Solve for a variable y<br> please show how<br> 2y=6x-8

Caroline , Colin and Sarah Share some money , Caroline gets 1/10 of the money. Colin and Sarah Share the rest in the ratio 2:7 w

Sati [7]

Answer:

1/5

Step-by-step explanation:

10/10-1/10=9/10=Colin and Sarah share

2x+7x=9x=Colin and Sarah share

9x=9/10

x=1/10

Colin=2x=2/10=1/5

6 0

3 years ago

Given the function h(x), determine the functions which correctly decompose h(x) into component functions f(x) and g(x) so that h

nataly862011 [7]

$\text{Hi there! :)}$

$\large\boxed{g(x) = 7x + 2\text{ , } f(x) = \sqrt{x} - 10}$

$\text{h(x) = f(g(x)), so determine what g(x) was substituted into f(x):}\\\\\text{Given the equation } h(x) = \sqrt{7x +2}- 10:\\\\\text{In the part of the equation with a variable, we see that "7x + 2" is in a square root:}$

$\text{Therefore, we can say that g(x) = 7x + 2:}\\\\\text{If h(x) = f(7x + 2), then f(x) must be:}\\\\f(x) = \sqrt{x} - 10$

$\text{The respective functions would be:}\\\\g(x) = 7x + 2\\\\f(x) = \sqrt{x} - 10$

7 0

3 years ago

Given the arithmetic series 2 4 6...=420. find the first term a and the common difference d

Trava [24]

First term is 2 and the common difference is the value by which it increases which is 2.

7 0

3 years ago

A 5.5-foot-tall woman walks at 4 ft/s toward a street light that is 27.5 ft above the ground. what is the rate of change of th

Citrus2011 [14]

Answer:

Rate at which the shadow is moving = -5 ft/s.

Step-by-step explanation:

I can do the second part for you:

If the distance of the woman from the wall is Xp , the length of the shadow is Xs and the distance from the tip of the shadow to the wall is X we have the relation:

X = Xp + Xs.

We need to find X' (the rate that the tip of the shadow is moving). at Xp = 16 and X'p = -4 ft/s.

We need a relation between X and Xp so we have to eliminate Xs.

By similar triangles 5.5 / 27.5 = Xs / x

1/5 = Xs/x

Xs = x /5 so substituting in the above relation:

X = Xp + X/5

4X/5 = Xp

X = 5Xp / 4

Taking derivatives:

X' = 5X'p / 4

Now X'p is given as - 4 so

X' = -20/4 = -5 ft/s.

3 0

3 years ago

This figure is made up of a quadrilateral and a semicircle.

vodomira [7]

Here the figure is made up of a quadrilateral and a semi circle.

ABCD is the quadrilateral here. We will find the sides of the quadrilateral by using the distance formula.

If (x₁, y₁) and (x₂, y₂) are two points given, then the distance between two points by using distance formula is,

$d =\sqrt({ x_{1}-x_{2})^2 +( y_{1} -y_{2} )^2}$

The co-ordinate of A is (-1,2) and co-ordinate of B is (-2,-1).

So the length of side AB = $\sqrt{(-1-(-2))^2+(2-(-1))^2}$

= $\sqrt{(-1+2)^2+(2+1)^2}$ (As negative times negative is positive)

= $\sqrt{(1)^2+(3)^2} =\sqrt{1+9} =\sqrt{10}$

The co-ordinate of C is (4,-3) and D is (5,0)

The length of side CD

= $\sqrt(4-5)^2+(-3-0)^2}$

= $\sqrt{(-1)^2+(-3)^2}$

= $\sqrt{1+9} =\sqrt{10}$

So the sides AB and CD are equal.

The length of side AD

= $\sqrt{(-1-5)^2+(2-0)^2}$

= $\sqrt{(-6)^2+(2)^2} =\sqrt{36+4} =\sqrt{40}$

The length of side BC

= $\sqrt{(-2-4)^2+(-1-(-3))^2}$

= $\sqrt{(-2-4)^2+(-1+3)^2}$

= $\sqrt{(-6)^2+(2)^2}=\sqrt{36+4} =\sqrt{40}$

So the lengths of the sides AD and BC are equal.

So the quadrilateral is a rectangle whose length is $\sqrt{40}$ and width is $\sqrt{10}$ .

Area of a rectangle = length × width

= $(\sqrt{40}) (\sqrt{10})$

= $\sqrt{(40)(10)}=\sqrt{400}$

= $20 unit^2$

Now the diameter of the semicircle is the side AD = $\sqrt{40}$

So, the radius of the semi-circle = $\frac{\sqrt{40}}{2}$

= $\frac{\sqrt{(4)(10)}}{2}$

= $\frac{(\sqrt{4})(\sqrt{10})}{2}$

= $\frac{2\sqrt{10}}{2}$ = $\sqrt{10}$

Area of semi-circle = $\frac{1}{2} \pi r^2$ , where r is the radius.

= $\frac{1}{2} \pi (\sqrt{10})^2$

= $\frac{1}{2} \pi (10)$

= $\frac{(\pi)(10)}{2}$

= $\frac{10\pi}{2} = 5\pi$ = $15.7 unit^2$ ( Approximately taken to the nearest tenth)

Total area of the figure = $(20+15.7) unit^2$ = $35.7 unit^2$

We have got the required answer.

Option a is correct here.

3 0

3 years ago

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Solve for a variable y please show how 2y=6x-8