I will try to solve your system of equations.
3
x
−
4
y
=
2
;
9
x
−
12
y
=
6
Step: Solve
3
x
−
4
y
=
2
for x:
3
x
−
4
y
+
4
y
=
2
+
4
y
(Add 4y to both sides)
3
x
=
4
y
+
2
3
x
3
=
4
y
+
2
3
(Divide both sides by 3)
x
=
4
3
y
+
2
3
Step: Substitute
4
3
y
+
2
3
for
x
in
9
x
−
12
y
=
6
:
9
x
−
12
y
=
6
9
(
4
3
y
+
2
3
)
−
12
y
=
6
6
=
6
(Simplify both sides of the equation)
6
+
−
6
=
6
+
−
6
(Add -6 to both sides)
0
=
0
Answer:
Infinitely many solutions.
L x W = 105
L + W = 26 so L = 26 - W
substitute L = 26 - W into L x W = 105
(26 - W) x W = 105
26W - W^2 = 105
W^2 - 26W + 105 = 0
(W - 21)(W - 5) = 0
W - 21 = 0; W = 21
W - 5 = 0; W = 5
The the dimensions of the rectangle are 5 ft and 21 ft.
Double check:
The sum of the length and the width is 26 feet: 21 + 5 = 26 feet
A rectangle has an area of 105 square feet: 21 x 5 = 105 square feet
Part A: 6m + 12 + 42m, which combines to form 48m + 12. Another expression is 12 + 48m, because using the commutative property of addition, it is equivalent.
Part B: As I stated earlier, using the commutative property of addition, your expression 12 + 48m is equivalent to 48m + 12.
Part C: If you substitute 2 for m, you will get 108. If they are talking about the main equation, then if you substitute 2 for m, you will have 6(2 + 2 + 14) = 108.
Answer:
0.6
Explanation: 60 over 100 would be 60/100, so when converting this into a decimal, the 60 would be in the hundreths place. Therefore, the decimal would be 0.6.
Hope this Helps!
Answer:
There are 33 multiple choice questions and 9 short answer questions on the test
Step-by-step explanation:
In this question, we are asked to calculate the number of multiple text answers and short answers given in a test, given that the test taker will attempt a number of questions and have a particular score.
Since we do not know the number of these questions individually, let’s represent them with variables. Let the number of multiple choice questions to be answered be x and the number of short answers questions to be given be y.
Mathematically,
x + y = 42. (I)
Also, the total points is 60, with multiple choice of 1 point each and short answers of 3 points each. Mathematically, this means;
x(1) + y(3) = 60.
x + 3y = 60. (ii)
Now let’s solve both 1 and 2 simultaneously.
From 1, let’s say y = 42-x and substitute this in 2
x +3(42-x) = 60
x + 126 -3x = 60
-2x = 60-126
2x = 66
x = 66/2
x = 33
From y = 42-x, we can substitute the value of x and get y.
y = 42-33
y = 9
