a line contains the points (4,2) and (0,-1). what is the equation of the line. a) y=2x -6
b)y= 3/4x -1
c) y= 1/4x + 1
d) y= 4/3x - 10/3

Two hundred percent (200%) is equivalent to whole number 2.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

We have the percentage 200%.

Converting percentage to whole number,

200/100,

= 2

2 is equivalent to 200%.

Therefore, 2 is equivalent to 200%.

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Linear function f with f(-3) = 1 and f(13) = 5 is given by   [tex]\rm f(x) = \dfrac{1}{4}x + \dfrac{7}{4}[/tex]  and this can be determined by using the given data.

Given :

f(-3) = 1 and f(13) = 5.

The generalised linear function is given by:

f(x)  = ax + b   --- (1)

Now, it is given that (f(-3) = 1) that means at (x = -3) the above function is equal to 1.

f(-3) = a(-3) + b

    1  = -3a + b

b = 1 + 3a   ---- (2)

Now, it is also given that (f(13) = 5) that means at (x = 13) the function (f(x) = ax + b) is equal to 5.

f(13) = 13a + b

5 = 13a + b

Now, put the value of 'b' in the above equation.

5 = 13a + 1 + 3a

4 = 16a

[tex]\rm a = \dfrac{1}{4}[/tex]

Now, put the value of 'a' in equation (2).

[tex]b = 1 +3\times \dfrac{1}{4}[/tex]

[tex]b = \dfrac{7}{4}[/tex]

Now, put the value of a and b in equation (1).

[tex]\rm f(x) = \dfrac{1}{4}x + \dfrac{7}{4}[/tex]

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Nathan can completely fill a bag of mixed nuts by calculating the total weight of the nuts, then dividing that total by 1.2 kg, which is the weight of nuts per bag. Any decimal in the result would be rounded down to give the number of full bags.

To determine the number of bags of mixed nuts Nathan can completely fill, you first need to calculate the total weight of all the nuts he bought. This is done by adding up the masses of all the different nuts mentioned in the table.

Let's assume that Nathan's total weight of nuts is 'T'. His plan is to fill each bag with 1.2 kg of nuts, thus the number of full bags he can make, denoted as 'B', is the total weight divided by the weight per bag. In other words, B = T / 1.2.

A key fact here is that this calculation will give a decimal if 'T' is not a multiple of 1.2. However, since he cannot create partial bags, you would round down any decimal to get the number of complete bags.

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Heather should be saving 1/36th of her annual salary for retirement. Based on her annual salary of $63,000, this amounts to about $1,750 per year or approximately $146 per month.

According to the information provided, Heather should be saving 1/36 of her annual salary for retirement. If Heather's annual salary is $63,000, she will need to find 1/36 of this total. In mathematical terms, this can be achieved by dividing $63,000 by 36. After calculating this, we get $1,750 yearly. However, Heather is interested in knowing how much she should save each month.

To find this, we need to take her annual saving of $1750 and divide it by 12 months. When we calculate this, we find that Heather should be saving approximately $146 per month. This is rounded to the nearest dollar. This is a simple and effective way to determine how much of one's salary should be allocated toward retirement savings each month based on a given fraction of that yearly salary.

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Without the height of the popcorn machine, the exact length cannot be calculated. The length is three-quarters of the height. If the height were known, the length would be determined by multiplying the height by 3/4.

To determine the length of the popcorn machine, we need to know the height of the machine since the length is expressed as a fraction of the height. Without the height measurement, we cannot calculate a specific length. However, if we were provided with the height (let's call it H), then we could easily find the length by multiplying the height by 3/4:

Length = (3/4) × H

For example, if the height of the popcorn machine were 4 feet, then the length would be calculated as follows:

Length = (3/4) × 4 feet = 3 feet

Therefore, the length of the popcorn machine is three-quarters of whatever its height is.

The percent of change from 14 inches to 26 inches is approximately 85.71 percent, calculated by using the formula for percent of change which is [(change in quantity)/(original quantity)] × 100.

