Step-by-step explanation:
Given expression is x⁴-kx²+4 =0
x−2 is a factor of the given expression.
So, x=2
Substitute in the equation, we get
2⁴-k(2)²+4
⇒16+4k+4=0
⇒4k=−20
⇒k=−5
Answer:
9. m(YZ) = 102°
10. m(JKL) = 192°
11. m<GHF = 75°
Step-by-step explanation:
9. First, find the value of x
4x + 3 = 3x + 15 (inscribed angle that are subtended by the same arc are equal based on the inscribed angle theorem)
Collect like terms
4x - 3x = -3 + 15
x = 12
4x + 3 = ½(m(YZ)) (inscribed angle of a circle = ½ the measure of the intercepted arc)
Plug in the value of x
4(12) + 3 = ½(m(YZ))
48 + 3 = ½(m(YZ))
51 = ½(m(YZ))
Multiply both sides by 2
51*2 = m(YZ)
102 = m(YZ)
m(YZ) = 102°
10. First, find the value of x.
7x + 5 + 6x + 6 = 180° (opposite angles in an inscribed quadrilateral are supplementary)
Add like terms
13x + 11 = 180
13x = 180 - 11
13x = 169
x = 169/13
x = 13
7x + 5 = ½(m(JKL)) (inscribed angle of a circle = ½ the measure of the intercepted arc)
Plug in the value of x
7(13) + 5 = ½(m(JKL))
96 = ½(m(JKL))
Multiply both sides by 2
2*96 = m(JKL)
m(JKL) = 192°
11. First, find x.
5x + 15 = ½(11x + 18) (inscribed angle of a circle = ½ the measure of the intercepted arc)
Multiply both sides by 2
2(5x + 15) = 11x + 18
10x + 30 = 11x + 18
Collect like terms
10x - 11x = -30 + 18
-x = -12
Divide both sides by -1
x = 12
m<GHF = 5x + 15
Plug in the value of x
m<GHF = 5(12) + 15
m<GHF = 60 + 15
m<GHF = 75°
Answer:
The answer is 21
Step-by-step explanation:
This should help you
Answer:
64°
Step-by-step explanation:
First, we have to find the angle situated in R, the addition of all angles in a triangle is 180° so that means:
x + 68 + 48 = 180
x = 180-116 = 64°
Now, remember that this angle (64°) is the same as this one = ?, thanks to one property.
So basically, that angle has the same value as that one.
? = 64°
Hope it was helpful ;)
Answer:
3
Step-by-step explanation:
P is the in-center
⇒PA=PE=PD because they are in-radius of the in-circle
We know that, tangent segments drawn from a point outside the circle are always equal in length
⇒DK=EK=7.2
In right triangle PKE,
using Pythagoras' Theorem : 
⇒
⇒
⇒
⇒
Therefore, 
