Answer:
1. n= 14
2. n=3
Step-by-step explanation:
For the first problem, let's break down the equation. The number being thought about can be represented by <em>n</em>. Then <em>n </em>is increased by 7, or simply put 7+ <em>n. </em>The sum is 21, so to find n you can use the equation 7 + n = 24 and solve for <em>n, </em>which is 14.
For problem two, the same strategy can be used. The number is <em>n, </em>multiplied by 9. So, 9 * <em>n</em> is equal to 27. Solve for n by isolating n, and the answer is 3.
Answer:
The models have tiles corresponding to x+8 and x+1
Step-by-step explanation:
We want to find the model that represents factors of

We split the middle term to get:

We factor by grouping to obtain:

We collect common factors again to get:

The models have tiles corresponding to x+8 and x+1
Answer:
Step-by-step explanation:
Given that a rectangle is constructed with its base on the x axis and two of its vertices on the parabola

This parabola has vertex at (0,100) and symmetrical about y axis.
Any general point above x axis can be written as (a,b) (-a,b) since symmetrical about yaxis.
Hence coordinates of any rectangle are

Length of rectangle = 2a and width = 
Area of rectangle = lw = 
To find max area, use derivative test.

Hence maxima when first derivative =0
i.e. when a =2
Thus we find dimensions of the rectangle are l =4 and w = 96
Maximum area = 
-(7x + 4)- 2x + 2 = 52
Distribute the negative sign:
-7x -4 - 2x + 2 = 52
Combine like terms:
-9x - 2 = 52
Add 2 to both sides:
-9x = 54
Divide by -9:
x = -6
Answer: x = -6