Given the function h(x)=x^2+14x+41, to solve by completing square we procced as follows;
x^2+14x+41=0
x^2+14x=-41
but;
c=(b/2)^2
and b=14
hence;
c=(14/2)^2=49
substituting the value of c in the expression we get:
x^2+14x+49=-41+49
x^2+14x+49=8
(x+7)^2=8
this can be written in vertex form;
h(x)=a(x-h)^2+k
where:
(h,k) is the vertex;
thus
(x+7)^2=8
h(x)=(x+7)^2-8
hence the vertex will be at the point:
(-7,-8)
Your answer to this question is definitely C!
Answer:
$386794
Step-by-step explanation:
To be able to find how much we get in 5 years, we need to base it off the initial salary value.
So in the first year we get.
$70,000
To get how much we get in the 2nd year we add the extra 5%.
2nd year salary = (1.05)70000
2nd year salary = 73500
Now we continue to do that until the 5th year
3rd year = (1.05)73500
3rd year = 77175
4th year = (1.05) + 77175
4th year = 81033.75
5th year = (1.05) + 81033.75
5th year = 85085.44
Now we add them all up to get the total.
70000 + 73500 + 77175 + 81033.75 + 85085.44 = $386794.19 or $386794
Answer:
1
Explanation:
According to the Unit Circle, sin π\6 is ½, so we plug this into the cosine function to get this:
cos π\6 - π\6 → cos 0 >> 1
If you are ever in need of assistance, do not hesitate to let me know by subscribing to my You-Tube channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.
** I do not have Unit Circle video uploaded yet, but if I need to, just notify me in the comments or on of course, You-Tube.
*** Plus, we need to make sure that the x-value falls in between 0 and π\2, which it did, so no need to worry.
Answer:
1) 22.5 A
2) 112 B
3) 430 L
4) 576 P
5) 486 L
6) 624 S
Code is A B L P L S
Step-by-step explanation:
1) Area of a triangle = 1/2 * base * height = 1/2 *5*9 = 22.5
2) Area of a parallelogram = base x height = 14 x 8 = 112
3) Area of a rectangular prism = 2(length * width) + 2*(length + height) + 2 *(length *height)
= 2(15x7 + 15*5 + 7*5)
= 2(105 + 75 + 35)
= 2 * 215
= 430
4) Volume of a triangular prism = 1/2 * base * length * height
= 1/2 * 8 * 16 * 9
= 576
5) A cube has six surfaces. Each surface has an area of s x s where s is the length of each side. In this case, each side has area of 9x9 = 81. Total surface area = 6 x 81 = 486 and that is the paper required
6) The trailer is a rectangular prism so its volume = length x width x height = 13 6 x 8 = 624
Now you have to look at each value and see which letter it corresponds to. For example answer 1) is 22.5 which lies between 0-100 so it gets letter A, answer (2) is 112 which lies in the range 101-200 so it gets the letter B and so on