Answer:
Question 1: y = 3/4x + 1/4.
Question 2: y = 6/5x + 7/5.
Step-by-step explanation:
Question 1: A line perpendicular to another line would have a slope that is the negative reciprocal of the other line. If the slope of the first line is -4/3, the slope of a line perpendicular to the first would have a slope of 3/4.
Since the line goes through (5, 4), we can just put the points into the equation, y = 3/4x + b.
4 = 3/4(5) + b
b + 15/4 = 4
b = 16/4 - 15/4
b = 1/4
So, the equation of the line is y = 3/4x + 1/4.
Question 2: 5x + 6y = -6
6y = -5x - 6
y = -5/6x - 1
As stated before, a line perpendicular to another will have a slope that is the negative reciprocal of the other. So, the slope of the other line is 6/5.
The line goes through (-2, -1), so we can put the points into the equation, y = 6/5x + b.
-1 = 6/5(-2) + b
b - 12/5 = -5/5
b = -5/5 + 12/5
b = 7/5
So, the equation of the line is y = 6/5x + 7/5.
Hope this helps!
Let the function be (3x+15)/(6-x) then the value of x exists at -5.
<h3>
What i
s the value of x?</h3>
Given: Rational Expression (3x+15)/(6-x)
To find the value of x when given a rational expression equivalent to 0.
To estimate the value of x, convey the variable to the left side and convey all the remaining values to the right side. Simplify the values to estimate the result.
Consider, (3x+15)/(6-x) = 0
3x + 15 = 0(6-x)
3x + 15 = 0
Subtract 15 from both sides of the equation, e get
3x + 15 - 15 = 0 - 15
simplifying the above equation, we get
3x = 0 - 15
3x = -15
Divide both sides by 3, then we get
x/3 = -15/3
x = -5
Therefore, the value of x exists at -5.
To learn more about the value of x refer to: brainly.com/question/11874663
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You can use this formula of arthenatic series to find sum to get the number of term
sum= n÷2 (2a+(n - 1)d)
n= number of tern = n
a= first term =
d= common difference
sum= 1113
you can find the number of series by putting in them
Since we know that <C is congruent to <E, we can say that: A. the two triangles are similar by SAS.
<h3>The properties of similar triangles.</h3>
In Geometry, two triangles are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.
Ratio = BC/AC = 6/3 = 2.
Ratio = FE/DE = 4/2 = 2.
Thus, the ratio of their corresponding sides are equal in magnitude i.e BC/AC ≡ FE/DE.
Since we know that <C is congruent to <E, we can say that the two triangles are similar by side, angle, side (SAS) criterion.
Read more on congruency here: brainly.com/question/11844452
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Answer:
6 units
Step-by-step explanation:
Remember the formula for the area of a rectangle: A = lw
What we know:
A=48
w = l-2
Substitute A for 48 and w for l-2 into the equation
A = lw
48 = l(l-2) Use the distributive property. Multiply over the brackets.
48 = l² - 2l
Rearrange the equation to standard form (0 = ax² + bx + c) to use quadratic formula.
0 = l² - 2l - 48
a = 1 ; b = -2 ; c = -48 State the variables for the quadratic formula
Substitute a, b and c to find the length:

Simplify


Split the equation at the ± for adding and subtracting. Then decide which answer is correct, or if both of them are possible answers.


This is "inadmissable", or impossible because the length can't be a negative value.


Length of the rectangle
Use the formula for the area of a rectangle
Substitute the length and area, then isolate "w" for the width
A = lw
48 = (8)w
48/8 = w
w = 6
Therefore the length of the rectangle is 6 units.