 400:

$25-3x=5\cdot (1.08)^x;$

plot graphs of the function $y=25-3x$ and $y=5\cdot (1.08)^x$ (see attached diagram);
find the common point of these two graphs: (6.663,5.01).

Conclusion: he needs nearly 6.663 years.

A woman making $1500 per month has her salary reduced by 10% because of sluggish sales. One year later, after a dramatic improvement in sales, she is given a 30% raise over her reduced salary. Find her salary after the raise.What percent change is this from the $1500 per month?

Answers

Answer:

after the raise, her salary is $1755 per month
this is a +17% change from her original salary

Step-by-step explanation:

The multiplier of her original salary to her reduced salary is ...

(1 - 10%) = 0.90

The multiplier of her reduced salary after her raise is ...

(1 +30%) = 1.30

The multiplier of her raised salary from her original salary is ...

(0.90)(1.30) = 1.17 = (1 +17%)

Her salary after the 17% raise is ...

1.17·1500/mo = $1755/mo

Answer:

17 %

Step-by-step explanation:

new salary=1500(0.9)(1.3) =1755 $

increase=1755-1500=255 $

% increase=(255/1500)×100=17

The coordinates A(5,-2), B(3,-1)C(-4,-4)D(-3,8), E(-1,4) form the vertices of a polygon when they are connected in order from A through E. Classify the polygon without plotting the points. Explain your answer

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Pentagon.
There are 5 points in this polygons, so that means 5 sides as well. The only polygons that have five points or five sides are pentagons.

Hope this helps :)

What is the domain of the relation? {(−4.5, 0), (−3, 9), (0.9, 0), (4, −7.8), (4, 0), (17, 3)} {0.9, 4, 17}

{−7.8, 0, 3, 9}

{−4.5, −3, 0.9, 4, 17}

{−4.5, −3}

Answers

Answer:

Domain of the relation is Option (c) : {−4.5, −3, 0.9, 4, 17}

A new pencil weighs 25 grams. After the pencil has been used for a while, it weighs 2 decagrams. How many grams of the pencil have been used up

Answers

5 grams of the pencil have been used up.

5 grams have been used up.

2 decagrams = 20 grams

You originated with 25.

25 - 5 = 20

Therefore the answer is 5 grams.

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