B. c = ((3)sin45°)/sin40°
Side a is given information: 3cm, and we can find angle A (which is the angle opposite side a) by subtracting the other two angles from 180 because the total interior angle measures of a triangle add to equal 180°.
Angle A = 180 - (95+45) = 40°.
This can be substituted into the equation for the law of sines.
sin(40)°/3 = sin(45)°/c
—Cross multiply
c•sin(40)° = 3•sin(45)°
—divide both sides by sin40 to get the variable c alone and we get:
c = (3)sin(45°)/sin(40°)
this also simplifies to 3.3 cm.
For the first roll, you expect that you would get number 3 of a die.
Next for the second roll, you expect that you would get an even number. Since there are 6 sides of a die, so the even numbers are only 2, 4 and 6.
9514 1404 393
Answer:
x = 2 1/3
Step-by-step explanation:
We can examine the equations to see where the solution lies.
<u>f(x) = (2/3) -x</u>
This has an x-intercept where y=0, at x=2/3. It has a y-intercept where x=0, at y=2/3. Its slope is -1.
<u>h(x) = 3 -2x</u>
This has an x-intercept where y=0, at x=3/2. It has a y-intercept where x=0, at y=3. Its slope is -2.
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In the first quadrant, the graph of h(x) is farther from the origin and steeper than the graph of f(x). The lines must cross in the 4th quadrant at some value of x that is greater than 3/2. The fraction in the definition of f(x) suggests that the solution will be a multiple of 1/3.
The attached table shows a couple of guesses at values of x that would make f(x) = h(x). We find that x = 7/3 is the solution we're looking for.
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<em>Additional comment</em>
Repetitive function evaluations are done conveniently and with fewer errors by a calculator or spreadsheet that can work with tables of values. Here, we have used a graphing calculator. These tools are readily available for free on almost any phone, tablet, or desktop computer platform.
Answer:
B.) 27ft
Step-by-step explanation:
The labeled points given: (5,18) and (1.5, 7.5)
Slope = (18 - 7.5)/(5-1.5) = 10.5 / 3.5 = 3
A linear model:
y - 18 = 3(x - 5)
y - 18 = 3x - 15
y = 3x + 3
If x = 8 seconds then the distance in feet (y) would be: (plug in x = 8 into the equation y = 3x + 3)
y = 3(8) + 3
y = 24 + 3
y = 27 ft
Answer:
B.) 27ft