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2 years ago

5a + 7b - 12a + 6c - 13b - 22a + 53c

Mathematics

2 answers:

Reptile [31]2 years ago

8 0

Answer:

-29a - 6b + 59c

Step-by-step explanation:

Combine like terms:

5a + 7b -12a + 6c -13b -22a + 53c

-29a + 7b + 6c - 13b + 53c

-29a + 7b + 6c - 13b + 53c

-29a -6b + 6c + 53c

-29a - 6b + 6c + 53c

-29a - 6b + 59c

Solution: -29a - 6b + 59c

Brainliest please! Visit my church's website at fbcinterlaken.org to learn more about God! It would mean a lot! Thank you and have a nice day! :)

Orlov [11]2 years ago

4 0

Answer:

-29a-6b+59c

Step-by-step explanation:

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The half-life of Carbon-14 is 5730 years. Suppose a fossil is found with 50% of Carbon-14 as compared to a living sample. How ol

melisa1 [442]

The answer is C. Because it takes 5730 years for half of a sample of carbon-14 atoms to decay. It says that 50% of the carbon atoms have decayed so that means that 5730 years have elapsed for that fossil.

I hope that helps.

4 0

2 years ago

Julian walked 6/10 of a mile to his friends house and another 35/100 mile to the store. He walked 1/4 of a mile back home. Julia

AveGali [126]

The statement, "Julian's sister said he walked 1/5 mile" cannot be agreed because Julian totally walked $1\frac{1}{5} \text{ or } \frac{6}{5}$ miles.

<u>Solution:</u>

Given that,

Julian walked 6/10 of a mile to his friends house
Another 35/100 mile to the store
He walked 1/4 of a mile back home

To find total distance walked by Julian we have to add the above stated values. That is, $\frac{6}{10} +\frac{35}{100} +\frac{1}{4}$

Factors of 10 = $5\times2$

Factors of 100 = $5\times2\times5\times2$

Factors of 4 = $2\times2$

Therefore, the least common factor of 10, 100 and 4 is 100. With like denominators we can operate on just the numerators,

$\frac{6\times10}{10\times10} +\frac{35\times1}{100\times1} +\frac{1\times25}{4\times1}\rightarrow\frac{60+35+25}{100}\rightarrow\frac{120}{100}$

$\Rightarrow\frac{120}{100}\rightarrow\frac{6}{5}$

Which can also be written as $1\frac{1}{5}$ .

So, from the above calculation it can be said that Julian walked $1\frac{1}{5} \text{ miles }$ .

3 0

2 years ago

John, Sally, and Natalie would all like to save some money. John decides that it

brilliants [131]

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

$b=\$300$

$y=100x+300$

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

$10\ years=10(12)=120 months$

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

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

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

$A=P(1+\frac{r}{n})^{nt}$

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

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

substitute in the formula above

$A=6,000(1+\frac{0.07}{1})^{1*t}\\ A=6,000(1.07)^{t}$

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

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

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

3 0

3 years ago

Lines d, e, and f are parallel. That means they have the same slope. Each of these lines has a slope of −3. Enter numbers to com

Sloan [31]

Answer:

Line d : y = -3x - 3

Line e : y = -3x - 2

Line f : y= -3x + 2

Step-by-step explanation:

Given that,

The slope of each line is -3.

Now,

We know that,

Equation of line is represented by y = mx + c

where m is the slope and c is the y-intercept.

Now,

Given that,

Line d goes through (0, - 3) and (- 1, 0).

So,

y-intercept of Line d is -3

∴ we get

Equation of Line d is : y = -3x -3

Now,

Given that,

Line e goes through (-1, 2) and (0, -2).

So,

y-intercept of Line e is -2

∴ we get

Equation of Line e is : y = -3x - 2

Now,

Given that,

Line f goes through (0, 2) and (1, -1).

So,

y-intercept of Line e is 2

∴ we get

Equation of Line f is : y = -3x + 2

6 0

2 years ago

1573-(640+30)+907 operaciones combinadas

igor_vitrenko [27]

Answer:

1810

640+30=670

1573-680=903

903+907=1810

6 0

2 years ago