what is the horizontal distance, d, from the edge of the pool to the point on the bottom of the pool

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Loftier School Math based on the topics required for the Regents Exam conducted by NYSED. The following are the worked solutions for the Geometry (Mutual Core) Regents High School Examination Jan 2019.

Geometry Common Cadre Regents New York State Exam - January 2019

The following are questions from the past newspaper Regents High School Geometry, Jan 2019 Exam (pdf). Scroll down the page for the step past step solutions.

Geometry - January 2019 Regents - Questions and solutions ane - 12
one. Later a dilation with middle (0, 0), the image of DB is D'B'. If DB = 4.5 and D'B' = 18, the calibration cistron of this dilation is
2. In the diagram below, ABC with sides of 13, 15, and 16, is mapped onto DEF after a clockwise rotation of 90° about point P.
3. On the set of axes beneath, ABC has vertices at A(-2,0), B(2,-4), C(4,2), and DEF has vertices at D(4,0), E(-4,8), F(-8,-4).
four. The figure beneath shows a rhombus with noncongruent diagonals.
Which transformation would not carry this rhomb onto itself?
five. In the diagram beneath of circumvolve O, points M, A, T, I, and Due east are on the circle, KAE and ITE are fatigued, KE ≅ EI, and EKA ≅ EIT.
6. In correct triangle ABC shown below, betoken D is on AB and signal E is on CB such that AC || DE.
If AB = xv, BC = 12, and EC = 7, what is the length of BD?
7. In rhomb VENU, diagonals VN and European union intersect at S.
If VN = 12 and EU = 16, what is the perimeter of the rhomb?
8. Given right triangle ABC with a right angle at C, yard∠B61°. Given right triangle RST with a right bending at T, thousand∠R = 29°.
ix. A vendor is using an eight-ft by 8-ft tent for a craft fair. The legs of the tent are nine ft tall and the summit forms a foursquare pyramid with a height of 3 ft
What is the volume, in cubic feet, of space the tent occupies?
x. In the diagram below of correct triangle KMI, altitude IG is fatigued to hypotenuse KM.
If KG 9 and IG 12, the length of is
eleven. Which three-dimensional figure will consequence when a rectangle 6 inches long and five inches wide is continuously rotated about the longer side?
12. Which statement about parallelograms is always true?

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Geometry - January 2019 Regents - Questions and solutions 13 - 24
thirteen. From a point on the ground i-half mile from the base of a historic monument, the angle of elevation to its superlative is 11.87°. To the nearest foot, what is the peak of the monument?
14. The area of a sector of a circle with a radius measuring 15 cm is 75π cm². What is the measure of the central angle that forms the sector?
fifteen. Betoken M divides AB so that AM:MB = one:2. If A has coordinates (-one,-3) and B has coordinates (8,9), the coordinates of M are
16. In the diagram below of triangle ABC, Ac is extended through point C to indicate D, and Be is drawn to AC.
17. In the diagram below of right triangle ABC, AC = 8, and AB = 17.
Which equation would determine the value of angle A?
eighteen. Francisco needs the three pieces of glass shown beneath to complete a stained glass window. The shapes, two triangles and a trapezoid, are measured in inches.
Drinking glass can exist purchased in rectangular sheets that are 12 inches wide. What is the minimum length of a canvass of glass, in inches, that Francisco must buy in guild to have plenty to complete the window?
nineteen. In the diagram of quadrilateral NAVY below, m∠YNA = xxx°, g∠YAN = 38°, m∠AVY = 94°, and m∠VAY = 46°.
Which segment has the shortest length?
xx. What is an equation of a circle whose center is (1,4) and diameter is 10?
21. On the set of axes below, ABC, altitude CG, and median CM are drawn.
Which expression represents the area of ABC?
22. In correct triangle ABC, m∠C = 90° and Ac ≠ BC. Which trigonometric ratio is equivalent to sin B?
23. As shown in the diagram below, the radius of a cone is ii.5 cm and its slant superlative is half-dozen.v cm
How many cubic centimeters are in the volume of the cone?
24. What is an equation of the image of the line y = 2/iii x - 4 after a dilation of a scale cistron of 3/4 centered at the origin?

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Geometry - January 2019 Regents - Questions and solutions Parts 2-four
25. Write an equation of the line that is parallel to the line whose equation is 3y + 7 = 2x and passes through the bespeak (2,6).
26. Parallelogram ABCD is next to rhombus DEFG, as shown beneath, and FC intersects AGD at H.
If yard∠B = 118° and m∠AHC = 138°, determine and land thou∠GFH
27. As shown in the diagram below, secants PWR and PTS are fatigued to circle O from external indicate P
If m∠RPS = 35° and mRS = 121°, determine and state mWT.
28. On the set of axes below, ABC is graphed with coordinates A(-2,-i), B(3,-one), and C(-ii,-4). Triangle QRS, the prototype of ABC, is graphed with coordinates Q(-v,2), R(-5,seven), and S(-eight,2).
Describe a sequence of transformations that would map ABC onto QRS.
29. Given points A, B, and C, use a compass and straightedge to construct betoken D so that ABCD is a parallelogram.
[Leave all construction marks.]
30. On the set of axes below, DEF has vertices at the coordinates D(ane,-1), E(3,4), and F(4,2), and point M has coordinates (3,1). Owen claims the median from point East must pass through betoken G.
Is Owen correct? Explain why.

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31. A walking path at a local park is modeled on the grid below, where the length of each grid foursquare is ten feet. The town needs to submit paperwork to pave the walking path. Determine and land, to the nearest foursquare foot, the expanse of the walking path.
32. A triangle has vertices A(-ii,4), B(half dozen,2), and C(one,-ane).
Prove that ABC is an isosceles right triangle.
[The apply of the prepare of axes below is optional.]
33. Theresa has a rectangular puddle xxx ft long, 15 ft broad, and iv ft deep. Theresa fills her puddle using urban center water at a charge per unit of $3.95 per 100 gallons of water.
Nancy has a circular pool with a bore of 24 ft and a depth of 4 ft. Nancy fills her pool with a water commitment service at a rate of $200 per 6000 gallons.
If Theresa and Nancy both fill their pools half dozen inches from the top of the pool, determine and state who paid more to fill her pool. [i ftⁱⁱⁱ water vii.48 gallons
34. As modeled in the diagram beneath, an access ramp starts on flat ground and ends at the showtime of the top step. Each step is 6 inches tall and 8 inches deep
If the angle of elevation of the ramp is 4.76°, determine and state the length of the ramp, to the nearest tenth of a human foot.
Make up one's mind and state, to the nearest tenth of a human foot, the horizontal distance, d, from the bottom of the stairs to the lesser of the ramp.
35. In the diagram of quadrilateral ABCD with diagonal AC shown below, segments GH and EF are drawn, AE ≅ CG, Be ≅ DG, AH ≅ CF, and AD ≅ CB. Prove: EF ≅ GH

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