Is the equation true, false or open? Explain.
8+4=-5+7
show your work
The equation is true.
Work:
8 + 4 = 12
-5 + 7 = 2
So the equation can be rewritten as 12 = 2, which is not true. Therefore, the equation is false.
Alternative explanation:
8 + 4 = 12
-5 + 7 = 2
12 and 2 are not equal, so the equation is false.
Which ordered pair is a solution of the equation y=-11x+4? Make sure you show work!
(0, -7)
(-1, -7)
(1, -7)
d. (2, 26)
show your work
To determine which ordered pair is a solution to the equation y = -11x + 4, we substitute the x and y values into the equation and check if it holds true.
For option (0, -7):
y = -11x + 4
-7 = -11(0) + 4
-7 = 4
This is not true, so (0, -7) is not a solution to the equation.
For option (-1, -7):
y = -11x + 4
-7 = -11(-1) + 4
-7 = 11 + 4
-7 = 15
This is not true, so (-1, -7) is not a solution to the equation.
For option (1, -7):
y = -11x + 4
-7 = -11(1) + 4
-7 = -11 + 4
-7 = -7
This is true, so (1, -7) is a solution to the equation.
For option (2, 26):
y = -11x + 4
26 = -11(2) + 4
26 = -22 + 4
26 = -18
This is not true, so (2, 26) is not a solution to the equation.
Therefore, the ordered pair (1, -7) is the only solution to the equation y = -11x + 4.
A plumber charges $65 per hour to fix a leak. What is an equation that relates the total cost of a leak repair c to the number of hours, h, it takes the plumber to fix the leak?
show your work
The equation that relates the total cost of a leak repair c to the number of hours h can be represented as:
c = 65h
In this equation, c represents the total cost of the leak repair in dollars and h represents the number of hours it takes the plumber to fix the leak. Since the plumber charges $65 per hour, the total cost is found by multiplying the number of hours by the cost per hour, which is 65.
Solve for x:
2x=-6
show your work
To solve for x in the equation 2x = -6, you can divide both sides of the equation by 2.
2x / 2 = -6 / 2
This simplifies to:
x = -3
Therefore, x is equal to -3.
Solve for x:
x+12=-15
show your work
To solve for x in the equation x + 12 = -15, you can subtract 12 from both sides of the equation.
x + 12 - 12 = -15 - 12
This simplifies to:
x = -27
Therefore, x is equal to -27.
Solve for p:
8p – 3 = 13
show your work
To solve for p in the equation 8p - 3 = 13, you can begin by adding 3 to both sides of the equation.
8p - 3 + 3 = 13 + 3
This simplifies to:
8p = 16
Next, divide both sides of the equation by 8 to isolate p.
(8p) / 8 = 16 / 8
This simplifies to:
p = 2
Therefore, p is equal to 2.
Solve for j:
8j – 5 + j = 67
show your work
To solve for j in the equation 8j - 5 + j = 67, you can first combine like terms on the left side of the equation by adding the two terms with j.
8j + j - 5 = 67
This simplifies to:
9j - 5 = 67
Next, you can isolate the variable j by adding 5 to both sides of the equation.
9j - 5 + 5 = 67 + 5
This simplifies to:
9j = 72
Finally, divide both sides of the equation by 9 to solve for j.
(9j) / 9 = 72 / 9
This simplifies to:
j = 8
Therefore, j is equal to 8.
Solve for x:
3(2x-5)=4x+33
To solve for x in the equation 3(2x-5) = 4x + 33, you can begin by distributing the 3 to both terms inside the parentheses:
6x - 15 = 4x + 33
Next, you can gather the x terms on one side of the equation and constants on the other side by subtracting 4x from both sides:
6x - 4x - 15 = 4x - 4x + 33
This simplifies to:
2x - 15 = 33
To isolate x, you can add 15 to both sides of the equation:
2x - 15 + 15 = 33 + 15
This simplifies to:
2x = 48
Finally, divide both sides of the equation by 2 to solve for x:
(2x) / 2 = 48 / 2
This simplifies to:
x = 24
Therefore, x is equal to 24.
Solve for x (literal equations):
c = b – bx
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To solve for x in the equation c = b - bx, we can start by isolating the term with x on one side of the equation.
First, we can subtract b from both sides of the equation:
c - b = b - bx - b
This simplifies to:
c - b = -bx
Now, we can multiply both sides of the equation by -1 to eliminate the negative sign in front of x:
(-1)(c - b) = (-1)(-bx)
This simplifies to:
b - c = bx
Finally, to isolate x, we can divide both sides of the equation by b:
(b - c) / b = (bx) / b
This simplifies to:
(b - c) / b = x
Therefore, x is equal to (b - c) / b.
Complete the table and state the rule.
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I'm sorry, but I cannot generate or complete a table as I am a text-based AI model. However, if you provide the incomplete table or specific values, I can help guide you through the process and explain the rule.
Complete the table and state the rule
input 0,blank,2,3,blank,5,6
output 0,3,blank,9,blank,15,blank
show your work
Using the given input-output pairs, we can complete the table as follows:
input | output
---------------
0 | 0
1 | 3
2 | 6
3 | 9
4 | 12
5 | 15
6 | 18
To determine the rule or pattern, we can observe that for each input value, the output is three times the input. Therefore, the rule for this table is y = 3x, where y represents the output and x represents the input.