Answer:
To solve the first inequality, you need to subtract 6 from both sides of the inequality, to obtain 4n≤12. This can then be cancelled down to n≤3 by dividing both sides by 4. To solve the second inequality, we first need to eliminate the fraction by multiplying both sides of the inequality by the denominator, obtaining 5n>n^2+4. Since this inequality involves a quadratic expression, we need to convert it into the form of an^2+bn+c<0 before attempting to solve it. In this case, we subtract 5n from both sides of the inequality to obtain n^2-5n+4<0. The next step is to factorise this inequality. To factorise we must find two numbers that can be added to obtain -5 and that can be multiplied to obtain 4. Quick mental mathematics will tell you that these two numbers are -4 and -1 (for inequalities that are more difficult to factorise mentally, you can just use the quadratic equation that can be found in your data booklet) so we can write the inequality as (n-4)(n-1)<0. For inequalities where the co-efficient of n^2 is positive and the the inequality is <0, the range of n must be between the two values of n whereby the factorised expresion equals zero, which are n=1 and n=4. Therefore, the solution is 1<n<4 and we can check this by substituting in n=3, which satisfies the inequality since (3-4)(3-1)=-2<0. Since n is an integer, the expressions n≤3 and n<4 are the same. Therefore, we can write the final answer as either 1<n<4, or n>1 and n≤3.
Answer:
x + y = 13
98x + 115y = z
Step-by-step explanation:
Let x represent the time spent taking class in Westside community college
Let y represent the time spent taking class in Pinewood community college
Let z represent the combined total amount paid for the class fees.
The total combined time for the two school is given as:
x + y = 13.
For the combined total amount; we multiply the price for each school with the time spent on the school and sum them together.
Westside: 
Pinewood: 
The combined total amount represented as z is given as:
z = 98x + 115y
The cost of the bond was 90/100 times $5,000, that is, $4,500 total.
<span>The annual interest is 5% of $5,000, that is, $250. </span>
<span>The current yield is 5% divided by (90/100), that is 5.555%; round to 5.6% as instructed. </span>
<span>The yield that real bond buyers would be more interested in is the yield to maturity, but this cannot be calculated without knowing the term (number of years). If it's a short term bond that will pay you back $5,000 in just a few years, that would add several percent to the yield, but if it's a 15-year bond the growth of the $4,500 to $5,000 adds only a fraction of 1% to the yield.</span>
Answer:
Step-by-step explanation:
Remark
Simple answer: you can't. I mean that you can't try to use 4 numbers, but you can solve the problem. You are going to have to redraw the diagram on another sheet of paper. Follow the directions below.
Directions for diagram extension.
Go to the right hand end of the 10 unit line.
Draw a line from the intersection point of the 10 unit line and 12 unit line
Draw this line so it is perpendicular to the 18 unit line. That will mean that the new line is parallel (and equal) to x
Mark the intersect point of the new line and the 18 unit line as B
Mark the intersect point of the 18 point line and the 12 unit line as C
Given and constructed
BC = 18 - 10 = 8
BC is one leg of the Pythagorean triangle.
The new x is the other leg of the Pythagorean triangle.
12 is the hypotenuse.
Formula
x^2 + 8^2 = 12^2
x refers to the new x which is equal to the given x
Solution
x^2 + 64 = 144 Subtract 64 from both sides
x^2 +64 - 64 = 144-64 Combine
x^2 = 80 Break 80 down.
x^2 = 4 * 4 * 5 Take the square root of both sides
x = 4*sqrt(5)
Comment
If you want the area it is 4*sqrt(5)(10 + 18)/2 = 56*sqrt(5)
Answer:
It will take him <u>20 days</u> to read a 300-page book.
Step-by-step explanation:
Given:
Stephen read a 90-page book in 6 days.
If he continues reading at that rate.
Now, to find the time it will take him to read a 300-page book.
So, we solve using unitary method:
If, Stephen read 90 pages in 6 days.
So, Stephen read 1 page in = 
days.
Thus, Stephen read 300 page in = 
Therefore, it will take him 20 days to read a 300-page book.
