Answer:
lateral area = 2320 m²
Step-by-step explanation:
The question wants us to calculate the lateral area of a square base pyramid. The square base pyramid has a side of 40 meters.The height is 21 meters.
Half of the square base is 40/2 = 20 meters . With the height it forms a right angle triangle. The hypotenuse side is the slant height of the pyramid.
Using Pythagoras's theorem
c² = a² + b²
c² = 20² + 21²
c² = 400 + 441
c² = 841
square root both sides
c = √841
c = 29 meters
The slant height of the pyramid is 29 meters.
The pyramid has four sided triangle. The lateral area is 4 multiply by the area of one triangle.
area of triangle = 1/2 × base × height
base = 40 meters
height = 29 meters
area = 1/2 × 40 × 29
area = 580
area of one triangle = 580 m²
Lateral area = 4(580)
lateral area = 2320 m²
Answer:
The y-intercept of points A and B is -2.
Step-by-step explanation:
Point A is the y-intercept. You can tell by looking at the x and seeing that it is 0. This means the point is the y-intercept.
Hope this helps!
-Luna
First, you have to find the equation of the perpendicular bisector of this given line.
to do that, you need the slope of the perpendicular line and one point.
Step 1: find the slope of the given line segment. We have the two end points (10, 15) and (-20, 5), so the slope is m=(15-5)/(10-(-20))=1/3
the slope of the perpendicular line is the negative reciprocal of the slope of the given line, m=-3/1=-3
step 2: find the middle point: x=(-20+10)/2=-5, y=(15+5)/2=10 (-5, 10)
so the equation of the perpendicular line in point-slope form is (y-10)=-3(x+5)
now plug in all the given coordinates to the equation to see which pair fits:
(-8, 19): 19-10=9, -3(-8+5)=9, so yes, (-8, 19) is on the perpendicular line.
try the other pairs, you will find that (1,-8) and (-5, 10) fit the equation too. (-5,10) happens to be the midpoint.
You could answer this question easily by applying synthetic division:
_______________
-5 / 4 14 -9
-20 30
---------------------------
4 -6 21
Answer:
4/11 of 2 1/2 = 4/11 * 5/2 = 20 / 22 = 10/11
a common denominator of 11 and 4 is 44
So 40 / 44 - 33 / 44 = 7/44
Check 4/11 * 2.5 = .909
3/4 = .75
difference = .909 - .750 = .159
7/44 = .159
