Answer:
6. E
7. D
8. 5,-8,34
Step-by-step explanation:
A. Parallel to the y-axis and passes through the point (3,5)
For it to be parallel to the y-axis, what this means is that it has an x-intercept and no y intercept.
So what this means is that x = 3 is our line so E is correct
B. Perpendicular to the y-axis means it is parallel to the x-axis
It means is has no x intercept and thus its x value at any point in time is zero
So the equation is y = -5
or simply y + 5 = 0 which means D is correct
C. It is parallel to the line 5x -8y + 12 = 0
Thus: 8y = 5x + 12
dividing both sides by 8
y = 5x/8 + 12/8
y = 5x/8 + 3/2
y = 5x/8 + 1.5
Comparing this with the general equation of a straight line ;
y = mx + c
where m is that slope, this means that 5/8 is the slope of the line
Mathematically if two lines are parallel, they have equal slopes.
So we can say the slope of the other line too is 5/8
Now to find the equation of the other line, we can use the point-slope method
y-y1 = m(x-x1)
where (x1,y1) in this case is (-2,3)
So we have;
y-3 = m(x-(-2))
y-3 = 5/8 (x + 2)
8(y-3) = 5(x + 2)
8y -24 = 5x + 10
5x + 10 + 24 -8y = 0
5x -8y + 34 = 0
So A, B, C = 5, -8, 34
Answer:
Only one says the mean s higher than the median, so choose that one.
Step-by-step explanation:
Putting them in order gets yout he following list
$99,000
$106,000
$122,000
$124,000
$130,000
$131,000
$114,000
$497,000
$450,000
The average changes if you increase or decrease any of the prices, thought he median does not unless you mess witht he middle value 130,000. Since it mentions the outliers lets look at those. The outliers are the last two because they are more than 3 times the next highest. So, increasing or decreasing these will effet the average in the same way. Also, keep in mind what the median is, and if the verage as is is higher or lower than it., that pretty much answers your question.
<h3>
Answer: Largest value is a = 9</h3>
===================================================
Work Shown:
b = 5
(2b)^2 = (2*5)^2 = 100
So we want the expression a^2+3b to be less than (2b)^2 = 100
We need to solve a^2 + 3b < 100 which turns into
a^2 + 3b < 100
a^2 + 3(5) < 100
a^2 + 15 < 100
after substituting in b = 5.
------------------
Let's isolate 'a'
a^2 + 15 < 100
a^2 < 100-15
a^2 < 85
a < sqrt(85)
a < 9.2195
'a' is an integer, so we round down to the nearest whole number to get 
So the greatest integer possible for 'a' is a = 9.
------------------
Check:
plug in a = 9 and b = 5
a^2 + 3b < 100
9^2 + 3(5) < 100
81 + 15 < 100
96 < 100 .... true statement
now try a = 10 and b = 5
a^2 + 3b < 100
10^2 + 3(5) < 100
100 + 15 < 100 ... you can probably already see the issue
115 < 100 ... this is false, so a = 10 doesn't work
Answer:
54.2 mph
Step-by-step explanation:
Since the drivers leave at the same time and travel in directions 90° from each other, their separation speed can be found using the Pythagorean theorem. Let c represent Cynthia's average speed. Then (c-10) will represent Tim's average speed. Their combined separation speed is 70 miles per hour, so we can write ...
70² = c² +(c -10)²
4900 = 2c² -20c +100 . . . . eliminate parentheses
c² -10c -2400 = 0 . . . . . . . . divide by 2; put in standard form
(c -5)² -2425 = 0 . . . . . . . . . rearrange to vertex form
c = 5 ±5√97 . . . . . . . . . . . . solve for c, simplify radical
c ≈ 54.244 ≈ 54.2 . . . . . . . use the positive solution
Cynthia's average speed was 54.2 miles per hour.
Set each expression from the parentheses equal to 0 separately like so:
Equation 1: x - 4 = 0
Equation 2: -5x + 1 = 0
Now for each equation solve for x!
Equation 1:
x +(- 4 + 4) = 0 + 4
x = 4
Equation 2:
-5x +( 1-1) = 0 - 1
-5x/ -5 = -1 / -5
x = 1/5
Check:
(4 - 4)(-5*4 + 1)
(0) (-20 + 1)
(0) (-19)
0 = 0 -------------------------> correct!
(1/5 - 4)(-5 * 1/5 + 1)
(-19/5)(-1 + 1)
(-19/5)(0)
0 = 0 -------------------------> correct!
smaller x = 1/5
larger x = 4
Hope this helped!
