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3 years ago

A bus travels 6/8 of a mile in 12 of a minute. How far will it travel in one minute?

Mathematics

1 answer:

Vitek1552 [10]3 years ago

6 0

Answer:

1/16 of a mile in one minute.

Step-by-step explanation:

1. you know that 3/4 mile = 12 mins and x mile = 1 min

2. To get 12 mins to 1 you divide the mins by 12

3. So you do the same for miles!

4. 3/4 miles divided by 12

5. which turns into 3/4 * 1/12

6. so your final answer would be 1/16 of a mile in one minute

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For the polynomial below, -1 is a zero of multiplicity of two.

mrs_skeptik [129]

Answer:

$h(x)=(x+1)^2(x-1-5i)(x-1+5i)$

Step-by-step explanation:

Given that -1 is a zero of multiplicity of two for the polynomial $h(x) = x^4+23x^2+50x+26.$ This means that $x-(-1)=x+1$ is twice the linear factor.

Rewrite the polynomial $h(x) = x^4+23x^2+50x+26$ as follows:

$h(x)\\ \\= x^4+23x^2+50x+26\\ \\=x^4+x^3-x^3-x^2+24x^2+24x+26x+26\\ \\=x^3(x+1)-x^2(x+1)+24x(x+1)+26(x+1)\\ \\=(x+1)(x^3-x^2+24x+26)\\ \\=(x+1)(x^3+x^2-2x^2-2x+26x+26)\\ \\=(x+1)(x^2(x+1)-2x(x+1)+26(x+1))\\ \\=(x+1)(x+1)(x^2-2x+26)$

Find linear factors of the quadratic polynomial $x^2-2x+26$ :

$D=(-2)^2-4\cdot 1\cdot 26=4-104=-100=100i^2\\ \\\sqrt{D}=\sqrt{100i^2}=10i\\ \\x_{1,2}=\dfrac{-(-2)\pm 10i}{2\cdot 1}=\dfrac{2\pm 10i}{2}=1\pm 5i$

Hence,

$x^2-2x+26=(x-(1+5i))(x-(1-5i))=(x-1-5i)(x-1+5i)$

and the initial polynomial factorization is

$h(x)=(x+1)^2(x-1-5i)(x-1+5i)$

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4 years ago

Read 2 more answers

If a game consists of picking a number from a bag of beans numbered 2, 2, 3, 4, and 5 and flipping a coin, which probabilities a

Semenov [28]

The true statement is (d) none of the above

<h3>Missing information</h3>

I. P(3 and tail)

II. P(even and head)

III .P(odd and head)

<h3>How to determine the equivalent probabilities?</h3>

We start by calculating each probability

There is only one 3 in the 5 numbers.

So:

P(3) = 1/5

The probability of a tail in a coin is:

P(Coin) = 1/2

So, we have:

P(3 and tail) = 1/5 * 1/2

P(3 and tail) = 1/10

There are three even numbers in the 5 numbers.

So:

P(even) = 3/5

The probability of a head in a coin is:

P(head) = 1/2

So, we have:

P(even and head) = 3/5 * 1/2

P(even and head) = 3/10

There are two odd numbers in the 5 numbers.

So:

P(odd) = 2/5

The probability of a head in a coin is:

P(head) = 1/2

So, we have:

P(odd and head) = 2/5 * 1/2

P(even and head) = 1/5

By comparing the results, none of the probabilities are equal.

Hence, the true statement is (d) none of the above