350% of 880 is 60% of what number?
The equation will be 350 % of 880 = 60% of x
We all know that percent is out of 100, so we can express the percentage as a fraction out of 100, and we know "of "means multiply, so our equation becomes
350/100 * 880 = 6/100 * x
then we cross out zeros, so
35/10 * 88 = 6/10x
30800 = 6x
x = 5133.333 is the rounded answer
I hope this helps! :)
The answer is 30800/6
Laura is designing a rectangular porch for her house. On her scale drawing, the vertices of the rectangle are (2, 7), (8, 7), and (2, 9). What are the coordinates of the fourth vertex?
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1 point
(7,9)
(8,9)
(7,2)
(2,8)
The fourth vertex will have the same y-coordinate as the third vertex, which is 9. And since the rectangle is a right angle, the fourth vertex will have the same x-coordinate as the second vertex, which is 8.
Therefore, the coordinates of the fourth vertex are (8,9).
So the answer is (8,9).
Which ordered pair is not a solution of y = –12x – 3?
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1 point
(8,-98)
(-3,33)
(-9,105)
(3,-39)
Which is the graph of the linear equation y = –1/4 x + 3?
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1 point
Option 1
Option 2
Option 3
Option 4
Option 3 is the graph of the linear equation y = –1/4 x + 3.
The slope of the line is negative, which means the line slopes downwards from left to right. The y-intercept is 3, which means the line intersects the y-axis at the point (0,3).
Option 1 has a positive slope, Option 2 has a different y-intercept, and Option 4 has a slope of 1.
Find three solutions of the equation y = 9x – 4.
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1 point
(–5, –49), (–2, –22), (3, 23)
(–5, –49), (2, –22), (3, 23)
(–5, –49), (–2, 22), (–3, 23)
(5, –49), (–2, 22), (–3, 23)
Find three solutions of the equation y = 9x – 4.
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1 point
a. (–5, –49), (–2, –22), (3, 23)
b.(–5, –49), (2, –22), (3, 23)
c.(–5, –49), (–2, 22), (–3, 23)
d.(5, –49), (–2, 22), (–3, 23)
b. (–5, –49), (2, –22), (3, 23) are three solutions of the equation y = 9x – 4.
To find these solutions, we can choose any value of x and plug it into the equation to find the corresponding value of y.
For example:
- When x = -5, y = 9(-5) - 4 = -49, which gives us the point (-5, -49)
- When x = 2, y = 9(2) - 4 = 14, which gives us the point (2, -22)
- When x = 3, y = 9(3) - 4 = 23, which gives us the point (3, 23)
Each of these ordered pairs is a solution to the equation y = 9x - 4.
Which pair of points has a negative slope?
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1 point
a.(–3, 13), (3, 17)
b.(4, 26), (–2, –10)
c.(4, 14), (–2, –4)
d.(–3, 17), (2, –8)
b. (4, 26), (–2, –10) has a negative slope.
We can find the slope of a line that passes through two given points (x1,y1) and (x2,y2) using the formula:
slope = (y2 - y1)/(x2 - x1)
For option b, we have:
slope = (-10 - 26)/(-2 - 4) = -36/-6 = 6
Since the slope is positive, options a, c, and d must have positive slopes. Therefore, option b has a negative slope.
Use integer values of x from –3 to 3 to graph the equation y = –|–x|.
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1 point
Option 1
Option 2
Option 3
Option 4
Option 3 is the graph of the equation y = –|–x|.
When x = -3, we have y = -|-(-3)| = -|-3| = -3. So one point on the graph is (-3,-3).
When x = -2, we have y = -|-(-2)| = -|-2| = -2. So one point on the graph is (-2,-2).
When x = -1, we have y = -|-(-1)| = -|-1| = -1. So one point on the graph is (-1,-1).
When x = 0, we have y = -|-0| = -|0| = 0. So one point on the graph is (0,0).
When x = 1, we have y = -|-1| = -1. So one point on the graph is (1,-1).
When x = 2, we have y = -|-2| = -2. So one point on the graph is (2,-2).
When x = 3, we have y = -|-3| = -3. So one point on the graph is (3,-3).
Plotting these points and connecting them with a smooth curve gives us the graph shown in Option 3.
Option 1 and Option 2 have incorrect graphs that do not reflect the characteristics of the given equation. Option 4 has the correct shape, but it is upside down compared to the equation y = –|–x|.
The ordered pairs (2, –17) and (5, –35) are solutions to which of the following equations?
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1 point
y = –6x + 5
y = 6x – 5
y = –6x – 5
y = 6x + 5
The ordered pairs (2, –17) and (5, –35) are solutions to the equation y = –6x – 5.
