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3 years ago

If a = 4 ft, c = 13 ft, and m∠B = 17°, what is the approximate area of ABC?

Mathematics

1 answer:

andre [41]3 years ago

8 0

Answer:

7.6 ft² ( to 1 dec. place )

Step-by-step explanation:

given 2 sides of a triangle and the angle between them, the area (A) is calculated using the formula

A = $\frac{1}{2}$ ac sin B

= 0.5 × 4 × 13 × sin 17° ≈ 7.6

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Photo above need help

Ira Lisetskai [31]

Answer:

m = 0

Step-by-step explanation:

<u>If two lines are parallel, their slopes are equal. </u>

The slope of x - axis is 0

(why?)

because, slope of a line is given by

$\boxed{\mathsf{slope\:of\:a\:line=tan \theta}}$

Θ is the angle made by the line with the x- axis.

Here, the line in question is the x- axis itself, and every line makes an angle of 0° with itself.

=> Θ = 0

=> tan Θ = 0

=> slope = 0

and the line in blue is parallel to the X- axis, therefore, it's slope is also 0

(also, a line makes an angle of 0° with the line it's parallel to)

$\mathfrak{\overline{There\:You\:Are!}}$

6 0

2 years ago

Read 2 more answers

1. A hotel manager buys 30 pillow cases and 25 shower curtains for $375. The manager then buys another 28 pillow cases and 35 sh

skad [1K]

Answer:

For #2: It's C. 17 nickels and 15 quarters.

Step-by-step explanation:

17*5= 85

15*25= 375

375+85= 460

add in the decimal:

17* 5 cents= $.85

15* 25 cents= $3.75

$3.75+ $.85= $4.60

7 0

2 years ago

Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

$b_n = a_{n+1} - a_n$

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

$2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)$

Then

$a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)$

$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

6 0

1 year ago

a projectile with an initial velocity of 48 feet per second is launched from a building 190 feet tall. the path of the projectil

nlexa [21]

I just graphed this equation, and it shows that the projectile will hit the ground at 5.3 seconds. I could be wrong but I'm going with the calculator is right I hope. I hope this helps you!

5 0

2 years ago

Read 2 more answers

If it is equal to (or) greater than 5, add ___ to previous digit.

Lisa [10]

Answer:

<h2>(b) 0 is the right answer.... </h2>

8 0

2 years ago