Answer:
Prove: ΔPYJ ≅ ΔPXK
Step-by-step explanation:
Overlapping triangles are said to be triangles that share at least part of a side or an angle.
To prove ΔPYJ is congruent to ΔPXK
First we would draw the diagram obtained from the given information.
Find attached the diagram.
Given:
JP = KP
PX = PY
From the diagram, ΔPYJ and ΔPXK share the line KJ (part of the side of each of the triangle)
KJ ≅ KJ (A reflexive property - the segment is congruent to itself)
In ∆PYJ
JP = KP + KJ
In ∆PXK
KP = JP + KJ
Since JP = KP
KP + KJ = JP + KJ
PJ ≅ PK
The overlapping section makes a smaller triangle KXJ
∠K = ∠J (opposite angles of congruent sides are equal)
In ∆PYJ: PY + YJ + PJ (sum of angles in a triangle)
In ∆PXK: PX + XK + PK (sum of angles in a triangle)
If ΔPYJ ≅ ΔPXK
PY + YJ + PJ = PX + XK + PK
XK ≅ YJ
Therefore, ΔPYJ ≅ ΔPXK
Answer: 615.4mm cube
Step-by-step explanation:
The volume of a cylinder is given as πr^2h
where r= radius
h = height
π = 3.14
From the question, diameter is 14mm and height is 4mm.
To get the radius, we divide the diameter by 2 which will give:
= 14mm/2 = 7mm
Volume= πr^2h
= 3.14 × 7^2 × 4
= 3.14 × 49 × 4
= 615.4mm cube
The volume of the cylindrical barrel is 615.4mm cube.
Answer:
The first pair shows equivalent expressions.
Step-by-step explanation:
3(x+2), you would have to distribute 3 among x and 2, also known as expanding the expression. So you'd do 3*x + 3*2, which equals 3x+6
The first equation is 3(x+2)=3x+6
Therefore, the first pair shows equivalent expressions.
Hey,
If you were to divide 137/7 it would be it would be 19 or if you wont a decimal it would be 19.5
I Hoped that Helped
