Answer:
C
Step-by-step explanation:
Add 10x to both sides:
-10x - 135 = 117 + 2x
-10x - 135 + 10x = 117 + 2x + 10x
-135 = 117 + 12x
Subtract 117 from both sides:
-135 - 117 = 117 + 12x - 117
-252 = 12x
Divide both sides by 12:
-21 = x
So the answer is C.
Hope this helps!
36x² - 100 = 4(9x²-25) = 4(3x+5)(3x-5)
B. 4(3x+5)(3x-5)
Step-by-step explanation:
Let's represent the number of mochas bought with the variable , and the number of lattes bought with the variable .
Since there are students, the total number of mochas and lattes bought must be . This can be represented with the following equation:
We can also set up another equation based on the total amount spent on the coffe:
If we rearrange the first equation, we can solve for :
If we substitute this into the second equation, we can solve for :
Subtituting this back into the original equation, we can solve for :
Therefore, 9 mochas and 14 lattes were bought.
Multiplying fractions is just multiplying the numerators together and the denominators together.
To find out which one is bigger, we need a common denominator. The LCM of 7 and 21 is 21, so convert the first fraction into a denominator of 21. 7 goes into 21 three times, multiply this to the numerator and denominator:
Now just compare the numerators to see which one is bigger.
therefore,
The correct answer is
the flagpole is <span>
33 feet high</span>.
Explanation:
Please refer to the attached picture.
We know:
CD = 40 feet
AC = 5 feet
∠BDC = α = 35°
Using trigonometry, we know that the definition of the tangent of an angle is the ratio between the opposite side and the adjacent side, therefore:
tan α = BC / CD
Solving for BC:
BC = CD · <span>tan α
= 40 </span>· tan (35)
= 28 feet
In order to find the height of the flagpole, we need to add the distance of the clinometer from the ground:
AB = BC + AC
= 28 + 5
= 33
Hence, the flagpole is
33 feet high.