Answer:
C
Step-by-step explanation:
Note that <em>x</em> is opposite to the given angle and we are also given the hypotenuse.
Since we have an angle and the side opposite to it and the hypotenuse, we can use the sine ratio. Recall that:
The opposite side is <em>x</em>, the hypotenuse is 15, and the angle is 53. Substitute:
Solve for <em>x: </em>
<em />
<em />
Use a calculator (make sure you're in Degrees Mode!). Hence:
Our answer is C.
Answer:
$6.75
Step-by-step explanation:
1: In this explanation, let's let one watermelon be w, and one orange be o.
2: From the passage, 1w + 5o = $11.
3: Also from the passage, 3w + 5o = $24.50
4: We can then use a simultaneous equation to work them out - both equations we have use 5 oranges.
3w + 5o = 24.5 (equation 1)
1w + 5o = 11 (equation 2)
5: We can now take the second equation away from the first :
3w - 1w = 2w, 5o - 5o = 0, 24.5 - 11 = 13.5
Now we know 2w = 13.5
6: If 2w = $13.50, one watermelon will be half of that, so $6.75
Hope this helps, let me know if you have any further questions :)
Equation:
x/3 = x/8 + 2/3
---
Multiply thru by 24 to get:
8x = 3x + 16
5x = 16
x = 3 1/5
========
<span>96 degrees
Looking at the diagram, you have a regular pentagon on top and a regular hexagon on the bottom. Towards the right of those figures, a side is extended to create an irregularly shaped quadrilateral. And you want to fine the value of the congruent angle to the furthermost interior angle. So let's start.
Each interior angle of the pentagon has a value of 108. The supplementary angle will be 180 - 108 = 72. So one of the interior angles of the quadrilateral will be 72.
From the hexagon, each interior angle is 120 degrees. So the supplementary angle will be 180-120 = 60 degrees. That's another interior angle of the quadrilateral.
The 3rd interior angle of the quadrilateral will be 360-108-120 = 132 degrees. So we now have 3 of the interior angles which are 72, 60, and 132. Since all the interior angles will add up to 360, the 4th angle will be 360 - 72 - 60 - 132 = 96 degrees.
And since x is the opposite (or congruent) angle to this 4th interior angle, it too has the value of 96 degrees.</span>
Answer:
We know that the equation of the circle in standard form is equal to <em>(x-h)² + (y-k)² = r²</em> where (h,k) is the center of the circle and r is the radius of the circle.
We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :
1 - We first group terms with the same variable :
(x²+8x) + (y²+22y) + 37 = 0
2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)
(x²+8x) + (y²+22y) = - 37
3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process <u><em>"completing the square"</em></u>.
x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²
y²+22y = (y²+22y+11²)-11² = (y+11)²-11²
4 - We plug the new values inside our equation :
(x+4)² - 4² + (y+22)² - 11² = -37
(x+4)² + (y+22)² = -37+4²+11²
(x+4)²+(y+22)² = 100
5 - We re-write in standard form :
(x-(-4)²)² + (y - (-22))² = 10²
And now it is easy to identify h and k, h = -4 and k = - 22 and the radius r equal 10. You can now complete the sentence :)
