Find the surface area of the prism. Length: 5 width: 8 height: 12 in

Find the missing side length BM. Round answer to the nearest tenth.

xenn [34]

Answer: BM = 21.4

Step-by-step explanation:

Considering the given triangle BMS, to determine angle BM, we would apply the sine rule. It is expressed as

m/SinM = s/SinS = b/SinB

Where m, s and b are the length of each side of the triangle and angle M, Angle S and angle B are the corresponding angles of the triangle.

From the information given,

Angle M = 102°

Angle B = 35°

Angle S = 180 - (102 + 35) = 43°

b = MS = 18

s = BM

Therefore

18/Sin 35 = BM/Sin 43

Cross multiplying, it becomes

BMSin35 = 18 × Sin 43

BM × 0.5736 = 18 × 0.6820

0.5736BM = 12.276

Dividing the left hand side and the right hand side of the equation by 0.5736, it becomes

0.5736BM/0.5736 = 12.276/0.5736

BM = 21.4

6 0

2 years ago

Lawrence wants to drive from Durban to Johannesburg 550km. If he travels at an average speed of 100km/hr, how long does he tale

Dafna1 [17]

Answer:

5.5hr

Step-by-step explanation:

Distance=550Km

Speed=100Km/hr

Speed=(Distance/Time)

Time=(Distance/Speed)

Time=550/100=5.5hr

8 0

3 years ago

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Describe the behavior of the function ppp around its vertical asymptote at x=-2x=−2x, equals, minus, 2.

insens350 [35]

Answer:

$x->-2^{-}, p(x)->-\infty$ and as $x->-2^{+}, p(x)->-\infty$

Step-by-step explanation:

Given

$p(x) = \frac{x^2-2x-3}{x+2}$ -- Missing from the question

Required

The behavior of the function around its vertical asymptote at $x = -2$

$p(x) = \frac{x^2-2x-3}{x+2}$

Expand the numerator

$p(x) = \frac{x^2 + x -3x - 3}{x+2}$

Factorize

$p(x) = \frac{x(x + 1) -3(x + 1)}{x+2}$

Factor out x + 1

$p(x) = \frac{(x -3)(x + 1)}{x+2}$

We test the function using values close to -2 (one value will be less than -2 while the other will be greater than -2)

We are only interested in the sign of the result

----------------------------------------------------------------------------------------------------------

As x approaches -2 implies that:

$x -> -2^{-}$ Say x = -3

$p(x) = \frac{(x -3)(x + 1)}{x+2}$

$p(-3) = \frac{(-3-3)(-3+1)}{-3+2} = \frac{-6 * -2}{-1} = \frac{+12}{-1} = -12$

We have a negative value (-12); This will be called negative infinity

This implies that as x approaches -2, p(x) approaches negative infinity

$x->-2^{-}, p(x)->-\infty$

Take note of the superscript of 2 (this implies that, we approach 2 from a value less than 2)

As x leaves -2 implies that: $x>-2$

Say x = -2.1

$p(-2.1) = \frac{(-2.1-3)(-2.1+1)}{-2.1+2} = \frac{-5.1 * -1.1}{-0.1} = \frac{+5.61}{-0.1} = -56.1$

We have a negative value (-56.1); This will be called negative infinity

This implies that as x leaves -2, p(x) approaches negative infinity

$x->-2^{+}, p(x)->-\infty$

So, the behavior is:

$x->-2^{-}, p(x)->-\infty$ and as $x->-2^{+}, p(x)->-\infty$

6 0

3 years ago

What is the median of the data set represented by the dot plot?

Butoxors [25]

So ur numbers are : 3,3,4,5,5,5,6,8,8

and the median (middle number) is 5 <==

because 2 dots above the 3 means u have 2 threes....and 1 dot above the 4 means there is 1 four..and so on

6 0

3 years ago

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Determine the slope of the line. Please explain the answer . If you hurry I’ll mark brainliest

Daniel [21]

Answer:

2/4

Step-by-step explanation:

Rise over run. you go up 2 and right 4

5 0

2 years ago

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