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:
2, 10, 50, 250
Step-by-step explanation:
Using the formula with a₁ = 2 , then
a₂ = 5a₁ = 5 × 2 = 10
a₃ = 5a₂ = 5 × 10 = 50
a₄ = 5a₃ = 5 × 50 = 250
The first 4 terms are 2, 10, 50, 250
From the table we have the points (-4, -2) and (-2, -10).
The formula of a slope:
Substitute:
<h3>Answer: The slope = -4.</h3>
Answer: 2
Step-by-step explanation:
try each value in the equation
2(0) + 1 = 3
0 + 1 = 3
1 ≠ 3
so 0 doesn’t work
2(1) + 1 = 3
2 + 1 = 3
3 = 3
this works, so the answer is 1
The answer is 20 stamps.
You can solve this by forming an equation with.
We know that she has a total of 50 at the end. So we will put the 50 stamps at the end of the equation and derive for the unknown.
She first gave 10 to her friend. This means we subtract first 10 from the unknown. Let x represent the unknown.
x-10
Afterwards Jane's mom bought her twice as many as she had at the beginning. So we know that we add twice as much as the unknown.
x-10+2x = 50
Now we solve. Let's arrange our terms by combining like terms:
3x - 10 = 50
Now we transpose the 10 to the other side of the equation:
3x = 50 + 10
3x = 60
And finally we transpose the 3 by the x to isolate x:
x = 60/3
= 20
She had 20 stamps in the beginning.
