Two rectangles are similar. One has a length of 10 cm and a width of 8 cm, and the other has a width of 7 cm. Find the length of the second rectangle. Round to the nearest tenth if necessary.
6.6 cm
8.8 cm
5.6 cm
10.1 cm
To find the length of the second rectangle, we can use the concept of similarity. Since the two rectangles are similar, their corresponding sides are proportional.
Using the given information, we can set up a proportion:
(length of first rectangle) / (width of first rectangle) = (length of second rectangle) / (width of second rectangle)
Plugging in the values, we get:
10 cm / 8 cm = (length of second rectangle) / 7 cm
Simplifying the proportion, we have:
5/4 = (length of second rectangle) / 7 cm
Cross multiplying, we get:
4 * (length of second rectangle) = 5 * 7 cm
4 * (length of second rectangle) = 35 cm
Dividing both sides by 4, we find:
(length of second rectangle) = 35 cm / 4
(length of second rectangle) ≈ 8.8 cm
Therefore, the length of the second rectangle is approximately 8.8 cm.
The correct answer is 8.8 cm.
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Van Gogh’s painting Starry Night measures 92 cm long by 73 cm high. You buy two posters, each showing an enlargement of the painting. The first poster measures 120 cm long by 100 cm high. The second poster measures 138 cm long by 109.5 cm high. Which of the following is true? (Hint: To be an accurate representation of the painting, would the the poster be similar to the painting?)
The first poster is not an accurate representation of the painting, but the second poster is an accurate representation.
Both posters are not accurate representations of the painting.
The first poster is an accurate representation of the painting, but the second poster is not an accurate representation.
Both posters are accurate representations of the painting.
To determine if the posters are accurate representations of the painting, we need to compare the ratios of their dimensions to the ratios of the painting's dimensions.
For the first poster:
Ratio of length: 120 cm / 92 cm = 1.3043
Ratio of height: 100 cm / 73 cm = 1.3699
For the second poster:
Ratio of length: 138 cm / 92 cm = 1.5
Ratio of height: 109.5 cm / 73 cm = 1.5
In both cases, the ratios of the poster's dimensions are not the same as the ratios of the painting's dimensions. Therefore, neither poster is an accurate representation of the painting.
The correct answer is: Both posters are not accurate representations of the painting.
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How did Mendeleev organize the elements to create a periodic table?
according to the year of their discovery
according to increasing mass and number of protons
alphabetically by element name
according to increasing mass and similar properties
Mendeleev organized the elements to create a periodic table according to increasing mass and similar properties. He noticed that when elements were arranged in order of increasing atomic mass, certain similarities in their chemical and physical properties appeared at regular intervals. This led Mendeleev to create a table where elements with similar properties were grouped together in columns, now known as groups or families. This arrangement is the basis for the modern periodic table.
Why is it unlikely to find pure alkali metals in nature?
They have low reactivity.
They are highly reactive.
They are made in the laboratory.
They are so rare.
The correct answer is: They are highly reactive.
Alkali metals are highly reactive elements because they have a single valence electron that is loosely held in their outermost energy level. This makes them very eager to donate or lose that one electron to achieve stability, which leads to their high reactivity. In nature, alkali metals are often found combined with other elements to form compounds rather than existing in their pure form. Examples include lithium in lithium carbonate and sodium in sodium chloride. Due to their extreme reactivity, it is unlikely to find alkali metals in their pure form in nature.