The factorization if the given expression 128 + 2d³ is 2(64 + d³).
<h3>Factorization</h3>
128 + 2d³
There are two parameters in the expression;
The common factors between 128 and 2d³ is 2
So,
128 + 2d³
= 2(64 + d³)
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Answer:
Step-by-step explanation:
Sum of angle in a triangle = 180°
<A+<B+<C = 180
Given <B = 50°
Substituting into the formula
<A+50+<C = 180
<A+<C = 180-50
<A+<C = 130°
Since the ∆ABC is an acute triangle, the angles <A and <C must be angles less than 90° since acute angles are angles less than 90°
The possible values of <A and <C that will be acute and give a sum of 130° are;
∠A= 58° and ∠C= 72°
∠A= 80° and ∠C= 50°
∠A= 60° and ∠C= 70°
You can see that all the Angles are less than 90° and their sum is 130°
Full question:
Linear Functions: Taking a Taxi
You take a trip to downtown Boston to walk the Freedom Trail with your family. After you walk through the Bunker Hill Memorial, your family decides to take a taxi to a restaurant for dinner. After 1 mile, the meter on the taxi says $4.75. It will cost $8.25 to go 3 miles. The cost varies linearly with the distance that you traveled. If you have $11 in your pocket, will you be able to take the cab 5 miles?
Answer:
Cannot go 5 miles having just $11
Step-by-step explanation:
Since the cost varies linearly with the distance that you traveled, to model the linear function for this problem we know that
1 mile = $4.75
And so to go x miles, we require $4.75x
Equation can therefore be modelled thus :
y=4.5x
Where y = total cost of transport in dollars
x= cost in dollars per mile
To find out if we can go 5 miles just having $11, we plug in 5 miles for x into the equation to find total cost of transport going 5 miles
y=4.5*5
y= $22.5
Therefore we cannot go 5 miles just having $11
Answer:
Number of $5 bills = 32
Number of $10 bills = 14
Number of $20 bills = 8
Step-by-step explanation:
Let x number of $5, y number of $10 and z number of $20
The number of $5 bills exceeds twice the number of $10 bills by 4.
Therefore, x = 2y + 4
The number of $20 bills is 6 fewer than the number of $10 bills.
Therefore, z = y - 6
A wallet contains $460 in $5, $10, and $20 bills.
Therefore,
5x + 10y + 20z = 460
Substitute x and y into equation
5(2y+4) + 10y + 20(y-6) = 460
10y + 20 + 10y + 20y - 120 = 460
40y - 100 = 460
40y = 460 + 100
40y = 560
y = 14
- Put the value of y into x = 2y + 4 and solve for x
x = 2(14) + 4
x = 32
- Put the value of y into z = y - 6 and solve for z
z = 14 - 6
z = 8
Hence, the each type of bills,
Number of $5 bills = 32
Number of $10 bills = 14
Number of $20 bills = 8
