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Arada [10]
3 years ago
10

Which of the following equations represents a line that is perpendicular to y = -4x + 9 and passes through the point, (4, 5)?

Mathematics
1 answer:
AURORKA [14]3 years ago
7 0
Perpendicular lines refers to a pair of straight lines that intercept each other. The slopes of this lines are opposite reciprocal, meaning that it's multiplication is equal to -1.

In this exercise is given the equation of a line and a point, and is asked to find the equation of the line that is perpendicular to the given one, and that passes through the given point.

The slope of the given line is -4, which means that the slope of a line perpendicular to this one, needs to be 1/4. Now you need to find the value of b or the y-intercept by substituting the given point into the formula y=mx+b, where letter m represents the slope.

y=mx+b                Substitute the values of the given point and slope
5=1/4(4)+b           Combine like terms
5=1+b                  Subtract 1 in both sides to isolate b
4=b

The equation of the line perpendicular to y=-4x+9 and that passes through the point (4,5) is y=1/4+4.




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A person stands 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 meters
In-s [12.5K]

Answer:

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

Step-by-step explanation:

Given that,

A person stand 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 m/s.

From Pythagorean Theorem,

(The distance between car and person)²= (The distance of the car from intersection)²+ (The distance of the person from intersection)²+

Assume that the distance of the car from the intersection and from the person be x and y at any time t respectively.

∴y²= x²+10²

\Rightarrow y=\sqrt{x^2+100}

Differentiating with respect to t

\frac{dy}{dt}=\frac{1}{2\sqrt{x^2+100}}. 2x\frac{dx}{dt}

\Rightarrow \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}. \frac{dx}{dt}

Since the car driving towards the intersection at 13 m/s.

so,\frac{dx}{dt}=-13

\therefore \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}.(-13)

Now

\therefore \frac{dy}{dt}|_{x=24}=\frac{24}{\sqrt{24^2+100}}.(-13)

               =\frac{24\times (-13)}{\sqrt{676}}

               =\frac{24\times (-13)}{26}

               = -12 m/s

Negative sign denotes the distance between the car and the person decrease.

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

8 0
2 years ago
Which pairs of angles in the figure below are vertical angles?
makvit [3.9K]

Answer:

thew answer is A DTN AND ATP

Step-by-step explanation:

its the correct answer and most reasonable

6 0
2 years ago
Read 2 more answers
If c = 4, evaluate the following expression: <br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7Bc%7D%20" id="TexFormula1" title=
mash [69]

Answer:

2 is the answer

Step-by-step

6 0
2 years ago
Part I: Describe the center and radius of the circle.
trasher [3.6K]

Answer:

Center (2,4) , radius=3, h=2 v=4 & r=3

Step-by-step explanation:

Ok so in order to find the center of the circle, use the graph (like you can see that the x is 2,if you count down from 5 to the left. the y is 4,because it's below 5 in the y pole).So the center is (2,4)

Now, in order to find the length of the radius, you need to do the following:

Take the center point (2,4) and the point where the circle ends (2,1) . Because radius is a straight, you can substract the y values of the two points : 4-1=3

As you can see in the equation, the h symbolizes the x of the center point and the v symbolizes the y.The r is the radius that we already found(3)

So it's shouldn't be a problem now to find the equation of the circle,simply replace the values with their numbers:

(x-2)^2 + (y-4)^2 = 9

4 0
3 years ago
Evaluate 90 divided by X to the second power + y
Arlecino [84]

Answer:  =34

=3⋅3⋅3⋅3

=81

For example, 3 to the power of -4:

=3−4

=134

=13⋅3⋅3⋅3

=181

=0.012346

Step-by-step explanation: the solution is expanded when the base x and exponent n are small enough to fit on the screen. Generally, this feature is available when base x is a positive or negative single digit integer raised to the power of a positive or negative single digit integer. Also, when base x is a positive or negative two digit integer raised to the power of a positive or

negative single digit integer less than 7 and greater than -7.

hopefully this is right :/

4 0
3 years ago
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