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seraphim [82]
3 years ago
10

What is the equation of the line that is perpendicular to the given line and has an x-intercept of -3?

Mathematics
1 answer:
Anvisha [2.4K]3 years ago
3 0

Answer:

y=-\frac{3}{2}x-\frac{9}{2}

Step-by-step explanation:

Let the equation of the perpendicular line is,

y = mx + b

where m = slope of the line

b = y-intercept

From the graph, slope of the line passing through (0, -1) and (3, 1),

m' = \frac{y_2-y_1}{x_2-x_1}

m' = \frac{1+1}{3-0}

m' = \frac{2}{3}

To get the slope (m) of this line we will use the property of perpendicular lines,

m × m' = (-1)

m × \frac{2}{3} = -1

m = -\frac{3}{2}

Equation of the perpendicular line will be,

y=-\frac{3}{2}x+b

x-intercept of the line is (-3) therefore, point on the line is (-3, 0)

0 = -\frac{3}{2}(-3)+b

b = -\frac{9}{2}=-4.5

Equation of the line will be,

y=-\frac{3}{2}x-\frac{9}{2}

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The sum of two consecutive even integers is at most seven more than half the sum of the next two consecutive even integers
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The sum of two consecutive even integers is at most seven more than half the sum of the next two consecutive even integers

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3 years ago
Part A: Factor x2y2 + 6xy2 + 8y2. Show your work. (4 points) Part B: Factor x2 + 8x + 16. Show your work. (3 points) Part C: Fac
skad [1K]

Answer:

Part A : y²(x + 2)(x + 4)

Part B: (x + 4) (x + 4)

Part C: (x + 4) (x - 4)

Step-by-step explanation:

Part A: Factor x²y²+ 6xy²+ 8y²

x²y²+ 6xy²+ 8y²

y² is very common across the quadratic equation , hence

= y² (x² + 6x + 8)

= (y²) (x² + 6x + 8)

= (y²) (x² + 2x +4x + 8)

= (y²) (x² + 2x)+(4x + 8)

= (y²) (x(x + 2)+ 4(x + 2))

= y²(x+2)(x+4)

Part B: Factor x² + 8x + 16

x² + 8x + 16

= x² + 4x + 4x + 16

= (x² + 4x) + (4x + 16)

= x( x + 4) + 4(x + 4)

= (x + 4) (x + 4)

Part C: Factor x² − 16

= x² − 16

= x² + 0x − 16

= x² + 4x - 4x - 16

= (x² + 4x) - (4x - 16)

= x (x + 4) - 4(x + 4)

= (x + 4) (x - 4)

6 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20%5Clarge%5Cfrak%7B%20%5Corange%7B%20Question%7D%7D" id="TexFormula1" title=" \large\frak{ \
SVEN [57.7K]

Answer:

\boxed{\sf distance \: between \:  the \: objects \: \: is  \: 2.5 \: cm}

Step-by-step explanation:

According to universal law of gravitation every object in the universe attracts every other particles that surrounds it with a force which is inversely proportional to the square of their distance of separation & directly proportional to

the product of their masses, given by standard formula.

A = G \cdot  \frac{m_1.m_2}{ {d}^{2} }

where A,d & G are force of attraction, distance of separation & proportionality constant respectively.

<em>Given:</em>

A1 = 2 units

d1= 5 cm

A2 = 8 units

<em>To find:</em>

Distance of separation when the force of attraction is 8 units d2 = ?

<em>Solution:</em>

Substituting the given values in above at each point,

A_1 = G \cdot  \frac{m_1.m_2}{ {d_1}^{2} }  \\ 2 = G \cdot  \frac{m_1.m_2}{ {5}^{2} }  \\  \sf similarly  \: at \:  second \:  point \:  of  \: attraction \\  A_2 = G \cdot  \frac{m_1.m_2}{ {d_2}^{2} }  \\ 8 = G \cdot  \frac{m_1.m_2}{ {d_2}^{2} }  \\  \sf \: \: dividing \:  both  \: of \:  the \:  equation \\  \frac{2}{8}  =  \frac{G \cdot  \frac{m_1.m_2}{ {5}^{2} }}{G \cdot  \frac{m_1.m_2}{ {d_2}^{2} } }  \\  \sf \: G \: m_1 and \: m_2  \: are \:   \: constant  \: hence  \\ \sf  they \:  can  \: be  \: cancelled \:  out  \\  \frac{2}{8}  =  \frac{ \frac{1}{ {5}^{2} } }{ \frac{1}{ {d_2}^{2} } }  \\  \sf rearranging \: above \: equation \\  \frac{1}{4}  =  \frac{{d_2}^{2} }{ {5}^{2} }  \\ {d_2}^{2}  =   \frac{ {5}^{2} }{4 }  \\ {d_2}^{2}  =  \frac{25}{4}   \\ {d_2}^{2}  = 6.25 \\  \sqrt{{d_2}^{2} }  =  \sqrt{6.25}  \\  \boxed{ \sf{d_2} = 2.5 \: cm}

<em>Answer:</em><em> </em><em>the distance between the two </em><em>objects </em><em>is </em><em>2</em><em>.</em><em>5</em><em> </em><em>cm</em><em>, if the attraction between them is 8 </em><em>units.</em>

<em><u>Learn more about universal law of gravitation here brainly.com/question/27244479</u></em>

<em>Thanks </em><em>for </em><em>joining </em><em>brainly </em><em>community</em><em>!</em>

7 0
2 years ago
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