What is the equation of a line that has a slope of one and passes through point (5,3)?

Mathematics

2 answers:

yanalaym [24]3 years ago

8 0

Answer:

The Equation of a line that is passing from the point (5,3) is y = x - 2

Step-by-step explanation:

The equation of a line that has a slope of one and passes through point (5,3) is as:

From given data,

slope = b = 1,
x 1= 5,
y 1= 3.

So by using the formula, y - y 1 = b ( x - x 1 ) now putting values in this formula,

y - y 1 = b ( x - x 1 )
y - ( 3 ) = 1( x - 5 )

=> y - 3 = x - 5,

=> y = x - 5 + 3,

=> y = x - 2.

The equation of a line that has a slope of one and passes through the point (5,3) is y = x - 2.

Katarina [22]3 years ago

5 0

To answer your question, it is shown in the image below:

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An ice cream store has the pricing shown below. You want to determine the best value. The height of the cone is 4.5 in and the d

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Solution:

Step 1:

We will calculate the volume of ice cream in the single scoop

The volume of the ice cream will be

$\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{2}{3}\pi r^3 \\ r=\frac{2in}{2}=1in(cone) \\ h=4.5in \\ r=\frac{3in}{2}=1.5in(radius\text{ of the hemisphere\rparen} \end{gathered}$

By substituting the values, we will have

$\begin{gathered} V=\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^{3} \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+\frac{2}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{14} \\ V=\frac{165}{14} \\ V=11.79in^3 \end{gathered}$

Step 2:

We will use the formula below to calculate the volume of the two scoops of ic cream

$\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{4}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5in+\frac{4}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{7} \\ V=\frac{132}{7} \\ V=18.86in^3 \end{gathered}$

Step 3:

We will use the formula below to calculate the volume of the three scoops of ic cream

$\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{6}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+2\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{297}{14} \\ V=\frac{363}{14} \\ V=25.93in^3 \end{gathered}$

For the first ice cream with one scoop