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3 years ago

What is 1/3d + 10 = 3/5d and please solve it step by step showing work.

Mathematics

2 answers:

Paladinen [302]3 years ago

5 0

The answer to this is 75/2

Ipatiy [6.2K]3 years ago

3 0

Answer: x = 75/2

Step-by-step explanation:

First, separate the 1/3d and 10 by subtracting 1/3d to the right side so the equation is now: 10 = 3/5d - 1/3d

Next, Make the two fractions have a common denominator: (3/5 = 9/15) and (-1/3 = -5/15) and solve to get 4/15x

Then, your equation should be 10= 4/15x

So now multiply the 10 by 4/15's reciprocal (15/4) to get the variable x by itself: 10 × 15/4 or

(10×15) / (4×1) to get x = 150/4 now simplify

4 can go into 150 twice so the simplified answer is 75/2 or 37.5 in decimal form

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Tracey paid $165 for an item that was originally priced at $570. What percent of the original price did Tracey pay? Round to the

kirza4 [7]

Answer:

Step-by-step explanation:

$\frac{165}{570}$ = 0.2894

multiply by 100 to turn into percentage

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3 years ago

Identify the percent of change as an increase or a decrease 12 inches to 36 inches, increases what is the percent of change ___%

Alisiya [41]

Answer:

It was an increase of 200%.

Step-by-step explanation:

In order to identfy the percent of the change we need to first find the absolute value, to do that we subtract the final value from the initial one. We have:

absolute difference = 36 - 12 = 24 inches

Since this value is positive it was an increase. Now we need to find the percentage at which it was increased, to do that we can use a rule of three in a way that the original value is 100% and the value we want to know is the percentage for the absolute increase. We do this as follows:

12 inches -> 100%

24 inches -> x %

12*x = 2400

x = 2400/12 = 200 %

It was an increase of 200%.

8 0

4 years ago

The points A BC :(2, 2,1), :(1,1,3), :(2,0,5) − are the vertices of a right triangle. The radius of the sphere with center at th

ElenaW [278]

Answer:

r=1

Step-by-step explanation:

First we need to know the length of each side of the triangle, so we use the formula of the vector modulus:

$|AB|= \sqrt{(b_{1}-a_{1})^{2}+(b_{2}-a_{2})^{2}+(b_{3}-a_{3})^{2}$

By doing so, we find:

$|AB|=\sqrt {6}\\|BC|=\sqrt {6}\\|AC|=2\sqrt {5}$

With this we know that the triangle is not right, but, we assume the longest side as the hypotenuse of the problem.

As we have two equal sides, we know that the line between point |AB| and the center of the hypotenuse is perpendicular, therefore, we can calculate it using Pythagoras theorem:

$|BC|^{2}=r^{2}+(\frac{|AC|}{2})^{2}\\\\r^{2}=|BC|^{2}-(\frac{|AC|}{2})^{2}\\\\r^{2}=(\sqrt{6})^{2}- (\frac{2\sqrt{5}}{2})^{2}\\\\r^{2}=6-5=1\\r=1$