Sally is having a problem with her puppy leaving the yard so she decides to build a new fence. The length of the yard is 8 feet
more than 4 times the width. She needs 106 feet of fencing to do the job. Find the length of the yard
1 answer:
Please check the attached file for the diagram of Sally's yard.
Let be the width of the yard.
Let be the length.
We are given that the length of the yard is 8 feet more than 4 times the width. Let us convert this into a mathematical equation.
4 times the width will be . Now, 8 feet, or 8 more than 4 times the width will be
. We know that this is the value of the length of the yard and thus we can write this as:
As we can see we have found the relationship between the length, and the width,
of the yard.
We have been told that the total length of the fence required for the yard is 106 feet. This obviously means that the perimeter of the rectangular yard is 106 feet.
Now, we know that the perimeter of a rectangle is given by:
Perimeter= this is because we know that the length,
is given by
.
Continuing further we get:
This is because Perimeter=length of the fence=106 (given)
Therefore,
or, so, we just now found the width of the yard which is 9 feet. We are required to find the length. We can easily find the length using the relationship between
and
which is:
giving us:
Thus the length of the fence is 44 feet.
You might be interested in
Hey there! I'm happy to help!
-----------------------------------------------------------------------------------------
<u>QUESTION 18</u>
Here is how you multiply a 2×2 matrix by a column vector (just one column matrix).
Once you get that final matrix, you add the rows which will give you a final column vector. Let's do it with this question, as we are multiplying together the matrices A and v.
So, your answer is .
-----------------------------------------------------------------------------------------
<u>QUESTION 14</u>
We have this equation of an ellipse and we need to solve for y. When we have a more complex equation to solve you get rid of the things furthest from the variable you are solving for first and then you get closer and closer to it.
We subtract from both sides.
We multiply both sides by 16.
We square root both sides.
We can take a four out of our root (because 16 is a perfect square so it can be simplified more).
y=
And we take out 1/5 (which is the square root of 1/25).
y=±
-----------------------------------------------------------------------------------------
<u>QUESTION 17</u>
We see that Sea Slugs have 3/10 matches won, so they have won 30% of their matches.
From now on, they will be winning 2/3 of their games. Let's look at the answer options.
A. If they play 15 more games, they will win 10 of them. Our total matches will be 25 (our original 10+15). So, we will have 13/25, which is equal to 52%, so this is incorrect.
B. If they play 10 more games they win 6 2/3 games (like that makes any sense) for a total of 9 2/3 games out of 20. This is about 48%, so this is incorrect.
C. If they play 40 games, they are winning fractional games again. They win 29 2/3 games out of 50 total, which is about 59%, but not quite 60. This is also incorrect.
D. If they play 45 matches, they will win 30 games. Add the original 10 and you have 40 games. Our total is 55. 40/55 is about 73%, so they have passed that 60% threshold, so this is the correct answer.
-----------------------------------------------------------------------------------------
<u>QUESTION 16</u>
Our question tells us that if we have two numbers x and y, and we add them, it has to be 24 or greater. By saying it can be equal to 24 or greater, we are going to be using a ≤ or ≥ sign. The opening of the arrow always faces the equal or greater quantity, and in this case it is x+y, so it will look like x+y≥24.
This eliminates answer choices B and D as they do not have the equal part on the inequality.
Product means to multiply, so it will be written as xy. It has to be less than 60, so in this case the greater quantity is 60, so the arrow will opening towards 60, so it will look like xy<60.
So, our final answer is A.
-----------------------------------------------------------------------------------------
<u>QUESTION 12</u>
You can only multiply matrices if the number of columns in the first matrix is equal to the number of rows in the second. So basically the two interior numbers have to be the same (a,b) and (b,c). So, if we follow this, we get these answers:
2×2 times 2×1 YES
2×1 times 2×2= NO
3×3 times 3×1= YES
3×1 times 3×3= NO
-----------------------------------------------------------------------------------------
Have a wonderful day and keep on learning! :D
The value of constant a is -5
Further explanation:
We will use the comparison of co-efficient method for finding the value of a
So,
Given
As it is given that
(x^2 - 3x + 4)(2x^2 +ax + 7) = 2x^4 -11x^3 +30x^2 -41x +28
In this case, co-efficient of variables will be equal, so we can compare the coefficients of x^3, x^2 or x
Comparing coefficient of x^3
So the value of constant a is -5
Keywords: Polynomials, factorization
Learn more about factorization at:
#LearnwithBrainly