Answer:
C. 60 degrees.
Step-by-step explanation:
Sin theta = opposite / hypotenuse
= 3 sqrt3 / 6
= sqrt3 / 2.
So theta = arcsin (sqrt3/2)
= 60 degrees.
Remember: Please Excuse My Dear Aunt Sally (PEMDAS)
In solving algebraic expressions, there is an order in which to solve it.
<span>1) perform the operation inside the </span>parenthesis<span> first </span>
<span>2) then perform the operation with the </span>exponents
<span>3) apply </span>multiplication<span> and </span>division<span> from left to right of the equation.</span>
<span>4) apply </span>addition<span> and </span>subtraction<span> from left to right of the equation.</span>
Answer:
C
Step-by-step explanation:
The picture
Answer: the area of the shaded region is 5x² + 28x + 23
Step-by-step explanation:
The formula for determining the area of the rectangle is expressed as
Area = length × width
The area of the smaller rectangle is
(x - 3)(x - 1)
We would apply the distributive property by multiplying each term in one bracket by each term in the other bracket. It becomes
x² - x - 3x + 1
x² - 4x + 1
The area of the bigger rectangle is
(3x + 6)(2x + 4)
6x² + 12x + 12x + 24
6x² + 24x + 24
The area of the shaded region would be
6x² + 24x + 24 - (x² - 4x + 1)
6x² + 24x + 24 - x² + 4x - 1
6x² - x² + 24x + 4x + 24 - 1
5x² + 28x + 23
Answer:
He bought 544 oranges and 1,360 apples
Step-by-step explanation:
Here, we want to know the number of oranges and apples bought
Let the number of oranges be x and the number of apples be y
Looking at their ratios;
x:y = 2:5
so;
x/y = 2/5
2y = 5x ••••••(i)
Now, he lost 3/4 of the apples ( by giving out)
What would be left with him is (1-3/4) = 1/4 * y = 0.25y
What is left with him out if the oranges will be; x-34
So now;
0.25y/x-34 = 2/3
3(0.25y) = 2(x-34) •••••••(ii)
From i, y = 5x/2 = 2.5x
Putting this into ii above, we have
3(0.25)(2.5x) = 2x - 68
1.875x = 2x-68
2x-1.875x = 68
0.125x = 68
x = 68/0.125
x = 544
But y = 2.5x
y = 2.5 * 544 = 1,360