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:
the first option, i took the test
Step-by-step explanation:
I think the correct answer from the choices listed above is option C. <span>C.Talia needs to factor out a negative from one of the groups so the binomials will be the same. She should do as follows:
</span><span>(15x2 – 3x) + (–20x + 4)
3x(5x – 1) + 4(–5x + 1)
</span>3x(5x – 1) - 4(5x - 1)
Answer:
A) 513 pumpkin
B) Ø = 42.2 degree
Step-by-step explanation:
Given that the triangle are of sides 45 ft, 75 ft, and 102 ft.
Let's first calculate the semi perimeter s of the triangle
S = ( a + b + c )/2
S = ( 45 + 75 + 102 )/2
S = 222/2 = 111
Area = sqrt root( s(s-a)(s-b)(s-c))
Area = sqrt root (111(66)(36)(9))
Area = 1540.66 square feet
If each pumpkin takes about 3 ft^2 of space.
The shelter display 1540.66/ 3 = 513.55
513 pumpkin
The measure of the middle-sized angle can be obtained by using cosine formula
75^2 = 45^2+102^2-2(45)(102)cosØ
5625 = 12429 - 9180cosØ
9180cosØ = 12429 - 5625
CosØ = 0.74118
Ø = 42.2 degree
