Answer: B) y=1/4x+7/2
Step 1: Slope
Knowing that the equation will be perpendicular to the one given will only give us the slope. Perpendicular means that the slope will be opposite to what it is now.
The opposite of -4 (the current slope) is 1/4. Even knowing only this will tell us that the answer is b, but I will continue to explain for when no options are given.
Step 2: Y-intercept
Now that we know the slope, the perpendicular aspect of this equation will no longer be of any help.
To find the y-intercept, we need to substitute y and x with the point given.
Our current equation is— y= 1/4x+b
Let’s substitute the point into this. The point (-2,3) tells us that the y-value is 3 and the x-value is -2.
y= 1/4x+ b
3=1/4(-2)+b
3 = -1/2 +b
+1/2 +1/2
__________
3 1/2 =b
Step 3: Improper fraction
Being that it is preferred to leave fractions improper, let’s turn 3 1/2 into an improper fraction. This will turn into 7/2 (comment below if you need an explanation of how to do this)
Final answer: now that we know that the slope is 1/4 and the y-intercept is 7/2, we know that our equation will be y=1/4x+7/2
Hope this helps comment below for more questions:)
According to the characteristics of <em>ticket</em> sales and the resulting system of linear equations we find that 122 children bought each one a ticket on Sunday.
<h3>How many children went to the movie theatre?</h3>
In this question we have a <em>word</em> problem, whose information must be translated into <em>algebraic</em> expressions to find a solution. Let be x and y the number of children and adults that went to the movie theatre, respectively.
We need two <em>linear</em> equations, one for the number of people assisting to the theatre and another for the total sales:
x - 4 · y = 0 (1)
6.30 · x + 9.50 · y = 1063.20 (2)
By algebraic procedures the solution to this system is: x = 122.559, y = 30.639. Since the number of tickets sold are integers, then we truncate each result: x = 122, y = 30.
According to the characteristics of <em>ticket</em> sales and the resulting system of linear equations we find that 122 children bought each one a ticket on Sunday.
To learn on systems of linear equations: brainly.com/question/27664510
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F(x) = 2(x)^2 + 5 * sqrt(x + 2)
f(2) = 2(2)^2 + 5 * sqrt(2 + 2)
f(2) = 2 * 4 + 5 * sqrt(4)
f(2) = 8 + 5 * 2
f(2) = 8 + 10
f(2) = 18
Use the distance formula
d = sqrt ((y2-y1)^2 + (x2-x1)^2))
= sqrt ( (5 sqrt2 - sqrt2)^2 + ( -3sqrt5 - sqrt5)^2)
= sqrt [( 4sqrt2)^2 + (4sqrt5)^2]
= sqrt (32 + 16*5) = sqrt 112 = sqrt16 * sqrt7 = 4 sqrt7
The answer is 4 sqrt7
Cos A cos B + sin A sin B