dolphinia

Hi there!

There are 4 integers for which there is no real solution. They are: 7, 8, 9, and 10. Therefore, the probability is \(\frac{4}{10}=\frac{2}{5}.\)

Aha tysm!

Great graph! thanks for helping! 

https://web2.0calc.com/questions/plz-help_78058

Let there be a number x such that multiplying each ratio by x gives the actual number of marbles there are of that color. We know \(1x+2x+3x+4x=180\), and we can simplify like terms to get \(10x=180\). Dividing by 10 gives \(x=18\), so to find the number of blue marbles we multiply \(3 \cdot 18=54\).

There are \(\boxed{54}\) blue marbles in the bag.

1. The formula for area of a triangle is \(A=\frac{1}{2}bh\). Plugging in the side lengths it's \(\frac{1}{2}(6)(8)=24\) square units.

2. The sum of the angles in a triangle is 180 degrees. The sum of the other two angles given is \(135+30=165\). So to find the unknown angle you subtract 180-165, which is 15. Therefore angle \(BAC=15º\).

1. Start by multiplying both sids of the equation by \(64a^3+7\) to get rid of the fraction. From there just do some regrouping to get the variable terms on one side and constant terms on the other.

2. Same here get rid of the fractions by multiplying the whole equation by the common denominator \(3a\), and from there just rearrange it and solve 

First, combine like terms on the right hand side: \(3a+4b=2a-6b+24\)

Then we rearrange the equation so that all the terms with \(b\) in it are on one side, and the rest (\(a\) terms and constants) are on the other side. So now we have \(-10b=a-24\)

Since we want to get b on its own, we divide by \(-10b\).

Thus \(b=-\frac{a-24}{10}\)

Hope that helped!

Thanks!

Makes so much sense now. Thank you!