Triangle a b c is shown with its exterior angles. line c b extends through point d. line b c extends to form exterior angle that is 135 degrees. angle c a b is 75 degrees. what is m∠abc? m∠abc = 15° m∠abc = 45° m∠abc = 60° m∠abc = 75°

m∠ABC = 45°

Step-by-step explanation:

See the attached figure.

As shown in the figure

Line C B extends through point D to form the exterior angle that is 135 degrees.

So, m∠ABD = 135°

But m∠ABC + m∠ABD = 180°

∴m∠ABC = 180° - m∠ABD = 180° - 135°= 45°

Also, we should know that

m∠ABD = m∠BAC + m∠ACB

So, m∠ACB = 135° - 75° = 60°

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Very important note:

If we replaced the location of B and C

SO, m∠ABC = 60° and m∠ACB = 45°

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d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt