Part 1: Answer:
(x+1)(x+1)(x-6) = x^3 - 4x^2 - 11x - 6
Step-by-step explanation:
To make r a root, include (x-r) as a factor. (-1+1)(-1+1)(-1-6) is zero even though (-1-6) isn't.
(6+1)(6+1)(6-6) is zero.
Part 2 Answer:
Standard form: y = -x^4 + 12
Degree 4
left end goes down, right end goes down.
Step by step: apply the definitions of standard form, polynomial degree, and "end behavior". In other words, read the textbook.
Part 3: Answer: x = 3, x = 8
Step by step:
x^2-11x = -24
x^2-11x+24 = 0
(x-3)(x-8) = 0
x = 3 or x = 8
Part 4a Answer:
quotient 2x^2 + x - 3
remainder 1
Step by step:
2x^2 + x - 3
___________________
x-4 ) 2x^3 - 7x^2 - 7x + 13
2x^3 - 8x^2
__________
0 + x^2 - 7x + 13
x^2 - 4x
____________
0 - 3x + 13
- 3x + 12
______
1
Part 4b answer:
quotient 2x^2 - 6x + 2
remainder -20
Step by step: you have to know exactly what you are doing. Refer to textbook or Wikipedia.
dividend 2x^3 +14x^2 - 58x
divisor x+10
leading coefficient of divisor must be 1
write coefficients of dividend at top
write coefficients of dividend at left
| 2 14 -58 0
-10 | -20 60 -20
___________
| 2 -6 2 -20
Coefficients of quotient are 2 -6 2
Remainder is -20
quotient = 2x^2 - 6x + 2
Answer:
the graph corresponds to function "D" 
Step-by-step explanation:
Since the graph shown corresponds to an exponential "decay" (the function decreases as we move from left to right), the base of the exponent has to be a number smaller than 1 (one). So we examine the only two options that give such (options C and D which have fractions as the base - 1/3 and 1/5 respectively)
From there, we analyze which of the two functions satisfies the crossing of the y-axis at (0,3) which is clearly shown in the graph:
We study both:
function C at x = 0 gives:
while function D at x = 0 gives:
Therefore, the graph corresponds to function "D"
2x(x+4)-1(x+4)
2x^2+8x-x-4
2x^2+7x-4
Answer:
638.32 yd²
Step-by-step explanation:
The surface area of any figure can be found by calculating the area of all the sides and finding the sum. In a rectangular pyramid, there is a rectangular base (l x w) and the same two triangles on one side and another two identical triangles on the other side.
Area of rectangle: A = l x w
Area of a triangle: A = 1/2(b)(h)
Rectangle: 16 x 13.4 = 214.4 yd²
Bottom/top triangles: 14.1 x 16 = 225.6 yd²
Side triangles: 14.8 x 13.4 = 198.32 yd²
Total: 198.32 + 225.6 + 214.4 = 638.32 yd²
Answer:
a. Life span increased
b. The median age could rise because of the improvement in medical technology. Also more advertisement of healthier life styles, such as eating healthy could have increase the median age.
c. No because this just shows the increase in life span not the decrease in children.
Step-by-step explanation:
a. more people on average lived longer lives. (explanation)
b. self explanatory I guess, my answer pretty much explained it.
c. life span of US citizens does not effect the children population. I guess you could say people lived longer lives to have more children, so possibly the number of children could have increased.
