Mathematics, 28.07.2019 22:00 needhhelp

Two angles of a triangle measure 40º each, and at least one side measures 10 inches. 1. how many possible triangles can be formed from these measurements? 2. draw diagrams of each triangle, and find the missing parts of each. 3. tell which law you used, and explain why you used it.

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1. Since we have 2 equal angles in our triangle, we will also have two equal sides. Given that the third side is fixed at 10 inches, we can only form two triangle with those measures.

2. Check the attached picture.

3. First, we are going to use the interior angle theorem to find the third angle of our triangle. Remember that the interior angle theorem says that the sum of the interior angles of a triangle is always 180°. Lets apply it to our triangle: we know that the measure of two of its angles is 40°; let A be our third angle:
A+40+40=180

Now that we have the three angles of our triangle, we can use the law of sines to find the sides of our first triangle:
$\frac{b}{sin40} = \frac{10}{sin100}$
$b= \frac{10sin40}{sin100}$
b=6.5

$\frac{c}{sin40} = \frac{6.5}{sin40}$
$c= \frac{6.5sin40}{sin40}$
c=6.5

Now, lets do the same for our second triangle:
$\frac{a}{sin100} = \frac{10}{sin40}$
$a= \frac{10sin100}{sin40}$
a=15.3

$\frac{c}{sin40} = \frac{15.3}{sin40}$
$c= \frac{15.3sin40}{sin40}$
c=15.3

We can conclude that we used the law of sines because the problem gave us tow angles and one side.
Two angles of a triangle measure 40º each, and at least one side measures 10 inches. 1. how many pos

Two angles of a triangle measure 40º each, and at least one side measures 10 inches. 1. how many pos

Answer from: Quest

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

the function given is y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 = -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

Answer from: Quest

answer: i think one of the answer is $150 and $300?

step-by-step explanation: