Answer:
-18.5
Step-by-step explanation:
find the gradient
40-77=-37
3-1=2
-37/2=-18.5
D=(7,3)=(xd,yd)→xd=7, yd=3
E=(8,1)=(xe,ye)→xe=8, ye=1
F=(4,-1)=(xf,yf)→xf=4, yf=-1
DE=sqrt[(xe-xd)^2+(ye-yd)^2]
DE=sqrt[(8-7)^2+(1-3)^2]
DE=sqrt[(1)^2+(-2)^2]
DE=sqrt[1+4]
DE=sqrt[5]
DE=2.236067978
DE=2.236
EF=sqrt[(xf-xe)^2+(yf-ye)^2]
EF=sqrt[(4-8)^2+(-1-1)^2]
EF=sqrt[(-4)^2+(-2)^2]
EF=sqrt[16+4]
EF=sqrt[20]
EF=sqrt[4*5]
EF=sqrt[4]*sqrt[5]
EF=2*sqrt[5]
EF=2*(2.236067978)
EF=4.472135956
EF=4.472
DF=sqrt[(xf-xd)^2+(yf-yd)^2]
DF=sqrt[(4-7)^2+(-1-3)^2]
DF=sqrt[(-3)^2+(-4)^2]
DF=sqrt[9+16]
DF=sqrt[25]
DF=5
The three sides are differents:
DE=2.236 different to EF=4.472 different to DF=5
Then the triangle scalene
Longest side is DF=5
DF^2=(5)^2→DF^2=25
DE^2=(sqrt[5])^2→DE^2=5
EF^2=(2*sqrt[5])^2=(2)^2*(sqrt[5])^2=4*5→EF^2=20
Square of the longest side: DF^2=25
Sum of the square of the other sides: DE^2+EF^2=5+20=25
The square of the longest side=25=Sum of the squares of the other sides, then the triangle is a right triangle
The triangle is right triangle and it is a scalene triangle
Answer: Option 3. right triangle
Count the number of positive integers less than 100 that do not contain any perfect square factors greater than 1.
Possible perfect squares are the squares of integers 2-9.
In fact, only squares of primes need be considered, since for example, 6^2=36 actually contains factors 2^2 and 3^2.
Tabulate the number (in [ ])of integers containing factors of
2^2=4: 4,8,12,16,...96 [24]
3^2=9: 9,18,....99 [11]
5^2=25: 25,50,75 [3]
7^2=49: 49,98 [2]
So the total number of integers from 1 to 99
N=24+11+3+2=40
=>
Number of positive square-free integers below 100 = 99-40 = 59
"mean" just means arithmetic average...
(22+11+10+14+10)/5=13.4
"median" is the center term (if there is one) or the average of the two center terms in an ordered sequence...so our elements ordered are:
10,10,22,14,22 Since there is a single middle term 22, 22 is the median.
"mode" just refers to the element that occurs most in the set...10 appears twice so 10 is the mode.
Answer:
1. X= 56
2. X= -11/2 (When you solve you get this if you need it as a mixed number it's X= -5 1/2
Step-by-step explanation:
simplifying means: Reducing to lowest terms.
To solve for x simplify both sides of the equation, then isolate the variable.
