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3 years ago

Consider the line 6x+4y=-5

1 answer:

8 0

$6x+4y=-5\implies 4y=-6x-5\implies y=\cfrac{-6x-5}{4} \\\\\\ y=-\cfrac{6x}{4}-\cfrac{5}{4}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{2}} x-\cfrac{5}{4}\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

$\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{-\cfrac{3}{2}} ~\hfill \stackrel{reciprocal}{-\cfrac{2}{3}} ~\hfill \stackrel{negative~reciprocal}{-\left( -\cfrac{2}{3} \right)\implies \cfrac{2}{3}}} \\\\[-0.35em] ~\dotfill\\\\ \textit{and a \underline{parallel line} to this one will also have a slope of }-\cfrac{3}{2}$

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The area of a rectangle is 56 cm. The length is 2 cm more than x and the width is 5 cm less than

Ira Lisetskai [31]

Answer:

<u>x = 6, length = 8 cm and width = 7 cm</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Area of a rectangle = 56 cm²

Length of the rectangle = x + 2

Width of the rectangle= 2x - 5

2. Solve for x. Round to the nearest whole number.

Area of a rectangle = Length * Width

(x + 2) (2x - 5) = 56

2x² + 4x - 5x -10 = 56

2x² - x - 66 = 0

Factoring, we have:

(2x + 11) * (x - 6) = 0

x₁ = 2x + 11 = 0 ⇒ 2x = -11; x₁ = - 5.5

x₂ = x - 6 = 0 ⇒ x₂ = 6

We picked x₂ because x₁ will give us negative values for length and width.

Length = 6 + 2 = 8 cm

Width = 2 * 6 - 5 = 12 - 5 = 7 cm

8 0

3 years ago

Write an equation that is perpendicular to and 3x+y=3 whose y-intercept 5. Anyone please help me, no link just explain how to do

Liula [17]

Answer:

$y = \frac{1}{3}x + 5$

Step-by-step explanation:

By definition, two lines are perpendicular if and only if their slopes are negative reciprocals of each other: $m = - \frac{1}{m_{2} }$ , or equivalently, $m_{1} * m_{2} = -1$ .

Given our linear equation 3x + y = 3 (or y = -3x + 3):

We can find the equation of the line (with a y-intercept of 5) that is perpendicular to y = -3x + 3 by determining the negative reciprocal of its slope, -3, which is $\frac{1}{3}$ .

To test whether this is correct, we can take first slope, $m_{1} = -3$ , and multiply it with the negative reciprocal slope $m_{2} = \frac{1}{3}$ :

$m_{1} * m_{2} = -1$

$-3 * \frac{1}{3} = -1$

Therefore, we came up with the correct slope for the other line, which is $\frac{1}{3}$ .

Finally, the y-intercept is given by (0, 5). Therefore, the equation of the line that is perpendicular to 3x + y = 3 is:

$y = \frac{1}{3}x + 5$

7 0

3 years ago

The low temperature in Leroy’s town one day was -4 F. The difference between the high temperature and the low temperature that d

Serggg [28]

2F
Not sure?????
.....

3 0

3 years ago

Read 2 more answers

A vending machine's coin box contains nickels, dimes, and quarters. The total number of coins in the box is 252 . The number o

ohaa [14]

Answer:

Step-by-step explanation :

N = number of nickels

D = number of dimes

Q = number of quarters

252 = N + D + Q <---- Equation 1

D = 3(N+Q) <---- Equation 2

24.85 = 0.05N + 0.10D + 0.25Q <---- Equation 3

We a have set of three linear equations to solve for three unknowns N, D, and Q.

Rearranging the equations we have :

N + D + Q = 252

3N - D + 3Q = 0

0.05N + 0.10 D + 0.25Q = 24.85

Solving the set of linear equations, we end up with :

N = 49

D = 189

Q = 14

(see the attached images for the entire solution)

8 0

2 years ago

6 Which equation has a solution of s = 9.5 ? F -5s = -47.5 G -3 + s = 12.5 H --2s 19 J –1 + s = 10.5

earnstyle [38]

Answer:

F. -5s = -47.5

Step-by-step explanation:

F. -5s = -47.5

s = -47.5 / -5

s = 9.5

This is the correct option

G. -3 + s = 12.5

s = 12.5 + 3

s = 15.5 (Incorrect option)

J. –1 + s = 10.5

s = 10.5 + 1

s = 11.5 (Incorrect option)

5 0

3 years ago