1)what is compound interest $660 at 3% compounded annually for 8 years

solve the equation. Justify each step. 5x - 11 = 34 Plzzz help me this needs to be explained in essay form.

Helga [31]

Answer:

x = 9

Step-by-step explanation:

5x -11 (+11) = 34 (+11)

5x = 45

5x ÷ 5 = 45 ÷ 5

x = 9

4 0

4 years ago

A hook in an office storage closet can hold no more than 6 pounds. An order of jumbo paperclips weighs 2 pounds and an

Westkost [7]

Answer:

the first graph: line passing through the points (3, 0) and (0,2), and the shaded region is below the line.

Explanation:

1) Find the expression that represents the situation.

The expression that represents the situation is an inequality:

Number of orders of paper clips: x
Weight of an order of paper clips: 2 lbs
Total weight of x orders of paper clips: 2x

Number of orders of packing tape: y
Weight of an order of packing tape: 3 lbs
Total weight of y orders of packing tape: 3y

Total weight of paper clips and packing tape in a bag: 2x + 3y

Maximum weight hold by the hook: 6 lbs

Hence, the total weight must be less than or equal to (≤) 6 lbs, which is:

2x + 3y ≤ 6

2) Graph of the inequality 2x + 3y ≤ 6

Line:

Border line: 2x + 3y = 6

x-intercept: y = 0 ⇒ 2x = 6 ⇒ x = 6 /2 ⇒ x = 3 ⇒ point (3,0)
y-intercept: x = 0 ⇒ 3y = 6 ⇒ y = 6 /3 ⇒ y = 2 ⇒ point (0,2)

Shaded region:

Symbol ≤ means that the line is included, which is represented with a solid line, and the region is below the line.

Conclusion: the graph is the line passing through the points (3, 0) and (0,2), and the shaded region is below the line, so that is the first graph of the picture.

Note: strictly speaking, you should include the restrictions that the variables x and y cannot be negative, with which the graph would be only on the first quadrant but those constrains are not handled in the problem.

The graph is also attached.

5 0

3 years ago

Read 2 more answers

A car is approaching a building. When it is 300 ft away, the angle of depression from the top of the building to the car is 42°.

labwork [276]

Answer: 333.2ft

Step-by-step explanation:

We can draw a triangle rectangle, where the distance between the base of the building and the car is one cathetus (300ft)

The height of the building is the other cathetus.

Now, we know that the angle of depression from the top of the building to the car is 42°

This angle is measured from a perpendicular line in from the building, so the "top angle" of the triangle rectangle will be:

90° - 42° = 48°

if we steep on this angle, the 300ft cathetus is the opposite cathetus and the height of the building is the adjacent cathetus.

Here we can use the relation:

Tan(A) = Opposite cathetus/adjacent cathetus:

Then:

Tan(48°) = H/300ft

Tan(48°)*300ft = H = 333.2ft

7 0

4 years ago

Read 2 more answers

A 10 foot ladder is leaning against a wall. Call x the distance from the top of the ladder to the ground, and call y the distanc

liq [111]

$-5.3\:\text{ft/s}$

Step-by-step explanation:

We start by applying the Pythagorean theorem to the ladder, with its length L as the hypotenuse:

$L^2 = 100\:\text{ft}^2 = x^2 + y^2$

where x is the vertical distance from the top of the ladder to the ground and y is the horizontal distance from the bottom of the ladder to the wall. Taking the derivative of the above expression with respect to time, we get

$0 = 2x\dfrac{dx}{dt} + 2y\dfrac{dy}{dt}$

Solving for dx/dt, we get

$\dfrac{dx}{dt} = -\left(\dfrac{y}{x}\right)\dfrac{dy}{dt} = -\left(\dfrac{\sqrt{L^2 - x^2}}{x}\right)\dfrac{dy}{dt}$

We know that

$\dfrac{dy}{dt} = 4\:\text{ft/s}$

when x = 6 ft. So the rate at which the top of the ladder is going down is

$\dfrac{dx}{dt} = -\left(\dfrac{\sqrt{100\:\text{ft}^2 - (6\:\text{ft})^2}}{6\:\text{ft}}\right)(4\:\text{ft/s})$

$\:\:\:\:\:\:\:= -5.3\:\text{ft/s}$

The negative sign means that the distance x is decreasing as y is increasing.

5 0

3 years ago

Christopher's best time in a race is four seconds faster than his second-best time. his second best time is 1 1/3 times slower t

a_sh-v [17]

If his best time is x, and the best time is smaller, then (1+1/3)*x=his second best time. If x+4=his second best time (since his second best time is 4 seconds slower), then (1+1/3)*x=x+4. Multiplying it out, we get (3/3+1/3)*x=x+4
=4x/3=x+4. Subtracting x from both sides, we get 4x/3-3x/3=x/3=4. Multiplying both sides by 3, we get x=12=his best time

8 0

4 years ago