Isaiah was given a gift card for a coffee shop. Each morning, Isaiah uses the card to buy one cup of coffee. The original amount of money on the gift card was $10 and each cup of coffee costs $2. Write an equation for A, A, in terms of x, x, representing the amount money remaining on the card after buying xx cups of coffee.

Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.

Solve each quadratic equation by factoring and using the zero product property. x^2 - 8x + 30 = 3x

Johnny rode his bike to a friends house 4 blocks down the street in his neighborhood. he immediately rode back home once he realized his friend was unable to play. what was his displacement for the total bike ride trip? what could you use as a reference point ? show the steps to solve this problem.