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2 years ago

Is it possible to create two triangles with congruent side lengths but different angle measurements?

1 answer:

8 0

Yes. If the side lengths are different, you can end up with different angle measurements (example: SSA~ property. You can have two sides that are the same but you can make two different triangles with those side lengths and that one angle.)

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A segment with endpoints A (3, 4) and C (5, 11) is partitioned by a point B such that AB and BC form a 2:3 ratio. Find B.

Dima020 [189]

Answer:

(3.8, 6.8)

Step-by-step explanation:

Point B:

Has coordinates (x,y)

AB and BC form a 2:3 ratio.

This means that:

$B - A = \frac{2}{2+3}(C - A)$

$B - A = \frac{2}{5}(C - A)$

We apply this both for the x-coordinate and for the y-coordinate.

x-coordinate:

x-coordinate of A: 3

x-coordinate of C: 5

x-coordinate of B: x

$B - A = \frac{2}{5}(C - A)$

$x - 3 = \frac{2}{5}(5 - 3)$

$x - 3 = \frac{4}{5}$

$x = 0.8 + 3 = 3.8$

y-coordinate:

y-coordinate of A: 4

y-coordinate of C: 11

y-coordinate of B: y

$B - A = \frac{2}{5}(C - A)$

$y - 4 = \frac{2}{5}(11 - 4)$

$y - 4 = \frac{14}{5}$

$y = 2.8 + 4 = 6.8$

Thus the correct answer is:

(3.8, 6.8)

7 0

2 years ago

Read 2 more answers

The Better Baby Buggy Co. has just come out with a new model, the Turbo. The market research department predicts that the demand

dlinn [17]

Answer:

$68

Step-by-step explanation:

We have been given the demand equation for Turbos as $q=-4p+544$ , where q is the number of buggies the company can sell in a month if the price is $p per buggy.

Let us find revenue function by multiplying price of p units by demand function as:

Revenue function: $pq=p(-4p+544)$

$pq=-4p^2+544p$

Since revenue function is a downward opening parabola, so its maximum point will be vertex.

Let us find x-coordinate of vertex using formula $\frac{-b}{2a}$ .

$\frac{-b}{2a}=\frac{-544}{2\times -4}$

$\frac{-b}{2a}=\frac{-544}{-8}$

$\frac{-b}{2a}=68$

The maximum revenue would be the y-coordinate of vertex.

Let us substitute $x=68$ in revenue formula.

$pq=-4(68)^2+544(68)$

$pq=-4*4624+544(68)$

$pq=-18496+36992$

$pq=18496$

Therefore, the company should sell each buggy for $68 to get the maximum revenue of $18,496.

8 0

2 years ago

A right triangle has side length that are consecutive integers of 12 feet what are the angles of the triangles

xxTIMURxx [149]

Your intention with the wording "consecutive integers of 12 feet" is not clear. Shown are triangles with sides 12 and 13 (a nice Pythagorean triple) as well as 11 and 12.