In triangle XYZ, XY¯¯¯¯¯¯¯¯=15, YZ¯¯¯¯¯¯¯=8, ∡X=(3w−35)°, and ∡Y=52°. In triangle RST, RS¯¯¯¯¯¯¯=15, RT¯¯¯¯¯¯¯=8, ∡R=(w+17)°, and ∡S=52°. Find the angle measure for each of the four angles whose measures are not known. A. ∡R=43°, ∡T=85°, ∡X=43°, ∡Z=85°

B. ∡R=64°, ∡T=64°, ∡X=64°, ∡Z=64°

C. ∡R=35°, ∡T=93°, ∡X=35°, ∡Z=93°

D. ∡R=52°, ∡T=76°, ∡X=52°, ∡Z=76°

A. ∡R=43°, ∡T=85°, ∡X=43°, ∡Z=85°

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. The types of triangles are scalene triangle, equilateral triangle, right angled triangle and obtuse triangle.

Cosine rule states that given a triangle with sides a, b, c and their corresponding angles opposite to the sides as A, B, C. Then:

In triangle XYZ, we can find XZ using cosine rule:

∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)

∠X + 52 + 85 = 180

∠X + 137 = 180

∠X = 43°

∠X = 3w - 35

3w - 35 = 43

3w = 78

w = 26

In triangle RST, using sine rule:

∠R = w + 17

∠R = 26 + 17

∠R = 43°

∠R + ∠S + ∠T = 180° (sum of angles in a triangle)

43 + 52 + ∠T = 180

∠T + 95 = 180

∠T = 85°

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.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

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

b)

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

c)

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.

d)

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.

e)

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.

f)

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.

g)

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

#15. square

step-by-step explanation:

because quadrilatural (idk how to spell it) means somthing that is not 3d or like, equal sides (or somthing like that   you know what i meanz)

hope this halps!

bai!