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strojnjashka [21]
3 years ago
7

Find the area of the triangle with the following measurements: B = 67°, a = 13 cm, c = 21 cm

Mathematics
1 answer:
Anarel [89]3 years ago
6 0

9514 1404 393

Answer:

  125.6 cm²

Step-by-step explanation:

The relevant area formula is ...

  Area = (1/2)ac·sin(B)

  Area = (1/2)(13 cm)(21 cm)·sin(67°) ≈ 125.6 cm²

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Let p be the plane in space that intersects the x-axis at −5, the y-axis at −2, and the z-axis at 5. Find a vector v¯¯¯ that is
Lana71 [14]

Let P be the plane that intersects

  • x-axis at point (-5,0,0);
  • y-axis at point (0,-2,0);
  • z-axis at point (0,0,5).

Write the equation of the plane P:

\left|\begin{array}{ccc}x-(-5)&y-0&z-0\\0-(-5)&-2-0&0-0\\0-(-5)&0-0&5-0\end{array}\right|=0\Rightarrow \left|\begin{array}{ccc}x+5&y&z\\5&-2&0\\5&0&5\end{array}\right|=0.

Then

-10(x+5)+10z-25y=0,\\ \\2(x+5)-2z+5y=0,\\ \\2x+5y-2z=-10.

The coefficients at variables x, y and z are the coordinates of perpendicular vector to the plane. Thus

\vec{v}=(2,5,-2)\perp P.

Answer: \vec{v}=(2,5,-2).

7 0
3 years ago
Explain work please
Softa [21]

Answer:

12 yards of silk

Step-by-step explanation:

okay so 1 yard = 36 inch so 2+3+6= 11 yards

now 1/2 of 36 is 18 inchs

6 inchs

and 1/3 of 36 is = 12

now add 12+18+6 = 36 = 1 extra yard so add that to 11 to get 12

4 0
3 years ago
Use the frequency distribution, which shows the number of American voters (in millions) according to age, to
a_sh-v [17]

Answer:

The probability that a voter chosen at random is in the 18 to 20 years old age range is =  4.2/ 134.8= 0.0311572

Step-by-step explanation:

We can find the probability by simply dividing the frequency of the ages range of 18-20 by the total frequency.

Ages                Frequency

18 to 20             4.2

21 to 24             7.8

25 to 34           20.8

35 to 44           23.7

45 to 64           50.1

<u>65 and over       28.2</u>

<u>∑                        134.8</u>

The probability of an event is given by the occurrence of an event by the total occurrences .

So

Here the occurrence of ages 18-20 is given by 4.2

and the total frequency is 134.8

The probability that a voter chosen at random is in the 18 to 20 years old age range is =  4.2/ 134.8= 0.0311572

7 0
3 years ago
what is the equation of a line, in point-slope form, that passes through (5, -3) and has a slope of 2/3? please help me
Brums [2.3K]

y + 3 = \frac{2}{3} (x - 5)

the equation of a line in point- slope form is

y - b = m ( x - a )

where m is the slope and (a, b) a point on the line

here m =\frac{2}{3} and (a,b) = (5 , - 3 )

y + 3 = \frac{2}{3} (x - 5 ) ← in point-slope form


3 0
3 years ago
Please help! I was absent!
lesya692 [45]
I got 6.3 not sure if Im right
7 0
3 years ago
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