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1 year ago

I need a simple but deep explanation on how to solve this

Mathematics

1 answer:

never [62]1 year ago

3 0

Let x be the missing side. Since we have a right triangle, we can apply Pythagorean theorem:

$x^2+8^2=10^2$

Remember that the hypotenuse (10 in our case) is always in front of the right angle. Then, from the last result, we have

$x^2+64=100$

By subtracting 64 to both sides, we get

$x^2=36$

then x is given by

$\begin{gathered} x=\sqrt[]{36} \\ x=6 \end{gathered}$

Therefore, the answer is: 6

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2. A right triangle has a hypotenuse of 15 cm. What are possible lengths for the two legs of the triangle? Explain your reasonin

dolphi86 [110]

Answer:

Two possible lengths for the legs A and B are:

B = 1cm

A = 14.97cm

Or:

B = 9cm

A = 12cm

Step-by-step explanation:

For a triangle rectangle, Pythagorean's theorem says that the sum of the squares of the cathetus is equal to the hypotenuse squared.

Then if the two legs of the triangle are A and B, and the hypotenuse is H, we have:

A^2 + B^2 = H^2

If we know that H = 15cm, then:

A^2 + B^2 = (15cm)^2

Now, let's isolate one of the legs:

A = √( (15cm)^2 - B^2)

Now we can just input different values of B there, and then solve the value for the other leg.

Then if we have:

B = 1cm

A = √( (15cm)^2 - (1cm)^2) = 14.97

Then we could have:

B = 1cm

A = 14.97cm

Now let's try with another value of B:

if B = 9cm, then:

A = √( (15cm)^2 - (9cm)^2) = 12 cm

Then we could have:

B = 9cm

A = 12cm

So we just found two possible lengths for the two legs of the triangle.

4 0

3 years ago

Help!!!!!!!!! Please!!!!

Sedaia [141]

your answer is letter A,

6 0

3 years ago

jacob wants to buy packets of fruit juice. on tuesday, he buys 8 packets of orange and 6 packets of Apple the packets make a tot

ioda

Answer:

Each packet of orange can make 2 cups of juice and each packets of Apple can make 3 cups of juice.

Step-by-step explanation:

Let number of cups of juice in each packet of orange be 'x'.

Let number of cups of juice in each pack of apples be 'y'.

Given:

On Tuesday;

Number of packets of oranges = 8

Number of packets of apples = 6 packets.

Amount of fruit juice = 34 cups

So we can say that;

Amount of fruit juice is equal to sum of Number of packets of oranges multiplied by number of cups of juice in each packet of orange and Number of packets of apples multiplied by number of cups of juice in each pack of apples.

framing in equation form we get;

$8x+6y=34 \ \ \ \ equation \ 1$

On Wednesday;

Number of packets of oranges = 14

Number of packets of apples = 6

Amount of fruit juice = 46 cups

So we can say that;

framing in equation form we get;

$14x+6y=46 \ \ \ \ equation \ 2$

Now Subtracting equation 1 from equation we get;

$14x+6y-(8x+6y)=46-34\\\\14x+6y-8x-6y=12\\\\6x=12$

Now dividing both side by 6 we get;

$\frac{6x}{6}=\frac{12}{6}\\\\x=2\ cups$

Now we will substitute the value of 'x' in equation 1 we get;

$8x+6y=34\\\\8\times2+6y=34\\\\16+6y=34$

Subtracting both side by 16 we get;

$16+6y-16=34-16\\\\6y= 18$

Now dividing both side by 6 we get;

$\frac{6y}{6}=\frac{18}{6}\\\\y=3$

Hence Each packet of orange can make 2 cups of juice and each packets of Apple can make 3 cups of juice.

5 0

3 years ago

What is the equation of the line that passes through the point (-5, 7)<br> and has a slope of –1/5?

Snowcat [4.5K]

The equation is y = -1/5x + 6

8 0

3 years ago

A bird flies at a top speed of 20,000 meters per hour. The bird flies 30,000 meters without stopping. a. For how many hours did

bazaltina [42]

Answer:

Step-by-step explanation:

7 0

2 years ago