Answer:
I. x + y = 9
II. x = 3
III. y/c = 1/4 --> y = 1/4*c
II and III in I
3 + 1/4*c = 9 --> c = 24
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The greatest common factor is the largest factor that both numbers contain. Let's look at the factors of these terms.
12x²: 1, 12, 2, 6, 3, 4, x, x
15x³: 1, 15, 3, 5, x, x ,x
We see that both of these numbers contain a 3 and 2 x's, so our GCF would be 3x².
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The P axis should go to atleast 15 because thats how many prizes he would need if he were to have 150 entrees. the E axis should have atleast to 150 because thats the supremum of entries
Answer: 49
Step-by-step explanation:
Given
The dimension of the block is ![24.5\ in.\times12.5\ in.\times 8\ in.](https://tex.z-dn.net/?f=24.5%5C%20in.%5Ctimes12.5%5C%20in.%5Ctimes%208%5C%20in.)
Each vase requires
of clay
The volume of clay block is
![\Rightarrow V=24.5\times 12.5\times 8\\\Rightarrow V=2450\ in.^3](https://tex.z-dn.net/?f=%5CRightarrow%20V%3D24.5%5Ctimes%2012.5%5Ctimes%208%5C%5C%5CRightarrow%20V%3D2450%5C%20in.%5E3)
Number of vases that can be made
![\Rightarrow n=\dfrac{2450}{50}\\\\\Rightarrow n=49\ \text{Vases}](https://tex.z-dn.net/?f=%5CRightarrow%20n%3D%5Cdfrac%7B2450%7D%7B50%7D%5C%5C%5C%5C%5CRightarrow%20n%3D49%5C%20%5Ctext%7BVases%7D)
Thus, 49 vases can be made
<h3>
Question: </h3><h3>
In the diagram below of Δ ABC, side BC is extended to point D, m∠A = x , m∠B = 2x+15, and m∠ACD = 5x+5 , what is m∠B ?</h3>
Answer: 3) m∠B = 25º
Step-by-step explanation:
Since m∠C is supplementary to m∠ACD
m∠C = 180º - m∠ACD
m∠C = 180º -(5·x + 5)
m∠C = 180º -5 -5·x
m∠C = 175º - 5·x
The sum of the angles of a triangle = 180º
m∠A + m∠B + m∠C = 180º
x + 2·x + 15º + 175º - 5·x = 180º
3·x - 5·x +190º = 180º
-2·x = 180º - 190º
-2·x = -10º
x = -10º/-2 = 5º
Now we can substitute this value of x in m∠B
m∠B = 2x+15
m∠B = 2·x + 15º = 2·5º + 15º = 10º + 15º = 25º
Answer: 3) m∠B = 25º
<h2><em>Spymore</em></h2>