Answer:
<h2>For c = 5 → two solutions</h2><h2>For c = -10 → no solutions</h2>
Step-by-step explanation:
We know
for any real value of <em>a</em>.
|a| = b > 0 - <em>two solutions: </em>a = b or a = -b
|a| = 0 - <em>one solution: a = 0</em>
|a| = b < 0 - <em>no solution</em>
<em />
|x + 6| - 4 = c
for c = 5:
|x + 6| - 4 = 5 <em>add 4 to both sides</em>
|x + 6| = 9 > 0 <em>TWO SOLUTIONS</em>
for c = -10
|x + 6| - 4 = -10 <em>add 4 to both sides</em>
|x + 6| = -6 < 0 <em>NO SOLUTIONS</em>
<em></em>
Calculate the solutions for c = 5:
|x + 6| = 9 ⇔ x + 6 = 9 or x + 6 = -9 <em>subtract 6 from both sides</em>
x = 3 or x = -15
Answer:
The 99% confidence interval is 
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The sample mean is 
The population standard deviation is 
From the question we are told the confidence level is 99% , hence the level of significance is
=> 
Generally from the normal distribution table the critical value of 
is
Generally the margin of error is mathematically represented as
=> 
Generally 95% confidence interval is mathematically represented as
=> 
=> 
Answer:
k
Step-by-step explanation:
Answer:
0.1228
Step-by-step explanation:
We use sine rule
where, in any triangle <em>ABC</em>, <em>a</em> is the side opposite ∠A, <em>b</em> is the side opposite ∠B and <em>c</em> is the side opposite ∠C.
Applying this to the question,
Answer:
5 cm and 13 cm
Step-by-step explanation:
Let b be the width of the rectangle.
Length = 3+2b
The area of the rectangle is 65 cm²
We need to find the dimensions of the rectangle. The area of a rectangle is given by :
A = lb
Neglecting the negative value, the width of the rectangle is 5 cm.
Length = 3+2b
=3+2(5)
=3+10
=13 cm
Hence, the dimensions of the rectangle are 5 cm and 13 cm.
