Is the equation true, false, or open?
9p + 8 = 10p + 7
(1 point)
Responses
Open; there is a variable.
Open; there is a variable.
True; the expressions are the same for all values of the variables.
True; the expressions are the same for all values of the variables.
False; the expressions are never the same.
Open; there is a variable.
To determine if the equation is true, false, or open, we need to compare the two sides of the equation and see if they are equal for all values of the variable.
In this case, we have the equation:
9p + 8 = 10p + 7
To solve this equation, we need to isolate the variable on one side of the equation. We can do this by subtracting 10p from both sides:
9p - 10p + 8 = 10p - 10p + 7
-p + 8 = 7
Next, we can subtract 8 from both sides to further isolate the variable:
-p + 8 - 8 = 7 - 8
-p = -1
To make the variable positive, we can multiply both sides of the equation by -1:
(-1)(-p) = (-1)(-1)
p = 1
Therefore, we have found that the value of the variable p is 1.
Since there is a specific value for the variable that satisfies the equation, the equation is not open. Thus, the correct answer is: False; the expressions are never the same.
To determine whether the equation is true, false, or open, let's start by comparing the expressions on both sides of the equation.
9p + 8 = 10p + 7
By comparing the terms, we see that the variable 'p' appears on both sides of the equation. Therefore, this equation is not a true or false statement, but an open equation. It means that there are values of 'p' for which the equation is true, and there are values for which it is false.
Which value is a solution of the equation 5 – 4x = –3?
(1 point)
Responses
0
0
2
2
–3
–3
one fourth
To find the solution to the equation 5 - 4x = -3, we can isolate the variable x.
First, let's subtract 5 from both sides:
5 - 4x - 5 = -3 - 5
-4x = -8
Next, divide both sides by -4 to solve for x:
(-4x) / (-4) = (-8) / (-4)
x = 2
Therefore, the value x = 2 is a solution to the equation 5 - 4x = -3. The correct answer is: 2.
Which ordered pair is a solution of the equation y = x – 2?
(1 point)
Responses
(3, 1)
(3, 1)
(1, 3)
(1, 3)
(–1, 3)
(–1, 3)
(3, –1)
(3, –1)
To determine which ordered pair is a solution of the equation y = x - 2, we simply substitute the values of x and y into the equation and see if it holds true.
Let's check the options:
1) (3, 1):
Plugging in x = 3 and y = 1 into the equation, we have:
1 = 3 - 2
1 = 1
This equation is true for (3, 1).
2) (1, 3):
Plugging in x = 1 and y = 3 into the equation, we have:
3 = 1 - 2
3 = -1
This equation is not true for (1, 3).
3) (-1, 3):
Plugging in x = -1 and y = 3 into the equation, we have:
3 = -1 - 2
3 = -3
This equation is not true for (-1, 3).
4) (3, -1):
Plugging in x = 3 and y = -1 into the equation, we have:
-1 = 3 - 2
-1 = 1
This equation is not true for (3, -1).
From our calculations, we see that only the ordered pair (3, 1) satisfies the equation y = x - 2. Therefore, the correct answer is: (3, 1).
Which ordered pair is a solution of the equation y = 3x?
(1 point)
Responses
(–2, –9)
(–2, –9)
(–8, –18)
(–8, –18)
(–8, –3)
(–8, –3)
(–10, –30)
To determine which ordered pair is a solution of the equation y = 3x, we can substitute the values of x and y into the equation and see if it holds true.
Let's check the options:
1) (-2, -9):
Plugging in x = -2 and y = -9 into the equation, we have:
-9 = 3(-2)
-9 = -6
This equation is not true for (-2, -9).
2) (-8, -18):
Plugging in x = -8 and y = -18 into the equation, we have:
-18 = 3(-8)
-18 = -24
This equation is not true for (-8, -18).
3) (-8, -3):
Plugging in x = -8 and y = -3 into the equation, we have:
-3 = 3(-8)
-3 = -24
This equation is not true for (-8, -3).
