<span>solve -2(2x + 5) - 3 = -3(x - 1)
-4x - 10 -3 = -3x + 3
-4x - 13 = -3x + 3
Add 3x to both sides
-4x - 13 +3x = -3x +3
Simplify
-x - 13 = 3
Add 13 to both sides
-x - 13 + 13 = 3 + 13
Simplify
-x = 16
multiply both sides by (-1)
x = -16</span>
A dime is worth 10 cents and a quarter is worth 25 cents.
Let D be the number of dimes and Q be the number of quarters.
Since the total amount of coins in the pocket is 32, then:
On the other hand, the total value of D dimes is 10D, while the total value of Q dimes is 25Q. Then, the total value of D dimes and Q cuarters is 10D+25Q, which must be equal to 545. Then:
Notice that we have found a 2x2 system of equations:
Solve the system using the substitution method. To do so, isolate D from the first equation and replace the expression for D into the second equation to obtain a single equation in terms of Q:
Replace back Q=15 into the expression for D to find the amount of dimes:
Therefore, the amount of dimes that the man has is 17.
Answer:
Step-by-step explanation:
Reasons:
3. The measures of supplementary angles add up to 180* (2)
5. Definition of Congruence (4)
6. Substitution Postulate (3,5)
EDIT: Your statement and proof column is cut off, so I can't see the other statements to completely fill in the reasons column.
The smallest amount of material needed is 54 square centimeters
<h3>How to determine the amount of material needed?</h3>
The given parameters are:
Volume = 36 cubic centimeters
Represent length with x, width with y and height with z.
So, we have
x = 3y
The volume is calculated as:
V = xyz
This gives
V = 3y²z
Substitute 36 for V
3y²z = 36
Divide by 3
y²z = 12
Make z the subject
z = 12/y²
The surface area is:
S = 2(xy + xz + yz)
This gives
S = 2(3y² + 3yz + yz)
Evaluate the like terms
S = 2(3y² + 4yz)
Expand
S = 6y² + 8yz
Substitute z = 12/y²
S = 6y² + 8y * 12/y²
This gives
S = 6y² + 96/y
Differentiate
S' = 12y - 96/y²
Set to 0
12y - 96/y² = 0
Multiply through by y²
12y³ - 96 = 0
Add 96 to both sides
12y³ = 96
Divide by 12
y³ = 8
Take the cube root of both sides
y = 2
Recall that:
x = 3y and z = 12/y²
This gives
x = 3 * 2 = 6
z = 12/2² = 3
Recall that:
S = 2(xy + xz + yz)
So, we have:
S = 2(6 * 2 + 3 * 3 + 2 * 3)
Evaluate
S = 54
Hence, the smallest amount of material needed is 54 square centimeters
Read more about surface areas at:
brainly.com/question/76387
#SPJ1
Answer:
y = x + 2
y =-x - 4
Step-by-step explanation:
Find the slope and y-intercept of each lines to write the equation in slope intercept form: y = mx + b where m is the slope and b is the y-intercept
