Answer:
Option B.
Step-by-step explanation:
The given inequalities are
We need to find the ordered pair which makes both inequalities true.
Check the above inequalities for each given ordered pair.
For (-3,5),
(False)
For (-2,2),
(True)
(True)
So, both inequalities are true for (-2,2). Option B is correct.
For (-1,-3),
(False)
For (0,-1),
(False)
Both inequalities are not true for (-3,5), (-1,-3) and (0,-1).
Therefore, the correct option is B.
Answer:
Step-by-step explanation:
The Side-Angle-Side method cana only be used when information given shows that an included angle which is between two sides of a ∆, as well as the two sides of the ∆ are congruent to the included side and two sides of the other ∆.
Thus, since John already knows that and
, therefore, an additional information showing that the angle between
and
in ∆ABC is congruent to the angle between
and
in ∆DEF.
For John to prove that ∆ABC is congruent to ∆DEF using the Side-Angle-Side method, the additional information needed would be .
See attachment for the diagram that has been drawn with the necessary information needed for John to prove that ∆ABC is congruent to ∆DEF.
Answer:
1) There were 33 $4,000 investors and 27 $8,000 investors.
2) The solution in x = 4, y = 9.
3) There were 24 nickels and 56 dimes.
Step-by-step explanation:
1) A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $4,000 or $8,000. If the partnership raised $348,000, then how many investors contributed $4,000 and how many contributed $8,000?
I am going to say that:
x is the number of investors that contributed 4,000.
y is the number of investors that contributed 8,000.
Building the system:
There are 60 investors. So:
In all, the partnership raised $348,000. So:
I am going to simplify by 4000. So:
Solving the system:
The elimination method is a method in which we can transform the system such that one variable can be canceled by addition. So:
I am going to multiply 1) by -1. So we have
By addition, the x are going to cancel each other
For x:
There were 33 $4,000 investors and 27 $8,000 investors.
2) Solve the system by row-reducing the corresponding augmented matrix.
This system has the following augmented matrix:
To help the row reducing, i am going to swap the first with the second line:
So we have:
Now, reducing the first column.
So we have:
Now we do:
And the matrix is:
Now to reduce the second column, we do:
.
So the solution is:
x = 4, y = 9.
3) A jar contains 80 nickels and dimes worth $6.80. How many of each kind of coin are in the jar?
I am going to say that x is the number of nickels and y is the number of dimes.
Each nickel is worth 5 cents and each dime is worth 10 cents.
Building the system:
There are 80 coins in all:
They are worth $6.80. So:
Solving the system:
I am going to divide 1) by -10, so we can cancel y. So:
Adding:
*(-100)
Also
There were 24 nickels and 56 dimes.