The problem statement tells you ∠MLK is 61°, so ∠LMK = 180° -68° -61° = 51°. Since a tangent is always perpendicular to a radius, triangles LJM and LJK are right triangles.
Trigonometry tells you ...
tangent = opposite / adjacent
so you can write two relations involving LJ.
tan(51°) = LJ/JM
tan(68°) = LJ/JK
The second equation can be used to write an expression for LJ that can be substituted into the first equation.
LJ = JK*tan(68°) = 3*tan(68°)
Substituting, we have
tan(51°) = 3*tan(68°)/JM
Multiplying by JM/tan(51°), we get
JM = 3*tan(68°)/tan(51°)
JM ≈ 6.01
The radius of circle M is about 6.01.
5 - 4 + 7x + 1 = 7x + (5 - 4 + 1) = 7x + 2
NO SOLUTIONS:
<em>5 - 4 + 7x + 1 = 7x + a </em><em>(a - any real number, except 2)</em>
ONE SOLUTION:
<em>5 - 4 + 7x + 1 = bx + c </em><em>(b - any real number, except 7, c - any real number)</em>
INFINITELY MANY SOLUTIONS:
<em>5 - 4 + 7x + 1 = 7x + 2</em>
Examples:
2x + 3 = 2x + 5 <em>subtract 2x from both sides</em>
3 = 5 FALSE <em>(NO SOLUTIONS)</em>
2x + 3 = x - 4 <em>subtract x from both sides</em>
x + 3 = -4 <em>subtract 3 from both sides</em>
x = -7 (<em>ONE SOLUTION)</em>
2x + 3 = 2x + 3 <em>subtract 2x from both sides</em>
3 = 3 TRUE <em>(INFINITELY MANY SOLUTIONS)</em>
Answer:
f= d/ 1+x
Step-by-step explanation:
Answer:
Variance, Range, Standard deviation, Inter-quartile range
Step-by-step explanation:
The most commonly used measure of variability in a data set include;
Variance and standard deviation - measures the variability of a data set about a fixed location, the mean. Variance is the square of the standard deviation.
Range - this is the difference between the largest and the smallest values in a data set.
Inter-quartile range is simply the difference between the third and the first quartile where the second quartile is the median.
Other measures include;
Downside semi-variance
Answer:
The number of sleeping bags bought is 17.
Step-by-step explanation:
If we let "x" be the number of the sleeping bags that were bought, we can make the following equation....
(5x)(12) + (x)(45) = 1785
By solving the equation we get....
(5x)(12) + (x)(45) = 1785
60x + 45x = 1785
105x = 1785
x = 1785 / 105
x = 17
There for the number of sleeping bags bough is 17.
