Pls help me find each measure on 1-8

9514 1404 393

Step-by-step explanation:

The diagonals of a rhombus are perpendicular bisectors of each other.

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1. KY is the long leg of right triangle KYR, whose hypotenuse is given as 13 and short leg as 5. If you do not recognize this as a 5-12-13 right triangle, you can find the longer leg using the Pythagorean theorem.

  KY² +RK² = RY²

  KY² = RY² -RK² = 169 -25 = 144

  KY = √144 = 12

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2. K is the midpoint of diagonal PY, so PK = KY = 12.

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3. As we have said, the diagonals cross at right angles.

  m∠YKZ = 90°

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4. PZ is parallel to RY, so the alternate interior angles created by diagonal ZR are congruent.

  m∠PZR = m∠YRZ = 67°

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5. We recognize that hypotenuse PQ of right triangle PQA is √2 times the side length AP. So, this is a "special right triangle" that is isosceles. The sides and hypotenuse have the ratios 1 : 1 : √2.

  AQ = AP = 3

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6. As in any isosceles right triangle, the acute angles are 45°.

  m∠APQ = 45°

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7. Each of the smaller acute angles is 45°. The diagonals bisect the corner angles, so each corner angle is 2×45° = 90°.

  m∠MNP = 90°

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8. A is the midpoint of PM, so PM is twice the length of AP.

  PM = 2×AP = 6

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

the car was traveling 40 mph before it started skidding. ( 2 points ) 17. was the driver were her brakes working at 75% efficiency or better? ( 2 points ) yes 29.

step-by-step explanation: