Hello,
Answer 1
Center=(-10,4)
radius=10
Step-by-step explanation:
a. ( p × q ) ( q + r )
= ( -24 × 12 ) ( 12 + -6 )
= 288 × 18
= 5184
b. ( p × r ) ( r - q )
= ( -24 × -6 ) ( -6 - 12 )
= ( 144 ) ( -18 )
= -2592
Simplifying
2x2 + 6x + 4 = 24
Reorder the terms:
4 + 6x + 2x2 = 24
Solving
4 + 6x + 2x2 = 24
Solving for variable 'x'.
Reorder the terms:
4 + -24 + 6x + 2x2 = 24 + -24
Combine like terms: 4 + -24 = -20
-20 + 6x + 2x2 = 24 + -24
Combine like terms: 24 + -24 = 0
-20 + 6x + 2x2 = 0
Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 3x + x2) = 0
Factor a trinomial.
2((-5 + -1x)(2 + -1x)) = 0
Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:
Simplifying
-5 + -1x = 0
Solving
-5 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5
Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5
Combine like terms: 0 + 5 = 5
-1x = 5
Divide each side by '-1'.
x = -5
Simplifying
x = -5
Add 4 to both sides
x - 4 < -3
x-4+4 < -3+4
x < 1
To graph this on a number line, plot an open circle at 1 on the number line. Do not fill in the open circle. Shade to the left of the open circle. The shaded region represents all x values smaller than 1.
The graph is shown below.
Answer:
Step-by-step explanation:
The diagonals of a rhombus are perpendicular to each other, so angles (2) and (3) are equal 90°.
To find angle (1), we can use the sum of internal angles in the left triangle with angles 52°, (1), and (2):
The diagonals of a rhombus bisects the angles, to the angle next to the angle of 52° is also 52°, then, in the upper triangle, we have:
