MATHEMATICS HIGH SCHOOL

A square acre of land is 4,840 square yards. The length of one side of the square is between which of the following?A 14 yd and 48 yd
B 69 yd and 70 yd
C 98 yd and 100 yd
D 124 yd and 139 yd

Answers

Answer 1
Answer: Hi there!

If we know the area is a square, we can use the formula for the area of a square to figure out what one side would be between. Knowing the value allows us to determine what it would be between. In this case, it is between 69 and 70.

WORK:
squareroot(4840) = 69.6

ANSWER:
Option B - 69 yd and 70 yd

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If f(x)=x^2-5 and g(x)=6x then g(f(x)) is equal to

Answers

g(x) = 6x 

g(f(x)) 
= 6((x^2) - 5) 
= (6x^2) - 30 

so its equal to
(6x^2) - 30
Plug f(x) as x in g(x) and you get 6(x^2-5), which is g(f(x)) = 6x^2-30.

When negative five is subtracted from a number the result is 10. Find the number.15
5
-5
-15

Answers

x = unknown number
x - (-5) = 10
x + 5 = 10
x = 5, or B.

Answer:

the answer is B

Graph the function f(x) = x3 − 15x2 + 68x − 96. Describe the graph. Include the y-intercept, x-intercepts, and the shape of the graph.

Answers

The function is a cubic function with y intercept at y = -96 and x-intercepts at x = 3, x = 4 and x = 8.
The graph is looks like an 'S' shape rotated to the left.
yintercept is where x=0
xint is where y=0
shape is 3rd degree and positive leading coefient
it goes from bottom left to top right

yint is -96
xint
factor
f(x)=(x-8)(x-4)(x-3)
xints are at (8,0) and (4,0) and (3,0)

What is the greatest common factor of 24 44 52 in prime factorizations?

Answers

24
/\
6 2
/\ \
3 2 2

44
/\
11 4
/ /\
11 2 2

52
/\
13 4
/ /\
13 2 2

I know that this is prime factorization, so the greatest common factor is 2 because that's the greatest number they all in common.

What is the value of i^97 - i

Answers

if\ i\ is\ the\ imaginary\ unit\ (i=√(-1)\Rightarrow i^2=-1):\n\ni^(97)-i=i(i^(96)-1)=i(i^(48\cdot2)-1)=i[(i^2)^(48)-1]=i[(-1)^(48)-1]\n\n=i(1-1)=i\cdot0=0\n\ntherefore\ \boxed{i^(97)-i=0}

this can also be explained as b on edg

Graph the solution of the inequality –3(x + 1) ≤ 6 on the number line.A. Number lines from minus five to five five by increament of one from left to right and each tick mark is labeled. Shaded part from close circle at minus three to infinity
B. Number lines from minus five by increament of one from left to right and each tick mark is labeled. Shaded part from open circle at minus three to infinity
C. Number lines from minus five by increament of one from left to right and each tick mark is labeled. Shaded part from minus infinity to close circle at minus three
D. Number lines from minus five by increament of one from left to right and each tick mark is labeled. Shaded part from minus infinity to open circle at minus three

Answers

Answer:  Choice A

Explanation

Let's solve for x.

-3(\text{x}+1) \le 6\n\n-3\text{x}-3 \le 6\n\n-3\text{x} \le 6+3\n\n-3\text{x} \le 9\n\n\text{x} \ge 9/(-3) \ \ \text{ ....... inequality sign flip}\n\n\text{x} \ge -3\n\n

The inequality sign flips whenever we divide both sides by a negative number.

The number line graph will have a closed filled in circle at -3 and shading to the right. This will visually mean "The solution set is either x = -3 or x > -3". In other words, we can pick -3 or larger.

The diagram is shown below.

The diagram matches with answer choice A
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