Alex is making a nut mixture to sell at the local farmer's market. he mixes 2 pounds of cashews with a nut mixture that is 40% cashews. the resulting mixture is 52% cashews. how many pounds of nut mixture does alex make?

mr. martinez mixes a 90% sugar cinnamon flavored solution with a 75% sugar cherry flavored solution to make 12 gallons of a new product. the new product is 85% sugar. how much of the cherry flavored solution did he use?

mr. acosta works in the lab at a pharmaceutical company. he needs 26 liters of a 36% acid solution to test a new product. his supplier only ships a 42% and a 29% solution. how much of the 42% solution will mr. acosta need to use?

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Mr. brettler is hanging up a 5-foot tall rectangular welcome sign in the gym. he has drawn a sketch on a coordinate grid. he has the lower vertices of the sign at (9, –3) and (–6, –3). where would the upper vertices be on the grid?

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)

The sum of the squares of two numbers is 8 . the product of the two numbers is 4. find the numbers.