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1 7/8 days

Matthew in one day can build 1/3 of the block.

Andy in one day can build 1/5 of the block.

Together in one day they can build 8/15 of the bolck. It means they need less than 1 day to build 7/15 of the block, which is 7/8 of the day. Thus, they need 1 day and 7/8 of the next day to build the block together.

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Andy solves problems 74 to 125 inclusive in a Math exercise How many problems does he solve?

125 - 73 = 52 problems


The ordered pair 2 16 is a solution for which of the following equations?

y = (x + 2)2 andy = (2x)2(x-2)2 + (y-16)2 = 0


If x equals -3 Andy equals 6 and z equals 8 what is 6y over x?

x = -3; y = 6; 6y/x = 6(6)/-3 = 36/-3 = -12


What is the length to the nearest tenth of the hypotenuse DF of a right triangle DEF if FE is 13 units long and angle F is 34 degrees?

Without seeing the diagram your question (as originally written) was incomplete and impossible to answer. If you had described your question (by rewriting it as I did) instead of blindly copying it, then the Answers community would have had all the necessary information to be able to answer your question and you would have got your homework done for you quicker. In fact, in rewriting the question you may actually have realised what was needed to be calculated and done it yourself - a very useful skill in being able to extract the required mathematics from the given information. Anyway, what is now obvious from the rewritten question is you have is the cosine ratio: cosine = adjacent/hypotenuse → cos F = FE / DF → DF = FE / cos F As you didn't bother to give us the required information, I can't be bothered to fill in the numbers and calculate the required value - you can do that. ----------------------------------------------------------------------------- What I was taught at pre-secondary school (some 40 odd years ago) to help remember the different trigonometric ratios: In a right angle triangle there are three sides to an angle: Opposite - the side opposite the angle Adjacent - the side adjacent to the angle which is not the hypotenuse. Hypotenuse - the side opposite the right angle There are three ratios: Tangent = Opposite / Adjacent Sine = Opposite / Hypotenuse Cosine = Adjacent / Hypotenuse To remember them, use this nonsense rhyme: Two Old Arabs Soft Of Heart Coshed Andy Hatchett The initial letter of each word in each line gives the ratio: Two Old Arabs → T = O / A → Tan = Opp / Adj Soft Of Heart → S = O / H → Sin = Opp / Hyp Coshed Andy Hatchett → C = A / H → Cos = Adj / Hyp


Find the two numbers whose product is 1 and whose sum is 1?

x + y = 1xy = 1y = 1 - xx(1 - x) = 1x - x^2 = 1-x^2 + x - 1 = 0 or multiplying all terms by -1;(-x^2)(-1) + (x)(-1) - (1)(-1) = 0x^2 - x + 1 = 0The roots are complex numbers. Use the quadratic formula and find them:a = 1, b = -1, and c = 1x = [-b + square root of (b^2 - (4)(a)(c)]/2a orx = [-b - square root of (b^2 - (4)(a)(c)]/2aSox = [-(-1) + square root of ((-1)^2 - (4)(1)(1)]/2(1)x = [1 + square root of (1 - 4]/2x = [1 + square root of (- 3)]/2 orx = [1 + square root of (-1 )(3)]/2; substitute (-1) = i^2;x = [1 + square root of (i^2 )(3)]/2x = [1 + (square root of 3)i]/2x = 1/2 + [i(square root of 3]/2 andx = 1/2 - [i(square root of 3)]/2Since we have two values for x, we will find also two values for yy = 1 - xy = 1 - [1/2 + (i(square root of 3))/2]y = 1 - 1/2 - [i(square root of 3)]/2y = 1/2 - [i(square root of 3)]/2 andy = 1 - [1/2 - (i(square root of 3))/2)]y = 1 - 1/2 + [i(square root of 3))/2]y = 1/2 + [i(square root of 3)]/2Thus, these numbers are:1. x = 1/2 + [i(square root of 3)]/2 and y = 1/2 - [i(square root of 3)]/22. x = 1/2 - [i(square root of 3)]/2 and y = 1/2 + [i(square root of 3)]/2Let's check this:x + y = 11/2 + [i(square root of 3)]/2 +1/2 - [i(square root of 3)]/2 = 1/2 + 1/2 = 1xy = 1[1/2 + [i(square root of 3)]/2] [1/2 - [i(square root of 3)]/2]= (1/2)(1/2) -(1/2)[i(square root of 3)]/2] + [i(square root of 3)]/2](1/2) - [i(square root of 3)]/2] [i(square root of 3)]/2]= 1/4 - [i(square root of 3)]/4 + [i(square root of 3)]/4 - (3i^2)/4; substitute ( i^2)=-1:= 1/4 - [(3)(-1)]/4= 1/4 + 3/4= 4/4=1In the same way we check and two other values of x and y.