To find the percent of change from one value to another, you apply the formula [(change in quantity)/(original quantity)] × 100. In this instance, the original quantity is 14 inches and it changed to 26 inches. Therefore, the change in quantity is 26 - 14 = 12 inches.

Now, substitute these values into the formula: (12/14) × 100 = 85.71% (approximately). This means the change from 14 inches to 26 inches represents an approximately 85.71 percent increase.

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Answer:

The vertices of image are (5,1), (2,-5) and (-4,-5).

Step-by-step explanation:

The vertices of triangle are (5,-1), (3,-5) and (-1,-5).

If a figure dilated by scale factor k centered at (a,b), then

[tex](x,y)\rightarrow (k(x-a)+a,k(y-b)+b)[/tex]

The figure after a dilation with a scale factor of 3/2 centered at (5, −5).

[tex](x,y)\rightarrow (\frac{3}{2}(x-5)+5,\frac{3}{2}(y+5)-5)[/tex]

The coordinates of image are

[tex](5,-1)\rightarrow (\frac{3}{2}(5-5)+5,\frac{3}{2}(-1+5)-5)\rightarrow (5,1)[/tex]

[tex](3,-5)\rightarrow (\frac{3}{2}(3-5)+3,\frac{3}{2}(-5+5)-5)\rightarrow (2,-5)[/tex]

[tex](-1,-5)\rightarrow (\frac{3}{2}(-1-5)+5,\frac{3}{2}(-5+5)-5)\rightarrow (-4,-5)[/tex]

Therefore vertices of image are (5,1), (2,-5) and (-4,-5).

The equivalent ratio to 8/24 is 1/3, which can be used to calculate that approximately 33.33% of students have at least 2 siblings. This demonstrates how to convert a ratio to a percentage by setting up a proportion with 100 as the denominator.

The ratio 8/24 represents the portion of students in a class who have at least 2 siblings. To find an equivalent ratio, one could simplify the given ratio by dividing both the numerator and the denominator by the same number. In this case, both 8 and 24 are divisible by 8, so dividing both by 8 yields the equivalent ratio 1/3. This ratio can also be used to express the percentage of students with at least 2 siblings. The calculation would be (1/3) * 100 to find the percentage, which gives us approximately 33.33%.

To further illustrate calculating percentages using equivalent fractions, we can take the original ratio (8/24) and set up a proportion with 100 as the denominator. The equation would be:

8/24 = X/100

where X represents the percentage of students. To solve for X, cross-multiply and divide:

(8 * 100) / 24 = 33.33%

This confirms that 33.33% is the percentage of students with at least 2 siblings. It is important to note that simplifying ratios and working with equivalent fractions is a useful skill in understanding data representation in statistics and mathematics.

the value of the fraction when x = 2 and y = 3 is approximately [tex]\( \frac{1}{31.6} \).[/tex]

To find the value of the fraction [tex]\( \frac{1}{2x^3 + 5.2y} \) when \( x = 2 \) and \( y = 3 \)[/tex], we substitute these values into the expression:

[tex]\[ \frac{1}{2(2)^3 + 5.2(3)} \][/tex]

[tex]\[ = \frac{1}{2(8) + 5.2(3)} \][/tex]

[tex]\[ = \frac{1}{16 + 15.6} \][/tex]

[tex]\[ = \frac{1}{31.6} \][/tex]

So, the value of the fraction when x = 2 and y = 3 is approximately [tex]\( \frac{1}{31.6} \).[/tex]

The probable question maybe:

What is the value of fraction 1 over 2x^3 + 5.2y when x = 2 and y = 3?

The average miles per gallon is given by the equation A = 65 miles per gallon

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the average miles per gallon be represented as A

Now , the equation will be

The total distance moped = 78 miles

The amount of gallons of gas for 78 miles = 1.2 gallons

Now , average miles per gallon = total distance moped / amount of gallons of gas for 78 miles

Substituting the values in the equation , we get

The average miles per gallon A = 78 / 1.2

The average miles per gallon A = 65 miles per gallon

Therefore , the value of A is 65 miles per gallon

Hence , the equation is A = 65 miles per gallon

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