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3 years ago

I WILL MARK BRAINIEST

Mathematics

1 answer:

yan [13]3 years ago

5 0

Answer:

x=20

Step-by-step explanation:

7x+2x=180(being straight angle )

9x=180

x=180/9

x=20

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The hypotenuse of a right triangle is 6 cm and one side is 2 cm longer than the other side. Find the length of each side to one

MA_775_DIABLO [31]

Answer:

The two legs of the right triangle are approximately 3.1 cm and 5.1 cm and the hypotenuse is 6 cm.

Step-by-step explanation:

Let x be one leg of the right triangle.

Since the other leg is two centimeters longer, it can be represented by the expression:

$x + 2 \text{ cm}$

According to the Pythagorean Theorem, for a right triangle:

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

Where c is the hypotenuse and a and b are the two legs.

The hypotenuse is given to be 6 cm and the two legs are x and (x + 2). Hence:

$(x)^2 + (x+2)^2 = 6^2$

Solve for x. Simplify:

$x^2 + (x^2 + 4x + 4) = 36$

Simplify:

$2x^2 + 4x + 4 = 36$

Subtract:

$2x^2 + 4x - 32 =0$

Divide:

$x^2 + 2x - 16 = 0$

The equation is not factorable, so we can consider using the quadratic formula:

$\displaystyle x = \frac{-b\pm\sqrt{b^2 -4ac}}{2a}$

In this case, a = 1, b = 2, and c = -16. Substitute:

$\displaystyle x= \frac{-(2)\pm\sqrt{(2)^2-4(1)(-16)}}{2(1)}$

And evaluate:

$\displaystyle \begin{aligned}x &= \frac{-2\pm\sqrt{68}}{2} \\ \\ &= \frac{-2\pm\sqrt{4\cdot 17}}{2} \\ \\ &= \frac{-2\pm2\sqrt{17}}{2} \\ \\ &= -1 \pm \sqrt{17} \end{aligned}$

Hence, our two solutions are:

$\displaystyle x = -1 + \sqrt{17} \approx 3.1\text{ or } x = -1 - \sqrt{17} \approx -5.1$

Lengths cannot be negative, so we can ignore the second solution.

Hence, the value of x or the first side length is about 3.1 centimeters.

Since the other side length is two centimeters longer, the other side is about 5.1 centimeters.

In conclusion, the two legs of the right triangle are approximately 3.1 cm and 5.1 cm and the hypotenuse is 6 cm.

4 0

3 years ago

Help. I have no idea how to do this

mr_godi [17]

Mhm.... Word problems.. So! Angle Side Angle :) proving that 2 triangles are equal.
You need to prove that DC is equal to BA. Now....
DB == AC.
which you can subtract BC from both sides!
DB-BC = AC-CB. leaving you with DC= AB

Now by Side Angle Side, The angles are =, 2 sides are equal, means the 2 triangles are equal :) If the triangles are equal, the 2 remaining sides must be equal

7 0

3 years ago

Coach leonardo used 9 1/2 meters of string to mark a soccer field for a game. He also used 2 2/5 meters of string to mark a spot

allsm [11]

Answer:

10 19/10 meters

Step-by-step explanation:

Step one:

given data

let the amount of string used for the soccer field be x

and the amount used for coach spot be y

Also, let the total string used be represented as T

Step two:

Hence the expression for the total is

T= x+y

T= 9 1/2+ 2 2/5

T= 9.5+ 2.4

T= 11.9

T= 119/10 meters

T= 10 19/10 meters

7 0

3 years ago

Experts/ace/trusted helpers helppp meee plzzzz

zubka84 [21]

The missing angle is: 25 degrees

4 0

3 years ago

What are the solutions of the quadratic equation 49x^2=9?

Flauer [41]

Simplifying 49x^2 + -9 = 0
Reorder the terms: -9 + 49x^2 = 0
Solving -9 + 49x^2 = 0 Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '9' to each side of the equation. -9 + 9 + 49x^2 = 0 + 9
Combine like terms: -9 + 9 = 0 0 + 49x^2 = 0 + 9 49x^2 = 0 + 9
Combine like terms: 0 + 9 = 9 49x^2 = 9
Divide each side by '49'. x^2 = 0.1836734694
Simplifying x^2 = 0.1836734694
Take the square root of each side: x = {-0.428571429, 0.428571429}

hope this helps!!

5 0

3 years ago