Rewrite the expression -2a(a+b-5)+3(-5a+2b)+b(6a+b-8)

Answers

Answer 1
Answer: First, think of it as 3 different expressions.Go through them one at a time. There is:
-2a(a+b-5)                    ]            +3(-5a+2b)          ]        +b(6a+b-8)
Multiply everything out.] Multiply everything out.  ]Multiply everything out
-2a x a = -2a²               ] +3 x -5a = -15a               ] +b x 6a = 6ab 
-2a x b = -2ab              ] +3 x 2b = 6b                    ] +b x b = b²
-2a x -5 = 10a              ] -15a + 2b = -15a+2b       ] +b x -8 = -8b                  -2a² + -2ab + 10a =  ]                                         ] 6ab + b² + -8b =
-2a²+-2ab+10a            ]                                         ] 6ab+b²+-8b
Now add everything up, but before that, remember these algebraic rules:
∞A.S.S. Add Same Signs, meaning positive add positive or negative add negative equals a positive number or 0. E.g 1+1=1 and -1+-2= 1
∞S.I.D. Subtract If Different, meaning a positive number add a negative number always equals a negative number or 0. E.g 1 + -2 = -1
∞You can only add up "similar terms", meaning you can add 'terms' ending in 'a' for example with another 'term' ending in 'a'. However. you cannot add a term ending in 'a' to an 'ab' or an 'a²'.
Following these rules, -2a²+-2ab+10a+-15a+2b+6ab+b²+-8b = 
4ab-5a-6b+b²-2a²

Hope that helps you and that it wasn't too tricky to understand. :)

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John, Sally, and Natalie would all like to save some money. John decides that itwould be best to save money in a jar in his closet every single month. He decides
to start with $300, and then save $100 each month. Sally has $6000 and decides
to put her money in the bank in an account that has a 7% interest rate that is
compounded annually. Natalie has $5000 and decides to put her money in the
bank in an account that has a 10% interest rate that is compounded continuously.


How much money have after 2 years?

How much money will sally have in 10 years?

What type of exponential model is Natalie’s situation?

Write the model equation for Natalie’s situation

How much money will Natalie have after 2 years?

How much money will Natalie have after 10 years

Answers

Answer:

Part 1) John’s situation is modeled by a linear equation (see the explanation)

Part 2)  y=100x+300

Part 3) \$12,300

Part 4) \$2,700

Part 5) Is a exponential growth function

Part 6) A=6,000(1.07)^(t)

Part 7) \$11,802.91

Part 8)  \$6,869.40

Part 9) Is a exponential growth function

Part 10) A=5,000(e)^(0.10t)    or  A=5,000(1.1052)^(t)

Part 11)  \$13,591.41

Part 12) \$6,107.01

Part 13)  Natalie has the most money after 10 years

Part 14)  Sally has the most money after 2 years

Step-by-step explanation:

Part 1) What type of equation models John’s situation?

Let

y ----> the total money saved in a jar

x ---> the time in months

The linear equation in slope intercept form

y=mx+b

The slope is equal to

m=\$100\ per\ month

The y-intercept or initial value is

b=\$300

so

y=100x+300

therefore

John’s situation is modeled by a linear equation

Part 2) Write the model equation for John’s situation

see part 1)

Part 3) How much money will John have after 10 years?

Remember that

1 year is equal to 12 months

so

10\ years=10(12)=120 months

For x=120 months

substitute in the linear equation

y=100(120)+300=\$12,300

Part 4) How much money will John have after 2 years?

Remember that

1 year is equal to 12 months

so

2\  years=2(12)=24\ months

For x=24 months

substitute in the linear equation

y=100(24)+300=\$2,700

Part 5) What type of exponential model is Sally’s situation?

we know that    

The compound interest formula is equal to  

A=P(1+(r)/(n))^(nt) 

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

P=\$6,000\n r=7\%=0.07\nn=1

substitute in the formula above

A=6,000(1+(0.07)/(1))^(1*t)\n  A=6,000(1.07)^(t)

therefore

Is a exponential growth function

Part 6) Write the model equation for Sally’s situation

see the Part 5)

Part 7) How much money will Sally have after 10 years?

