A piece of iron sheet is 30 decimeters long and 23.4 decimeters wide. How many triangle signboards can you make if you use it to make a bottom of 9 decimeters and a height of 7.8 decimeters? How did you get it? How did you get it

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• 1. As shown in the figure, point D is a point on the diameter CA extension line of ⊙ o, point B is on ⊙ o, and ab = ad = Ao. (1) prove that BD is the tangent of ⊙ o; (2) if point E is a point on inferior arc BC, AE and BC intersect at point F, and the area of △ bef is 8, cos ∠ BFA = 23, calculate the area of △ ACF
• 2. P is in the angle AOB. Points m and N are the symmetric points of point P about OA and ob respectively. The perimeter of triangle PEF is 15. Find the length of M and n
• 3. In isosceles trapezoid ABCD, AD / / BC, Mn are the midpoint of ADBC, EF are the midpoint of BM, cm As shown in the figure, in isosceles ladder ABCD, AD / / BC, m and N are the midpoint of AD and BC respectively, e and F are the midpoint of BM and cm respectively (1) If the quadrilateral menf is a square, please explore the quantitative relationship between the height of the isosceles trapezoid ABCD and the base BC, and prove your conclusion
• 4. Known circle C: [X-1] ^ 2 + [Y-2] ^ 2 = 2. Point P [2. - 1] is tangent to circle C through point P, PA, Pb ah, is tangent point 【1】 Find the linear equation of PA and PB [2] find the length of tangent PA [3] find the sine length of ∠ PAB [4] find the linear equation of ab?
• 5. It is known that the moving point P of two points m (4.0) n (1.0) on the plane satisfies the equation PM = 2pn (1) to find the locus C of the moving point P. (2) if the point Q (a, 0) is a point in the locus C, any linear L intersection LOCUS C passes through Q at two points AB, it is proved that the value of vector QA multiplied by vector QB is only related to a; Let f (a) = vector QA multiplied by vector QB to find the value range of F (a)
• 6. In the equation 4x-3y = 5, use the algebraic expression of X to express y, and get y =; use the algebraic expression of y to express x, and get X=
• 7. Let the volume of the triangular prism abc-a1b1c1 be V, P and Q be the points on the side edges Aa1 and CC1 respectively, and PA = qc1, then the volume of the pyramid b-apqc is () A. 16vB. 14vC. 13vD. 12v
• 8. Given a square b square + a square + b square + 16 = 10ab, which a square + b square = how much
• 9. Let a = {X-Y, x + y, XY} B = {X & sup2; + Y & sup2;, - X & sup2; - Y & sup2;, 0} if a = B, find the value of real number x, y Come on, speed up
• 10. If we know that one part of a + a = 3, then the value of one part of a & # 178; + A & # 178; is?
• 11. Are all odd numbers prime
• 12. A triangle cloth area is 120 square decimeters, the bottom is 30 decimeters, how many decimeters is the height
• 13. Given that 14a2 + 9b2 − a + 12b + 5 = 0, find the value of (a − 2) 2A2 − B2
• 14. The bottom of a cone is 8 cm in diameter and 6 cm in height. It is filled with water. Pour all the water into the bottom. The area is 12.56 How many centimeters is the water depth in a square centimeter cylindrical container?
• 15. F (x) = LG (1 + 2 ^ x + 4 ^ XA) / 3, where a ∈ R, if f (x) is meaningful when x ∈ (- infinity, 1], find the value range of A
• 16. The area of a triangle is equal to that of a square. The side length of the square is 12cm, the bottom of the triangle is 18cm, and its height is () cm
• 17. How to deal with the problem that the equal sign can't be obtained when seeking the maximum value in the basic inequality Root XY ≥ 2 root 3 / 5 If and only if x = y = 2 radical 3 / 5, the minimum value of radical XY is 2 radical 3 / 5, At the same time, if 3x = 4Y (x ≠ y), what is the minimum value of root XY? Can only the above conditions be answered? If x, y satisfy x + 3Y = 5xy, then the minimum value of 3x + 4Y is?
• 18. In RT △ ABC, the bisector of acute angle a intersects with the bisector of the adjacent complementary angle of acute angle B at point D, then ∠ ADB=______ Degree
• 19. Simplification ratio Less difficult, no points
• 20. The radius of a circle is 4 decimeters, and its circumference is______ Decimeter, area is______ Square decimeter