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3 years ago

prove that if two circles are tangent externally then the common internal tangent bisects a common external tangent.

Mathematics

1 answer:

Scilla [17]3 years ago

5 0

Explanation:

Consider the attached diagram.

Circles A and B have mutual tangents CF and DE that intersect at point F.

We know that the two tangents to a circle from an external point are congruent, so ...

FE≅ FC

FD ≅ FC

By the transitive property of congruence, both segments congruent to FC are congruent to each other:

FD ≅ FE

Therefore, CF is a bisector of DE.

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The number N of cars produced at a certain factory in 1 day after t hours of operation is given by Upper N (t )equals 800 t minu

Elden [556K]

Answer:

The cost C as a function of t is C(t) = 30,000 + 6,400,000 t - 40,000 t²

Step-by-step explanation:

The function N(t) = 800 t - 5t², represents the number of cars produced at a time t hours in a day, where 0 ≤ t ≤ 10

The function C(N) = 30,000 + 8,000 N, represents the cost C (in dollars) of producing N cars

We need to find The cost C as a function of the time t

That means Substitute N in C by its function by other word find the composite function (C о N)(t)

∵ C(N) = 30,000 + 8,000 N

∵ N(t) = 800 t - 5 t²

- Substitute N in C by 800 t - 5 t²

∴ C(N(t)) = 30,000 + 8000(800 t - 5 t²)

- Multiply the bracket by 8000

∴ C(N(t)) = 30,000 + 8000(800 t) - 8000(5 t²)

∴ C(N(t)) = 30,000 + 6,400,000 t - 40,000 t²

- C(N(t) = C(t)

∴ C(t) = 30,000 + 6,400,000 t - 40,000 t²

The cost C as a function of t is C(t) = 30,000 + 6,400,000 t - 40,000 t²

5 0

3 years ago

Cameron went into a grocery store and bought 4 apples abd 7 mangoes, costing a total of $17.75. Gavin went into the same grocery

rusak2 [61]

Answer:

7.00

Step-by-step explanation:

you subtract the 2 totals.

6 0

3 years ago

What is the quadratic equation to this question

-BARSIC- [3]

Answer:

f(x) = 4x − 12

Step-by-step explanation:

It's not quadratic. It's linear. Each time x increases by 1, f(x) increases by 4. So the slope is 4. The y-intercept (when x=0) is -12. The equation of the line is therefore:

f(x) = 4x − 12

5 0

3 years ago

Help help help help help

Mkey [24]

Answer:

x = 42

Step-by-step explanation:

The marked angles are supplementary, so their sum is 180°.

(2x +8) +(2x +4) = 180

4x +12 = 180 . . . . . . . . . simplify

x +3 = 45 . . . . . . . divide by 4 (because we can)

x = 42 . . . . . . subtract 3

_____

<em>Additional comment</em>

A "two-step" linear equation like this one is usually solved by subtracting the unwanted constant, then dividing by the coefficient of the variable. Here, we have done those steps in reverse order. This makes the numbers smaller and eliminates the coefficient of the variable. Sometimes I find it easier to solve the equation this way.

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2 years ago

Use the quadratic formula to solve the equation <br> X^2+9X+20=0

lions [1.4K]

Answer:

x=-4

x=-5

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers