36x² - 100 = 4(9x²-25) = 4(3x+5)(3x-5)
B. 4(3x+5)(3x-5)
<u>Answer-</u>
<em>The polynomial function is,</em>
<u>Solution-</u>
The zeros of the polynomial are 2 and (3+i). Root 2 has multiplicity of 2 and (3+i) has multiplicity of 1
The general form of the equation will be,
( ∵ (3-i) is the conjugate of (3+i) )
Therefore, this is the required polynomial function.
To solve any equation, you do whatever you need to do
to wind up with the unknown quantity all alone on one side.
BUT ... whatever you do to one side of the equation, you must
also do to the other side.
Here, we have the
he original equation: -15 = a/5
Multiply each side by 5 : -75 = a
and bada-bing, THERE's the solution !
Answer: a) Yes, there is enough fance
b) 58.1° and 47.9°
c) The city will not approve, because 1/3 of the area is just 2220.5ft²
Step-by-step explanation:
a) using law of cosines: x is the side we do not know.
x² = 126² + 110² - 2.126.110.cos74°
x² = 20335.3
x = 142.6 ft
So 150 > 142.6, there is enough fance
b) using law of sine:
sin 74/ 142.6 = sinα/126 = sinβ/110
sin 74/ 142.6 = sinα/126
0.006741 = sinα/126
sinα = 0.849
α = sin⁻¹(0.849)
α = 58.1°
sin 74/ 142.6 = sinβ/110
sin 74/ 142.6 = sinβ/110
0.006741 = sinβ/110
sinβ = 0.741
β = sin⁻¹(0.741)
β = 47.9°
Checking: 74+58.1+47.9 = 180° ok
c) Using Heron A² = p(p-a)(p-b)(p-c)
p = a+b+c/2
p=126+110+142.6/2
p=189.3
A² = 189.3(189.3-126)(189.3-110)(189.3-142.6)
A = 6661.5 ft²
1/3 A = 2220.5
So 2300 > 2220.5. The area you want to build is bigger than the area available.
The city will not approve
First we have to find the vertex (h,k) h is also x and it also is the a xis symmetry
1st: group the number
(X2+6x)-9
2nd: use b/2
6/2 = 3 , 3^2= 9
(X2+6x+9)-9-9
(X2 + 3)-18
Vertex is 3,-18 so the symmetry is 3