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3 years ago

How to find the measure of a triangle?

Mathematics

2 answers:

gulaghasi [49]3 years ago

8 0

Is it 1/2×b×h
to find the area
or
base×height

AleksAgata [21]3 years ago

6 0

Hi there! :)

Answer:

The answer is D. 83°

Step-by-step explanation:

You should know that the interior angles of a triangle always add up to 180°.

So, what you will need to do, is add all 3 angles together and create an equation (equal to 180). Then you need to solve this equation by isolating "x":

(8x + 12) + (55 - 3x) + (10x + 23) = 180

Get rid of all the parentheses

8x + 12 + 55 - 3x + 10x + 23 = 180

Add all similar terms together

8x - 3x + 10x = 15x

12 + 55 + 23 = 90

15x + 90 = 180

Subtract "90" from each side of the equation → 180 - 90 = 90

15x = 90

Divide each side of the equation by "15" → 90 ÷ 15 = 6

x = 6

Since you now know that the value of "x" is 6, you can now find the measure of the angle at George's position by replacing the "x" by 6:

10x + 23 = Measure of the angle at George's position

10(6) + 23

Multiply 10 by 6 → 10 × 6 = 60

60 + 23

Add 60 and 23 together → 60 + 23 = 83

83 = Measure of the angle at George's position

There you go! I really hope this helped, if there's anything just let me know! :)

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a surveyor measures the distance to the two landmarks as shown in the diagram what is the distance d. between the landmarks

Inessa [10]

<h3>The distance between two landmarks is 123 meters</h3>

Solution:

We have to find the distance between two landmarks

Use the law of cosines

The third side of a triangle can be found when we know two sides and the angle between them

$c^2 = a^2 + b^2 - 2ab\ cos c$

Here, angle between 90 meters and 130 meters is 65 degrees

From figure,

a = 90

b = 130

c = d

Therefore,

$d^2 = 90^2 + 130^2 - 2(90)(130)\ cos 65\\\\d^2 = 8100 + 16900 - 23400\ cos\ 65\\\\d^2 = 25000 - 23400 \times 0.4226\\\\d^2 = 25000 - 9889.267\\\\d^2 = 15110.73\\\\d = 122.92\\\\d \approx 123$

Thus, the distance between two landmarks is 123 meters

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3 years ago

In the system of equations below, which variable would it be easiest to solve for?

Maru [420]

Answer:

<h3> The first: The easiest to solve for is x in the first equation.</h3>

Step-by-step explanation:

To get x from first equation you just need to subtract 4y from both sides.

The rest of variables needs two operations to get variable - subtracting and then dividing.

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2 years ago

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In Wellington, a city of 360,000 citizens, there has been an outbreak of vampires and werewolves There are 3,000 people infected

Alex17521 [72]

Answer:

0.0286 or 2.86%

Step-by-step explanation:

The total number of people that have werewolfism is 21,000.

Of those 21,000, 600 also have vampirism, while the remaining 20,400 do not. Therefore, the probability that someone has vampirism, given that they have werewolfism is:

$P(V|W)=\frac{N_{V\cap W}}{N_W}\\P(V|W)=\frac{600}{21,000} \\P(V|W)=0.0286=2.86\%$

The probability is 0.0286 or 2.86%.

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3 years ago

Find the 7th term of the geometric sequence -5, 15, 45, 135, 405,...

katovenus [111]

Answer:

1,215

Step-by-step explanation:

Because if you think of it it multiplies by 3x so 3x5=? 15! 15x3=? 45! 45x3=? 405! 405x=3? 1,215! 1,215x3=? 3,645! anyways, I can go on and on I hope this answer was right!

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3 years ago

(secx)dy/dx=e^(y+sinx), please help me solve the differential equation. Thanks :)

nalin [4]

First, you must know these formula d(e^f(x) = f'(x)e^x dx, e^a+b=e^a.e^b, and d(sinx) = cosxdx, secx = 1/ cosx

(secx)dy/dx=e^(y+sinx), implies dy/dx=cosx .e^(y+sinx), and then
dy=cosx .e^(y+sinx).dx, integdy=integ(cosx .e^(y+sinx).dx, equivalent of
integdy=integ(cosx .e^y.e^sinx)dx, integdy=e^y.integ.(cosx e^sinx)dx, but we know that d(e^sinx) =cosx e^sinx dx,
so integ.d(e^sinx) =integ.cosx e^sinx dx,
and e^sinx + C=integ.cosx e^sinxdx
finally, integdy=e^y.integ.(cosx e^sinx)dx=e^2. (e^sinx) +C
the answer is
y = e^2. (e^sinx) +C, you can check this answer to calculate dy/dx

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3 years ago

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