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deff fn [24]
3 years ago
8

How many solutions does a triangle with side lengths a = 4, A = 112º and b =9 have?​

Mathematics
1 answer:
Ainat [17]3 years ago
7 0

Answer:

This case has NO solutions.

Step-by-step explanation:

Notice that you are in a case of an obtuse triangle (one of its angles is larger than 90 degrees), the side opposite to the obtuse triangle is shorter than the side adjacent to the angle, so no actual triangle can be formed.

This can be found by simply trying to apply the Law of Sines to solve for the value of angle "B" opposite to side "b":

\frac{sin(A)}{a} =\frac{sin(B)}{b}\\sin(B)=\frac{b\,sin(A)}{a}\\sin(B)=\frac{9\,sin(112^o)}{4}\\\\sin(B)=2.086

As shown above, we get an impossible mathematical condition (also call an absurd), since the sine of an angle cannot give a value larger than 1 (one).

Therefore, there is no angle we can find to build a triangle with the given data.

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First you have to multiply the 0.6 of the small shakers times two which gives us 1.2 the amount of salt of the large shakers. divide the 18.6 by 1.2 which is 15.5 the amount going into the 8 shakers. Then subtract 15.5 from 18.6 which gives us 3.1. Then you divide that by 0.6 = 5. 5 small shakers can be filled with the remaining salt.
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3 years ago
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line w passes through point (-6,-7) and has a slope 1/2. what is the equation for the line in point-slope form?
Elena L [17]

Answer:

y + 7 = \frac{1}{2} (x + 6)

Step-by-step explanation:

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{1}{2} and (a, b ) = (- 6, - 7 ) , then

y - (- 7) = \frac{1}{2} (x - (- 6) ) , that is

y + 7 = \frac{1}{2} (x + 6)

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2 years ago
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Evaluate the function.<br> f(x) = -x2-12 find f(-3)
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Write an equation for a line parallel to y=3x-3 and passing through the point (4,15)
Andrews [41]

Hello!

To find the equation of a line parallel to y = 3x - 3 and passing through the point (4, 15), we need to know that if two lines are parallel, then their slopes are equivalent.

This means that we create a new equation in slope-intercept form, which includes the original slope, which is equal to 3.

In slope-intercept form, we need a y-intercept. So, we would substitute the given ordered pair into the new equation with the same slope and solve.

Remember that slope-intercept form is: y = mx + b, where m is the slope and b is the y-intercept.

y = 3x + b (substitute the ordered pair (4, 15))

15 = 3(4) + b (simplify)

15 = 12 + b (subtract 12 from both sides)

3 = b

Therefore, the equation for the line parallel to the line y = 3x - 3, and passing through the point (4, 15) is y = 3x + 3.

8 0
3 years ago
What is the value of 1/2 of 2/3 of 3/4 of 4/5 of 5/6 of 6/7 of 7/8 of 8/9 of 9/10 of 1000?
Alenkasestr [34]

Answer:

it's 100

Step-by-step explanation:

9/10 of 1000 is 900, 8/9 of 900 is 800, 7/8 of 800 is 700, 6/7 of 700 is 600, 5/6 of 600 is 500, 4/5 of 500 is 400, 3/4 of 400 is 300, 2/3 of 300 is 200, and 1/2 of 200 is 100 which makes 100 the value of 1/2 of 2/3 of 3/4 of 4/5 of 5/6 of 6/7 of 7/8 of 8/9 of 9/10 of 1000? I hope this makes sense.

5 0
3 years ago
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