Step-by-step explanation:
Let us consider the task to find the angle between vectors ES and EJ (the first letters are taken to name the vectors).
\overrightarrow{ES} = (4;4) - (4; -3) = \overrightarrow{(0; 7)}
ES
=(4;4)−(4;−3)=
(0;7)
\overrightarrow{EJ} = (-5; -4) - (4; -3) = \overrightarrow{(-9; -1)}
EJ
=(−5;−4)−(4;−3)=
(−9;−1)
cos \alpha=\frac{\overrightarrow{ES}*\overrightarrow{EJ}}{|\overrightarrow{EJ}|*|\overrightarrow{ES}|}cosα=
∣
EJ
∣∗∣
ES
∣
ES
∗
EJ
cos(a) = (0*(-9)+7*(-1)) / (7*9.055) = -0.11043;
a = 96,34°
Solution: 96 degrees.
Let's call that number x, twice the number will be 2x, sum of it and 5 is, 2x+5. So if this expression is at most 15, it means, it can be only less than 15 and equal to 15. Let's show this as an inequality.
Let's solve.
![x\quad \in \quad \left[ -\infty ,5 \right]](https://tex.z-dn.net/?f=x%5Cquad%20%5Cin%20%5Cquad%20%5Cleft%5B%20-%5Cinfty%20%2C5%20%5Cright%5D%20)
If the number is a natural number. The values it can take is,
![x\quad \in \quad \left[ 0,1,2,3,4,5 \right]](https://tex.z-dn.net/?f=x%5Cquad%20%5Cin%20%5Cquad%20%5Cleft%5B%200%2C1%2C2%2C3%2C4%2C5%20%5Cright%5D%20)
Answer:
56°
Step-by-step explanation:
a straight line is 180° and 124° subtracted from 180° is 56°
Answer: 1436 units cubed (3.14) or 1437 units cubed (π)
Step-by-step explanation:
answer depends on if you substitute in 3.14 for π or not
9514 1404 393
Answer:
Step-by-step explanation:
When the 12-cup bag of sugar is divided evenly, each baker gets 6 cups.
There is no dot on Noah"s graph for 6 cups of sugar, so you have to extrapolate the given set of dots to see where it might be. You notice that each dot is 1/2 cup of flour more than the one to its left, so you expect that Noah will use 3 cups of flour for 6 cups of sugar.
__
Similarly, the table for Lin does not have an entry for 6 cups of sugar. Again, the next entry can be figured using the relations between previous entries. Here, each row for sugar goes up by 1 1/2 cups, so the next row would be 4 1/2 + 1 1/2 = 6 cups. And the rows for flour go up by 1 cup, so the next row for flour (for 6 cups of sugar) would be 4 cups of flour.
Lin will use 4 cups of flour for 6 cups of sugar.
__
<em>Alternate solution</em>
The relationship are proportional in both cases, so you can read the value for a smaller amount (2 cups or 3 cups of sugar), then multiply the value by an appropriate multiplier (3 or 2) to get the number of cups of flour for 6 cups of sugar.
Noah: 1 flour for 2 sugar ⇒ 3 flour for 6 sugar
Lin: 2 flour for 3 sugar ⇒ 4 flour for 6 sugar
