Answer:
y= 3/5x+ 6.2
Step-by-step explanation:
the slope is change in y over change in x.
-4-(-1) divided by 3-8 will be -3/-5 = 3/5
For the y-intercept, plug in x and y values. I will use (3,8).
8= 3/5(3)+b
8= 9/5+b
(subtract 9/5 from both sides)= 6 and 1/5 or 6.2 as a decimal.
First we rewrite the table:
20 30
50 75
80 120
150 ?
We observe that for each 30 number of hops, the distance increases by 45 feet.
We must find the slope of the line:
m = (y2-y1) / (x2-x1)
m = (75-30) / (50-20)
m = 1.5
Then, the line is:
y = 1.5x
We substitute x = 150
y = 1.5 * (150)
y = 225
Answer:
Find the ratio of hops to distance traveled (1: 1.5), then multiply 150 by 1.5.
Answer:
a*b = 1/2
a/ b = 8/9
Step-by-step explanation:
a = 0.66666 and b = 0.75
To multiply it we write the decimal numbers in fraction form
a= 0.666666...
Multiply by 10 on both sides
10 a = 6.66666...
a = 0.66666...
Subtract the second equation
9a = 6
divide by 9 on both sides

so 0.6666 = 2/3
Now we convert 0.75 into fraction form

Multiply top and bottom by 100 to remove decimal

so 0.75 is 3/4
a= 2/3 and b = 3/4


Answer:
log_4(256)=4
log_4(1/1024)=-5
log_4(16)=2
log_4(1/256)=-4
Step-by-step explanation:
We want to write a number, x, such that
Log_4(y)=x.
In exponential form that is 4^x=y.
So first number is x=4.
4^4=256 which means log_4(256) is 4 as a logarithm with base 4.
The second number is x=-5.
4^-5=1/4^5=1/1024 which means log_4(1/1024) is -5 as a logarithm with base 4.
The third number is x=2.
4^2=16 so log_4(16) is 2 as a logarithm with base 4.
The fourth number is x=-4.
Since 4^4=256 then 4^-4=1/256 which means -4 as a logarithm with base 4 is log_4(1/256).
Answer:
The simplified expressions are (<em>x</em> + <em>y·</em>z' + <em>t</em>) and <em>x·</em>(<em>x</em> + <em>y</em>' + <em>z</em>) respectively.
Step-by-step explanation:
The expressions provided are:

(i)
Simplify the first expression with as few symbols as possible:


(ii)
Simplify the second expression with as few symbols as possible:


Thus, the simplified expressions are (<em>x</em> + <em>y·</em>z' + <em>t</em>) and <em>x·</em>(<em>x</em> + <em>y</em>' + <em>z</em>) respectively.