A) Height -7 = base
B) .5 * height * base = 60
Substituting A into B
B) .5 * height * (height -7) = 60
B) .5*height^2 -3.5*height = 60
B) .5*height^2 -3.5*height -60 = 0
Using the quadratic formula:
Height = 15
Subtracting 7 gives us the base length
Base = 8
**************************************************************
Double-Check
.5 * 15 * 8 = 60
Answer:

Step-by-step explanation:
We can use exponent rules to try and simplify this expression down.
Exponent rules tell us that
.
This means that since we have the same base on both terms (7 and 7), we can add the exponents to get a simplified expression.

So our simplified expression is
.
Hope this helped!
sin2x =12/13
cos2x = 5/13
tan2x = 12/5
STEP - BY - STEP EXPLANATION
What to find?
• sin2x
,
• cos2x
,
• tan2x
Given:
tanx = 2/3 = opposite / adjacent
We need to first make a sketch of the given problem.
Let h be the hypotenuse.
We need to find sinx and cos x, but to find sinx and cosx, first determine the value of h.
Using the Pythagoras theorem;
hypotenuse² = opposite² + adjacent²
h² = 2² + 3²
h² = 4 + 9
h² =13
Take the square root of both-side of the equation.
h =√13
This implies that hypotenuse = √13
We can now proceed to find the values of ainx and cosx.
Using the trigonometric ratio;
![\sin x=\frac{opposite}{\text{hypotenuse}}=\frac{2}{\sqrt[]{13}}](https://tex.z-dn.net/?f=%5Csin%20x%3D%5Cfrac%7Bopposite%7D%7B%5Ctext%7Bhypotenuse%7D%7D%3D%5Cfrac%7B2%7D%7B%5Csqrt%5B%5D%7B13%7D%7D)
![\cos x=\frac{adjacent}{\text{hypotenuse}}=\frac{3}{\sqrt[]{13}}](https://tex.z-dn.net/?f=%5Ccos%20x%3D%5Cfrac%7Badjacent%7D%7B%5Ctext%7Bhypotenuse%7D%7D%3D%5Cfrac%7B3%7D%7B%5Csqrt%5B%5D%7B13%7D%7D)
And we know that tanx =2/3
From the trigonometric identity;
sin 2x = 2sinxcosx
Substitute the value of sinx , cosx and then simplify.
![\sin 2x=2(\frac{2}{\sqrt[]{13}})(\frac{3}{\sqrt[]{13}})](https://tex.z-dn.net/?f=%5Csin%202x%3D2%28%5Cfrac%7B2%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%29%28%5Cfrac%7B3%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%29)

Hence, sin2x = 12/13
cos2x = cos²x - sin²x
Substitute the value of cosx, sinx and simplify.
![\begin{gathered} \cos 2x=(\frac{3}{\sqrt[]{13}})^2-(\frac{2}{\sqrt[]{13}})^2 \\ \\ =\frac{9}{13}-\frac{4}{13} \\ =\frac{5}{13} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ccos%202x%3D%28%5Cfrac%7B3%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%29%5E2-%28%5Cfrac%7B2%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%29%5E2%20%5C%5C%20%20%5C%5C%20%3D%5Cfrac%7B9%7D%7B13%7D-%5Cfrac%7B4%7D%7B13%7D%20%5C%5C%20%3D%5Cfrac%7B5%7D%7B13%7D%20%5Cend%7Bgathered%7D)
Hence, cos2x = 5/13
tan2x = 2tanx / 1- tan²x






OR

Hence, tan2x = 12/5
Therefore,
sin2x =12/13
cos2x = 5/13
tan2x = 12/5
The answer is b hope it helped
Answer:
It would take 5.5 months for the two cable companies to cost the same.
Step-by-step explanation:
50x + 100 = 60x + 45
-45 -45
50x + 55 = 60x
-50x -50x
55 = 10x
/10 /10
x = 5.5