Answer:
70
Step-by-step explanation:
From the question given above, the following data were obtained:
TU = 8x + 11
UV = 12x – 1
Next, we shall determine the value of x.
From the question:
U is the midpoint. This means that TU and UV are equal i.e
TU = UV
With the above idea in mind, we shall determine the value of x as follow:
TU = UV
TU = 8x + 11
UV = 12x – 1
8x + 11 = 12x – 1
Collect like terms
11 + 1 = 12x – 8x
12 = 4x
Divide both side by the coefficient of x i.e 4
x = 12/4
x = 3
Next, we shall determine the length of TU and UV. This can be obtained as follow:
TU = 8x + 11
x = 3
TU = 8(3) + 11
TU = 24 + 11
TU = 35
UV = 12x – 1
x = 3
UV = 12(3) – 1
UV = 36 – 1
UV = 35
Finally we shall determine the length of TV. This can be obtained as follow:
TV = TU + UV
TU = 35
UV = 35
TV = 35 + 35
TV = 70
Therefore, the distance between my house and grandma's house is 70.
NOTE: Assume the distance is measured in kilometer (km)
This means that I will travel 70 km from grandma's house to my house.
Answer as an inequality: 
Answer in interval notation: [2, 7]
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Explanation:
The range is the set of all possible y outputs of a function.
The lowest point occurs when y = 2
The highest point occurs when y = 7
The range is the set of every y value between 2 and 7, including the endpoints.
The range as an inequality is 
It is equivalent to [2, 7] in interval notation. The square brackets include each endpoint.
Answer:
180 cards
Step-by-step explanation:
45x 4= 180
Answer:
It means that 20 times x is 5
also the answer to that problem (20x=5) is 1/4
Step-by-step explanation:
20x means
20 * x
and since 20 * x = 5
divide 5 and 20
5/20 = 1/4
Answer:
- <u><em>P = 0.40x + 0.50y</em></u>
Explanation:
The <em>objective function</em> is the function that you want to optimize: usually minimize in the case of costs, and maximize in the case of revenues or profits.
In this case, you know the <em>profits</em> that a manufacturer earns from two types of <em>bottled coffe drinks</em>: <em>cappuccinos</em> and <em>cafés au lait</em>.
Each bottle of <em>cappuccino earns a profit of $0.40</em> and each bottle of <em>café au lait earns a profit of $0.50</em>.
Then:
- using the variable x for the number bottles of cappuccino produced, the profit earned from x bottles is 0.40x, and
- using the variable y for the number of bottles of café au lait the produced, the profit earned from y bottles is 0.5y.
The total profit earned, P, is the sum of the profits earned from each type of bottled coffee drinks:
That is the <em>objective function</em>, i.e. the function that the manufacturer must try to maximize subject to the corresponding constraints.
