Answer:
x = 2√3 ≈ 3.464
Step-by-step explanation:
The side marked x is opposite the given 30° angle. The side marked 6 is adjacent to that angle. The trig function relating opposite and adjacent sides of a right triangle is ...
Tan = Opposite/Adjacent
Filling in values, we have ...
tan(30°) = x/6
Multiplying by 6 gives ...
x = 6tan(30°) = 6(√3/3)
x = 2√3 ≈ 3.464
Answer:
Each girl earned 2 points
Each boy earned 5 points
Step-by-step explanation:
Let x represent the number of points one girl earned
Let y represent the number of points one boy earned
4x + 2y = 28
4x - 2y = 12
8y = 40
y = 5 points
4x + (2)(5) = 28
4x + 20 = 28
4x = 8
x = 2 points
Each girl earned 2 points
Each boy earned 5 points
Tiffany Baldwin's pre-tax deductions are the parts of her salary that
she does not have to pay income tax on. Those include the parts of her
salary that already go to taxes, which are her federal income tax, state
income tax, and her FICA (Social Security and Medicare) taxes. Those
taxes are $25 + $11 + ($800 x .0765) = $97.20. Baldwin's other pre-tax
deduction is her contribution to her 401K retirement account, which is
$800 x .02 = $16. So, her total pre-tax deductions for a week are $97.20
+ $16 = $113.20. The amount she has taken out for her gym membership is
"post-tax", meaning she still has to pay income tax on that $20 every
week, so this is not included.
We can Notice that the Angles in the Given Triangle ABC are Equal
The Given Triangle ABC is an Equilateral Triangle
We know that an Equilateral Triangle has Equal Sides
let us take any two sides
AC = BC
4x - 30 = 2x + 20
2x = 50
x = 25
<u>Verification :</u>
we got x = 25
AC = 4x - 30 = 4(25) - 30 = 100 - 30 = 70
BC = 2x + 20 = 2(25) + 20 = 50 + 20 = 70
AB = 3x - 5 = 3(25) - 5 = 75 - 5 = 70
We Got All sides Equal to 70
So, x = 25 is correct value
First you eliminate the 2y and -2y since they cancel each other out then you add the 6x+5x and 14+8, then you are left with 11x=22, then divide both sides by 11 leaving you with x=11, hope this helps!