All categories

3 years ago

Please help with this math problem! :)

Mathematics

1 answer:

miskamm [114]3 years ago

8 0

Answer:

Step-by-step explanation:

Diagonals intersect at 90

2z - 8 = 90

2z = 90 + 8

2z = 98

z = 98/2

z = 49

Adjacent sides are congruent

5x - 12 = 3x + 2

5x = 3x + 2 + 12

5x = 3x + 14

5x - 3x = 14

2x = 14

x = 14/2

x = 7

3x + 2 = 3*7 + 2

= 21 + 2

= 23

Use Pythagorean theorem to find y

16² + y² = 23³

256 + y² = 529

y² = 529 - 256 = 273

y = √273

y = 16.52

You might be interested in

Need the answer in 20 min !! Ty

kirill115 [55]

Answer:

Step-by-step explanation:

6 0

2 years ago

Find out the number of combinations and the number of permutations for 8 objects taken 6 at a time. Express your answer in exact

umka2103 [35]

Solution:

The permutation formula is expressed as

$\begin{gathered} P^n_r=\frac{n!}{(n-r)!} \\ \end{gathered}$

The combination formula is expressed as

$\begin{gathered} C^n_r=\frac{n!}{(n-r)!r!} \\ \\ \end{gathered}$

where

$\begin{gathered} n\Rightarrow total\text{ number of objects} \\ r\Rightarrow number\text{ of object selected} \end{gathered}$

Given that 6 objects are taken at a time from 8, this implies that

$\begin{gathered} n=8 \\ r=6 \end{gathered}$

Thus,

Number of permuations:

$\begin{gathered} P^8_6=\frac{8!}{(8-6)!} \\ =\frac{8!}{2!}=\frac{8\times7\times6\times5\times4\times3\times2!}{2!} \\ 2!\text{ cancel out, thus we have} \\ \begin{equation*} 8\times7\times6\times5\times4\times3 \end{equation*} \\ \Rightarrow P_6^8=20160 \end{gathered}$

Number of combinations:

$\begin{gathered} C^8_6=\frac{8!}{(8-6)!6!} \\ =\frac{8!}{2!\times6!}=\frac{8\times7\times6!}{6!\times2\times1} \\ 6!\text{ cancel out, thus we have} \\ \frac{8\times7}{2} \\ \Rightarrow C_6^8=28 \end{gathered}$

Hence, there are 28 combinations and 20160 permutations.

7 0

1 year ago

Suppose a car going 65 mph is traveling north parallel to a train going 50 mph. Once the front of the car is as far north as the

scoray [572]

Answer:

0.75 Miles

Step-by-step explanation:

To find the answer we have to find the difference in the distance the train and car travelled

65/60 is 1.083333 which is miles per minute then multiplied by 3 is 3.25 mile gone in 3 minutes

For the train it is 50/60 which is 0.833333 and the times 3 is 2.5 miles in three minutes

3.25 miles minus 2.5 miles is 0.75 miles so that is how long the train is