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3 years ago

Find GH. write answer as an internet or as a decimal rounded to the nearest tenth ty

Mathematics

1 answer:

LiRa [457]3 years ago

8 0

Answer:

We can use trigonometric ratios to solve this

$cos(24)=GH/IH\\cos(24)=GH/5\\5 cos(24)=GH\\$

Using a cosine calculator we find that cos(24)=0.91354546 and 0.91354546 x 5=4.56

GH=4.5677273 or 4.57 rounded

Step-by-step explanation:

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Solve elimination 5x+y=9 10x-7y=-18

k0ka [10]

To solve this system by addition, notice that if we add these two equations together, neither one of our variables will cancel out.

In this situation, we need to set things up so that when we do add our two equations together, one of the variables will cancel out.

Notice that we have a 10x in our second equation. if we had a -10x in our first equation, then the x's would cancel out.

To create a -10x, we can multiply the top equation by -2 to get a -10x.

From there, rewriting our equation gives us -10x - 2y = -18.

Now the x's cancel. Just add the equations together

now to get the two-step equation -9y = -36.

Solving from here, y = 4.

Now plug y into either one of the equations

to find that x =1.

So our solution is (1,4).

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3 years ago

((W to the power of 2)) to the power of 4

UkoKoshka [18]

X^2^4 = x^8

Just multiply then 2 and 4 to get 8

8 0

3 years ago

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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.

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3 years ago

Determine which ordered pair is a solution of y = x2-2.

hodyreva [135]

Answer:

(-1 , -1)

Step-by-step explanation:

y = x²-2

(-1 , -1)

y = (-1)² - 2 = 1 - 2 = -1

7 0

3 years ago

Harry cycles 8 kilometres in 30 minutes. Calculate his average speed, in km/h.

TiliK225 [7]

It would be 16km/1 hour

7 0

3 years ago

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