4) (-10, -30):
Plugging in x = -10 and y = -30 into the equation, we have:
-30 = 3(-10)
-30 = -30
This equation is true for (-10, -30).
From our calculations, we see that only the ordered pair (-10, -30) satisfies the equation y = 3x. Therefore, the correct answer is: (-10, -30).
Which ordered pair is a solution of the equation y = –7x + 2?
(1 point)
Responses
(1, 2)
(1, 2)
(8, –54)
(8, –54)
(5, –35)
(5, –35)
(1, –7)
To determine which ordered pair is a solution of the equation y = -7x + 2, we can substitute the values of x and y into the equation and see if it holds true.
Let's check the options:
1) (1, 2):
Plugging in x = 1 and y = 2 into the equation, we have:
2 = -7(1) + 2
2 = -7 + 2
2 = -5
This equation is not true for (1, 2).
2) (8, -54):
Plugging in x = 8 and y = -54 into the equation, we have:
-54 = -7(8) + 2
-54 = -56 + 2
-54 = -54
This equation is true for (8, -54).
3) (5, -35):
Plugging in x = 5 and y = -35 into the equation, we have:
-35 = -7(5) + 2
-35 = -35 + 2
-35 = -33
This equation is not true for (5, -35).
4) (1, -7):
Plugging in x = 1 and y = -7 into the equation, we have:
-7 = -7(1) + 2
-7 = -7 + 2
-7 = -5
This equation is not true for (1, -7).
From our calculations, we see that only the ordered pair (8, -54) satisfies the equation y = -7x + 2. Therefore, the correct answer is: (8, -54).
Nick and his cousin Sara have the same birthday, but Nick is four years older than Sara. Let the variable x represent Nick’s age and y represent Sara’s age. Which graph represents the relationship between Nick’s age and Sara’s age?
(1 point)
Responses
The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages.The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 0 comma 4 right parenthesis, left parenthesis 2 comma 6 right parenthesis, and left parenthesis 4 comma 8 right parenthesis.
Image with alt text: The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 0 comma 4 right parenthesis, left parenthesis 2 comma 6 right parenthesis, and left parenthesis 4 comma 8 right parenthesis.
The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages.The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 0 comma 0 right parenthesis, left parenthesis 4 comma one-half right parenthesis, and left parenthesis 8 comma 1 right parenthesis.
Image with alt text: The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 0 comma 0 right parenthesis, left parenthesis 4 comma one-half right parenthesis, and left parenthesis 8 comma 1 right parenthesis.
The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages.The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left-parenthesis 0 comma 0 right-parenthesis, left-parenthesis one-half comma 4 right-parenthesis, and left-parenthesis 1 comma 8 right-parenthesis.
Image with alt text: The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left-parenthesis 0 comma 0 right-parenthesis, left-parenthesis one-half comma 4 right-parenthesis, and left-parenthesis 1 comma 8 right-parenthesis.
The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages.The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 4 comma 0 right parenthesis, left parenthesis 6 comma 2 right parenthesis, and left parenthesis 8 comma 4 right parenthesis.
Image with alt text: The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 4 comma 0 right parenthesis, left parenthesis 6 comma 2 right parenthesis, and left parenthesis 8 comma 4 right parenthesis.
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The correct graph representation of the relationship between Nick's age and Sara's age is the first one described:
The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points (0, 4), (2, 6), and (4, 8).
This graph represents the fact that Sara's age (y) is always 4 years less than Nick's age (x). As Nick's age increases, Sara's age also increases in a consistent manner.
Solve the equation.–3 = z + 4(1 point)Responses z = 4z = 4z = –4z = –4z = –7z = –7z = 7z = 7
To solve the equation -3 = z + 4, we can isolate the variable z.
First, let's subtract 4 from both sides of the equation:
-3 - 4 = z + 4 - 4
-7 = z
Therefore, the solution to the equation -3 = z + 4 is z = -7. The correct answer is: z = -7.
Solve the equation.
z – 4 = –8
(1 point)
Responses
z = –2
z = –2
z = 32
z = 32
z = –4
z = –4
z = –12
z = –12
To solve the equation z - 4 = -8, we can isolate the variable z.
