Answer:
8² = 4² + 5² - 2(4)(5) cos(P)
which is the third option
Explanation:
The general rule of cosine is:
a² = b² + c² - 2bc*cos(A)
In our triangle:
a is substituted by p = 8 cm
b is substituted by n = 4 cm
c is substituted by m = 5 cm
A is substituted by P which we want to find
Replace the variables in the general equation with the givens as follows:
p² = n² + m² - 2mn*cos(P)
8² = 4² + 5² - 2(4)(5) cos(P)
Hope this helps :)
Answer:
Microscopes cost $44 and Dissection Kits cost $11
Step-by-step explanation:
Using the information given, we can make the system of equations:
30x+48y=1848
x represents the price of microscopes and y represents the price of dissection kits.
We also know that microscopes will be 4x the price of dissection kits. Therefor:
x=4y
We can plug these two equations together to find the answer.
30(4y)+48y=1848
120y+48y=1848
168y=1848
y=11
Using the y-value, can find the x-value.
x=4(11)
x=44
Answer:
Step-by-step explanation:
4/5 x - 2 > 3/10 * 2x
4/5 x - 2 > 3/5 x
4/5 x - 2 - 3/5x> 0
1/5x > 2
x > 10
See the attached image for the graph. The piecewise function is simply a collection of functions glued together to form a sort of "frankenstein function" of sorts. Here's how it works. If x is between 0 and 1 (including 0 but excluding 1), then f(x) = -2 for all x values mentioned. This is exactly what the first row of the piecewise function says. Then the second line says "if x is between 1 and 2, including both endpoints, then f(x) = 3-x". Finally the last line says f(x) = 1 as long as x is larger than 1 but smaller than 4. The value x = 4 is allowed for this piece but x = 1 is not allowed.
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Now onto function evaluation. We want to evaluate f(1) so we need to find f(x) when x = 1. If x = 1, then we'll use the second piece because the first piece excludes x = 1. So
f(x) = 3-x
f(1) = 3-1
f(1) = 2
is the first answer for the function evaluation section.
The value of f(3) is equal to 1 since we resort to using the third piece of the piecewise function (x = 3 is in the range from x = 2 to x = 4)
The value of f(-5) is undefined simply because we're out of the range defined by the piecewise function. The smallest x can get is x = 0.
Finally, f(2) is equal to 1 since...
f(x) = 3-x
f(2) = 3-2
f(2) = 1
again we use the second piece of the piecewise function because x = 2 is in the range 1 <= x <= 2
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In summary:
f(1) = 2
f(3) = 1
f(-5) = undefined
f(2) = 1
Once again have a look at the graph to see how the points match up. I've color-coded the graph so that each piece is a different color. The first piece is in red, the second in blue, the third in green. Note the open hole at point B to indicate "don't include this point as part of the graph".
48/3 = 16. On the second day she sold 16 notebooks.
16-2(she sold two more each day) = 14
16+2=18
Day 1=14
Day 2=16
Day 3=18