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3 years ago

Passes through (-4, 2 ) and parallel to y = 1/2x + 5

Mathematics

2 answers:

lord [1]3 years ago

7 0

Answer:

y = 1/2x + 4

Step-by-step explanation:

Lines that are parallel have the same gradient....in which its 1/2

Equation of the line that is parallel to y = 1/2x + 5 and passes through (-4,2)

(y - 2) = 1/2(x + 4)

2(y - 2) = x + 4

; 2y - 4 = x + 4

Equation of the line,

y = 1/2x + 4

kirill115 [55]3 years ago

3 0

Answer:

$\large\boxed{y=\dfrac{1}{2}x+4}$

Step-by-step explanation:

$\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\===========================\\\\\text{We have}\ k:y=\dfrac{1}{2}x+5\to m_1=\dfrac{1}{2}\\\\\text{Let}\ l:y=m_2x+b.\\\\l\ \parallel\ k\iff m_2=m_1\to m_2=\dfrac{1}{2}.\\\\l:y=\dfrac{1}{2}x+b\\\\\text{Put the coordinates of the given point (-4, 2) to the equation of a line:}\\\\2=\dfrac{1}{2}(-4)+b\\\\2=-2+b\qquad\text{add 2 to both sides}\\\\4=b\to b=4\\\\\text{Finally:}\\\\y=\dfrac{1}{2}x+4$

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3 years ago

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Elan Coil [88]

Answer:

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2 years ago

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iren2701 [21]

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3 years ago

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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

nignag [31]

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