In parallelogram HIJK, the meſsure of angle H is 57 degrees. What is the

Mathematics

1 answer:

goldfiish [28.3K]3 years ago

3 0

Answer:

is 31

Step-by-step explanation:

cuz u have to divdie it to get your answer.

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A rectangle with a length of L and a width of W has a diagonal of 10 inches. Express the perimeter P of the rectangle as a funct

KatRina [158]

<h2>Answer:</h2>

The expression which represents the perimeter P of the rectangle as a function of L is:

$Perimeter=2(L+\sqrt{100-L^2})$

<h2>Step-by-step explanation:</h2>

The length and width of a rectangle are denoted by L and W respectively.

Also the diagonal of a rectangle is: 10 inches.

We know that the diagonal of a rectangle in terms of L and W are given by:

$10=\sqrt{L^2+W^2}$

( Since, the diagonal of a rectangle act as a hypotenuse of the right angled triangle and we use the Pythagorean Theorem )

Hence, we have:

$10^2=L^2+W^2\\\\i.e.\\\\W^2=100-L^2\\\\W=\pm \sqrt{100-L^2}$

But we know that width can't be negative. It has to be greater than 0.

Hence, we have:

$W=\sqrt{100-L^2}$

Now, we know that the Perimeter of a rectangle is given by:

$Perimeter=2(L+W)$

Here we have:

$Perimeter=2(L+\sqrt{100-L^2})$

7 0

4 years ago

Find the coordinates of the vertices of the figure formed by each system of inequalities. x + y < 9 x - 2y < 12 y < 2x

Vladimir [108]

Answer:

b. (10, -1), (-6, -9), (2, 7)

Step-by-step explanation:

One way to solve this problem is by graphing (see attachment). In fact, that actually is the easiest way to do this.

First, graph x + y < 9 (red part on the attachment). To do this, isolate the y so that it's like a regular linear equation: y < -x + 9. Graph the line y = -x + 9 first, and then choose a point either on the left or right of the line to plug in for x and y.

Let's just choose (0, 0), which is on the left of the line: 0 < -0 + 9 ⇒ 0 < 9. Since this is a true statement, we know that we should shade the left side of the equation, and not the right side.

Now, graph x - 2y < 12 (blue part on the attachment). It's the same process here as the first inequality. For this one, we find that we also shade to the "left" of the line (it's more "up" than "left", but you get the idea).

Finally, graph y < 2x + 3 (green part on the attachment). Again, it's the same process. For this, we shade to the right.

Now look at the three points that they intersect at: they are (2, 7), (-6, -9), and (10, -1). The answer is thus B.