Answer:
Step-by-step explanation:
We can use the Polynomial Remainder Theorem. It states that if we divide a polynomial P(x) by a <em>binomial</em> in the form (x - a), then our remainder will be P(a).
We are dividing:
So, a polynomial by a binomial factor.
Our factor is (x + k) or (x - (-k)). Using the form (x - a), our a = -k.
We want our remainder to be 3. So, P(a)=P(-k)=3.
Therefore:
Simplify:
Solve for <em>k</em>. Subtract 3 from both sides:
Factor:
Zero Product Property:
Solve:
So, either of the two expressions:
Will yield 3 as the remainder.
Complete question :
Suppose that of the 300 seniors who graduated from Schwarzchild High School last spring, some have jobs, some are attending college, and some are doing both. The following Venn diagram shows the number of graduates in each category. What is the probability that a randomly selected graduate has a job if he or she is attending college? Give your answer as a decimal precise to two decimal places.
What is the probability that a randomly selected graduate attends college if he or she has a job? Give your answer as a decimal precise to two decimal places.
Answer:
0.56 ; 0.60
Step-by-step explanation:
From The attached Venn diagram :
C = attend college ; J = has a job
P(C) = (35+45)/300 = 80/300 = 8/30
P(J) = (30+45)/300 = 75/300 = 0.25
P(C n J) = 45 /300 = 0.15
1.)
P(J | C) = P(C n J) / P(C)
P(J | C) = 0.15 / (8/30)
P(J | C) = 0.5625 = 0.56
2.)
P(C | J) = P(C n J) / P(J)
P(C | J) = 0.15 / (0.25)
P(C | J) = 0.6 = 0.60
Answer:
Step-by-step explanation:
We can prove that a tangent will always be perpendicular to the radius touching it. So, the other angle in the diagram is 
.
Because all the angles of a triangle sum to 
, we have that 
.
We combine like terms on the left side to get 
.
We subtract 
on both sides to get 
.
So, 
and we're done!
-2m - 5m = -7m
-7m - 8 = 3 -7 + m
3 - 7 = -4
-7m - 8 = m - 4
-7m - 8 + 8 = m - 4 + 8
-7m = m + 4
-7m - m = m + 4 - m
-8m = 4
-8m/-8 = 4/ -8
FINAL = m= -1/2 = -0.5
Answer:
The answer is 35.5 square units
Step-by-step explanation:
The shape represents a rectangle, a small triangle removed from it at the upper right corner and a bigger triangle is attached to it at the upper left corner.
We get this formula:
A(shape) = A(rectangle) - A(small triangle) + A(big triangle)
SO LET'S FIND EACH!
A(rectangle)= length x width
length= 8 units
width= 4 units
We get:
A(rectangle) =8x4= 32 square unit
A(small triangle)= (base x height)/2
base= 1 unit
height= 1 unit
We get:
A(small triangle) = (1x1)/2 = 1/2 = 0.5 square units
A(big triangle)= (base x height)/2
base= 2 units
height= 4units
We get:
A(big triangle)= (2x4)/2 = 8/2 = 4 square units
For the final result:
A(shape) = 32 - 0.5 + 4 = 35.5 square units
