1. Which representation does not show y as a function of x?
A) Answer F
B) Answer G
C) Answer H
D) Answer J
2. Which set of ordered pairs represents y as a function of x?
A) {(-9, 2), (0, 6), (1, -2), (-3, 6)}
B) {(-1, 0), (4, 3), (-7, -3), (-1, -8)}
C) {(3, 2), (-4, -2), (3, 1), (-4, 1)}
D) {(5, 4), (2, 3), (1, 1), (2, 4)}
the pic is for question 1
Applying the rules that makes a relation a function:
1. The relation that doesn't represent y as a function of x is: D. Answer J.
2. The only set of ordered pairs showing a relation that represents y as a function of x is: A) {(-9, 2), (0, 6), (1, -2), (-3, 6)}.
Recall:
A relation is a function if every input value (x-value) has only one possible y-value that is related to or corresponds to.Let's analyze each relation given:
1. All the relations in F, H, and G all have only one y-value assigned or related to every x-value (input). Hence, they all represent y as a function of x.
The graph in J does not represent y as a function of x because of the following:
x =-3 has two y-values, -2, and -3x = -2 has two y-values, 0, and -1.x = -1 has two y-values, 1, and 2.x = 0 has two y-values, 3, and 4.Therefore, answer J does not represent a function.
2. Same rule of a function applies here.
From the set of ordered pairs given, only the set of ordered pairs in A represents y as a function of x because it every of its x-values has only one possible y-value assigned to them.The rest set of ordered pairs have more than one y-values assigned to some of their x-values.In summary:
1. The relation that doesn't represent y as a function of x is: D. Answer J.
2. The only set of ordered pairs showing a relation that represents y as a function of x is: A) {(-9, 2), (0, 6), (1, -2), (-3, 6)}.
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In triangle abc, ab=36, bc=18, and ac=22. Sketch and label the triangle. List the angles in order from smallest to largest.
The angles of the triangle in order from smallest to largest are a, b and c
How to determine the angles of the triangle in order from smallest to largest?
From the question, we have the following parameters that can be used in our computation:
ab = 36, bc = 18 and ac = 22
By definition
The angle opposite a bigger length will be largr than the angle opposite a smaller length
The angles opposite the above lengths are
c, a and b
When ordered, we have
a, b and c
Hence, the angles in the required order are a, b and c
Aiden is trying to pick up some lawn mowing jobs over the weekend to make extra money for a school trip. Each lawn in his neighborhood takes an average of 40 minutes to mow, and Aiden has no more than 11 hours, or 660 minutes, of available time to mow lawns. If Aiden mows his grandparents' farm which takes him 110 minutes, and x represents the number of lawns he mows in his neighborhood, which inequality represents this situation?
Answer: [tex]110 + 40x \leq 660[/tex]
Step-by-step explanation:
Here, x represents the number of lawns he mows in his neighborhood,
Since, He takes 110 minutes in working with his grandfather.
And, after this he mows in his neighborhood,
Also, Each lawn in his neighborhood takes an average of 40 minutes to mow,
Thus, the total time taken by him = 110 + 40 x
Aiden has no more than 11 hours, or 660 minutes,
Thus time taken by him can not be exceed to 660 minutes,
Therefore, [tex]110 + 40x \leq 660[/tex]
Which is the required inequality.
What number is 1/10 as great as .7
Answer: The required number is 0.07.
Step-by-step explanation: We are given to find the number that is [tex]\dfrac{1}{10}[/tex] as great as 0.7.
Let the required number be represented by x.
Then, according to the given information, we have
[tex]x=\dfrac{1}{10}\times0.7\\\\\Rightarrow x=0.07.[/tex]
Thus, the required number is 0.07.
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Help! I an stuck on this and have no idea what to do
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3-74. Mentally calculate the following products. Use the rule for decimal multiplication to write an equation in which the decimal point is written in the correct location. Homework Help ✎ (−0.04)(−0.1) (0.03)(−0.02) (0.7)(0.4) Stacey said, “Stephanie, look at my answer to the last problem, 0.7 · 0.4 = 0.28. Usually when I multiply, I get a bigger answer than the numbers I start with. Twenty-eight hundredths, 0.28, is less than either 0.4 or 0.7. I must have made a mistake.” Stephanie responded, “Well, one half times one half is one fourth, and one fourth is less then one half. I think when you multiply by a fraction or decimal less than one, you get less than you started with.” Write a sentence or two about who you think is correct and why.
Final answer:
Stephanie is right; when you multiply decimals less than one, the result is smaller than the original numbers. The multiplication of (-0.04)(-0.1) is 0.004, (0.03)(-0.02) is -0.0006, and (0.7)(0.4) is 0.28. These examples illustrate the rule correctly.
Explanation:
Stephanie is correct in her explanation to Stacey. When multiplying two numbers where one or both numbers are less than one, the product will be smaller than the original numbers. This is because you are essentially taking a fraction of each number. Let's confirm this by calculating the products of the given examples.
Multiplication of Negative Decimals: The product of negative decimals will be positive (since a negative times a negative equals a positive). For (-0.04)(-0.1), the product is 0.004.Multiplication of Mixed Decimals: The product of a positive and a negative decimal will be negative. For (0.03)(-0.02), the product is -0.0006.Multiplication of Positive Decimals: As in Stacey's example, (0.7)(0.4) equals 0.28, which is indeed less than either 0.4 or 0.7 because you're multiplying fractions of a whole number.Moreover, in scientific notation, moving the decimal and using placeholders is crucial for accurate answers. Multiplying 2.4 by 100 moves the decimal two places to the right, giving us 240.
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Answer:
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Step-by-step explanation:
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A conversion factor is a ratio used to convert quantities measured in different units. It consists of a fraction with equivalent amounts expressed in two different units. This tool enables conversions by multiplying the quantity needing conversion by the appropriate conversion factor.
A conversion factor is a ratio that compares two quantities that are measured in different units. This mathematical tool is essential for converting from one unit of measure to another. Essentially, a conversion factor is a fraction that has equivalent quantities in the numerator and the denominator, but they are expressed in different units. For instance, if we know that 1 inch equals 2.54 centimeters, we can write the conversion factor as either 1 inch/2.54 cm or 2.54 cm/1 inch, depending on the direction of the conversion we need to make.
To use a conversion factor, you multiply the quantity you want to convert by the conversion factor. This will cancel out the original units and introduce the new units, effectively converting the quantity. For example, to convert 10 inches to centimeters, you would multiply 10 inches by the conversion factor of 2.54 cm/1 inch to get 25.4 centimeters.
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