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3 years ago

What’s the line contains the point (-5,7) and is perpendicular to a line with a slope of 5/3

Mathematics

2 answers:

inysia [295]3 years ago

7 0

Slope. perp. -3/5

y - 7 = -3/5(x + 5)

y - 7 = -3/5x - 3

y = -3/5x + 4

11Alexandr11 [23.1K]3 years ago

5 0

Answer:

$\large\boxed{y=-\dfrac{3}{5}+4}$

Step-by-step explanation:

$\text{Let}\ k:y=m_1x+b_1,\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\===========================\\\\\text{We have}\ m_1=\dfrac{5}{3},\ \text{therefore}\ m_2=-\dfrac{1}{\frac{5}{3}}=-\dfrac{3}{5}.\\\\l:y=-\dfrac{3}{5}x+b\\\\\text{Put the coordinates of the point (-5, 7) to the equation of a line }\ l:\\\\7=-\dfrac{3}{5}(-5)+b\\\\7=3+b\qquad\text{subtract 3 from both sides}\\\\4=b\to b=4\\\\\text{Fimally we have the equation:}\\\\l:y=-\dfrac{3}{5}+4$

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4 0

2 years ago

Translate the phrase into an expression: 11 more than one third of a number

skelet666 [1.2K]

1/3x+11.
1/3 of a number can be shown as 1/3x, since the number is not identified.

We can represent 11 more as +11.
This, our expression is 1/3x+11

Hope this helps!

5 0

3 years ago

Use substitution to solve the following system of equations. What is the value of y? {3x+2y=12{5x−y=7 A) y = -3B) y = 3C) y = -2

Vlad [161]

<em>Answer</em>

B) y = 3

<em>Step-by-step explanation</em>

Given the system of equations:

$\begin{gathered} 3x+2y=12\text{ \lparen eq. 1\rparen} \\ 5x-y=7\text{ \lparen eq. 2\rparen} \end{gathered}$

Isolating x from equation 1:

$\begin{gathered} 3x+2y-2y=12-2y \\ 3x=12-2y \\ \frac{3x}{3}=\frac{12-2y}{3} \\ x=\frac{12}{3}-\frac{2}{3}y \\ x=4-\frac{2}{3}y\text{ \lparen eq. 3\rparen} \end{gathered}$

Substituting equation 3 into equation 2 and solving for y:

$\begin{gathered} 5(4-\frac{2}{3}y)-y=7 \\ 5\cdot4-5\cdot\frac{2}{3}y-y=7 \\ 20-\frac{10}{3}y-y=7 \\ 20-\frac{13}{3}y=7 \\ 20-\frac{13}{3}y-20=7-20 \\ -\frac{13}{3}y=-13 \\ (-\frac{3}{13})\cdot-\frac{13}{3}y=(-\frac{3}{13})\cdot-13 \\ y=3 \end{gathered}$

6 0

1 year ago

A town has a population of 19000 and grows at 4.5% every year. To the nearest tenth of a year, how long will it be until the pop

steposvetlana [31]

Answer:

If the population grows by 4% each year then

the population in any given year is 104% of

the previous year or 1.04 times as much

P(t) = P0(1.04)t

P(t) is population at time t years

P0 = initial population = 11,000

t = number of years = 15

P(15) = 11,000(1.04)15

P(15) = 19,810 people

Step-by-step explanation:

3 0

3 years ago

What is the median of these numbers 12 13 15 16 19 32

uysha [10]

Answer:

15 1/2 or 15.5

Step-by-step explanation:

the median is just the numer in the middle (numerical order) so, because you end up with both 15 and 16, the rational number between them is 15.5

4 0

2 years ago