By using trigonometric relations, we will see that:
AC = 15.6 in
AB = 8.4 in.
<h3>
How to get the measures of the other two sides of the right triangle?</h3>
Here we have the right triangle where:
B = 90°
C = 40°
BC = 10 in.
Notice that is the adjacent cathetus to the angle C, then we can use the two relations:
- sin(a) = (adjacent cathetus)/(hypotenuse).
- tan(a) = (opposite cathetus)/(adjacent cathetus).
Where:
- hypotenuse = AC
- opposite cathetus = AB.
Then we will have:
sin(40°) = 10in/AC.
AC = 10in/sin(40°) = 15.6 in
tan(40°) = AB/10in
tan(40°)*10in = AB = 8.4 in.
So we can conclude that for the given right triangle we have:
AC = 15.6 in
AB = 8.4 in.
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Answer:
B (3, 13.5)
Step-by-step explanation:
Using point (0,0) and (15, 67.5) we can find the slope(gradient).
(y - y¹) / (x - x¹) = (67.5 - 0) / (15 - 0)
= 67.5 / 15 = 4.5
slope = 4.5
using the point given in option A (0, 4.5) with point (15, 67.5) to calculate the slope it gives 4.2 which is not equal to what we calculated.
using the option B (3, 13.5) with (15, 67.5) gives a slope of 4.5 which is equal to the slope of the line.
Cramer's rule works as follows:
x+3y=16
3x+y=8
Then
x=Dx/D
y=Dy/D
where Dx,Dy,D are 2x2 matrices formed from of coefficients and right hand side.
D=
1 3
3 1
=1-9=-8
Dx=matrix D with first column replaced by the vector [16,8]=
16,3
8 1
=16-24
=-8
Dy=matrix D with second column replaced by the vector [16,8]=
1 16
3 8
=8-48
=-40
Therefore
x=-8/-8=1
y=--40/-8=5
Check:
x+3y=1+3(5)=16
3x+y=3(1)+5=8 ok.
The completely factored expression of 2x^2 + 4x + 3xy + 6y is (2x + 3y)(x + 2)
<h3>How to factor the polynomial?</h3>
The expression is given as:
2x^2 + 4x + 3xy + 6y
Group the expression into two
[2x^2 + 4x] + [3xy + 6y]
Factor out each group
2x(x + 2) + 3y(x + 2)
Factor out x + 2
(2x + 3y)(x + 2)
Hence, the completely factored expression of 2x^2 + 4x + 3xy + 6y is (2x + 3y)(x + 2)
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Odd integers would include: -1, 1, and 3.
