Step-by-step explanation:
the answer is in the image
4 cos² x - 3 = 0
4 cos² x = 3
cos² x = 3/4
cos x = ±(√3)/2
Fixing the squared cosine doesn't discriminate among quadrants. There's one in every quadrant
cos x = ± cos(π/6)
Let's do plus first. In general, cos x = cos a has solutions x = ±a + 2πk integer k
cos x = cos(π/6)
x = ±π/6 + 2πk
Minus next.
cos x = -cos(π/6)
cos x = cos(π - π/6)
cos x = cos(5π/6)
x = ±5π/6 + 2πk
We'll write all our solutions as
x = { -5π/6, -π/6, π/6, 5π/6 } + 2πk integer k
Answer:
y = -4
Step-by-step explanation:
-2x + 5y = 8
Let x=-14
-2(-14) +5y = 8
28 +5y = 8
Subtract 28 from each side
28-28 +5y = 8-28
5y = -20
Divide by 5
5y/5 = -20/5
y = -4
Answer:
$12.31
Step-by-step explanation:
Think of the original rate of pay as being 100%.
If your rate is increasing by 7%, it will now be 107% of the original rate (since 100% + 7% = 107%)
To find 107% of $11.50, convert 107% into a decimal
⇒ 107% = 107/100 = 1.07
then multiply this by the original rate to get the new increased rate:
⇒ $11.50 × 1.07 = $12.305
Rounding this to the nearest hundred = $12.31
Alternatively, you can find 7% of $11.50 and then add this to $11.50.
⇒ 7% = 7/100 = 0.07
Therefore, 7% of $11.50 = 0.07 × $11.50 = $0.805
Add this to the original rate:
$11.50 + $0.805 = $12.305
Rounding this to the nearest hundred = $12.31
Answer:
240 = 2 x 2 x 2 x 2 x 3 x 5 or 2^4x3x5
Step-by-step explanation:
240
/ \
2 120 (240 = 2 x 120)
/ \
2 60 (120 = 2 x 60)
/ \
2 30 (60 = 30 x 2)
/ \
2 15 (30 = 2 x 15)
/ \
3 5