Answer:
4^{10}
Step-by-step explanation:
Complete the exponents first.
4*4=16
4*4*4*4*4*4*4*4=65536
65536 *16= 1048576
The answer is
You can also find this if you add the exponents.
WILL GIVE THE BRAINLEST Find the surface area of the triangular prism
1 answer:
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Answer:
∠HGJ = 35°
Step-by-step explanation:
Although the question is somewhat incomplete, I have tried to reconstruct the question as much as possible to aid understanding (attached is the pictorial representation of the rhombus).
Firstly, it is important to note that rhombuses are parallelograms which have all sides equal and whose diagonals are perpendicular to each other. In addition to this, their diagonals bisect one other.
Mathematically, |EF| = |FG| = |GH| = |HE|
Another property which rhombuses have is that their opposite angles are equal.
Mathematically, ∠E = ∠G, ∠H = ∠F
The adjacent angles in a rhombus are supplementary. This means that the sum of angles closest to each other is 180°.
Mathematically, ∠E + ∠F = 180°, ∠F + ∠G = 180°, ∠G + ∠H = 180°,
∠H + ∠E = 180°
The question gave us ∠GHE and asked us to find ∠HGJ (denoted as θ in the picture attached). Note that ∠GHE means ∠H. That is, ∠GHE ⇒ ∠H
∠GHE or ∠H = 110°
From the properties of rhombuses (earlier stated), we know that adjacent angles in a rhombus are supplementary
Mathematically,
∠GHE + ∠FGH ⇒ 110° + ∠FGH = 180° ⇒ ∠FGH = 180° - 110°
∠FGH or ∠G = 70°
To calculate for ∠HGJ, we divide ∠FGH by 2, we have:
∠HGJ = ∠FGH ÷ 2 = 70° ÷ 2
∠HGJ = 35°
Answer:
Graph B
No
Inside
Step-by-step explanation:
Let, the number of apples = x and number of peaches = y.
It is given that the farmer can afford maximum of 54 acres.
Thus, x + y ≤ 54.
Also, apples require 3000 gallons of water and peaches require 800 gallons of water each day.
Since, maximum amount of water is 80,000 gallons per day,
We get, 3000x + 800y ≤ 80,000.
It is required to maximize the profit given by z = 3400x + 1600y.
Thus, the system of equations becomes,
z = 3400x + 1600y
3000x + 800y ≤ 80,000.
x + y ≤ 54.
Plotting these equations gives the following graph.
We can see that the graph obtained is equivalent to Graph B.
Further, we know that the maximum value of the objective function z = 3400x + 800y is obtained at the boundary point of the solution region.
Thus, any point inside the solution region will give a feasible solution not maximum solution.
Hence, ( 30,20 ) will not maximize the profit as it lies inside the solution region.
