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3 years ago

Michael runs 3.5 miles in 30 minutes. If he continues at this rate for 2 hours, determine his rate of change.

Mathematics

1 answer:

mezya [45]3 years ago

5 0

Remember d=rt
so its 3.5=r(0.5)

divide 3.5 by 0.5, which is 7. His rate is 7 miles per hour.

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Write y=-(3/5)x-2 in standard form using integers please thank you

juin [17]

Y= -3/5x - 2 Add -3/5x to both sides
3/5x +y= -2 Multiply both sides by 5 because 5 is the denominator.
By multiplying by 5 you can cancel out and make it a real number.
5(3/5x +y) = -2(5)

3x + 5y= -10 is the answer.

5 0

3 years ago

Please help very urgent

Alik [6]

Answer:

32, 16, 8, 4, 2, 1

Explanation:

The geometric mean can be represented by $\sqrt[n]{x_{1} • x_{2} • x_{3} • .. x_{n}}$ .

Which is the mean of the product of n numbers, used to find the average of a geometric progression.

Don't get confused by geometric mean, it is only asking you about the next numbers in the geometric sequence given the first and sixth term.

The explicit rule for a geometric sequence can be modeled by:

$a_{n} = a_{1} • r^{n-1}$

Where $a_{n}$ is the nth term, $a_{1}$ is the first term in the sequence, n is the term number, and r is the common ratio.

Since we already know the first term, $a_{1}$ will simply be 32.

Since we know it's geometric, there will be an exponential relationship, which means that we will use the geometric mean to find the common ratio.

There are 6 total terms, r is raised to the n – 1 so 6 – 1 = 5, and that will be the degree of this root.

$\sqrt[5]{\frac{a_{6}}{a_{1}}}$ =

$\sqrt[5]{\frac{1}{32}}$ =

$\frac{1}{2}$ .

Therefore: $r = \frac{1}{2}$ .

Using all the information we have, we can find the explicit rule:

$a_{n} = a_{1} • r^{n-1}$

$a_{1}$ = 32
$r = \frac{1}{2}$

$a_{n} = a_{1} • r^{n-1}$ →

$\boxed{a_{n} = 32 • (\frac{1}{2})^{n-1}}$

________________________________

We can test that this works by substituting the number location of the term you want to find.

For instance:

$a_{1} = 32 • (\frac{1}{2})^{1-1}$

$a_{1} = 32 • (\frac{1}{2})^{0}$

$a_{1} = 32 • 1$

$a_{1} = 32$

$a_{6} = 32 • (\frac{1}{2})^{6-1}$

$a_{6} = 32 • (\frac{1}{2})^{5}$

$a_{6} = 32 • \frac{1}{32}$

$a_{6} = 1$

3 0

3 years ago

Read 2 more answers

Please answer this for me correctly. THANK YOU!!

Leona [35]

Answer:

Hope this helps!

5 0

2 years ago

What is the common denominator of 2/4 and 7/8

Ivenika [448]

Answer:

Step-by-step explanation:

$\dfrac 24 = \dfrac{ 2 \times 2}{4 \times 2} = \dfrac 4 8$

5 0

2 years ago

At Rosedale Middle School, 11.25% of the

LUCKY_DIMON [66]

Answer:

162

Step-by-step explanation:

8 0

2 years ago