For t=10 years

substitute  the value of t in the exponential growth function

A=6,000(1.07)^(10)=\$11,802.91 

Part 8) How much money will Sally have after 2 years?

For t=2 years

substitute  the value of t in the exponential growth function

A=6,000(1.07)^(2)=\$6,869.40

Part 9) What type of exponential model is Natalie’s situation?

we know that

The formula to calculate continuously compounded interest is equal to

A=P(e)^(rt) 

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

P=\$5,000\nr=10\%=0.10

substitute in the formula above

A=5,000(e)^(0.10t)

Applying property of exponents

A=5,000(1.1052)^(t)

 therefore

Is a exponential growth function

Part 10) Write the model equation for Natalie’s situation

A=5,000(e)^(0.10t)    or  A=5,000(1.1052)^(t)

see Part 9)

Part 11) How much money will Natalie have after 10 years?

For t=10 years

substitute

A=5,000(e)^(0.10*10)=\$13,591.41

Part 12) How much money will Natalie have after 2 years?

For t=2 years

substitute

A=5,000(e)^(0.10*2)=\$6,107.01

Part 13) Who will have the most money after 10 years?

Compare the final investment after 10 years of John, Sally, and Natalie

Natalie has the most money after 10 years

Part 14) Who will have the most money after 2 years?

Compare the final investment after 2 years of John, Sally, and Natalie

Sally has the most money after 2 years

Find the area of a parallelogram with base B and height H b = 87 cm

h = 18.6 cm

Answers

area =hb
h=18.6
b=87
area=(18.6)(87)
a=1618.2 cm^2

The area would be 1618.2 cm. I think I am not positive.

Ben, Cam, and Justin are lumberjacks. The number of trees they chop down is given by b+2c+3j, where b is the number of hours Ben spends chopping, c is the number of hours Cam spends chopping, and j is the number of hours Justin spends chopping. How many trees do they chop down after Ben spends 8 hours chopping, Cam spends 3 hours chopping, and Justin spends 4 hours chopping?

Answers

Answer: There are 26 trees which they chop down .

Explanation:

Since we have given that

the number of trees they chop down is given by

b+2c+3j

Where 'b' denotes number of hours Ben spends chopping,

'c' denotes number of hours Cam spends chopping,

'j' denotes number of hours Justin spends chopping.

Now, we have also given that,

Number of hours Ben spends chopping = 8

Number of hours Cam spends chopping = 3

Number of hours Justin spends chopping = 4

Now, we put the value of all these variable in the above expression ,we'll get

8+2* 3+3* 4=8+6+12=26

Hence, there are 26 trees which they chop down .

Substitute the values into the equation...
b = 8 so 8+2c+3j
c = 3 if 8+2(3)+3j or 8+6+3j
j = 4 8+6+3(4) or 8+6+12
Add this all together and you get...
26 trees

Which is bigger 5200ft 145in or 1mi 40in

Answers

5200ft 145in is less than 1mi 40in because 1mi 40in is equal to 5283.33 ft 

suzy had 10L of water. She wanted to pour an equal amount of water into 5 thermoses. How many liters did she pour into each thermos?

Answers

Divide 10 by 5.

10/5=2

2 liters per thermus.
Agreed. 10 divided by 5 is equally 2. 2 litres per thermos.

Tell me a number that is greater than 832,458 but less than 832,500

Answers

the answer is 832,459
Well, first we have to see how many numbers can go in-between those numbers.
So 832,458 - 832,500 = 42

So 42 numbers can go in-between that number here is all of them:

832,459
832,460
832,461
832,462
832,463
832,464
832,465
832,466
832,467
832,468
832,469
832,470
832,471
832,472
832,473
832,474
832,475
832,476
832,477
832,478
832,479
832,480
832,481
832,482
832,483
832,484
832,485
832,486
832,487
832,488
832,489
832,491
832,492
832,493
832,494
832,495
832,496
832,497
832,498
832,499

Hope I Helped You!!!