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goldenfox [79]
3 years ago
15

The perimeter of an isosceles triangle is 25 ft. The length of the third side is 2 ft less than the length of one of the equal s

ides. Find the measurement of the three sides of the triangle.
Mathematics
1 answer:
Fittoniya [83]3 years ago
8 0

Answer:

The side lengths are 9, 9 and 7.

Step-by-step explanation:

The sum of the 2 equal sides plus the shorter side is 25 ft.

Representing these unknowns:

2 sides are of length s, and the third (shortest) side is then s - 2.

Thus,  s + s + (s - 2) = 25, or 3s = 27.  Thus, s = 9 and s-2 = 7

The side lengths are 9, 9 and 7.

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Solve the equation if 0 degrees&lt;=x&lt;=360 degrees.<br> tanx=sqrt 3
storchak [24]

Answer:

Step-by-step explanation:

hello :

tanx = √3        0°≤x≤360°

x = 60°

x=240°

4 0
3 years ago
A complex number, represented by z = x + iy, may also be visualized as a 2 by 2 matrix
Marat540 [252]

Answer:

Step-by-step explanation:

A) Suppose that we have the complex numbers

z= x + iy \quad \text{and} \quad \\\\ \tilde{z}=\tilde{x} + i \tilde{y}

Remember that to sum complex numbers, we sum the real parts of the two numbers to get the real part and the imaginary parts of the two numbers to get the imaginary part. Hence,  

z+\tilde{z} = (x + i y) + (\tilde{x} + i \tilde{y}) = (x + \tilde{x})+i (y+\tilde{y})

On the other hand, if we sum the matrix visualizations of z \quad \text{and} \quad \tilde{z} we get

\left[\begin{array}{cc}x &y\\-y&x\end{array}\right] + \left[\begin{array}{cc}\tilde{x}&\tilde{y}\\ -\tilde{y}&\tilde{x}\end{array}\right] = \left[\begin{array}{cc}x + \tilde{x}& y + \tilde{y}\\-(y+\tilde{y})&x+\tilde{x}\end{array}\right]

which is the matrix visualization of z + \tilde{z}.

To multiply two complex numbers, we use the distributive law to multiplly and then separete the real part from the imaginary part

z \cdot \tilde{z}= (x + iy) \cdot (\tilde{x} + i \tilde{y})=(x \tilde{x} + i x \tilde{y} + i \tilde{x} y - y\tilde{y} ) = (x\tilde{x}-y\yilde{y})+i(x\tilde{y}+\tilde{x}y)

Again, if we multiply the matrix visualizations of z \quad \text{and} \quad \tilde{z} we get

\left[\begin{array}{cc}x&y\\-y&x\end{array}\right]\left[\begin{array}{cc}\tilde{x}&\tilde{y}\\-\tilde{y}&\tilde{x}\end{array}\right] = \left[\begin{array}{cc}x\tilde{x}-y\tilde{y}&x\tilde{y}+y\tilde{x}\\-y\tilde{x}-x\tilde{y}&x\tilde{x}-y\tilde{y}\end{array}\right]

which is the matrix viasualization of z\cdot\tilde{z}.

B)  Since the usual matrix operations are consisten with the usual addition and multiplication rules in the complex numbers, we can use them to find the multiplicative inverses of a complex number z=x+iy.

We are looking for the complex number z^{-1}=(x+iy)^{-1} which in terms of matrices is equivalent to find the matrix

\left[\begin{array}{cc}x&y\\-y & x\end{array}\right]^{-1}= \dfrac{1}{x^{2}+y^{2}} \left[\begin{array}{ccc}x&-y\\y&x\end{array}\right]    

Hence,

z^{-1}=\dfrac{1}{x^2 +y^2} (x-iy)=\dfrac{1}{|z|^2}(x-iy)

6 0
3 years ago
My question is: 1x - 47y = 310
musickatia [10]

Answer:

x-intercept(s):  

(

310

,

0

)

y-intercept(s):  

(

0

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−

310

47

)

Step-by-step explanation:

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fredd [130]

Answer:

Step-by-step explanation:

(9 - 7)/(4 + 2) = 2/6 = 1/3 is the slope of the line

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