Find the slope of each line

Final answer:

The parachutist's speed of 12 miles per hour can be converted to feet per second by using conversion factors (1 mile equals 5280 feet, and 1 hour equals 3600 seconds).

The resultant speed is approximately 17.6 feet per second.

Explanation:

To convert the parachutist's speed from miles per hour to feet per second, utilize the known conversion factors for miles to feet and hours to seconds. Bread down the problem into two conversions: first, convert miles to feet (1 mile is equivalent to 5280 feet).

Next, convert hours to seconds (1 hour is equivalent to 3600 seconds). The given speed is 12 miles per hour: start the conversion by multiplying it by the number of feet in a mile, then dividing that result by the number of seconds in an hour.

Step 1: Convert miles to feet: 12 miles * 5280 feet/mile = 63360 feet

Step 2: Convert hours to seconds: 1 hour/3600 seconds

From Step 1&2, combine the results to find the speed in feet per second:

63360 feet ÷ 3600 seconds = 17.6 feet per second

So, the parachutist is falling at a speed of 17.6 feet per second.

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Answer:

A  = 222 units^2

Step-by-step explanation:

To find the area of this trapezoid, first draw an imaginary horizontal line parallel to AD and connecting C with AB  (Call this point E).  Below this line we have the triangle CEB with hypotenuse 13 units and vertical side (21 - 16) units, or 5 units.  Then the width of the entire figure shown can be obtainied using the Pythagorean Theorem:

(5 units)^2 + CE^2 = (13 units)^2, or 25 + CE^2 = 169. Solving this for CE, we get |CE| = 12.

The area of this trapezoid is

A = (average vertical length)(width), which here is:

       (21 + 16) units

A  = --------------------- * (12 units),   which simplifies to:

                  2

A = (37/2 units)(12 units)  =  A  = 37*6 units  =  A  = 222 units^2

Compound interest is the addition of interest. The interest that is needed to be paid by Jim in the 4 years of tenure is $2253.98.

What is compound interest?

Compound interest is the addition of interest on the interest of the principal amount. It is given by the formula,

We know that the Principal amount received by Jim is $2000, while the interest that Jim needs to pay is 3% quarterly, therefore, he needs to pay the interest 4 times a year. Thus, the value of n is 4.

Now, we know all the values therefore, substitute the values in the formula of compound interest,

Hence, the interest that is needed to be paid by Jim in the 4 years of tenure is $2253.98.

Learn more about Compound Interest:

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Answer:

$2253.98

Step-by-step explanation:

Jim received a $2000 loan from his bank. The loan accrues 3% interest every 3 months.

P=2000

r= 3%=0.03  and t= 4 years

interest every 3 months so n= 4

Answer:

The slope is 3/4 and the y-intercept is -5.

Step-by-step explanation:

Your equation is already in slope-intercept form, so all you have to do is look at it. Slope-intercept form looks like y = mx + b, where m is the slope and b is the y-intercept. Hope that helps!

Answer:

Translated according to the rule (x, y) →(x + 7, y + 1) and reflected across the x-axis

Step-by-step explanation:

We are given Pentagon ABCDE.

with vertices as:

A (-4,-2) , at B(-6,-3) at C (-5,-6), at D (-2,-5) at E (-2,-3)

and the pentagon A'B'C'D'E' with vertices as:

A'(3,1) , B'(1,2) , C'(2,5) , D'(5,4) and E'(5,2).

Clearly we could observe that the image is formed by the translation and reflection of the pentagon ABCDE.

First the Pentagon is translated by the rule:

(x,y) → (x+7,y+1) so that the pentagon is shifted to the fourth coordinate  and then it is reflected across the x-axis to get the transformed figure in the first coordinate plane as Pentagon A'B'C'D'E'.

Hence, the answer is:

Translated according to the rule (x, y) →(x + 7, y + 1) and reflected across the x-axis