Answer: the height of the television screen is 20 inches
Step-by-step explanation:
The diagram of the rectangular television screen is shown in the attached photo. The rectangle is labelled as ABCD. The diagonal forms a right angle triangle, ABC. This means that angle B is 90 degrees. The height it labelled as h. To determine h, we will apply Pythagoras theorem. Pythagoras theorem is expressed as
Hypotenuse ^2 = opposite ^2 + adjacent ^2
From the diagram,
hypotenuse = 29 inches
Adjacent = 21 inches. Therefore,
29^2 = 21^2 + h^2
h^2 = 29^2 - 21^2 = 841 - 441
h = √400
h = 20 inches
I'll do the first one to get you started
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The equation x^2 + x - 6 = 0 is the same as 1x^2 + 1x + (-6) = 0. It is in the form ax^2 + bx + c = 0
We see that a = 1, b = 1, c = -6. Those values will be plugged into the quadratic formula (see attached image for steps).
The answers are x = -3 and x = 2. The order of the roots does not matter.
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To factor 1x^2 + 1x - 6, we need to find two numbers such that they add to 1 (the x coefficient) and multiply to -6 (the constant term)
Two such numbers are 3 and -2. This is found through trial and error.
Note how 3 plus -2 = 1 and 3 times -2 = -6.
So x^2 + x - 6 = 0 becomes (x+3)(x-2) = 0. You can use the FOIL rule to get x^2+x-6 back again.
Now use the zero product property to solve
(x+3)(x-2) = 0
x+3 = 0 or x-2 = 0
x = -3 or x = 2
which are the two solutions we got when we used the quadratic formula.
<span>
<span>
</span><span><span>
Tour
Price
# of Customers
Tour Income
Operating Cost Profit or Loss
</span>
<span>
100
40 4000
6000
-2000
</span>
<span>
150 35 5250
6000
-750
</span>
<span>
200 30
6000
6000
0
</span>
<span>
250 25 6250 6000
250
</span>
<span>
300 20 6000 6000
0
</span>
<span>
350
15 5250 6000
-750
</span>
<span>
400 10 4000 6000
-2000
</span>
<span>
450 5
2250
6000
-3750
</span>
<span>
500
0 0
6000 -6000
The company should offer the tour price of 250 to earn a profit. any price less or more than 250 will either give them 0 profit or a loss.
</span></span></span>
The answer is D. 3/8 in 1/2 hour, multiply by 2, since 1/2 times 2 is 1, meaning 1 hour. You will get 6/8, by simplifying that, you get 3/4.
An easy way to find an endpoint when the midpoint is given is to simply count the distance from the given endpoint to the midpoint, and go that distance from the midpoint in the opposite direction of the other endpoint. Using your problem as an example:
The y value doesn't change, so we only need to worry about x.
From 1 to -4, you go left 5 (-4 - 1 = -5). So, do that again, and you get -9.
Therefore, the coordinates of the other endpoint are (-9, -2), or B.
<em>Hope this helps! :)</em>
