Which values are solutions to the inequality below?check all that apply x^2 >49 A. 6 B.20 C.-7 D.-5 E.-16 F. 7

1 answer:

4 0

Well the square root of 49 is 7 so anything with an absolute value over 7 would work and if it is greater than or equal to, than 7 and -7 also work :)

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Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = 4x − 4 at (1, 0).

larisa86 [58]

We are given the following:
- parabola passes to both (1,0) and (0,1)
 - slope at x = 1 is 4 from the equation of the tangent line 

First, we figure out the value of c or the y intercept, we use the second point (0, 1) and substitute to the equation of the parabola. When x = 0, y = 1. So, c should be equal to 1. The parabola is y = ax^2 + bx + 1 

Now, we can substitute the point (1,0) into the equation,
0 = a(1)^2 + b(1) + 1
0 = a + b + 1
a + b = -1 

The slope at x = 1 is equal to 4 which is equal to the first derivative of the equation.
We take the derivative of the equation ,
y = ax^2 + bx + 1
y' = 2ax + b

x = 1, y' = 2
4 = 2a(1) + b
4 = 2a + b 

So, we have two equations and two unknowns, 
2a + b = 4 
a + b = -1

Solving simultaneously,
a = 5 
b = -6

Therefore, the eqution of the parabola is y = 5x^2 - 6x + 1 .

6 0

3 years ago

The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel: A quadrilateral ABCD is shown with the

algol [13]

A Quadrilateral A B C D in which Sides AB and DC are congruent and parallel.

The student has written the following explanation

Side AB is parallel to side DC so the alternate interior angles, angle ABD and angle BDC, are congruent. Side AB is equal to side DC and DB is the side common to triangles ABD and BCD. Therefore, the triangles ABD and CDB are congruent by SAS.

The student has also written

angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB form a pair of alternate interior angles. Therefore, AD is congruent and parallel to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.

Postulate SAS completely describes the student's proof.

Because if in a quadrilateral one pair of opposite sides are equal and parallel then it is a parallelogram.