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4 years ago

SOLVE y = 3x – 2 x – y = 4 BY USING SUBSTITUTION!! SHOW ALL WORK! HELPPP!

Mathematics

1 answer:

Nataly [62]4 years ago

5 0

Answer:

y=3x-2..... i

x-y=4...... ii

x-4=y

Substituting the value of y in equation i,

x-4=3x-2

2-4=3x-x

-2=2x

x=-1.

From ii,

-1-4=y

y=-5.

x=-1, y=-5

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Both the La Plata river dolphin (Pontoporia blainvillei) and

Citrus2011 [14]

Answer:

1. A sperm whale is 3 orders of magnitude heavier than a La Plata river dolphin; 2. The radius of the larger ball is one (1) order of magnitude bigger than the radius of the smaller ball; 3. The volume of the larger ball is 3 orders of magnitude bigger than the volume of the smaller ball.

Step-by-step explanation:

If we expressed a number as:

$\\ N = a * 10^{b}$ (1)

Where

$\\ \frac{1}{\sqrt{10}} \leq a < \sqrt{10}$ (2)

$\\ 1 \leq a < 10$ (3)

Then, b represents the order of magnitude of such a number (Order of magnitude (2020), in Wikipedia).

The order of magnitude can be defined as "...the smallest power of ten needed to represent a quantity" (Weisstein, Eric W. "Order of Magnitude". From MathWorld--A Wolfram Web Resource).

Having gathered all this information, we can proceed as follows:

<h3>First case</h3>

The La Plata river dolphin weighs between 30 and 50kg and the sperm whale weighs between 35,000 and 40,000kg.

Then, considering (1) and (3) to express the dolphin and whale's weight (since in this way the order of magnitude is the same as the exponent part in the scientific notation):

$\\ 30kg \leq Dolphin_{weight} \leq 50kg$

$\\ 3*10^{1}kg \leq Dolphin_{weight} \leq 5*10^{1}kg$

$\\ 35000kg \leq Whale_{weight} \leq 40000kg$

$\\ 3.5*10^{4}kg \leq Whale_{weight} \leq 4.0*10^{4}kg$

Since the range for the weights are in the same order of magnitude for both dolphin and whale (considering the definition above):

$\\ Dolphin_{weight} = 10^{1}\;(order\;of\;magnitude=1)$

$\\ Whale_{weight} = 10^{4}\;(order\;of\;magnitude=4)$

Then

$\\ \frac{Whale_{weight} = 10^{4}}{Dolphin_{weight} = 10^{1}}$

$\\ \frac{Whale_{weight}}{Dolphin_{weight}} = \frac{10^{4}}{10^{1}}$

$\\ \frac{Whale_{weight}}{Dolphin_{weight}} = 10^{4-1}$

$\\ \frac{Whale_{weight}}{Dolphin_{weight}} = 10^{3}$

Thus

A sperm whale is 3 orders of magnitude heavier than a La Plata river dolphin.

<h3>Second case</h3>

Following the same reasoning, we can conclude that the radius of the larger ball is one (1) order of magnitude bigger than the radius of the smaller ball:

$\\ \frac{Larger\;ball_{radius}}{Smaller\;ball_{radius}} = \frac{10^{1}}{10^{0}}$

$\\ \frac{Larger\;ball_{radius}}{Smaller\;ball_{radius}} = 10^{1-0} = 10^{1}$

<h3>Third case</h3>

For this case, we need to calculate the volume of a sphere for both radii (1cm and 10cm).

The volume of a sphere is

$\\ V_{sphere} = \frac{4}{3}*\pi*R^{3}$

Then, the volume of the ball of radius 1cm is:

$\\ V_{radius=1} = \frac{4}{3}*\pi*(1cm)^{3}$

$\\ V_{radius=1} \approx 4.19*10^{0}cm^{3}$

And, the volume of the ball of radius 10cm is:

$\\ V_{radius=10} = \frac{4}{3}*\pi*(10cm)^{3}$

$\\ V_{radius=10} \approx 4.19*10^{3}cm^{3}$

Thus

$\\ \frac{10^{3}}{10^{0}} = 10^{3}$

As a result, the volume of the larger ball is 3 orders of magnitude bigger than the volume of the smaller ball.

4 0

3 years ago

The coordinate plane below shows the graph of a linear function of x. Which of the following equations best describes the functi

Vitek1552 [10]

Answer: Its A

Step-by-step explanation:

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2 years ago

What is the length of the arc on a circle with radius 20 in. intercepted by a 15° angle?

AnnyKZ [126]

Length of arc = (15/360) * 2*3.14*20 = 5.23 ins

circumference of the circle = 2*3.14*24 = 150.72

angle at center from 10 ft arc = (10/150.72) * 360 = 23.89 degrees

6 0

3 years ago

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What is C’ T’ if there was a rotation ?

Simora [160]

Answer: The Answer Is 4) Hope it Helps!

Step-by-step explanation:

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4 years ago

Calculate the amount and compound interest on

mart [117]

Answer:

Below in bold.

Step-by-step explanation:

i) Amount = 15000(1 + 0.10)^2 = 18,150.

Interest = 3,150.

ii) Amount = 15620(1 + 0.08/2)^(3/2*2)

= 15620(1 + 0.04)^3

= 17,570.38.

Interest =1,950.38.

iii) Amount = 100000(1 + 0.04/4)^(3)

= 100000(1 + 0.01)^3

= 103,030.1

Interest = 3030.1.

7 0

3 years ago