SOLUTION: adult tickets to the aquarium costs $22 each while child tickets cost $15 each. If a large group bought 32 tickets and paid $543, how many child ...

Step-by-step explanation:

7 0

3 years ago

A vertex of square is at(1,1) and its two parallel sides are y=x and y=x+1. find the equation of the remaining sides.Show your w

belka [17]

Answer:

$\displaystyle y = - x + 2$

$y = - x +1$

Step-by-step explanation:

we are given a vertex of a square i.e (1,1)

and the equations of the two parallel sides

notice that, the given vertex coordinates satisfy one of the parallel side i.e y=x which means that (1,1) points lie on one of Parallel sides

remember that,

every angles of a square is 90°

therefore,

we need to figure out the remaining Perpendicular line of the given Parallel sides so

let's figure out the perpendicular line of y=x line

recall that,

Parallel lines have the same slope thus

$\displaystyle m_{ \rm perpedicular} = - 1$

since we are given a vertex the equation of the perpendicular line should be

$\displaystyle y - 1 = - 1(x - 1)$

distribute:

$\displaystyle y - 1 = - x + 1$

add 1 to both sides:

$\displaystyle y = - x + 2$

to figure out the second perpendicular line we can consider the coordinates (0.5,0.5) of y=x equation

so the slope of the perpendicular line is -1

and the equation:

$y - 0.5 = - 1(x - 0.5)$

distribute:

$y - 0.5 = - x +0 .5$

add 0.5 to both sides:

$y = - x +1$

and we are done!

4 0

3 years ago

21. Reason When you multiply any number

Anettt [7]

Answer:

Because multiplying a number by one will just give you the same number over and over again

Step-by-step explanation:

Example: 1 x 56 = 56

4 0

3 years ago

Read 2 more answers

Complete the equations of the line through (-9,7) and (-6,-3)

lbvjy [14]

In point slope form, the equation is y-7=(-10/3)(x+9). In slope-intercept form, it is y=(-10/3)x-23.

First find the slope of the line. The formula for slope is
m=(y₂-y₁)/(x₂-x₁)

Using our points, we have
m=(-3-7)/(-6--9) = -10/3

Plug this into point slope form:
y-y₁=m(x-x₁)
y-7=(-10/3)(x--9)
y-7=(-10/3)(x+9)

Using the distributive property:
y-7=(-10/3)*x+(-10/3)*9
y-7=(-10/3)x-90/3
y-7=(-10/3)x-30

Add 7 to both sides:
y=(-10/3)x-23

3 0

3 years ago