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2 years ago

I NEED HELP ASAP PLEASE

Mathematics

1 answer:

zavuch27 [327]2 years ago

4 0

16 miles for 1 gallón. Kkjudt divide 130 to 5

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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

What is the value of x? enter your answer in the box

antiseptic1488 [7]

Answer:

2(x+10) = 3x-30 (reason: vertical angles are congruent)

2x+20 = 3x-30

20 = 1x-30

1x = 20+30

1x = 50

x = 50

5 0

2 years ago

Read 2 more answers

Convert 9/20 into a decimal using long division

Mice21 [21]

Answer:

0.45

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Which one of the following are true

Lady bird [3.3K]

I say B it intercepts both axis

4 0

2 years ago

If the range of f(x)= square root mx and the range of g(x)=m square root x are the same, which statement is true about the value

AveGali [126]

M can be any positive real number.

Explanation:

From f(x) = √(mx) ; if x is posive m has to be positive; if x is negative m has to be negative; if x is cero m can have any value, and the range will always be 0 or positve

From g(x) = m √x; x can only be 0 or positive and the range will have the sign of m.

Given we concluded that the range of f(x) can only be 0 or positive, then me can only be 0 or positive.

3 0

2 years ago