<h3>
Answer:</h3>
42. 29°
43. 3x³ +2x² -3x +10
44. 20a² +68a
<h3>
Step-by-step explanation:</h3>
42. The right-angle corner tells you the two marked angles are complementary — they sum to 90°.
(-3x +20)° + (-2x +55)° = 90°
-5x +75 = 90 . . . . . . . . . . collect terms, divide by °
-5x = 15 . . . . . . . . . . . . . . . subtract 75
x = -3 . . . . . divide by the coefficient of x
The angle of interest is (-3x+20)°. Filling in the found value for x, we have ...
(-3·(-3) +20)° = 29° = m∠BDC
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43. The distributive property is useful for multiplying polynomials.
(x +2)(3x² -4x +5) = x(3x² -4x +5) +2(3x² -4x +5)
= 3x³ -4x² +5x +6x² -8x +10 . . . . . eliminate parentheses
= 3x³ +2x² -3x +10
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44. Area is the product of length and width, so this becomes a problem in multiplying polynomials.
area = (5a +17)(4a) = 20a² +68a . . . . area in square feet
Problema Solution
Terrance and Jesse are training for a long-distance race. Terrance trains at a rate of 6 miles every half hour, and Jesse trains at a rate of 2 miles every 15 minutes.
How long will each person take to run a total of 50 miles at the given rates?
Answer provided by our tutors
d = 50 mi the distance
t1 = the time of Terrance
t2 = the time of Jesse
Terrance trains at a rate of 6 miles every half hour thus his rate is:
v1 = 6/0.5 = 12 mph
Jesse trains at a rate of 2 miles every 15 minutes thus his rate is:
v2 = 2/(15/60) = 8 mph
since speed = distance/time follows time = distance/speed:
t1 = d/v1
t1 = 50/12
t1 = 4 1/6 hr
t1 = 4 hr 10 min
t2 = d/v2
t2 = 50/8
t2 = 6 1/4 hr
t2 = 6 hr 15 min
Terrance will run 4 hours and 10 minutes.
Jesse will run 6 hours and 15 minutes.
There is one clock that shows the right time so we do not have to worry about the one which is always correct.
Talking about the second clock that loses a minutes in every 24 hours (or in a day), so after 60 days (since it has lost 60 minutes because it is losing 1 minute everyday) it will show 11:00 a.m when it is exactly the noon.
So this way, in total it will take 
days before it shows the correct noon.
Now, the third clock gains a minute every 24 hours (or in a day) , after 60 days (when it has gained 60 minutes or a complete hour) it will show 1:00 p.m when it is exactly the noon.
This way, it will take days (since it has gained a minute everyday) when it shows the correct noon.
Therefore, it will take 1440 days before all the three clocks show the correct time again.
The function (fg)(x) is a composite function
The value of the function (fg)(x) is 2x^3 + 7x^2 - 19x - 20
<h3>How to determine the function (fg)(x)?</h3>
The functions are given as:
f(x) = 2x^2 - 3x - 4 and g(x) = x + 5.
To calculate (fg)(x), we make use of
(fg)(x) = f(x) * g(x)
So, we have:
(fg)(x) = (2x^2 - 3x - 4) * (x + 5)
Expand
(fg)(x) = 2x^3 - 3x^2 - 4x + 10x^2 - 15x - 20
Collect like terms
(fg)(x) = 2x^3 - 3x^2 + 10x^2 - 4x - 15x - 20
Evaluate
(fg)(x) = 2x^3 + 7x^2 - 19x - 20
Hence, the function (fg)(x) is 2x^3 + 7x^2 - 19x - 20
Read more about composite function at:
brainly.com/question/10687170
2nd term = 3 - 14 = -11
3rd tern = -11-14 = -25 answer
