Hello from MrBillDoesMath!
Answer:
4( x + 1.5)^2 + 0
Discussion:
4x^2 + 12x + 9 = => factor "4" from first 2 terms
4 (x^2 + 3x) + 9 = => complete the square, add\subtract (1.5)^2
4(x^2 + 3x + (1.5)^2) - 4 (1.5)^2 + 9 =
4 ( x + 1.5)^2 + ( 9 - 4(1.5)^2) = => as (1.5)^2 = 2.25
4 ( x + 1.5)^2 + ( 9 - 4(2.25)) = => as 4 ( 2.25) = 9
4 ( x+ 1.5)^2 + 0
Thank you,
MrB
Answer:
3(x - 4)
Step-by-step explanation:
Given
3x - 12 ← factor out 3 from each term
= 3(x - 4)
<span>The surface area of a sphere is equal to [4 x Pi x R^2]. In other words, four multiplied by 3.14 multiplied by the radius squared. If the radius of a sphere is 15 yards, the approximate surface area is [4 x 3.14 x (15x15)] = [12.5 x 225] = [2,812 yd^2]. The surface area of a sphere with radius 15 yd is approximately 2,800 yards.</span>
Let x represent amount invested in the higher-yielding account.
We have been given that a man puts twice as much in the lower-yielding account because it is less risky. So amount invested in the lower-yielding account would be 
.
We are also told that his annual interest is $6600 dollars. We know that annual interest for one year will be principal amount times interest rate.
, where,
I = Amount of interest,
P = Principal amount,
r = Annual interest rate in decimal form,
t = Time in years.
We are told that interest rates are 6% and 10%.
Amount of interest earned from lower-yielding account: 
.
Amount of interest earned from higher-yielding account: 
.
Let us solve for x.
Therefore, the man invested $30,000 at 10%.
Amount invested in the lower-yielding account would be 
.
Therefore, the man invested $60,000 at 6%.
Answer:
21. The slope is 50.
22. 0
23. y=50x
24. $2600
Step-by-step explanation:
21. The slope of the line is 50. Slope is defined as "rise over run". As the line increases, each segment moves up the y-axis by $50, and to the right on the x-axis 1 segment. (Work: 50 divided by 1)
22. The y-intercept is (0, 0), or simply 0. If you look at the graph you can see that the line crosses the y-axis at the origin. This makes the y-intercept equal to 0.
23. The slope tells you that the student makes $50 every week. The y-intercept is 0. Using the formula y=mx+b, an appropriate equation would be y=50x.
24. The equation found in problem 23 can me used to determine how much a student makes (y) after "x" weeks. Substitute 52 for x to solve for y. This becomes y=50(52). This can be simplified to y=2600. This means that after 52 weeks, the student will have made $2,600.
