Answer:1. The measure of angle P is 53. 2. The value of x is 25.
3. The length of each side of the triangle is 30 cm.
Step-by-step explanation:
1. (3x +2) + (3x + 2 ) + (5x -11) =180 Angle Q and P have the same measures because it is an isosceles triangle that is why you have three expressions.
So x =17 and 3(17)+ 2 =53
2. (2x +10) + (2x+10) + (2x + 10)= 180 this is because the second triangle is an equilateral triangle which means all it have the same measures.
solve for x. and x is 25.
3.The third triangle is also an equilateral triangle so you will make the expressions equal each other and solve for y .
1/10y + 11= 3/5y -4
y= 30
Answer:
u = 40° , v = 40° and x = 100°
Step-by-step explanation:
i) from the rule of triangle we know that the sum of all three angles = 180°
ii) 100° + 40° + y = 180°. Therefore y = 40°. where y is the angle adjacent to v.
iii) from theorem on parallel lines we can say that u = y =40°
iv) from the properties of parallel lines we get v = 40° as interior alternate angles are equal.
v) again from the properties of parallel lines we get u = 40°
vi) using the triangle property as in i) we can see that u + v + x =180° therefore 40° + 40° + x = 180°. Therefore x = 100°.
vii) Therefore u = 40° , v = 40° and x = 100°
the center is at the origin of a coordinate system and the foci are on the y-axis, then the foci are symmetric about the origin.
The hyperbola focus F1 is 46 feet above the vertex of the parabola and the hyperbola focus F2 is 6 ft above the parabola's vertex. Then the distance F1F2 is 46-6=40 ft.
In terms of hyperbola, F1F2=2c, c=20.
The vertex of the hyperba is 2 ft below focus F1, then in terms of hyperbola c-a=2 and a=c-2=18 ft.
Use formula c^2=a^2+b^2c
2
=a
2
+b
2
to find b:
\begin{gathered} (20)^2=(18)^2+b^2,\\ b^2=400-324=76 \end{gathered}
(20)
2
=(18)
2
+b
2
,
b
2
=400−324=76
.
The branches of hyperbola go in y-direction, so the equation of hyperbola is
\dfrac{y^2}{b^2}- \dfrac{x^2}{a^2}=1
b
2
y
2
−
a
2
x
2
=1 .
Substitute a and b:
\dfrac{y^2}{76}- \dfrac{x^2}{324}=1
76
y
2
−
324
x
2
=1 .
0.
It is impossible for 151 to be selected, as it is outside the range of numbers (1 to 100) that can be selected. Therefore the probability is 0.
Answer:
180ft
Step-by-step explanation:
By using the formula, we do Pi (3) x the radius which is 6² then x by the height, so, we do 3 x 6² x 5. 6² is 36. 3 x 36 = 108. Next, we do 5 x 108. This gives us 540. Now, we have to divide by 3. This makes our answer 180ft.
