Answer:
LN=64 units
Step-by-step explanation:
step 1
Find the value of x
we know that
LN=LM+MN -----> equation A
see the attached figure to better understand the problem
we have
LN=12x+16
LM=10x+8
MN=5x-4
substitute the values in the equation A
12x+16=(10x+8)+(5x-4)
Solve for x
12x+16=15x+4
15x-12x=16-4
3x=12
x=4
step 2
Find the value of LN
LN=12x+16
LN=12(4)+16=64 units
Answer: <em>7m⁴n²</em>
Step-by-step explanation:
<em>Find the GCF of 21m⁵n² and 28m⁴n².</em>
<em>Find the prime factors of each term in order to find the greatest common factor (GCF).</em>
<em>21m⁵n² = </em><em><u>7</u></em><em> · 3 · </em><em><u>m</u></em><em> · </em><em><u>m</u></em><em> · </em><em><u>m</u></em><em> · </em><em><u>m</u></em><em> · m · </em><em><u>n</u></em><em> · </em><em><u>n</u></em>
<em>28m⁴n² = </em><em><u>7</u></em><em> · 2 · 2 · </em><em><u>m</u></em><em> · </em><em><u>m</u></em><em> · </em><em><u>m</u></em><em> · </em><em><u>m</u></em><em> · </em><em><u>n</u></em><em> · </em><em><u>n</u></em>
<em>The product of these common prime factors will be the Greatest Common Factor: </em><em><u>7</u></em><em> · </em><em><u>m</u></em><em> · </em><em><u>m</u></em><em> · </em><em><u>m</u></em><em> · </em><em><u>m</u></em><em> · </em><em><u>n</u></em><em> · </em><em><u>n</u></em><em> = 7m⁴n²</em>
Answer:
45.3 megabytes
Step-by-step explanation:
242 x 18.7%
= 242 x 0.187 = 45.254 = 45.3 megabytes
Answer:
We should add 2.4 quarts of pure orange juice to 3.6 quarts 10% orange juice to make 6 quarts of 40% orange juice.
Explanation:
Let p represent number of quarts of pure orange juice and q represent number of quarts of 10% orange juice.
We have total quarts required = 6
So, p+q =6 --------------------equation 1
The orange content of 6 quarts = 40 % = 6 x 40/100 = 2.4 quarts.
Orange content in p pure juice = p quarts.
Orange content in q, 10% juice = q x 10/100 = 0.1 q quarts
So we have, p + 0.1 q = 2.4 --------------------equation 2
Equation 1 - Equation 2 gives
0.9 q = 6 -2.4
q = 3.6 quarts
p + 3.6 = 6
p = 2.4 quarts
So we should add 2.4 quarts of pure orange juice to 3.6 quarts 10% orange juice to make 6 quarts of 40% orange juice.
we know that
An isosceles triangle has two equal sides and two equal angles
If the isosceles triangle is a right triangle
then
The measure of the angles are


so

we have

Substitute and solve for the hypotenuse

therefore
<u>the answer is</u>