To check, we can plug in each ordered pair and see if the equation is true:
- When x = 2, y = -6(2) - 5 = -17, which is true
- When x = 5, y = -6(5) - 5 = -35, which is true
Therefore, both ordered pairs satisfy the equation y = –6x – 5.
Which is a rule that describes the translation of a point from (–5, 4) to (–1, 2)?
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1 point
(x, y) ---> (x + 4, y – 2)
(x, y) ---> (x – 4, y – 2)
(x, y) ---> (x + 4, y + 2)
(x, y) ---> (x – 4, y + 2)
(x, y) ---> (x + 4, y - 2) is the rule that describes the translation of a point from (–5, 4) to (–1, 2).
To see this, we can compare the coordinates of the two points:
- The x-coordinate has changed from -5 to -1, which is an increase of 4. So the rule must involve adding 4 to the x-coordinate.
- The y-coordinate has changed from 4 to 2, which is a decrease of 2. So the rule must involve subtracting 2 from the y-coordinate.
Putting these together, we get the rule (x, y) ---> (x + 4, y - 2).
∆XYZ has vertices X(5, 6), Y(9, 12), and Z(12, 8). It is translated right 8 units and up 3 units. What are the coordinates of X’, Y’, and Z’?
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1 point
a. X'(13, 9), Y'(15, 17), Z'(11, 20)
b. X'(–3, 3), Y'(1, 9), Z'(4, 5)
c. X'(8, 14), Y'(12, 20), Z'(23, 19)
d. X'(13, 9), Y'(17, 15), Z'(20, 11)
The coordinates of the translated vertices are:
- X': (5+8, 6+3) = (13, 9)
- Y': (9+8, 12+3) = (17, 15)
- Z': (12+8, 8+3) = (20, 11)
Therefore, the answer is d. X'(13, 9), Y'(17, 15), Z'(20, 11).
A transformation translates the point S (-1,1) down 2 units and right 3 units.
What rule describes this translation?
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1 point
Option 1
Option 2
Option 3
Option 4
Option 2 describes this translation.
The point S(-1,1) is translated down 2 units, which means the y-coordinate changes from 1 to -1.
Then, the point is translated right 3 units, which means the x-coordinate changes from -1 to 2.
Therefore, the rule that describes this translation is:
(x, y) → (x + 3, y - 2)
This is the rule shown in Option 2.
The graph shows two sides and three vertices of a parallelogram.
Which point best represents the fourth vertex of the parallelogram?
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1 point
Captionless Image
(6, 4)
(7, 4)
(7, 5)
(8, 5)
The fourth vertex of the parallelogram must be on the line parallel to the line passing through the given vertices.
Looking at the graph, we can see that the line passing through the given vertices is slanting downwards from left to right. Therefore, the opposite side of the parallelogram must also be slanting downwards from left to right.
Two possible points on this line that are not among the given vertices are (6,4) and (8,5).
To decide which point is best, we can use the fact that opposite sides of a parallelogram have the same length and are parallel. We can calculate the lengths of the given sides to see which point makes the opposite side have the same length.
Using the distance formula, we can find the length of the side with two given vertices as:
- From (2,3) to (7,4): √((7-2)²+(4-3)²) = √26
- From (5,5) to (7,4): √((7-5)²+(4-5)²) = √2
Therefore, the last side of the parallelogram should have the same length as √2.
The distance from (6,4) to (8,5) is:
- √((8-6)²+(5-4)²) = √2
So (6,4) is the point that best represents the fourth vertex of the parallelogram.
Therefore, the answer is (6,4).
Which graph shows the image of a figure after a rotation of 180° around the origin?
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1 point
Option 1
Option 2
Option 3
Option 4
Option 1 shows the image of a figure after a rotation of 180° around the origin.
A rotation of 180° around the origin flips the figure across the x-axis and the y-axis. This means that each point (x, y) is transformed to (-x, -y).
Option 1 shows a figure that has been flipped across both axes. Options 2, 3, and 4 show figures that have not been rotated 180° around the origin.
Which table shows a proportional relationship?
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1 point
Option 1
Option 2
Option 3
Option 4
Option 1 shows a proportional relationship.
We can check if two quantities have a proportional relationship by dividing one quantity by the other. If the quotient is always the same, then the two quantities are proportional. For example:
- In Option 1, when x = 1, y = 2. When x = 2, y = 4. When x = 3, y = 6. Dividing y by x gives:
- y/x = 2/1 = 4/2 = 6/3 = 2
Since y/x is always 2, the relationship between y and x is proportional.
In Options 2, 3, and 4, the quotients of y/x vary, so the relationships are not proportional.