Aaron has punchcards for her favorite tea house and her favorite coffee shop she currently has three punches on the TV punchcard and nine punches on the coffee punchcard given her regular routine she consistently earn seven new punches per week on the T punchcard and four on the coffee punch card before too long here and will have the same number punches on each card how long will that take how many punches or Aaron have on each card

The answers to the questions are;

The duration it will take for TV and coffee punch cards to have the same number of punches is 2 weeks

In 2 weeks Aaron will have an equal number of 17 punches on each (TV and coffee) card.

Step-by-step explanation:

TV = 3 + 7·x

Coffee = 9 + 4·x

Solving for x, we have

This gives 9 - 3 = 7·x - 4·x

6 = 3·x and

x = 2

Therefore in 2 weeks the number of punches on the TV and coffer punch cards will be equal

Also the number of punches on each card at the instant equal number of punches per cards is;

Number of punches on the TV card in 2 weeks =3 + 7·2 = 17

Number of punches on the coffee card in 2 weeks = 9 + 4·2 =17

That is Aaron has 17 punches on each card

That is Aaron will have 17 punches on each card in 2 weeks time.

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²

step-by-step explanation:

hihi so drawing these 2 triangles is fairly simple. all that's left is finding the height of each one. luckily, we have a side length and an angle, so there is a trig function we can use to solve for the height. the easiest one to use would be tangent, since we have 2/3 things needed to find and the third needed is what we are solving for. tan(73°) * 30 ~= 98.13 and tan(73°) * 35 ~= 114.45