<PRE><B>Question 1137015</B>
The trowel shown is in the shape of an isosceles triangle.Find the polynomial that represents its height if the area of the trowel is represented by the polynomial 6+18t+t^2+3t^3 square inches. 
The height is blank but the base is t^2+6 that what the picture shows. 
The height is ____ in 


the formula for the area of a triangle is A = 1/2 * b * h.


A is the area.
b is the base.
h is the height.


the area is given as 6 + 18t + t^2 + 3t^3 square inches


re-arrange this in descending order of degree and the area if given as 3t^3 + t^2 + 18t + 6.


the base is given as t^2 + 6.


A = 1/2 * b * h becomes 3t^3 + t^2 + 18t + 6 = 1/2 * (t^2 + 6) * h


divide both sides of this equation by t^2 + 6 and you get (3t^3 + t^2 + 18t + 6) / (t^2 + 6) = 1/2 * h.


perform the division on the left side of the equal sign and you get (3t + 1) = 1/2 * h


multiply both sides of this equation by 2 and solve for h to get h = 6t + 2.


the height of the isosceles triangle is 6t + 2.


that&#39;s your solution.


A = 1/2 * b * h becomes A = 1/2 * (t^2 + 6) * (6t + 2), where t^2 + 2 is the base and 6t + 2 is the height.


multiply out the right side of the equation and you will find that it is equal to 3t^3 + t^2 + 18t + 6 which is the area of the triangle.


the attached worksheet shows the result of the division of 3t^3 + t^2 + 18t + 6 by t^2 + 6


&lt;img src = &quot;http://theo.x10hosting.com/2019/032001.jpg&quot; alt=&quot;$$$&quot; &gt;



---------------------------


2) the moon is about 240,000 miles from earth.


a) write this in scientific notation. 


240,000 is equal to 2.4 * 10^5.


your decimal point starts immediately after 240,000 to get 240,000.


you move it to the left 5 places to get it immediately after the 2.


that&#39;s the same as dividing 240,000 by 10^5.


so, you get 2.4 = 240,000 / 10^5.


multiply both sides of that equation by 10^5 and you get 2.4 * 10^5 = 240,000.


you can use your calculator to confirm.


you can make the calculator divide (2.4 * 10^5) by 240,000 and the calculator will tell you that the answer is 1.


any time you divide something by itself, the answer will be 1.


b)if a rocket traveled at 4*10^4 miles per hour, how long would it take for it to reach the moon? Use scientific notation and exponent rules to find the answer.


the moon is 2.4 * 10^5 miles away from the earth.


if the rocket travels at 4 * 10^4 miles per hour, then to figure out how long it would take to get to the moon, you need to divide 2.4 * 10^5 by 4 * 10^4.


there are several ways to do this, but let&#39;s try this way.


(2.4 * 10^5) / (4 * 10^4) is equal to (2.4 / 4) * (10^5 / 10^4).


10^5 / 10^4 is equal to 10^(5-4) which is equal to 10^1 which is equal to 10.


you get (2.4 / 4) * 10.


this is equal to (2.4 * 10) / 4 which is equal to 24 / 4 which is equal to 6.


the rocket would take 6 hours to get to the moon.


4 * 10^4 miles per hour times 6 = 24 * 10^4 miles.


if you divide 24 by 10, you need to multiply 10^4 by 10 to keep the same value.


therefore 24 * 10^4 is equal to (24 / 10) * (10^4 * 10) which is equal to 2.4 * 10^5.


your solution is that it will take 6 hours for the rocket to get to the moon.


</PRE>