By hypothesis, the price of the shoes is represented by x, and the price of the hat is represented by y.
"Devin spent a total of $64 dollars for shoes and a hat" can be represented by the equation x + y = 64
"The shoes cost $6 more than the hat" can be represented by the equation x=y+6
We can now create a system:
x + y = 64 (1)
x = y + 6 (2)
Let's use the value of x from equation 2 and replace in equation (1):
x + y = 64
y + 6 + y = 64
2y + 6 = 64
Subtract 6 from each side to have the variables on a side and the numbers on the other:
2y + 6 = 64
2y + 6 - 6 = 64 - 6
2y = 58
Then divide both sides by 2 to have the variable y alone on the first side and its value on the other side:
(2y)/2 = 58/2
y = 29
We found the value of y.
Now let's use the value of y in equation (1), in order to find the value of x:
x = y + 6
x = 29 + 6
x = 35
We found the value of x.
So the price of the shoes is x = $35 and the price of the hat is y = $29.
You can recheck your answer (very important):
x + y = 29 + 35 = 64 (David spent a total of $64 dollars for shoes and a hat)
y + 6 = 29 + 6 = 35 = x (The shoes cost $6 more than the hat)
Hope this Helps! :)
Answer:
1/4
Step-by-step explanation:
The slope of a line is the steepness of a line.
The slope of a perpendicular line is always the negative reciprocal of the slope of the line it is perpendicular with.
Since line C has a slope of -4, the negative reciprocal of that is 1/4.
Reciprocals are two numbers that multiply together to get 1.
For example, -1/4*-4/1=1
Therefore the negative recipricol is 1/4
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Hello!
A city council member wanted to know how her constituents felt about a planned rezoning. She randomly selected 75 names from the city phone directory and conducted a phone survey.
Identify the population and sample in this setting.
The population of interest is confirmed by all the individuals or experimental units that the researcher wants to study. The sample is normally a portion of the population randomly selected and representative of it. Since in most cases it is impossible to study the whole population the sample is taken. Then after the experiment is conducted, the conclusions reached are extrapolated to the whole population.
Normally is easier to identify the sample first and then the population, in this example, the sample is "75 names from the city phone directory" then the population will be "people registered in the city phone directory"
The correct option is the first one.
> The population is everyone listed in the city phone directory; the sample is the 75 people selected. CORRECT
> The population is residents of the city; the sample is the registered voters in the city. INCORRECT
> The population is registered voters in the city; the sample is everyone listed in the city phone directory. INCORRECT
I hope this helps!
Answer:
62.8319 ≈ 62.8 inches
Step-by-step explanation:
