Answer:
<h2>5 units</h2>
Step-by-step explanation:
A right angled triangle is a triangle that has one of this angles to be 90°. According to the ΔABC, the angle at B is 90°.
Area of a triangle = 1/2 * base * height
According to the diagram shown, the base is BC and the height is AB which is the required side.
Area of the triangle = 1/2 * BC * AB
Given area of the triangle = 10 square units
BC = 4 units
AB is the required length.
Substituting this values into the formula above;
10 = 1/2 * 4 * AB
10 = 2AB
Dividing both sides by 2
2AB/2 = 10/2
AB = 5 units
Hence the length of AB is 5 units.
if Martha is not earning money to pay it back, it would be negative. Each week, she loses -9.72 dollars. so -9.72 x 3 weeks = your problem. I'll let you take it from there and solve the rest
<span>A freight train completes its journey of 150 miles 1 hour earlier if its original speed is increased by 5 miles/hour. What is the train’s original speed?
***
let x=original speed
x+5=increased speed
travel time=distance/speed
..
lcd:x(x+5)
150(x+5)-150x=x(x+5)
150x+750-150x=x^2+5x
x^2+5x-750=0
(x-25)(x+30)=0
x=25
What is the train’s original speed? 25 mph</span>
Half the distance of AC (6)
Answer:
y = -2
Step-by-step explanation:
To find the equation of the tangent we apply implicit differentiation, and then we take apart dy/dx
The equation is
implicit differentiation give us
![\frac{d}{dx}[y^2(y^2-4)=x^2(x^2-5)]\\\\2y\frac{dy}{dx}(y^2-4)+y^2(2y\frac{dy}{dx})=2x(x^2-5)+x^2(2x)\\\\4y^3\frac{dy}{dx}-8y\frac{dy}{dx}=2x^3-10x+2x^3\\\\\frac{dy}{dx}=\frac{4x^3-10x}{4y^3-8y}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5By%5E2%28y%5E2-4%29%3Dx%5E2%28x%5E2-5%29%5D%5C%5C%5C%5C2y%5Cfrac%7Bdy%7D%7Bdx%7D%28y%5E2-4%29%2By%5E2%282y%5Cfrac%7Bdy%7D%7Bdx%7D%29%3D2x%28x%5E2-5%29%2Bx%5E2%282x%29%5C%5C%5C%5C4y%5E3%5Cfrac%7Bdy%7D%7Bdx%7D-8y%5Cfrac%7Bdy%7D%7Bdx%7D%3D2x%5E3-10x%2B2x%5E3%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7B4x%5E3-10x%7D%7B4y%5E3-8y%7D)
But we know that
Hence, for the point (0,-2) and by replacing for dy/dx
Hence m=0, that is, the tangent line to the point is a horizontal line that cross the y axis for y=-2. The equation is:
y=(0)x+b = -2
HOPE THIS HELPS!!
