Y = x + 1......slope = 1, y int = 1
y = x + 2.....slope = 1, y int = 2
In y = mx + b form, the slope can be found in the m position and the y int can be found in the b position.
if the equations have the same slope, but different y int, then u have a set of parallel lines which never cross...therefore they have no solution and are inconsistent
Answer:
4.30 inches
Step-by-step explanation:
Given data
Volume of basket ball= 334cubic inches
We know that the expression for the volume of a sphere is given as
Volume of sphere= 4/3πr^3
334= 4/3πr^3
334=4/3*3.142*r^3
334=4.189*r^3
r^3= 334/4.189
r^3=79.73
cubic root both sides
r= ∛79.73
r=4.30 inches
Answer:
Step-by-step explanation:
Judging by the context, you are looking for the angle x of a triangle, where the other two angles are 76 and 49. The sum of a triangle's angles is always 180, so
76 + 49 + x = 180
125 + x = 180
x = 55
Answers:
a) The Area of the swimming pool.
b) 9 meters wide, 12 meters long.
c) 9, 12 & multiplication.
d) 9 • 12
e) 108
Answer:
Area of trapezium = 4.4132 R²
Step-by-step explanation:
Given, MNPK is a trapezoid
MN = PK and ∠NMK = 65°
OT = R.
⇒ ∠PKM = 65° and also ∠MNP = ∠KPN = x (say).
Now, sum of interior angles in a quadrilateral of 4 sides = 360°.
⇒ x + x + 65° + 65° = 360°
⇒ x = 115°.
Here, NS is a tangent to the circle and ∠NSO = 90°
consider triangle NOS;
line joining O and N bisects the angle ∠MNP
⇒ ∠ONS = = 57.5°
Now, tan(57.5°) =
⇒ 1.5697 =
⇒ SN = 0.637 R
⇒ NP = 2×SN = 2× 0.637 R = 1.274 R
Now, draw a line parallel to ST from N to line MK
let the intersection point be Q.
⇒ NQ = 2R
Consider triangle NQM,
tan(∠NMQ) =
⇒ tan65° =
⇒ QM =
QM = 0.9326 R .
⇒ MT = MQ + QT
= 0.9326 R + 0.637 R (as QT = SN)
⇒ MT = 1.5696 R
⇒ MK = 2×MT = 2×1.5696 R = 3.1392 R
Now, area of trapezium is (sum of parallel sides/ 2)×(distance between them).
⇒ A = () × (ST)
= () × 2 R
= 4.4132 R²
⇒ Area of trapezium = 4.4132 R²