A mother is 26 years older than her daughter. The daughter is one-third her mother's age. How old is each now? When will the mot
1 answer:
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In this attached picture according to the conditions of the problem we have an isosceles trapezoid and since we know that legs are equal (AD=BC=5 cm), we have to calculate bases and height in order to find the area. Working with the triangle BCD, we apply Pythagoras theorem and find that CD = = 10 cm. Since BDC is a right triangle, applying theorem for the area of triangles, we find that
and BF=
. Since ABCD is an isosceles trapezoid, triangles ADE and BFC are congruent with Angle Side Angle theorem. Then, DE=FC and with the help of Pythagoras theorem, DE=FC=2.5 cm. Then, AB=EF=5 cm and the area of the trapezoid is
Answer:
The equation of the axis of symmetry is x =
The coordinates of the vertex are ( ,
) ⇒ 2nd answer
Step-by-step explanation:
The quadratic function y = ax² + bx + c is represented graphically by a parabola which has a minimum/maximum vertex (h , k), where
- h =
and k is value y at x = h
- The axis of symmetry of the parabola is a vertical line passes through the vertex point and its equation is x = h
- The minimum/maximum value of the function is (h , k)
∵ y = 4x² + 5x - 1
∵ The form of the quadratic function is y = ax² + bx + c
∴ a = 4 , b = 5 , c = -1
∵ The coordinates of the vertex points are (h , k)
∵ h =
∴ h =
- To find k substitute x in the function by
∵ k = 4 ( )² + 5(
) - 1
∴ k = 4 ( ) + (
) - 1
∴ k = -
- 1
∴ k =
∴ The coordinates of the vertex are ( ,
)
∵ The equation of the axis of symmetry is x = h
∵ h =
∴ The equation of the axis of symmetry is x =
Answer:
C)
Step-by-step explanation:
Group the similar terms together:
Add/Subtract the w:
Add/Subtract the numbers: