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2 years ago

Write the equation of a line that is parallel to y = 1/2x - 4 and that passes through the point (9, -6)

Mathematics

1 answer:

timofeeve [1]2 years ago

7 0

//To have the lines parallel, the gradients must be the same.

y -- 6 = 1/2 (x - 9)
y + 6 = 1/2 x -9/2
y = 1/2 x - 10.5

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What is the slope of the line through (-1,8) and (3,-4)?

laila [671]

Hey there!!

How do we find slopes ?

Slope = $\frac{y2-y1}{x2-x1}$

We are given with two co-ordinates :

(-1,8) and (3,-4)

Hence, the slope is :

$\frac{-4-8}{3+1}$

... $\frac{-12}{4}$ = -3

The slope is -3.

Hope my answer helps!

4 0

2 years ago

What is the equation of a circle with a center located at (-3, 4) and a diameter of 14?

AnnZ [28]

Answer: (x + 3)^2 + (y - 4)^2 = 49

Step-by-step explanation:

The equation of a circle given the center and radius: (x - h)^2 + (y - k)^2 = r^2

Given: center (-3,4) ; h = -3 and k = 4

diameter = 14

To find the radius: divide the diameter by 2 = 14/2 = 7 = r

Center: (-3,4) and radius: 7

Equation of a circle: (x - h)^2 + (y - k) ^2 = r^2

Substitute h = -3, k = 4, r = 7

(x - (-3))^2 + (y - 4)^2 = 7^2

Answer:

Equation of the circle: (x + 3)^2 + (y - 4)^2 = 49

7 0

3 years ago

What is the maximum height of of Anna's golf ball? The equation is y=x−0.04x2.

elena-s [515]

Given:

The height of a golf ball is represented by the equation:

$y=x-0.04x^2$

To find:

The maximum height of of Anna's golf ball.

Solution:

We have,

$y=x-0.04x^2$

Differentiate with respect to x.

$y'=1-0.04(2x)$

$y'=1-0.08x$

For critical values, $y'=0$ .

$1-0.08x=0$

$-0.08x=-1$

$x=\dfrac{-1}{-0.08}$

$x=12.5$

Differentiate y' with respect to x.

$y''=(0)-0.08(1)$

$y''=-0.08$

Since double derivative is negative, the function is maximum at $x=12.5$ .

Substitute $x=12.5$ in the given equation to get the maximum height.

$y=(12.5)-0.04(12.5)^2$

$y=12.5-0.04(156.25)$

$y=12.5-6.25$

$y=6.25$

Therefore, the maximum height of of Anna's golf ball is 6.25 units.

7 0

2 years ago

The perimeter of a rectangle is 64 units. Can the length X of a rectangle be 20 units when it's width y is 11 units

Blababa [14]

Nope. Perimeter = sum of all sides

P = 20 + 11 + 20 + 11 = 62 and not 64

So, it is not possible.

4 0

2 years ago

Janna spends 1.25 hours of her 8 hour work day answering email messages. What percentage of the work day is this time

dusya [7]

1.25 divided by 8 =0.15635×100=15.6% or round up to 16%

3 0

2 years ago