General Idea:
(i) Assign variable for the unknown that we need to find
(ii) Sketch a diagram to help us visualize the problem
(iii) Write the mathematical equation representing the description given.
(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE
Applying the concept:
Given: x represents the length of the pen and y represents the area of the doghouse
<u>Statement 1: </u>"The pen is 3 feet wider than it is long"
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<u>Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"</u>
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<u>Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."</u>
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<u>Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."</u>
Conclusion:
The systems of equations that can be used to determine the length and width of the pen and the area of the doghouse is given in Option B.
length is 8m
Width is 6.5m
<u>Explanation:</u>
Let, width = b
So, length = 2b-5
area = 52
We know,
area of rectangle = length X width
So, 
= 
On solving the above equation, we get
Width, b = 6.5m
length, l = 8m
Answer:
FD≈25.94.. rounded = 26
Step-by-step explanation:
FD²=12²+(4x+11)²
FD²=144+16x²+88x+121
FD²=265+16x²+88x
also
FD²=12²+(13x-16)²
FD²=144+169x²-416x+256
FD²=400+169x²-416x
thus
265+16x²+88x = 400+169x²-416x
16x²-169x²+88x+416x+265-400 = 0
-153x²+504x-135 = 0
we will solve this quadratic equation by suing the quadratic formula to find x
x=(-504±sqrt(504²-4(-153)(-135)))/2(-153)
x=(-504±
)/2(-153)
x=(-504±
)/-306
x=(-504±
)/-306
x=(-504±414)/-306
x=(-504+414)/-306 and x=(-504-414)/-306
x=-90/-306 and x=-918/-306
x= 5/17 , 3
substituting x by the roots we found
check for 5/17:
4x+11 = 4×(5/17)+11 = (20/17)+11 = (20+187)/17 = 207/17 ≈ 12.17..
13x-16 = 13×(5/17)-16 = (65/17)-16 = (65-272)/17 = -207/17 ≈ -12.17..
check for 3:
4x+11 = 4×3+11 = 12+11 = 23
13x-16 = 13×3-16 = 23
thus 3 is the right root
therfore
ED=23 and CD=23
FD²=FE²+ED² or FD²=FC²+CD²
FD²=12²+23²
FD²=144+529
FD²=673
FD=√673
FD≈25.94.. rounded = 26
Answer:
Results:
0.1432
0.0045
0.0905
0.0483
Step-by-step explanation:
Step a:
P(A or 10, A or 10) = 20/52 * 19/51 = 5/13 / 19/51 = 95/663 = 0.1432
Step b:
P(A A) = 4/52 * 3/51 = 1/13 * 1/17 = 1/221 = 0.0045
Step c:
P(10 10) = 16/52 * 15/51 = 4/13 * 5/17 = 20/221 = 0.0905
Step d:
P(A 10 or 10 A) = 2 * 4/52 * 16/51 = 2/13 * 16/51 = 32/663 = 0.0483
As well we get the probability by subtracting a, b and c:
P(blackjack): 0.1432 - 0.0905 - 0.0045 = 0.0482
Answer:
good question
Step-by-step explanation:
