Combine the like terms to simplify the expression: 5 + 7 + 15xy^2 + 9y^3 + 10x –13xy^2 – 3x – 8y^3. a. y^6 + 2x^2y^2 + 10x + 12 b. y^3 + 2xy^2 + 7x + 12 c. y^3 + 2xy^2 + 10x + 1 d. y^3 –2xy^2 + 10x + 15

It is important to remember that in simplifying expressions, you can only add or subtract like terms. Also, you have to follow PEMDAS. For the expression, 

5 + 7 + 15xy^2 + 9y^3 + 10x –13xy^2 – 3x – 8y^3

We can combine all the constants, xy^2 terms, y^3 terms and x terms which will yield,

12 + 2xy^2 + y^3 + 7x

Therefore the correct answer is option B.

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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