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3 years ago

18. What is the slope of the linear function associated with the sequence {12, 9, 6, 3} for x = 1, 2, 3, 4?

Mathematics

1 answer:

Aloiza [94]3 years ago

4 0

Answer:

D) -3

Step-by-step explanation:

Slope of a linear function:

The slope of a linear function is the amount by which y changes when x increases by 1.

In this question:

When x = 1, y = 12

When x = 2, y = 9

When x = 3, y = 6

When x = 4, y = 3

So each time x increases by 1, y decreases by 3, which means that the slope is -3, and the answer is given by option D.

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Paul and jose are trying to measure the height of a tree. paul is standing 19m from the foot of the tree and measures the angle

Nina [5.8K]

The firts thig we are going to do is create tow triangles using the angles of elevation of Paul and Jose. Since the problem is not giving us their height we'll assume that the horizontal line of sight of both of them coincide with the base of the tree.
We know that Paul is 19m from the base of the tree and its elevation angle to the top of the tree is 59°. We also know that the elevation angle of Jose and the top of the tree is 43°, but we don't know the distance between Paul of Jose, so lets label that distance as $x$ .
Now we can build a right triangle between Paul and the tree and another one between Jose and the tree as shown in the figure. Lets use cosine to find h in Paul's trianlge:
$cos(59)= \frac{19}{h}$
$h= \frac{19}{cos(59)}$
$h=36.9$
Now we can use the law of sines to find the distance $x$ between Paul and Jose:
$\frac{sin(43)}{36.9} = \frac{sin(16)}{x}$
$x= \frac{36.9sin(16)}{sin(43)}$
$x=14.9$

Now that we know the distance between Paul and Jose, the only thing left is add that distance to the distance from Paul and the base of the tree:
$19m+14.9=33.9m$

We can conclude that Jose is 33.9m from the base of the tree.

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3 years ago

If sin theta = -0.7660, which of the following represents an approximate value of tan theta, for 180 degrees < theta < 270

Elis [28]

We have that
sin ∅=-0.7660

the sin ∅ is negative
so
∅ belong to the III or IV quadrant
but
180°< ∅ < 270°
hence
∅ belong to the III quadrant
sin ∅=-0.7660
sin² ∅+cos² ∅=1
cos² ∅=1-sin² ∅------> cos² ∅=1-(0.7660)²-----> 0.4132
cos ∅=√0.4132-----> cos ∅=0.6428
the value of cos ∅ is negative-------> III quadrant
cos ∅=-0.6428

tan ∅=sin ∅/ cos ∅----> tan ∅=-0.7660/-0.6428----> tan ∅=1.1917

the answer is
tan ∅ is 1.1917

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