Answer:
DE ≈ 14.91
Step-by-step explanation:
Make use of the relationships between sides and angles in a right triangle. These are summarized by the mnemonic SOH CAH TOA:
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
__
The side DE is opposite the angle 19°, so the sine or tangent relation will be involved. The sine relation requires you know hypotenuse EF. The tangent relation requires you know adjacent side DF.
The only common side between triangles CDF and DEF is side DF. That side is opposite the given 61° angle. The given side length (CF = 24) is adjacent to the 61° angle.
This means you have enough information to use these relations:
tan(61°) = DF/CF = DF/24
DF = 24·tan(61°)
and
tan(19°) = DE/DF
DE = DF·tan(19°) = (24·tan(61°))·tan(19°) . . . . . use DF from above
DE ≈ 24(1.804048)(0.344328) ≈ 14.908
The length of DE is about 14.91.
Answer:
The third graph is correct for the inequality 2x + 3y > -3
Step-by-step explanation:
The slope of the graph is –2/3.
The y-intercept is –1
The area above the dashed be line is shaded.
To verify, choose a coordinate in the shaded area, substitute the values for x and y. Calculate and check.
For example: (1,1)
2(1) + 3(1) > –3
2 + 3 > –3
5 > –3 True.
9514 1404 393
Answer:
the multiplicity is 4
Step-by-step explanation:
The graph shows a root at x = -2 that has a multiplicity of 2. You know the multiplicity is even, because the graph does not cross the x-axis. The multiplicity is 2 because the general shape of the graph in that area matches that of a quadratic (parabola).
The multiplicity of the root at x=4 is also an even number, because the x-axis is not crossed. However, the graph is significantly flatter at that point (than at x=-2), meaning the multiplicity is greater than 2. It is at least 4.
When we draw a graph with a multiplicity of 6 at x=4, we find the ratio of the peaks near x=-4 and x=0 to be different from that shown here. The suggests that the multiplicity of the root at x=4 is exactly 4.
Answer:
378 marbles are blue, and 270 marbles are red
Step-by-step explanation:
The total number of ratio units must be multiplied by 6 to get the total number of marbles. Hence the number of blue marbles is 63×6 = 378, and the number of red marbles is 45×6 = 270.
Answer:
It would last 7 1/2 weeks if i'm correct
