All categories

2 years ago

Find the indicated side of the right triangle.

Mathematics

1 answer:

Advocard [28]2 years ago

8 0

Answer:

?=9

Step-by-step explanation:

We have a special right triangle, the 45-45-90 triangle.

In a 45-45-90 triangle, the side lengths are x, and the hypotenuse is x√2.

Since we know that the side length is 9, this means that:

$x=9\\\text{Hypotenuse}=x\sqrt2\\\text{Hypotenuse}=9\sqrt2$

The ? is 9.

You might be interested in

You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the co

Norma-Jean [14]

Choosing the first tile:

At first, there are 7 tiles.

You are interested in choosing a 5. There is only one tile with a 5.

p(5) = 1/7

Choosing the second tile:

After the 5 has been taken, now there are 6 tiles left.

Only one tile has the number 6.

p(6) = 1/6

The overall probability of choosing a 6 after a 5 is the product of the individual probabilities:

p( 5 then 6) = 1/7 * 1/6 = 1/42

Answer: The probability of choosing a 5 and then a 6 is 1/42

7 0

2 years ago

Can you please answer this question

tamaranim1 [39]

$3tan^{2} \theta +7sec\theta=3$
First I converted the equation terms into sine and cosine.
$tan^{2}\theta = \frac{sin^{2}\theta}{cos^{2}\theta}$ and $sec\theta= \frac{1}{cos\theta}$
Substitution:
$\frac{3sin^2\theta}{cos^2\theta} + \frac{7}{cos\theta} =3$
Common Denominator Created:
$\frac{3sin^2\theta}{cos^2\theta} + \frac{7cos\theta}{cos^2\theta} =3$
Multiply each term by the LCD:
$3sin^2\theta+7cos\theta=3cos^2\theta$
Substitution: Recall ⇒ $sin^2\theta =1-cos^2\theta$
$3(1-cos^2\theta)+7cos\theta=3cos^2\theta$
Distribute and collect all terms on one side:
$6cos^2\theta-7cos\theta-3=0$
Factor and set each factor equal to 0:
$(2cos\theta-3)(3cos\theta+1)=0$
$2cos\theta-3=0$ ⇒ $theta=cos^{-1} \frac{3}{2}$
$3cos\theta+1=0$ ⇒ $theta=cos^{-1} \frac{-1}{3}$
The 2nd factor provides only possible answer 109.5 degrees

4 0

3 years ago

The owner of an auto repair shop studied the waiting times for customers who arrive at the shop for an oil change. The following

labwork [276]

Answer:

(d)0.6

Step-by-step explanation:

(a)Frequency Distribution

$\left|\begin{array}{c|c}$Waiting Time(in Minutes)&$Frequency\\-----------&--\\0-4&4\\5-9&8\\10-14&5\\15-19&2\\20-24&1\\--&--\\Total&20\end{array}\right|$

(b)The relative frequency distribution.

$\left|\begin{array}{c|c}$Waiting Time(in Minutes)&$Relative Frequency\\-----------&--\\0-4&4/20=0.2\\5-9&8/20=0.4\\10-14&5/20=0.25\\15-19&2/20=0.1\\20-24&1/20=0.05\\--&--\\Total&1\end{array}\right|$

(c)The cumulative frequency distribution.

$\left|\begin{array}{c|c|c}$Waiting Time(in Minutes)&$Frequency&$Cumulative Frequency\\-----------&--&---\\0-4&4&4\\5-9&8&12\\10-14&5&17\\15-19&2&19\\20-24&1&20\\--&--&--\\Total&20\end{array}\right|$