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3 years ago

14

Write the equation of the line that passes through the points (8, –1) and (2, –5) in standard form, given that the point-slope f

orm is y + 1 =2/3 (x – 8).

1 answer:

Nitella [24]3 years ago

7 0

Answer:

you have to fisrt solve the equation of the buttonm part the find the common number between 5 to 8

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

Inessa [10]

Answer:

1. <em>Axis of symmetry</em>: x = 3

2. <em>Vertex:</em> (3,5)

3. <em>Solution of the equation</em>:

<u />

x-intercepts:

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

y-intercept: (0, -4)

Explanation:

<u>1. Equation:</u>

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

<u>2. </u><em><u>Axis of symmetry:</u></em>

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:

$x=3$

<em><u>3. Vertex</u></em>

<em><u /></em>

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)

<u>4. Find the x-intercepts</u>

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:

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

<u>5. Find the y-intercept</u>

<u />

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

4 years ago

Please calculate the volume of the triangular prism (MIDDLE SCHOOL MATH)

k0ka [10]

Answer:

52.374 cm*3

Step-by-step explanation:

the upper triangle is equal to the bottom triangle

Btw fyi the formula of calculating the value of a prism is:

area of the base × height

3 0

3 years ago

Alexander invested $320 in an account paying an interest rate of 1.5% compounded annually. Assuming no deposits or withdrawls we

boyakko [2]

Answer:

The amount is $418.35 and the interest is $98.35

Step-by-step explanation:

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3 years ago

A drinking glass has a height of 4 inch a length of 2 and a width of 2 inch while a baking pan has a width of 4 inch a length of

Alex Ar [27]

The answer would be two glasses

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3 years ago

-1/2y=1/2x+5 and y=2x+2

Anettt [7]

I assume this is the intersection of two lines, i.e. -1/2y is (-1/2)y. Please tell me if it's really -1/(2y).

(-1/2)y=(1/2)x+5

Multiplying both sides by -2

y = - x - 10

The other equation is

y = 2x + 2

We can equate them to find the meet

y = - x - 10 = 2x + 2

-3x = 12

x = -4

y = 2x + 2 = -6

Check: (-1/2)y=3, (1/2)x+5=3, equal, good

2x+2=2(-4)+2=-6=y, good

Answer: x=-4, y=-6

6 0

3 years ago