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Travka [436]
3 years ago
13

Let segments a p and b p be tangent segments. what is the length of segment a p if b p equals 12 cm?

Mathematics
1 answer:
algol [13]3 years ago
8 0

Answer:

Measure of line segment ap = 12 cm

Step-by-step explanation:

Given:

Two line segments (tangents) from a common point (p).

Considering p as a common point.

Measure of length bp = 12 cm

We have to find the measure of length ap.

According to the theorem.

Two-Tangent Theorem:

When two segments are drawn tangent to a circle from the same point outside the circle, the segments are equal in length.

So,

We can say that both the line segments from point p are equal.

Measure of ap = 12 cm

A diagram is also attached with this.

Measure of segment ap = 12 cm

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Which of the following proves these triangles are congruent
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In one day, a book store earned $199 in sales for 4 copies of a new cookbook and 5 copies of a new science fiction novel. On the
Marina86 [1]

Answer:

The cookbook costs $36 per copy while the science fiction costs $11 per copy

Step-by-step explanation:

Here in this question, we are interested in calculating the price of the cookbook and the price of the science fiction novel.

Since we do not know the price of each, we start by assigning variables to stand in for these unknown prices.

Let the price of the cookbook be $x , while the price of the science fiction be $y

Now, on the first day, 4 copies of the cookbook and 5 copies of the fiction;

mathematically that would be 4 * x and 5 * y

We add both and sum to be $199

Thus we have;

4x + 5y = 199 ••••••••••(i)

On the second day;

3 copies of cookbook 3 * x = 3x with 4 copies of science fiction 4 * y

Adding both yielded 152;

Thus, we have ;

3x + 4y = 152••••••••••(ii)

So we need to solve both equations simultaneously to get the values of x and y

4x + 5y = 199

3x + 4y = 152

Multiply equation i by 3 and equation ii by 4

3 * 4x + 5y = 199

4 * 3x + 4y = 152

12x + 15y = 597

12x + 16y = 608

Now, subtract multiplied equation ii from multiplied equation i

(12x-12x) + (15y-16y) = (597-608)

-y = -11

y = 11

To get x, simply substitute in any of the equations;

let’s use equation 1

4x + 5y = 199

4x + 5(11) = 199

4x + 55 = 199

4x = 199-55

4x = 144

x = 144/4

x = 36

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3 years ago
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