Answer:
Below.
Step-by-step explanation:
Substitute x = 3 into each polynomial and see if the value of the polynomial is zero. If it is zero then x-3 is a factor.
Try number 1:
a(x) = x^3 - 2x^2 - 4x + 3
a(3) = 3^3 - 2(3)^2 - 4(3) + 3
= 27 - 2(9) - 12 + 3
= 27 - 18 - 12 + 3
= 9 - 18 - 9
= 27 - 27
= 0
So a(x) has (x-3) is a factor of a(x)
The other 3 polynomials are solved in the same way.
Answer:
The second: 
Step-by-step explanation:
![f (x) =4x^2+6x-3\\\\f (x) =4(x^2+\frac64x]-3\\\\f (x) =4[x^2+2\cdot x\cdot\frac34+(\frac34)^2-(\frac34)^2]-3\\\\f (x) =4[(x+\frac34)^2-(\frac34)^2]-3\\\\f (x) =4(x+\frac34)^2-4(\frac34)^2-3\\\\f (x) =4(x+\frac34)^2-\frac94-\frac{12}4\\\\\underline{f (x) =4(x+\frac34)^2-\frac{21}4}](https://tex.z-dn.net/?f=f%20%28x%29%20%3D4x%5E2%2B6x-3%5C%5C%5C%5Cf%20%28x%29%20%3D4%28x%5E2%2B%5Cfrac64x%5D-3%5C%5C%5C%5Cf%20%28x%29%20%3D4%5Bx%5E2%2B2%5Ccdot%20x%5Ccdot%5Cfrac34%2B%28%5Cfrac34%29%5E2-%28%5Cfrac34%29%5E2%5D-3%5C%5C%5C%5Cf%20%28x%29%20%3D4%5B%28x%2B%5Cfrac34%29%5E2-%28%5Cfrac34%29%5E2%5D-3%5C%5C%5C%5Cf%20%28x%29%20%3D4%28x%2B%5Cfrac34%29%5E2-4%28%5Cfrac34%29%5E2-3%5C%5C%5C%5Cf%20%28x%29%20%3D4%28x%2B%5Cfrac34%29%5E2-%5Cfrac94-%5Cfrac%7B12%7D4%5C%5C%5C%5C%5Cunderline%7Bf%20%28x%29%20%3D4%28x%2B%5Cfrac34%29%5E2-%5Cfrac%7B21%7D4%7D)
To set the equation,we can first find how much price would be raised within a year:
=500×(1+7%)
=500×1.07
As the years go by the increase would accumulate,and the equation would be:
Hope it helps!
Answer:
Peter ran 33 laps.
Step-by-step explanation:
Multiply Evelyn's 44 laps by 75% or 0.75 to get your answer.
44(0.75)=33
A right triangle is a type of triangle which contains a right triangle. To be a right triangle, it should satisfy the Pythagorean Theorem which relates the three sides of the triangle. In this triangle, the longest side is called as the hypotenuse. To determine the hypotenuse, we use the Pythagorean Theorem which is expressed as follows:
c^2 = a^2 + b^2
where c is the hypotenuse
We calculate as follows:
c^2 = a^2 + b^2
c^2 = 6^2 + 5^2
c^2 = 61
c = √61
Therefore, the hypotenuse of the right triangle with sides 6 and 5 would be √61 which, clearly, is longer than the two sides.
