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3 years ago

Find the area of the shape shown below.

Mathematics

1 answer:

Rama09 [41]3 years ago

7 0

Answer:

Step-by-step explanation:

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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 length of the hypotenuse? If necessary, round to the nearest tenth.

N76 [4]

Answer:

7 feet

Step-by-step explanation:

Pythagorean theorem

sqrt(4.5^2 + 5.3^2) = hypotenuse

sqrt(48.34) = hypotenuse

6.95269732 = hypotenuse

round to nearest tenth

7 feet = the length of the hypotenuse

7 0

2 years ago

Read 2 more answers

Find the point-slope equation of the line with slope -3 that passes through the point (2, -10).

MatroZZZ [7]

Answer:

Step-by-step explanation

(-y-y1)/(x-x1)= m

y-(-10)/(x-2)= -3

y= -3x -4

4 0

2 years ago

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A garden shed is 5 m from back to front; the back wall is 1.9 m high and the tool

krek1111 [17]

Answer:

yagni

Step-by-step explanation:

de bo dam me ha te cu te mala panga uh hu ayeee

7 0

2 years ago

A bag contains 35 coins, some dimes and some quarters. The total amount of money in the bag is $4.85. How many dimes and how man

miskamm [114]

Answer:

9 quarters and 26 dimes

Step-by-step explanation:

your welcome :)

5 0

10 months ago