All categories

3 years ago

What is the missing leg length

Mathematics

2 answers:

Rom4ik [11]3 years ago

8 0

Answer:

b = 16

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

12^2 + b^2 = 20^2

144+b^2 = 400

Subtract 144 from each side

b^2 = 400-144

b^2 = 256

Take the square root of each side

sqrt(b^2) = sqrt(256)

b = 16

Nana76 [90]3 years ago

4 0

The answer is 16 meters

You might be interested in

Write the statement in the if then form perpendicular lines intersect to form right angles

kvv77 [185]

Answer: If perpendicular lines intersect, then they form right angles.

Step-by-step explanation:

You take the first part, "perpendicular lines intersect", and add the "if" to it. Then, you take the second part, "to form right angles", and add the "then" in front of it to get your answer, "If perpendicular lines intersect, then they form right angles."

Hope it helps! :)

8 0

3 years ago

During which interval was the bicyclists speed the greatest?

den301095 [7]

Answer:

The first our to the second hour

8 0

3 years ago

HALLP QUICKKKK

Rina8888 [55]

To solve this we are going to use the formula for speed: $S= \frac{d}{t}$
where
$S$ is the speed
$d$ is the distance
$t$ is the time

Let $S_{l}$ be the speed of the boat in the lake, $S_{a}$ the speed of the boat in the river, $t_{l}$ the time of the boat in the lake, and $t_{a}$ the time of the boat in the river.

We know for our problem that the current of the river is 2 km/hour, so the speed of the boat in the river will be the speed of the boat in the lake minus 2km/hour:
 $S_{a}=S_{l}-2$
We also know that in the lake the boat sailed for 1 hour longer than it sailed in the river, so:
 $t_{l}=t_{a}+1$

Now, we can set up our equations.
Speed of the boat traveling in the river:
 $S_{a}= \frac{6}{t_{a} }$
But we know that $S_{a}=S_{l}-2$ , so:
$S_{l}-2= \frac{6}{t_{a} }$ equation (1)

Speed of the boat traveling in the lake:
$S_{l}= \frac{15}{t_{l} }$
But we know that $t_{l}=t_{a}+1$ , so:
$S_{l}= \frac{15}{t_{a}+1}$ equation (2)

Solving for $t_{a}$ in equation (1):
$S_{l}-2= \frac{6}{t_{a} }$
$t_{a}= \frac{6}{S_{l}-2}$ equation (3)

Solving for $t_{a}$ in equation (2):
$S_{l}= \frac{15}{t_{a}+1}$
$t_{a}+1= \frac{15}{S_{l}}$
$t_{a}=\frac{15}{S_{l}}-1$
$t_{a}= \frac{15-S_{l}}{S_{l}}$ equation (4)

Replacing equation (4) in equation (3):
$t_{a}= \frac{6}{S_{l}-2}$
$\frac{15-S_{l}}{S_{l}}=\frac{6}{S_{l}-2}$

Solving for $S_{l}$ :
$\frac{15-S_{l}}{S_{l}}=\frac{6}{S_{l}-2}$
$(15-S_{l})(S_{l}-2)=6S_{l}$
$15S_{l}-30-S_{l}^2+2S_{l}=6S_{l}$
$S_{l}^2-11S_{l}+30=0$
$(S_{l}-6)(S_{l}-5)=0$
$S_{l}=6$ or $S_{l}=5$

We can conclude that the speed of the boat traveling in the lake was either 6 km/hour or 5 km/hour.

3 0

4 years ago

How do I get started?

natita [175]

I think this is right maybe

6 0

4 years ago

Gouilleul Sequence.

harkovskaia [24]

Answer:

Step-by-step explanation:

No idea what a gouilleul Sequence is, but hopefully it will help to show how I would find the answer.

A geometric sequence means a term is multiplied by something over and over So say we start with 100 and the common ratio is .5 then the sequence would go 100,50,25,12.5,6.25 and so on. Another way of writing it is:

100*.5^0 = 100

100*5^1 = 50

100*.5^2 = 100*.25 = 25

and so on.

ANyway, here we have the first and fourth term. so that's 3.5*x^0 and 3.5*x^3. Keep in mind the exponent will be n-1 when the term you want to find is the nth term. Anyway, we know 3.5*x^3 = 28, so we just use algebra to find x, which is the common ratio.

3.5*x^3 = 28

x^3 = 8

x = 2

So the common ratio is 2, or in other words it keeps doubling. You could try it real quick, keep doubling the starting term 3.5

3.5, 7, 14, 28 and 28 is the fourth term.

So we know the common ratio. you could just add the four terms listed then for part b, but there is an equation, for in case they ask you to find the sum of say the first 100 terms. that wouldn't be fun. Anyway, the formula is a((1-r^n)/(1-r)) where a is the starting term, r is the common ratio and n is the number term. In your case that's 3.5((1-2^4)/(1-2)) = 52.5. You can actually check since it's only 4 terms. 3.5 + 7 + 14 + 28 = 52.5.

If you want to know how that formula was gotten let em know and I can explain or give a link to a video or something to show.

6 0

3 years ago