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3 years ago

If the door to the library is at (2, 4), the door to the mall is at (8, 2), and one

Mathematics

1 answer:

guapka [62]3 years ago

5 0

Answer:

6 miles

Step-by-step explanation:

The distance formula is expressed as;

D = √(x2-x1)²+(y2-y1)²

D = √(2-4)²+(8-2)²

D = √(-2)²+(6)²

D = √4 + 36

AD = √40

AD = 6.32

Hence the approximate distance between the library and the mall is 6 miles

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Compare the fraction 1:24,000 to the fraction 1:3,168,000; which is the largest rational number

gulaghasi [49]

Answer:

$\frac{1}{24,000}$

Step-by-step explanation:

we know that

When we compare positive fractions with the same numerator, the largest rational number will be the fraction with the lowest denominator

In this problem we have

$\frac{1}{24,000}$ and $\frac{1}{3,168,000}$

Both numerator are equal

Compare the denominators

$24,000 < 3,168,000$

therefore

$\frac{1}{24,000}$ is the largest rational number

7 0

3 years ago

Choose Yes or No to tell whether each expression is equivalent to –43p – 25.

Rashid [163]

Answer:

–43p + (–25) is EQUIVALENT to –43p – 25.

Step-by-step explanation:

<u>The options are MISSING.</u>

The needed options are:

1. 25 – 43p

2. 25 – 43p

3. –25p –43

4. –43p + (–25)

Now, here the given expression is: –43p – 25

Taking each option and simplifying it , we get:

1. 25 – 43p

Here, the second term is NEGATIVE, but the first term (25) is POSITIVE.

⇒ 25 – 43p ≠ –43p – 25

Hence, 25 – 43p is NOT EQUIVALENT.

2. 25 – 43p

Here, the second term is NEGATIVE, but the first term (25) is POSITIVE.

⇒ 25 – 43p ≠ –43p – 25

Hence, 25 – 43p is NOT EQUIVALENT.

3. –25p –43

Here, the variable p is multiplied with (-25) and NOT (-43).

⇒ –25p –43 ≠ –43p – 25

Hence, –25p –43 is NOT EQUIVALENT.

4. –43p + (–25)

Here, both the given terms (43) and (25) are NEGATIVE.

Also, the varibale p is multiplied with (-43)

⇒ –43p + (–25) = –43p – 25

Hence, –43p + (–25) is EQUIVALENT.

5 0

3 years ago

Situation:

stepan [7]

Answer:

t = 6162 years

Step-by-step explanation:

This equation takes the form of

$N=N_{0}e^{kt}$

We are given everything but the amount of C-14 at time t = 0. But we can figure it out from the info we ARE given. We are told that when the spear head is found it contains 54% of its original amount of C-14. Notice we are dealing in percents. If 54% remains when it is found, it started out with 100% of its amount. That's our N value. Filling in:

$100=54e^{.0001t}$

Our goal is to get that t down from the exponential position that it is currently in. To do that we will need to eventually take the natural log of both sides, because ln's and e's "undo" each other, much like squaring "undoes" a square, or dividing "undoes" multiplication. So we take the natural log of both sides. On the right side, notice that when we take the natural log, the e disappears; it's "undone", gone. Before that, though, we will simplify by dividing both sides by 54. 100/54 = 1.851851852. So, altogether...

$ln(1.851851852)=.0001t$