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Stells [14]
3 years ago
9

The perimeter of XYZ is ___ units.

Mathematics
1 answer:
In-s [12.5K]3 years ago
7 0

Look at the picture.

ZY = 5+3=8

For XY and ZX use the Pythagorean theorem.

XY^2=3^2+4^2\\\\XY^2=9+16\\\\XY^2=25\to XY=\sqrt{25}\\\\XY=5

ZX^2=5^2+4^2\\\\ZX^2=25+16\\\\ZX^2=41\to ZX=\sqrt{41}

The perimetero fo XYZ:

P_{\triangle XYZ}=8+5+\sqrt{41}=\boxed{13+\sqrt{41}}

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Problem PageQuestion Flying against the jetstream, a jet travels 3050 miles in 5 hours. Flying with the jetstream, the same jet
goblinko [34]

Answer: the rate of the jet in still air is 685 mph and the rate of the jetstream is 75 mph

Step-by-step explanation:

Let x represent the rate of the jet in still air.

Let y represent the rate of the jet jetstream.

Distance = speed × time

Flying against the jetstream, a jet travels 3050 miles in 5 hours. This means that the total speed of the jet would be (x - y) mph. Therefore,

3050 = 5(x - y)

3050/5 = x - y

x - y = 610 - - - - - - - - - - - - - -1

Flying with the jetstream, the same jet travels 3800 miles in 4 hours. This means that the total speed of the jet would be (x + y) mph. Therefore,

3800 = 4(x + y)

3800/5 = x + y

x + y = 760 - - - - - - - - - - - - - -2

Adding equation 1 to equation 2, it becomes

2x = 1370

x = 1370/2 = 685mph

Substituting x = 685 into equation 1, it becomes

685 - y = 610

y = 685 - 610 = 75mph

3 0
3 years ago
1)Sheyna drive to the lake and back. It took two hours less time to get there than it did to get back. The average speed on the
ipn [44]

Answer:

8 hours

Step-by-step explanation:

Given:

Sheyna drives to the lake with average speed of 60 mph and

v_1 = 60\ mph

Sheyna drives back from the lake with average speed of 36 mph

v_2 = 36\ mph

It took 2 hours less time to get there than it did to get back.

Let t_1 be the time taken to drive to lake.

Let t_2 be the time taken to drive back from lake.

t_2-t_1 = 2 hrs ..... (1)

To find:

Total time taken = ?

t_1+t_2 = ?

Solution:

Let D be the distance to lake.

Formula for time is given as:

Time =\dfrac{Distance}{Speed }

t_1 = \dfrac{D}{60}\ hrs

t_2 = \dfrac{D}{36}\ hrs

Putting in equation (1):

\dfrac{D}{36}-\dfrac{D}{60} = 2\\\Rightarrow \dfrac{5D-3D}{180} = 2\\\Rightarrow \dfrac{2D}{180} = 2\\\Rightarrow D = 180\ miles

So,

t_1 = \dfrac{180}{60}\ hrs = 3 \ hrs

t_2 = \dfrac{180}{36}\ hrs = 5\ hrs

So, the answer is:

t_1+t_2 = \bold{8\ hrs}

8 0
3 years ago
Find the midpoint of the segment with the given endpoints (5,-9) and (-2,-2)
QveST [7]
Another way to solve this is to use the Midpoint Formula.  The midpoint of a segment joining points (x_1,y_1) and (x_2,y_2) is

\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} \right)

So the midpoint of your segment is

\left(\frac{5+(-2)}{2},\frac{-9+(-2)}{2}\right) = \left(\frac{3}{2},-\frac{11}{2} \right)

Perhaps it helps to see that the x-coordinate of the midpoint is just the average of the x-coordinates of the points.  Ditto for the y-coordinate of the midpoint; just average the y's.
6 0
3 years ago
In a set of 25 aluminum castings, four castings are defective (D), and the remaining twenty-one are good (G). A quality control
lianna [129]

Answer:

The sample space for selecting the group to test contains <u>2,300</u> elementary events.

Step-by-step explanation:

There are a total of <em>N</em> = 25 aluminum castings.

Of these 25 aluminum castings, <em>n</em>₁ = 4 castings are defective (D) and <em>n</em>₂ = 21 are good (G).

It is provided that a quality control inspector randomly selects three of the twenty-five castings without replacement to test.

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

{n\choose k}=\frac{n!}{k!(n-k)!}

Compute the number of samples that are possible as follows:

{25\choose 3}=\frac{25!}{3!\times (25-3)!}

      =\frac{25\times 24\times 23\times 22!}{3!\times 22!}\\\\=\frac{25\times 24\times 23}{3\times 2\times 1}\\\\=2300

The sample space for selecting the group to test contains <u>2,300</u> elementary events.

6 0
3 years ago
What is the answer <br> A.<br> B.<br> C.<br> D.
RUDIKE [14]

Answer:

B.

Step-by-step explanation:

The opposite of 5/2 is -5/2 which is -2 1/2 and the opposite of -1/2 is 1/2.

4 0
2 years ago
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