ANSWER: x=5/3, -1. Good luck. Hope this suffices.
Explanation for x=-1: |9x-3|=12. Lets take the absolute value brackets away for a sec. Add 3 to both sides 9x-3+3=-12+3, simplify: 9x=-9, divide both sides by nine:9x/9=-9/9. And that means that x=-1.
Explanation for x=5/3: |9x-3|=12. Add 3. 9x-3+3=12+3. Simplify: 9x=15. Divide both sides by 9. 9x/9=15/9. Simplify: x=5/3
Answer:
8
Step-by-step explanation:
8•4=32 it's not that bad
Answer:
D. About 800 years
Step-by-step explanation:
Use the half-life equation:
A = A₀ (½)ⁿ
where A is the final amount,
A₀ is the initial amount,
and n is the number of half-lives.
0.90A₀ = A₀ (½)ⁿ
0.90 = (½)ⁿ
To solve for n, take log of both sides:
log 0.9 = n log 0.5
n = (log 0.9) / (log 0.5)
n = 0.152
It takes 0.152 half-lives. The half-life of carbon-14 is 5730 years.
0.152 × 5730 years = 871 years
The closest answer is D.
Answer:
x = π/2 + πk
Step-by-step explanation:
cot² x csc² x + 2 csc² x − cot² x = 2
Multiply both sides by sin² x:
cot² x + 2 − cos² x = 2 sin² x
Add cos² x to both sides:
cot² x + 2 = 2 sin² x + cos² x
Pythagorean identity:
cot² x + 2 = sin² x + 1
Subtract 1 from both sides:
cot² x + 1 = sin² x
Pythagorean identity:
csc² x = sin² x
Multiply both sides by sin² x:
1 = sin⁴ x
Take the fourth root:
sin x = ±1
Solve for x:
x = π/2 + 2πk, 3π/2 + 2πk
Which simplifies to:
x = π/2 + πk
Answer: Option B and option D.
Step-by-step explanation:
We know that a quadrilateral is a 2-dimensional closed shape that has four sides.
By definition the diagonals of a quadrilateral are the lines that connect two non-adjacent vertices.
The following quadrilaterals have diagonals that are perpendicular to each other (also known as perpendicular bisector diagonals), which means that they form four angles of 90 degrees (right angles): <em>Rhombus and Square.</em>
Therefore the answers are: the option B and the option D.
