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pentagon [3]
3 years ago
11

Edgar said 3/5 is equivalent to 18/32. Check his work by making a table of equivalent ratios.

Mathematics
1 answer:
Katen [24]3 years ago
4 0

Answer:

In a nutshell, \frac{3}{5} is not equivalent to \frac{18}{32}.

Step-by-step explanation:

Now we proceed to demonstrate that Edgar's statement is false:

1) \frac{3}{5} Given

2) \frac{3}{5} \times \frac{2}{2} Modulative property/Existence of multiplicative inverse

3) \frac{6}{10} \frac{a}{b}\times \frac{c}{d} = \frac{a\cdot b}{c\cdot d}

4) \frac{6}{10}\times \frac{3}{3} Modulative property/Existence of multiplicative inverse

5) \frac{18}{30} \frac{a}{b}\times \frac{c}{d} = \frac{a\cdot b}{c\cdot d}/Result

In a nutshell, \frac{3}{5} is not equivalent to \frac{18}{32}.

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The median of the values in a data set is y. If 48 were subtracted from each
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Answer would be D.

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The altitude (i.e., height) of a triangle is increasing at a rate of 2 cm/minute while the area of the triangle is increasing at
s344n2d4d5 [400]

Answer:

A = 1/2 B H       area = 1/2 base X height

B = 2 A / H = 2 * 99 / 12 = 16.5 cm

dA / d t = 1/2 * (B dH / dt + H dB / dt)

dB / dt = (2 dA / dt - B dH / dt) / H

dB / dt = (2 * 1.5 cm^2 / min - 16.5 cm * 2 cm / min) / 12 cm

dB / dt = (3 - 33) / 12 cm/min = -2.5 cm/min

4 0
3 years ago
Prove that an = 4^n + 2(-1)^nis the solution to
olga nikolaevna [1]

Answer:

See proof below

Step-by-step explanation:

We have to verify that if we substitute a_n=4^n+2(-1)^n in the equation a_n=3a_{n-1}+4a_{n-2} the equality is true.

Let's substitute first in the right hand side:

3a_{n-1}+4a_{n-2}=3(4^{n-1}+2(-1)^{n-1})+4(4^{n-2}+2(-1)^{n-2})

Now we use the distributive laws. Also, note that (-1)^{n-1}=\frac{1}{-1}(-1)^n=(-1)(-1)^{n} (this also works when the power is n-2).

=3(4^{n-1})+6(-1)^{n-1}+4(4^{n-2})+8(-1)^{n-2}

=3(4^{n-1})+(-1)(6)(-1)^{n}+4^{n-1}+(-1)^2(8)(-1)^{n}

=4(4^{n-1})-6(-1)^{n}+8(-1)^{n}=4^n+2(-1)^n=a_n

then the sequence solves the recurrence relation.

4 0
3 years ago
A is directly proportional to b. When a is 6, b is 72. Find b when a is 8. 3
adelina 88 [10]

Answer:

a)  <em>"K" is proportional Constant   K= 0.0833</em>

<em>b)     The value of b = 99.639</em>

Step-by-step explanation:

<u><em>Explanation</em></u> :-

Given   'a' is directly proportional to 'b'

                     a ∝ b

                <em>  a  =  k b ....(i)</em>

<em>where "K" is proportional Constant</em>

<u><em>Case(i)</em></u><em>:-</em>

<em>when a =6  and b=72</em>

<em>               a  =  k b     </em>

<em>          ⇒ 6 = k (72)</em>

<em>        ⇒  </em>K = \frac{6}{72} = \frac{1}{12} = 0.0833<em>      </em>

<u><em>Case(ii)</em></u><em>:-      </em>

<em> Given  a = 8.3  </em>

<em>           a  =  k b     </em>

<em>⇒   8.3 = 0.0833 ×b</em>

<em>⇒  </em>b = \frac{8.3}{0.0833} = 99.639<em></em>

<u><em>Final answer</em></u><em>:-</em>

a)<em>"K" is proportional Constant   K= 0.0833</em>

<em>b)     The value of b = 99.639</em>

<em></em>

<em></em>

<em></em>

<em></em>

6 0
3 years ago
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