Answer:
x = 6
Step-by-step explanation:
The volume (V) of the triangular prism is calculated as
V = Al ( A is the area of the triangular end and l is its length )
A = bh = 0.5 × 9 × 4 = 18 cm² , then
V = 18 × 12 = 216 cm³
The volume of a cube is
V = s³ ( s is the side length ) , so
s³ = x³ = 216 ( take the cube root of both sides )
x = = 6
Answer:
1. Given
2. Diagonals of a parallelogram bisect each other.
3. Vertical angles are equal.
4. Definition of parallelogram.
5. If lines parallel, then alternate interior angles are equal.
6. ASA
7. CPCTE
Step-by-step explanation:
Statement 1:
The first statement is a parallelogram ABCD, which is already given in the question. So, reason 1 is: Given.
Statement 2:
BT and TD are equal because for a parallelogram, its diagonal bisect each other. Here, BD and AC are the diagonals of parallelogram ABCD. So, the diagonals bisect each other at T. Hence,
Statement 3:
Angles 1 and 2 is a pair of vertical angles. A pair of vertical angles are always equal to each other.
Statement 4:
A parallelogram is a quadrilateral whose opposite sides are parallel and equal. Hence, is because of the definition of a parallelogram.
Statement 5:
Angles 3 and 4 is a pair of alternate interior angles. If two lines are parallel, then the alternate interior angles are always equal.
Statement 6:
The triangles BET and DFT are now congruent because:
i.Angle-
ii. Side -
iii. Angle -
Therefore, by ASA postulate the two triangles are congruent.
Statement 7:
As the two triangles are congruent, then their corresponding parts are also equal.
So, by CPCTE,
<u>Given</u>:
Given that the graph of the equation of the line.
The line that is perpendicular to the given line and passes through the point (2,-1)
We need to determine the equation of the line perpendicular to the given line.
<u>Slope of the given line:</u>
The slope of the given line can be determined by substituting any two coordinates from the line in the slope formula,
Substituting the coordinates (-1,3) and (2,2), we get;
Thus, the slope of the given line is
<u>Slope of the perpendicular line:</u>
The slope of the perpendicular line can be determined by
Substituting , we get;
simplifying, we get;
Thus, the slope of the perpendicular line is 3.
<u>Equation of the perpendicular line:</u>
The equation of the perpendicular line can be determined using the formula,
Substituting and the point (2,-1) in the above formula, we have;
Thus, the equation of the perpendicular line is
Hence, Option d is the correct answer.
