State which of the following ordered pairs is a function.


Set A: (-1, 0), (-2, 1), (4, 3), (3, 4)

Set B: (1, 4), (2, 3), (3, 2), (4, 1)

Set C: (2, 1), (3, 2), (2, 3), (1, 4)

a. Set A

b. Set B

c. Both Set A and Set B

d. Set C

Answer:

Roots are -3, 2

Step-by-step explanation:

y = −x^2 − x + 6

To find out the roots we set y=0 and solve for x

0 = -x^2 -x+6

Factor out -1

0=-1(x^2+x-6)

divide both sides by -1

x^2 +x -6=0, factor x^2 +x-6

product is -6 and sum +1

3* (-2) = -6

3-2= 1

so factors are 3 and -2

x^2 +x -6=0

(x+3)(x-2)=0

Set each factor =0 and solve for x

x+3 =0 , so x=-3

x-2=0, so x= 2

Roots are -3, 2

Answer: The correct option is B.

Explanation:

The given expression is,

[tex]\sqrt[4]{9^{\frac{1}{2}}}x[/tex]

Use the property of radical expression [tex]\sqrt[n]{x} =x^{\frac{1}{n} }[/tex].

[tex]\sqrt[4]{9^{\frac{1}{2}}}x=(9^{\frac{1}{2})^{\frac{1}{4}}}x[/tex]

Use the property, [tex](x^m)^n=x^{mn}[/tex]

[tex]\sqrt[4]{9^{\frac{1}{2}}}x=9^{\frac{1}{2\times 4}x[/tex]

[tex]\sqrt[4]{9^{\frac{1}{2}}}x=9^{\frac{1}{8}x[/tex]

Therefore, the correct option is B.

Final answer:

Option b is the situation where opposite quantities combine to make zero. David used 2 1/2 liters of water (which is equivalent to 5/2 liters) to make lemonade, resulting in no water left, indicating the quantities have combined to make zero.

Explanation:

The question asks which scenario involves opposite quantities that combine to make zero. Let's examine the given options:

a. Eva adding quarters to her piggy bank on different days does not involve opposite quantities, as both actions are additive and result in an increase in the number of quarters.

b. David having 2 1⁄2 liters of water and using 5/2 liters for lemonade represents a scenario where opposite quantities combine to make 0. It's because 2 1⁄2 is a mixed number equivalent to 5/2, so when 5/2 liters of water are used, the quantities are opposite (one positive and the other negative) and they cancel each other out, leaving 0 liters.

The correct answer to which scenario involves opposite quantities that combine to make zero is b. David made lemonade using all of the water he had, ending with none left.

Option b, where David uses 5/2 liters of water for lemonade from an initial 2 1/2 liters, demonstrates opposite quantities combining to make 0. These quantities are the same, and when subtracted from each other, result in zero.

The question asks which of the given situations involve opposite quantities that combine to make 0. Option b represents such a situation. David had 2 1⁄2 liters of water, and then he used exactly 5/2 liters for lemonade, which are opposite quantities when considering addition and subtraction, since 5/2 liters is the equivalent of 2 1/2 liters.

To further explain, when David uses the 5/2 liters of water for lemonade, this amount is subtracted from the initial 2 1⁄2 liters, leading to a remainder of 0 liters. This is an example of performing an operation with opposite quantities where the result is zero.

[tex] 6\cdot5\cdot4=120 [/tex]

The number of ways the first 3 positions can be filled when there are 6 horses is given by combination and the value of P is 5 ways

What are Combinations?

The number of ways of selecting r objects from n unlike objects is:

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

Let the number of ways be represented as C

Now , the value of C is given by

The number of horses in the race = 6 horses

The number of positions = 3 positions

So , the number of ways the 6 horses can take 3 positions is given by combination and the equation is

⁶C₃ = 6! / ( 6 - 3 )! ( 3 ) !

On simplifying the equation , we get

⁶C₃= ( 6 x 5 x 4 x 3 x 2 x 1 ) / ( 4 x 3 x 2 x 1 ) ( 3 x 2 x 1 )

⁶C₃= ( 6 x 5 ) / ( 3 x 2 )

⁶C₃= 5 ways

Hence , The number of ways the is given by combination and the value of P is 5 ways

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A line of best fit is useful during data analysis for the following reasons:

Identifying Trends and Relationships:

The line helps visualize the overall direction and tendency of the data points. It reveals patterns and trends that might be difficult to see when looking at individual data points alone. This allows you to understand the relationship between two variables and how they might be correlated.

