Recall that
![\cos(90-x)^\circ=\sin x^\circ](https://tex.z-dn.net/?f=%5Ccos%2890-x%29%5E%5Ccirc%3D%5Csin%20x%5E%5Ccirc)
which tells you that
![\cos40^\circ=\cos(90-50)^\circ=\sin50^\circ](https://tex.z-dn.net/?f=%5Ccos40%5E%5Ccirc%3D%5Ccos%2890-50%29%5E%5Ccirc%3D%5Csin50%5E%5Ccirc)
, so in fact
![\cos40^\circ=\sin50^\circ=\dfrac{10}{15}](https://tex.z-dn.net/?f=%5Ccos40%5E%5Ccirc%3D%5Csin50%5E%5Ccirc%3D%5Cdfrac%7B10%7D%7B15%7D)
Attached is an image demonstrating why the identity is true.
Answer:
C
Step-by-step explanation:
Given
(3x² + 5x - 8) + (5x² - 13x - 5) ← remove the parenthesis
= 3x² + 5x - 8 + 5x² - 13x - 5 ← collect like terms
= 8x² - 8x - 13 → C
Answer:
ABC ~ EDF
Step-by-step explanation:
By the order of the letters, we can determine which triangles are similar.
We know that Angle D is congruent to Angle B. So we have to look for a set of triangles where D and B have the same place holders.
For example, if D is the first letter, then B also has to be the first letter.
The same thing applies for Angle E, and Angle A, since they are congruent to each other.
Wherever Angle E is, Angle A has to be in that same place holder.
Triangle ABC, has Angle B, as the second angle. Therefore we know the similar triangle has to be _D_.
Similarly, Angle A is congruent to Angle E, so we know that Angle E has to be in the first place holder. ED_
By process of elimination we know that the only corresponding angles left are C and F, they must be congruent. So the last thing to write is F.
Triangle ABC ~ Triangle EDF
Given:
Let the cost of chocolate bar be 'x'.
![\text{Cost of Peanut butter bar=x+0.07}](https://tex.z-dn.net/?f=%5Ctext%7BCost%20of%20Peanut%20butter%20bar%3Dx%2B0.07%7D)
![\begin{gathered} 5(x+0.07)+6(x)=6.40 \\ 5x+0.35+6x=\text{6}.40 \\ 11x=6.40-0.35 \\ x=\frac{6.05}{11} \\ x=0.55 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%205%28x%2B0.07%29%2B6%28x%29%3D6.40%20%5C%5C%205x%2B0.35%2B6x%3D%5Ctext%7B6%7D.40%20%5C%5C%2011x%3D6.40-0.35%20%5C%5C%20x%3D%5Cfrac%7B6.05%7D%7B11%7D%20%5C%5C%20x%3D0.55%20%5Cend%7Bgathered%7D)
Cost of chocolate bar is $0.55
To answer this question you will need to calculate the amount of interest he earns in a year, apply the discount on the sale price, and calculate the sales tax on the discounted price. Then you will take the amount in his bank account minus the sale price with tax.
Each of the steps is shown in the attached work.
He will have $111 left is his account.