Perpendicular means the two lines' slopes are negative reciprocal to each other. the slope of the given line is 1/3, therefore the slope of the perpendicular line is -3/1, which is -3
use the point-slope form: the given point is (4,1), so (y-1)=-3(x-4)
you can stop right here or you can write it into slope intercept form:
y-1=-3x+12
y=-3x+13
The distance between the two adjacent gas stations will be 5 miles.
<h3>What is the difference between a ratio and a proportion?</h3>
A ratio is an ordered pair of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two ratios are specified to be equal.
Distance between city airport and the train station = 45 miles
Stations equally spaced between the airport and train station=9
Let the space between two gas stations will be x;
x = 45/9
x=5 mile.
Hence, the distance between the two adjacent gas stations will be 5 miles.
To learn more about the ratio, refer to the link;
brainly.com/question/14335762
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Answer:
D) 4
Step-by-step explanation:
−9 + 12 + (unknown) + −8 = −1
<em>Start by going through and testing each option</em>
−9 + 12 + 2 + −8 =
3 + 2 + −8 =
5 + −8 =
−3
−3 ≠ −1
<em>A) 2 is not possible.</em>
−9 + 12 + −2 + −8 =
3 + −2 + −8 =
1 + −8 =
−7
−7 ≠ −1
<em>B) </em>−<em>2 is not possible.</em>
−9 + 12 + −4 + −8 =
3 + −4 + −8 =
−1 + −8 =
−9
−9 ≠ −1
<em>C) </em>−4<em> is not possible.</em>
<em>From this, D is looking like the answer. But to be sure, test it.</em>
−9 + 12 + 4 + −8 =
3 + 4 + −8 =
7 + −8 =
−1
−1 = −1
<em>D) 4 is the answer.</em>
Answer:
Step-by-step explanation:
Both expressions are examples of the <em>distributive property</em>, which basically says "if I have <em>this </em>many groups of some size and <em>that</em> many groups of the same size, I've got <em>this </em>+ <em>that</em> groups of that size altogether."
To give an example, if I've got <em>3 groups of 5 </em>and <em>2 groups of 5</em>, I've got 3 + 2 = <em>5 groups of 5 </em>in total. I've attached a visual from Math with Bad Drawings to illustrate this idea.
Mathematically, we'd capture that last example with the equation
. We can also read that in reverse: 3 + 2 groups of 5 is the same as adding together 3 groups of 5 and 2 groups of 5; both directions get us 8 groups of 5. We can use this fact to rewrite the first expression like this: 
.
This idea extends to subtraction too: If we have 3 groups of 4 and we take away 1 group of 4, we'd expect to be left with 3 - 1 = 2 groups of 4, or in symbols: 
. When we start with two numbers like 15 and 10, our first question should be if we can split them up into groups of the same size. Obviously, you could make 15 groups of 1 and 10 groups of 1, but 15 is also the same as <em>3 groups of 5</em> and 10 is the same as <em>2 groups of 5</em>. Using the distributive property, we could write this as 
, so we can say that 
.
Answer:
40
Step-by-step explanation:
Plug in 12 for u, 7 for x, and 4 for y in the given expression:
u + xy = 12 + (7)(4)
Remember to follow PEMDAS. First, multiply, and then add:
u + xy = 12 + (7 * 4) = 12 + (28) = 40
40 is your answer.
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