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3 years ago

Need help with this problem its really complicated for me

Mathematics

1 answer:

ddd [48]3 years ago

8 0

You can write a proportion because the two triangles are similar

$\frac{x}{x-2}$ = $\frac{x + x + 5}{x + 1 + x - 2}$ (the second fraction is longer because I added the full lengths of the larger triangle) cross multiply to get (x)(x + 1 + x - 2) = (x - 2)(x + x + 5)

which simplifies to (x)(2x - 1) = (x - 2)(2x + 5)

then 2x² - x = 2x² + 5x -4x - 10

then 2x² - x = 2x² + x - 10

then 2x² = 2x² + 2x - 10

subtract 2x² from both sides to get 0 = 2x - 10

add 10 to both sides to get 10 = 2x

divide both sides by 2 to get 5 = x

You might be interested in

What is the value of z?

UNO [17]

Answer:

z =23

Step-by-step explanation:

The three angles in a triangle add to 180 degrees.

62+95+z = 180

Combine like terms

157 +z = 180

Subtract 157 from each side

157-157 +z = 180-157

z =23

3 0

3 years ago

A carpenter has a rectangular wooden board. The diagonal of the board is 18 inches long and one side of the board is 12 inches l

BaLLatris [955]

In this question, it is given that the diagonal of the board is 18 inches long and one side of the board is 12 inches long.

Let the other side is of length b inches .

Now we use pythagorean identity, which is

$a^2 + b ^2 = c^2$

Here, a = 12 and c=18

Substituting these values, we will get

$12^2 + b^2 = 18^2 \\ 144 + b ^2 = 324 \\ b^2 = 324-144 \\ b^2 = 180 \\ b= \sqrt{180} \\ b = 13.4164 inches$

And the formula of perimeter is

$Perimeter = 2(Sum\ of \ legs)$

Substituting the values of the two legs, we will get

$Perimeter = 2(12+13.4164) = 50.83 inches$

3 0

3 years ago

Read 2 more answers

The perimeter of a rectangular pool is 326 M if the length of the pool is 87 M what is its width

sveta [45]

Half the perimeter is equal to the length plus the width.

326 /2 = 163

Length + width = 163

87 + width = 163

Width = 163 - 87

Width = 76 meters

4 0

2 years ago

Please. Answer Fast! Use composition to determine if G(x) or H(x) is the inverse of F(x) for the

s344n2d4d5 [400]

Answer:

A. H(x) is an inverse of F(x)

Step-by-step explanation:

The given functions are:

$F(x)=\sqrt{x-2}$

$G(x)=(x-2)^2$

$H(x)=x^2+2$

We compose F(x) and G(x) to get:

$(F\circ G)(x)=F(G(x))$

$(F\circ G)(x)=F((x-2)^2)$

$(F\circ G)(x)=\sqrt{(x-2)^2-2}$

$(F\circ G)(x)=\sqrt{x^2-4x+4-2}$

$(F\circ G)(x)=\sqrt{x^2-4x+2}$

$(F\circ G)(x)\ne x$

Hence G(x) is not an inverse of F(x).

We now compose H(x) and G(x).

$(F\circ H)(x)=F(H(x))$

$(F\circ H)(x)=F(x^2+2)$

$(F\circ H)(x)=\sqrt{x^2+2-2}$

We simplify to get:

$(F\circ H)(x)=\sqrt{x^2}$

$(F\circ H)(x)=x$

Since $(F\circ H)(x)=x$ , H(x) is an inverse of F(x)

3 0

2 years ago

Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:

ryzh [129]

First find the critical points of f :

$f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7$

$\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1$

$\dfrac{\partial f}{\partial y}=6y=0\implies y=0$

so the point (1, 0) is the only critical point, at which we have

$f(1,0)=-7$

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

$f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t$

Find the critical points of g :

$\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0$

$\implies\sin t=0\text{ OR }1+5\cos t=0$

$\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi$

where n is any integer. We get 4 critical points in the interval [0, 2π) at

$t=0\implies f(10,0)=155$

$t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299$

$t=\pi\implies f(-10,0)=235$

$t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299$

So f has a minimum of -7 and a maximum of 299.

4 0

3 years ago