First, let's add 4 to both sides of the equation:
z - 4 + 4 = -8 + 4
z = -4
Therefore, the solution to the equation z - 4 = -8 is z = -4. The correct answer is: z = -4.
Solve the equation.
2.8 = 2y
(1 point)
Responses
y = 1.4
y = 1.4
y = 0.5
y = 0.5
y = 2.8
y = 2.8
y = 0.6
To solve the equation 2.8 = 2y, we can isolate the variable y.
First, let's divide both sides of the equation by 2:
2.8 / 2 = 2y / 2
1.4 = y
Therefore, the solution to the equation 2.8 = 2y is y = 1.4. The correct answer is: y = 1.4.
Solve the equation.
–7 = Start Fraction z over 3 End Fraction
(1 point)
Responses
z = –seven-thirds
z = – Image with alt text: seven-thirds
z = 2
z = 2
z = –21
z = –21
z = 21
To solve the equation -7 = z/3, we can isolate the variable z.
First, let's multiply both sides of the equation by 3 to eliminate the fraction:
3 * -7 = 3 * (z/3)
-21 = z
Therefore, the solution to the equation -7 = z/3 is z = -21. The correct answer is: z = -21.
Solve the equation.
negative four equals two-fifths x
(1 point)
Responses
x = 10
x = 10
x = –10
x = –10
x = –1
x = –1
x = 1
x = 1
To solve the equation "negative four equals two-fifths x", we can isolate the variable x.
First, let's multiply both sides of the equation by the reciprocal of two-fifths, which is 5/2:
(-4) * (5/2) = (2/5) * (x)
-20/2 = 2/5 * x
-10 = 2/5 * x
Now, we can solve for x by multiplying both sides by the reciprocal of 2/5, which is 5/2:
-10 * (5/2) = (2/5 * x) * (5/2)
-25 = x
Therefore, the solution to the equation "negative four equals two-fifths x" is x = -25. The correct answer is: x = -25.
thats not a choice
I apologize for the incorrect response. Let's go through the options again.
The equation is: -4 = (2/5)x
1) x = 10:
-4 = (2/5)(10)
-4 = 4
This equation is not true for x = 10.
2) x = -10:
-4 = (2/5)(-10)
-4 = -8
This equation is not true for x = -10.
3) x = -1:
-4 = (2/5)(-1)
-4 = -2/5
This equation is not true for x = -1.
4) x = 1:
-4 = (2/5)(1)
-4 = 2/5
This equation is not true for x = 1.
None of the given choices satisfy the equation. I apologize for the mistake.
dawg one of those has to be it which is it
Apologies for the confusion. Let's go through the options again to find the correct solution.
The equation is: -4 = (2/5)x
1) x = 10:
-4 = (2/5)(10)
-4 = 4
This equation is not true for x = 10.
2) x = -10:
-4 = (2/5)(-10)
-4 = -8
This equation is not true for x = -10.
3) x = -1:
-4 = (2/5)(-1)
-4 = -2/5
This equation is not true for x = -1.
4) x = 1:
-4 = (2/5)(1)
-4 = 2/5
This equation is not true for x = 1.
None of the given choices satisfy the equation. I apologize for the repeated mistake. The correct answer is none of the options provided.
dawg it HAS to be one of those, just pick one holy crap
I apologize for the confusion. If we look at the options again, it seems that "x = -10" is the only choice left. Let's check if it satisfies the equation:
-4 = (2/5)(-10)
-4 = -20/5
-4 = -4
Since the equation holds true when we substitute x = -10, the correct answer is x = -10. I apologize for the previous incorrect responses.
Which equation is an identity?
(1 point)
Responses
11 – (2v + 3) = –2v – 8
11 – (2 v + 3) = –2 v – 8
5w + 8 – w = 6w – 2(w – 4)
5 w + 8 – w = 6 w – 2( w – 4)
7m – 2 = 8m + 4 – m
7 m – 2 = 8 m + 4 – m
8y + 9 = 8y – 3