Answer:
7. parallel: k = 3
perpendicular: k = -4/3
8. $1300
Step-by-step explanation:
7.
Rewrite each equation as the slope-intercept form of a linear equation:
y = mx + b (where m is the slope and b is the y-intercept)
8y = 12x + 6
⇒
4y = k(2x + 10)
⇒ 4y = 2kx + 10k
⇒
If the graphs are parallel their slopes will be the same.
If the graphs are perpendicular then the product of their slopes will be -1.
8. Create a linear equation, where x is the number of coffee mugs and y is the total cost (in dollars).
Choose 2 ordered pairs from the table: (10, 110) and (20, 195)
Let = (10, 110)
Let = (20, 195)
Use the slope formula to find the slope m:
Now use the point-slope form of linear equation:
Substitute x = 150 into the equation and solve for y:
Therefore, the total cost of ordereing 150 mugs is $1300
Radical 64 is the same as saying the sqrt(64)
The answer is 8
Answer:
Step-by-step explanation:
Let the hypotenuse of the smaller triangle be h units.
Then; from the Pythagoras Theorem.
From the smaller triangle;
and
From the second triangle, let the other other shorter leg of the second triangle be s units.
Then;
and
We now use the double angle property;
we plug in the values to obtain;
To find the median, order the numbers in the data set from least to greatest (or greatest to least, either one works) and then find the number in the middle. If there are 2 numbers in the middle, find their mean.
Step 1: Ordering the numbers.
<span>Original: 100, 88, 76, 78, 92, 94, 84, 98, 82, 90
Ordered: </span>76, 78, 82, 84, 88, 90, 92, 94, 98, 100
Step 2: Find the median (middle number).
The median is the number in the center.
Count in from each side equally to find the middle number.
76, 78, 82, 84, 88, 90, 92, 94, 98, <span>100
</span>78, 82, 84, 88, 90, 92, 94, 98
82, 84, 88, 90, 92, 94
84, 88, 90, 92
88, 90
88 and 90 are the middle numbers.
Since there are 2 numbers in the middle, we must find their mean.
Step 3: Find the mean of the 2 middle numbers.
Mean is also known as average.
To find this, add up the numbers and then divide by the amount of numbers there are.
In this case, that means adding 88 and 90 then dividing their sum by 2.
This can be represented by the equation (88 + 90) ÷ 2.
88 + 90 = 178
178 ÷ 2 = 89
89 is the final answer, it is the median.
Answer:
The median of this data set is 89.
Hope this helps!