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3 years ago

Find three rational numbers between 1/3 and 5/6

1 answer:

6 0

First we need to know the meaning of a rational number. A rational number is any number that terminates and doesn't repeat as a decimal, and can be represented as a fraction.

I would say it's 3/6, 4/6, and 5/6, you can also have 2/6 since they can be expressed as a ratio and are between 1/3 and 5/6. (1/3 is equal to 2/6)

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8x + 20y = 20<br> 14x + 35y = k<br> For the above system of equations to be consistent, k must equal

Goshia [24]

Answer:

Step-by-step explanation:

The equations will be "consistent" when they describe lines that are not parallel.

<h3>Slopes</h3>

The slope of a line whose equation is written in this form is the opposite of the ratio of the y-coefficient to the x-coefficient:

line 1 slope = -8/20 = -2/5

line 2 slope = -14/35 = -2/5

These lines have the same slope, so will be parallel unless they have the same y-intercept.

<h3>Y-intercept</h3>

The y-intercept of each line is the ratio of the constant to the y-coefficient:

line 1 y-intercept = 20/20 = 1

line 2 y-intercept = k/35

We want these lines to have the same y-intercept so that they are not inconsistent. This requires ...

k/35 = 1

k = 35

For the equations to be consistent, we must have k = 35.

<em>Additional comment</em>

Linear equations are generally categorized as "consistent" or "inconsistent," and "dependent" or "independent."

Equations are "inconsistent" if there are no values of the variables that satisfy all of the equations. They are "dependent" if they describe exactly the same relation between the variables. "Consistent" equations may be "dependent" (describing the same line, as here), or "independent" (describing lines with different slopes.)

7 0

2 years ago

Rewrite the form In exponential form:<br> Log100 = x

andrey2020 [161]

Answer:

$10^x=100$

Step-by-step explanation:

You know how subtraction is the <em>opposite of addition </em>and division is the <em>opposite of multiplication</em>? A logarithm is the <em>opposite of an exponent</em>. You know how you can rewrite the equation 3 + 2 = 5 as 5 - 3 = 2, or the equation 3 × 2 = 6 as 6 ÷ 3 = 2? This is really useful when one of those numbers on the left is unknown. 3 + _ = 8 can be rewritten as 8 - 3 = _, 4 × _ = 12 can be rewritten as 12 ÷ 4 = _. We get all our knowns on one side and our unknown by itself on the other, and the rest is computation.

We know that $3^2=9$ ; as a logarithm, the <em>exponent</em> gets moved to its own side of the equation, and we write the equation like this: $\log_3{9}=2$ , which you read as "the logarithm base 3 of 9 is 2." You could also read it as "the power you need to raise 3 to to get 9 is 2."

One historical quirk: because we use the decimal system, it's assumed that an expression like $\log1000$ uses <em>base 10</em>, and you'd interpret it as "What power do I raise 10 to to get 1000?"

The expression $\log100=x$ means "the power you need to raise 10 to to get 100 is x," or, rearranging: "10 to the x is equal to 100," which in symbols is $10^x=100$ .

(If we wanted to, we could also solve this: $10^2=100$ , so $\log100=2$ )

6 0

3 years ago

If y = 7x − 5, which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs?

BaLLatris [955]

Answer:

Correct option is C). {(0, −5), (2, 9), (−3, −26)}

Step-by-step explanation:

Given function is f(x)=7x-5.

Here, Options are given ordered pair

Let, x=0

f(x)=7x-5

f(0)=7(0)-5

f(0)=(-5)

The ordered pair is (0,-5)

Let, x=2

f(x)=7x-5

f(2)=7(2)-5

f(2)=9

The ordered pair is (2,9)

Let, x=(-3)

f(x)=7x-5

f(-3)=7(-3)-5

f(-3)=(-26)

The ordered pair is (-3,-26)

Thus, Correct option is C). {(0, −5), (2, 9), (−3, −26)}

8 0

4 years ago

Estimate the following difference by rounding each number to the nearest hundred.

Arte-miy333 [17]

1348.5 rounds down to 1300 because 4 is less than 5
567.21 rounds up to 600 because 6 is greater than 5
1300-600=700

8 0

4 years ago

Read 2 more answers

19 is 25% of what number?

zepelin [54]

Answer:

19/25 * 100 = 76%

Step-by-step explanation:

3 0

3 years ago