Find the area and perimeter of the composite shape..

Y=-x^2+6x-4 Find the Axis of Symmetry and the Vertex, Also solve the whole equation.

Inessa [10]

Answer:

1. Axis of symmetry: x = 3

2. Vertex: (3,5)

3. Solution of the equation:

x-intercepts:

$(3-\sqrt{5},0) \\\\(3+\sqrt{5},0)$

y-intercept: (0, -4)

Explanation:

1. Equation:

$y=-x^2+6x-4$

2. Axis of symmetry:

That is the equation of a parabola, whose standard form is:

$y=ax^2+bx+c$

Where:

$a=-1;b=6;c=-4$

The axis of symmetry is the vertical line with equation:

$x=-b/2a$

Substitute $a=-1,\text{ and }b=6$

$x=-6/[(2)(-1)]=-6/(-2)=3$

Thus, the axis of symmetry is:

$x=3$

3. Vertex

The x-coordinate of the vertex is equal to the axys of symmetry, i.e x = 3.

To find the y-xoordinate, substitute this value of x into the equation for y:

$y=-x^2+6x-4\\\\y=-(3)^2+6(3)-4=-9+18-4=5$

Therefore, the vertex is (3, 5)

4. Find the x-intercepts

The x-intercepts are the roots of the equation, which are the points wher y = 0.

$y=-x^2+6x-4=0$

Use the quadratic equation:

$x=\frac{-b\pm \sqrt{b^2-4ac} }{2a} \\\\x=\frac{-6\pm\sqrt{(-6)^2-4(-1)(-4)} }{2(-1)}\\\\x_1=3-\sqrt{5} \\\\x_2=3+\sqrt{5}$

5. Find the y-intercept

The y-intercet is the value of y when x=0:

$y=-x^2+6x-4\\\\y=-(0)^2+6(0)-4=-4$

7 0

3 years ago

Which ordered pairs in the form (x, y) are solutions to the equation 7x−5y=28?

belka [17]

Answer:7x + -5y = -28

(-4, _)

(1, _)

(_, 14)

Step-by-step explanation:

6 0

2 years ago

HELP please! ‍♂️ Last one is 0.5 < x < 1.5 And none

Ket [755]

1.5 is lesser than 0.5. Oh, wait nevermind I meant to say -1.5 is lesser than 0.5

3 0

2 years ago

In a shipment of airplane parts 3% are known to be defective . If 15 parts are found to be defective how many parts are in the s

marissa [1.9K]

If 3% out of 100% are defective it would be 3 out of every 100, and 3 multiplied by 5 is 15. Then you multiply 100 by 5 and its 500 so out of 500 parts 15 would be defective

3 0

2 years ago

Read 2 more answers

A new college, The University of Discrete Structures, is opening in Boulder! Ioana and Rachel are its founders and are holding a

Rama09 [41]

Answer:

(a) 9 buildings

(b) 2^n -1

Step-by-step explanation:

The number of distinct non-empty subsets of b objects is 2^b -1. Since the subsets are distinct, each could represent a list of the buildings, from the set of b buildings, in which a student is taking courses.

(a) For 8 buildings, 2^8 -1 = 255 students could enroll. for 9 buildings, 2^9-1 = 511 students could enroll.

For 500 students, 9 buildings are required.

__

(b) The maximum number of students for n buildings is ...

2^n -1

3 0

3 years ago