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andre [41]
3 years ago
6

A mixture of paint calls for 1/3 cups of red paint and 1/2 cup of yellow paint. How many cups of red paint would be needed for e

very 1 cup of yellow paint?
Mathematics
1 answer:
KatRina [158]3 years ago
8 0

Step-by-step explanation:

1 cup of yellow paint = 2×1/2 cup.

and that requires then also 2×1/3 Co red paint.

so, 1 cup of yellow paint mixes with 2/3 cups of red paint.

2 and 3 have a smallest common multiple (smallest number that is divisible by both numbers without remainder) of 6.

so, we need to get 6 units of each for a whole number ratio :

6×1/2 = 3 cups of yellow paint mix with 6×1/3 = 2 cups of red paint.

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Show work and Factor 4x^2+xy-18y^2
grigory [225]

Answer:

4x^2+xy-18y^2=(4x+9y)\,(x-2y)

Step-by-step explanation:

Let's examine the following general product of two binomials with variables x and y in different terms:

(ax+by)\,(cx+dy)= ac\,x^2+adxy+bcxy+bdy^2

so we want the following to happen:

a\,c = 4\\ad+bc=1\\bd--18

Notice as well that ad+bc =1 means that those two products must differ in just one unit so, one of them has to be negative, or three of them negative. Given that the product bd=-18, then we can consider the case in which one of this  (b or d) is the negative factor. So let's then assume that a\,\,and \,\,c are positive.

We can then try combinations for  a\,\,and \,\,c  such as:

a = 4;\,\,c=1\\a=2;\,\,c=2\\a=1;\,\,c=4

Just by selecting the first one (a=4;\,\,c=1)

we get that 4d_b=1\\b=-4d-1

and since

bd=-18\\(-4d-1)\,d=-18\\-4d^2-d=-18\\4d^2+d-18=0

This quadratic equation give as one of its solutions the integer: d = -2, and consequently,

d=-18/(-2)\\d=9

Now we have a good combination of parameters to render the factoring form of the original trinomial:

a=4; \,\,b=9;\,\,c=1;\,\,d=-2

which makes our factorization:

(4x+9y)\,(x-2y)=4x^2+xy-18y^2

6 0
3 years ago
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Darya [45]

Answer:

2 - √3

Step-by-step explanation:

tan45 = 1

tan60 = √3

2 tan 45 - tan 60​

2(1) - √3

=> 2 - √3

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Answer is D or the last choice
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