12x - 3x + 90 = 12x + 57
X = ?

What is x ?

x = 11

General Formulas and Concepts:

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Write equation

12x - 3x + 90 = 12x + 57

Step 2: Solve for x

Combine like terms:                         9x + 90 = 12x + 57Subtract 9 on both sides:                 90 = 3x + 57Subtract 57 on both sides:               33 = 3xDivide 3 on both sides:                     11 = xRewrite:                                              x = 11

Step 3: Check

Plug in x to verify it's a solution.

Substitute:                         12(11) - 3(11) + 90 = 12(11) + 57Multiply:                             132 - 33 + 90 = 132 + 57Subtract:                            99 + 90 = 132 + 57Add:                                    189 = 189

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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