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3 years ago

What about linear equations

Mathematics

1 answer:

Charra [1.4K]3 years ago

5 0

Answer:

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

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Mike and Beth both write the decimal 0.8 (0.88888...)as a fraction. Mike: 45 Beth: 89 Which student wrote the correct fraction?

fenix001 [56]

Answer:

see the explanation

Step-by-step explanation:

we have

0.888...

This is a <u>repeating decimal</u> (Is a decimal that has a digit, or a block of digits, that repeat over and over and over again without ever ending)

Convert to fraction number

Let

x=0.888...

10x=8.888...

Subtract 0.888... from 8.888... to remove the decimal

10x-x=8.888...-0.888...

9x=8

Solve for x

x=8/9

therefore

Mike fraction is incorrect

because 4/5=0.8

0.8 is a <u>terminating decimal </u>(It's a decimal with a finite number of digits)

Mike's mistake was considering the number as a terminating decimal instead of a repeating decimal

Beth is correct

because

If you divide 8/9

the result is 0.8888888...

3 0

2 years ago

Combine the rational expressions into a single fraction and reduce it in the lowest terms.

Lostsunrise [7]

Answer:

13. -3 14. (x+1)(2x-7) / (x-6)(x+3)

Step-by-step explanation:

5 0

3 years ago

A coordinator will select 6 songs from a list of 9 songs to compose an event's musical entertainment lineup. How many different

g100num [7]

Answer:

84 different lineups are possible

Step-by-step explanation:

The order in which the songs are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

6 musics from a set of 9. So

$C_{9,6} = \frac{9!}{6!(9-6)!} = 84$

84 different lineups are possible

4 0

3 years ago

The function f(x) varies inversely with x and f(x)=8 when x=3

Sedaia [141]

Answer:

$12$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form $y*x=k$ or $y=k/x$

In this problem we have

For $x=3$ -----> $f(x)=8$

Find the value of k

$f(x)*x=k$

substitute the value of x and f(x)

$8*3=k$

$k=24$

therefore

the equation is equal to

$f(x)=24/x$

For $x=2$ -------> substitute in the equation and find the value of f(x)

$f(x)=24/2=12$

6 0

3 years ago

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im stupid. honestly. just help me pls. this is probably really easy but i aint done any maths in over a month so ion remember ho

KATRIN_1 [288]

Answer:

19 coins

Step-by-step explanation:

We know that mean is the sum of all the elements divided by the number of elements there are: m = t/n, where m is the mean, t is the total sum, and n is the number of elements.

Here, we are given the mean number of coins for all 27 + 18 = 45 children is 16, so m = 16 and n = 45. Then:

m = t/n

16 = t/45

t = 720

This t means that the total number of coins that all the boys and girls have is 720 coins.

Now, we also know the mean number of coins for the boys only, which is 14. Since there are 27 boys, then:

m = t/n

14 = t/27

t = 378

This t means the total number of coins all the boys have.

Subtracting 378 from 720, we get 342, which is the total number of coins the girls have. We also know there are 18 girls, so:

m = t/n

m = 342 / 18 = 19

Thus, the mean is 19 coins.

7 0

3 years ago

Read 2 more answers