Segment length geometry honors

Mathematics

1 answer:

kipiarov [429]3 years ago

6 0

Answer:

x = 15

Step-by-step explanation:

Assuming you require the value of x

The product of the external part and the whole of one secant is equal to the external part and the whole of the other secant, that is

9(9 + x) = 8(8 + 19), that is

81 + 9x = 8 × 27 = 216 ( subtract 81 from both sides )

9x = 135 ( divide both sides by 9 )

x = 15

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220 student enter a spelling bee after the first round 40 students were eliminated there will be 180 students competing in round

solniwko [45]

Initial number of students: 220

Final number of students : 180

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Officials begin to release water from a full man-made lake at a rate that would empty the lake in 10 weeks, but a river that can

Romashka [77]

Answer:

It takes 20 weeks to empty the lake

Step-by-step explanation:

Some rate, let's call it $R_{empty}$ empties the lake in 10 weeks and a river (with rate $R_{river}$ can fill the lake in 20 weeks. The idea behind the solution of this type of problem is always set the rate to the same units. Let's see this:

$R_{empty}=\frac{1\ lake}{10\ weeks}$ which implies that this rate empties 0.1 of the lake per week, thus, $R_{empty}=0.1/week$ .

Using the same idea, we can obtain that the filling rate of the river is:

$R_{river}=\frac{1\ lake}{20\ weeks} = 0.05 /week$

Since both rates are acting at the same time, the total rate of flowing water (either in or out the lake) would be given by:

$R_{total}=R_{empty}+R_{river}\\R_{total}= -0.1 + 0.05=-0.05/week$ , which means that the lake is being empty at a rate of -0.05 week and using the rule of three: