Math 9th grade<br> Number 17.

given that oa=2x+9y ob=4x+8y and cd= 4x-2y, explain the geometrical relationships between the straight lines ab and cd mathswatc

tangare [24]

The geometrical relationships between the straight lines ab and cd

is the straight line ab is parallel to the straight line cd

Step-by-step explanation:

Let us revise some notes:

If a line is drawn from the origin and passes through point A (a , b), then the equation of OA = ax + by
If a line is drawn from the origin and passes through point B (c , d), then the equation of OB = cx + dy
To find the equation of AB subtract OB from OA, then AB = (c - a)x + (d - b)y
The slope of line AB = $\frac{-coefficient(x)}{coefficient(y)}$

∵ oa = 2 x + 9 y

∵ ob = 4 x + 8 y

∵ ab = OB - OA

∴ ab = (4 x + 8 y) - (2 x + 9 y)

∴ ab = 4 x + 8 y - 2 x - 9 y

- Add like terms

∴ ab = (4 x - 2 x) + (8 y - 9 y)

∴ ab = 2 x + -y

∴ ab = 2 x - y

∵ The slope of ab = $\frac{-coefficient(x)}{coefficient(y)}$

∵ Coefficient of x = 2

∵ Coefficient of y = -1

∴ The slope of ab = $\frac{-2}{-1}=2$

∵ cd = 4 x - 2 y

∵ Coefficient of x = 4

∵ Coefficient of y = -2

∴ The slope of cd = $\frac{-4}{-2}=2$

∵ Parallel lines have same slopes

∵ Slope of ab = slope of cd

∴ ab // cd

The geometrical relationships between the straight lines ab and cd

is the straight line ab is parallel to the straight line cd

Learn more;

You can learn more about the parallel lines in brainly.com/question/10483199

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4 0

3 years ago

Find an equation of the circle that has center (-4,3) and passes through (6,-4).

kumpel [21]

Answer:

$(x+4)^2+(y-3)^2=149$

Step-by-step explanation:

The equation of a circle is $(x-h)^2+(y-k)^2=r^2$ where $(h,k)$ is the center of the circle and $r$ is the radius of the circle.

Given that $(h,k)\rightarrow(-4,3)$ and it passes $(6,-4)$ , their distance between each other must the radius of the circle, so we can use the distance formula to find the radius:

$d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\\\d=\sqrt{(-4-3)^2+(6-(-4))^2}\\\\d=\sqrt{(-7)^2+10^2}\\\\d=\sqrt{49+100}\\\\d=\sqrt{149}$

Therefore, if the length of the radius is $r=\sqrt{149}$ units, then $r^2=149$ , making the final equation of the circle $(x+4)^2+(y-3)^2=149$

5 0

3 years ago

If F(x) = 5x - 7 and G(X) = x2 - 41, what is G(F(x))?

Viktor [21]

C is the answer to this

4 0

3 years ago

Solve the system by substitution. <br><br> y= 4x + 22<br> y= -7x<br><br> (__,__)

Margarita [4]

Answer:

Step-by-step explanation:

Isolate the term of x and y from one side of the equation.

y=4x+22 and y=-7x

y=-7x=4x+22

Solve.

-7x=4x+22

x=2

Substitute.

y=-7x, x=-2

y=-7(-2)

Solve.

Multiply.

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Therefore, the final answer is (-2,14).

I hope this helps you! Let me know if my answer is wrong or not.

4 0

3 years ago

An open box is to be made out of a 12-inch by 20-inch piece of cardboard by cutting out squares of equal size from the four corn

Natali5045456 [20]

Answer:

Length = 15.14, width = 7.14 and height = 2.43 inches.

( correct to the nearest hundredth).

Step-by-step explanation:

Let the lengths of the squares cut out be x inches.

Then the width of the box will be 12 - 2x and the length will be

20 - 2x inches.

The height of the box is x inches.

Volume V = x(20-2x)(12-2x)

To find the value of x when V is a maximum we find the derivative and equate it to zero.

V = x( 240 - 64x + 4x^2)

V = 4x^3 - 64x^2 + 240x

dV/dx = 12x^2 - 128x + 240 = 0

4(3x^2 - 32x + 60) = 0

This won't factor so we use the formula:

x = [-(-32) +/- √((-32)^2 - 4*3*60)] / 6

= 8.24, 2.43.

So one of these gives a maximum Volume.

The second derivative

d^2V/dx^2 = 24x - 128

When x = 8.24, this = 69.6 (positive) so this gives a minimum.

x = 2.43 gives a negative value ( -49.7) so this is the maximum

So the dimensions are:-

length = 20 - 2(2.43) = 15.14

width = 12 - 2(2.43) = 7.14

height = 2.43.

7 0

3 years ago

Math 9th grade Number 17.