Answer:
-5 < x < 9
Step-by-step explanation:
By Hinge theorem,
"If two sides of a triangle are congruent to the two sides of another triangle, and the included angle of one triangle is larger than the included angle of the second, then the 3rd side of triangle one will be larger than the third side of the second"
23 > 21
Therefore, 42° > (3x + 15)°
42° - 15° > 3x
27 > 3x
9 > x
And (3x + 15) > 0
3x > -15
x > -5
Therefore, range for x will be,
-5 < x < 9
Answer: Domain:
{
1
,
3
,
4
,
6
,
8
}
Step-by-step explanation:
The domain is the set of all the values of
x
.
Answer:
The slope of the line that passes through points ( -10, -8 ) and ( -8, -16 ) is -4.
Explanation:
Points given = ( -10, -8) and ( -8, -16)
Slope = ?
( -10, -8 ) : x1 = -10 and y1 = -8
( -8, -16 ) : x2 = -8 and y2 = -16
We know,
slope = y2 - y1 / x2 - x1
Slope = -16 - ( -8) / -8 - (-10)
slope = -16 + 8 / -8 + 10
slope = -8 / 2
slope = -4
Therefore, slope of the line that passes through points ( -10, -8 ) and ( -8, -16 ) is -4.
Step-by-step explanation:
Answer:
x = 3
, y = 5
Step-by-step explanation:
Solve the following system:
{3 y - 7 x = -6 | (equation 1)
3 y - 3 x = 6 | (equation 2)
Subtract 3/7 × (equation 1) from equation 2:
{-(7 x) + 3 y = -6 | (equation 1)
0 x+(12 y)/7 = 60/7 | (equation 2)
Multiply equation 2 by 7/12:
{-(7 x) + 3 y = -6 | (equation 1)
0 x+y = 5 | (equation 2)
Subtract 3 × (equation 2) from equation 1:
{-(7 x)+0 y = -21 | (equation 1)
0 x+y = 5 | (equation 2)
Divide equation 1 by -7:
{x+0 y = 3 | (equation 1)
0 x+y = 5 | (equation 2)
Collect results:
Answer: {x = 3
, y = 5
