How do you know that calculating 80% of the regular price gives you the same result as subtracting 20% from the regular price

What is the equation of a line parallel to y=1/2×+6 that passes through (-4,1)

IgorC [24]

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

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

so we're really looking for the equation of a line whose slope is 1/2 and passes through (-4 , 1)

$(\stackrel{x_1}{-4}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{(-4)}) \\\\\\ y-1=\cfrac{1}{2}(x+4)\implies y-1=\cfrac{1}{2}x+2\implies y=\cfrac{1}{2}x+3$

5 0

2 years ago

Keith won a cash prize in an art competition. He gave his mother 2/5 of the money he won. Of the remainder, 1/4 was given to his

USPshnik [31]

Answer:

300 dollars

Step-by-step explanation:

Let the original amount = x

x - 2/5x was what his mother's share looked.

5/5 x - 2/5 x

3/5x is what is left.

3/5 x - 1/4 * 3/5 x - 2/3x * 3/5 = his sister's share and his brothers

3/5x - 1/4*3/5 x - 2/3 * 3/5 = 15

3/5x * (1 - 1/4 - 2/3) = 15

3/5 x 5/60 = 15

15 / 300 * x = 15

1/20 x = 15

x = 15 * 20

x = 300

7 0

2 years ago

The sum of 3 integers is 194. the sum of the first and second integers exceeds the third by 80. The third integer is 45 less tha

kirill115 [55]

Let
x = first integer
y = second integer
z = third integer
First equation: x + y + z = 194
Second equation: x + y = z + 80
Third equation: z = x - 45

Let's find the values of x, y and z.
Substitute 3rd eq to 1st eq:
x + y + x - 45 = 194
2x + y = 45 + 194
y = -2x + 239

Plug in both we have solved for y and the 3rd eq to the 2nd eq to find x
x + (-2x + 239) = (x - 45) + 80
x - 2x - x = -45 + 80 - 239
-2x = -204
x = -204/-2
x = 102

Solving for y,
y = -2(102) + 239
y = 35

Solving for z,
z = 102 - 45
z = 57

5 0

3 years ago

joel is laying pipe for a sprinkler system before he plants his lawn . the lawn is a rectangle, 15 feet long and 8 feet wide. he

Nadya [2.5K]

Answer:

The length of the pipe = 17 feet

Step-by-step explanation:

length = 15 feet

width = 8 feet

Pythagorean theorem,

(diagonal)² = (length)² +(width)² {all angles of rectangle are 90°}

= 15² + 8²