Making Predictions:

The line of best fit can be used to estimate the value of a variable based on the value of another. This allows us to make predictions about future trends and outcomes.

Simplifying Data Interpretation:

The line provides a concise summary of the data, making it easier to understand and interpret. It eliminates the need to analyze every data point individually, saving time and effort. This is particularly beneficial when dealing with large datasets.

Identifying Outliers:

Deviations from the line of best fit can highlight data points that are significantly different from the overall trend. This can help identify outliers that might be caused by errors, unusual events, or other factors.

The sound of a jet at takeoff is [tex]10^{8}[/tex] times more intense than the sound of a normal conversation.

The sound intensity of a jet at takeoff is [tex]10^{8}[/tex]times more intense than the sound of a normal conversation.

To calculate this, you need to find the difference in intensity between the jet at takeoff and a normal conversation, which is [tex]10^{14}[/tex] – [tex]10^{6}[/tex] = [tex]10^{8}[/tex]

Therefore, the sound of a jet at takeoff is [tex]10^{8}[/tex] times more intense than the sound of a normal conversation.

The snail traveled 31,464 inches.

To convert the distance traveled by the snail from miles to inches, we need to convert miles to feet and then feet to inches. We know that there are 2,280 feet in a mile. So, the snail travels 1.15 miles x 2,280 feet/mile = 2,622 feet. Next, we know that there are 12 inches in a foot. So, the snail travels 2,622 feet x 12 inches/foot = 31,464 inches.

The slope of a line parallel to the line with the equation 3x - 4y = 8 is 3/4, which is option C.

To find the slope of a line parallel to the given line, first, we need to write the equation of the given line in slope-intercept form, which is y = mx + b, where m is the slope, and b is the y-intercept. Starting with the equation 3x - 4y = 8, we rearrange it to solve for y:

3x - 4y = 8
-4y = -3x + 8
y = (3/4)x - 2

The slope of the original line is therefore 3/4. Lines that are parallel to each other have the same slope. Therefore, the slope of a line parallel to the given line is also 3/4, which is option C.

Given that angles X and Y are parallel, and that angle X measures 150 degrees, angle Y would also measure 150 degrees, as corresponding angles are equal in measure when lines are parallel.

The subject in the question is Mathematics. Specifically it involves the topic of geometry, and concepts of parallel lines and angles. Given angles X and Y are parallel and the measure of angle X is 150 degrees, the measure of angle Y, by properties of parallel lines, would also be 150 degrees, as corresponding angles are equal.

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Answer: It's B)(in^2 hope I helped.

Answer:

just did test, answer is 61 gallons

Step-by-step explanation:

The unit rate is calculated by dividing the total quantity by the given time unit. For Mitch who ate 45 hot dogs in 3 minutes, his unit rate was 15 hot dogs per minute.

Unit rate is the ratio of a quantity to one, such as miles per hour or cost per item. To find Mitch's unit rate of hot dogs eaten per minute, we divide the total number of hot dogs by the time taken. In this case, Mitch ate 45 hot dogs in 3 minutes, so his unit rate is 45 hot dogs / 3 minutes = 15 hot dogs per minute.

The slant height for the given pyramid to the nearest whole unit si,

⇒ 14 cm

Given that;

Pyramid base : 12 cm

Height : 8 cm

Now, Let the value of slant height = a

Hence, We can formulate;

a² = 12² + 8²

a² = 144 + 64

a² = 208

a = √208 cm

a = 14.4 cm

a = 14 cm

Thus, The slant height for the given pyramid to the nearest whole unit si,

⇒ 14 cm

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Answer:

The Scatter Plot is shown below:

Step-by-step explanation:

Scatter Plot is the graphical representation of two-dimension data. It is plot to see the relation between two data values.

Here both X and Y has discrete or continuous data types.

By the scatter plot, we see that as we increase the value of X, value of Y also get increases. Thus, both has Positive Correlation.