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3 years ago

What is the answer and how do I solve?

Mathematics

1 answer:

8_murik_8 [283]3 years ago

4 0

Because it is a 90° angle and the legs are congruent, the legs intersect with the hypotenuse at the same angle, so the other, unnamed angle at the bottom left is equal to x.

Now we can state that:

2x + 90 = 180
2x = 90
x = 45

You might be interested in

The equations in the triangle consist of (2x +1) and (5x +5)

Ainat [17]

2x + 1 + 5x + 5 + 90 = 180
7x + 96 = 180
7x = 180 - 96
7x = 84
x = 12

6 0

3 years ago

Solve the following differential equation: (2x+5y)dx+(5x−4y)dy=0 *Hint: they are exact C=.

Tpy6a [65]

Answer with Step-by-step explanation:

The given differential equation is

$(2x+5y)dx+(5x-4y)dy=0$

Now the above differential equation can be re-written as

$P(x,y)dx+Q(x,y)dy=0$

Checking for exactness we should have

$\frac{\partial P}{\partial y}=\frac{\partial Q}{\partial x}$

$\frac{\partial P}{\partial y}=\frac{\partial (2x+5y)}{\partial y}=5$

$\frac{\partial Q}{\partial x}=\frac{\partial (5x-4y)}{\partial x}=5$

As we see that the 2 values are equal thus we conclude that the given differential equation is exact

The solution of exact differential equation is given by

$u(x,y)=\int P(x,y)dx+\phi(y)\\\\u(x,y)=\int (2x+5y)dx+\phi (y)\\\\u(x,y)=x^2+5xy+\phi (y)$

The value of $\phi (y)$ can be obtained by differentiating u(x,y) partially with respect to 'y' and equating the result with P(x,y)

$\frac{\partial u}{\partial y}=\frac{\partial (x^2+5xy+\phi (y)))}{\partial y}=Q(x,y))\\\\5y+\phi '(y)=(5x-4y)\\\\\phi '(y)=5x-9y\\\\\int\phi '(y)\partial y=\int (5x-9y)\partial y\\\\\phi (y)=5xy-\frac{9y^2}{2}\\\\\therefore u(x,y)=x^2+10xy-\frac{9y^2}{2}+c$

5 0

3 years ago

Solve.

Serggg [28]

Answer:

The solution is (4, 0)

Step-by-step explanation:

Using Linear combination method to solve:

$2d + e = 8\\d - e = 4\\$

Since "e" have the same coefficient in both equation with opposite operator; we will add.

$(2d + d) + (e - e) = (8 + 4)\\3d = 12\\$

Divide both side by coefficient of d which is 3

$\frac{3d}{3} = \frac{12}{3} \\d = 4\\$

Since d = 4; put 'd' into any of the equation to get 'e'

$2d + e = 8\\2(4) + e = 8\\8 + e = 8\\e = 8 - 8\\e = 0\\$

Therefore, the solution is (4, 0)

5 0

4 years ago

Can i get help on this one ? im almost running our of points i would give 50 but i need more ;-; anyway

JulsSmile [24]

Answer:

Step-by-step explanation:

Let x = third side

Using the Triangle Inequality theorem which states that the sum of two sides of a triangle must be longer than the third side and the difference of the two sides is the lower limit of the third side, the answer to your question is that the third side must be between 3 and 13, or written using inequalities, 3 < third side (or x) < 13 is the range.

4 0

3 years ago

How to Write 3/9 in simplest form.

White raven [17]

To write it in simplest form, you must find a common factor.

In $\frac{3}{9}$ , 3 is a factor of both 3 and 9

3÷3=1 and 9÷3=3

So $\frac{3}{9} = \frac{1}{3}$

$\frac{1}{3}$ is your answer in simplest form.

3 0

3 years ago