Answer:
The number of pages that Polina read was 90 and the number of pages that Marcus read was 18
Step-by-step explanation:
Let
x -----> number of pages that Polina read
y ----> number of pages that Marcus read
we know that
x+y=108 ----> equation A
x=5y -----> equation B
substitute equation B in equation A and solve for y
Find the value of x
therefore
The number of pages that Polina read was 90 and the number of pages that Marcus read was 18
Answer:
The correct answer is 10 and 14
When we are given 3 sides, we try to solve the angles first by using the
law of cosines
cos (A) = [b^2 + c^2 - a^2] / (2 * b * c)
cos (A) = [43^2 + 17^2 -27^2] / (2 * 43 * 17)
cos (A) = [1,849 + 289 -729] /
<span>
<span>
<span>
1,462
</span></span></span>cos (A) = 1,409 / 1,462
cos (A) =
<span>
<span>
<span>
0.96374829001368
Angle A = 15.475
Now that we have one angle, we next can use the
Law of Sines
sin(B) / side b = sin(A) / side a
sin(B) = sin(A) * sideb / sidea
</span></span></span><span>sin(B) = sin(15.475) * 43 / 27
</span><span>sin(B) = 0.26682 * 43 / 27
sin (B) = </span><span>0.424935555555</span>
Angle B = 25.147 Degrees
Remember the arc sine (<span>0.424935555555) also equals </span>
<span>
<span>
<span>
154.85
</span></span></span>Finally, calculating the third angle is quite easy
Angle C = 180 - Angle (A) - Angle(B)
Angle C = 180 - 15.475 - 154.85
Angle C = 9.675
Source:
http://www.1728.org/trigtut2.htm
Parallel lines share the same slope, so the slope of the parallel line in this case must be 
.
Point-slope form is 
, where 
is the slope and 
is any known point on the line.
Plug in the values. 
Simplify and distribute. 
Subtract 1 from both sides. 
Answer:
3/4 or a 75% chance
Step-by-step explanation:
Out of 4 cards ( 2 3 4 5), here are the cards greater than 3: 4, and 5. That leaves you with a 2/4 chance of drawing one of them. (2 cards, 4 in total).
Then, picking a 4 out of 4 cards is a 1/4 chance; since that is one card out of 4 total possibilities.
1/4 + 2/4 = 3/4. Or, a 75% chance.
