Answer:
D. 28.54
Step-by-step explanation:
To find the area of the shaded region, find the area of the circle and divide it in 4. This will the area of the portion with the triangle.
Now, find the area of the triangle and subtract the two. The resulting value will be the area of the shaded region.
Circle:
Divide by 4 for the area of the section with the triangle.
314/4 = 78.5
Triangle:
Subtract the two, 78.5 - 50 = 28.5.
Answer:
x = - 3
y = - 2
Step-by-step explanation:
Start with the second equation. Switch
3y = 2x Divide by 3
3y/3 = 2x/3
y = 2x/3
Now go to the first equation. Put the value for y in the first equation.
x - 3(2x/3) = 3 Cancel the 3s on the left.
x - 2x = 3 Combine
-x = 3 Multiply by -1
-1(-x) = 3(-1)
x = - 3
Now go back to the original equation I have called the second equation
2x = 3y
2(-3) = 3y Put in - 3 for x
- 6 = 3y Divide by 3
-6 / 3 = y
y = - 2
Answer:
I have no clue... I'm very sorry...
Step-by-step explanation:
Answer: the perimeter of the larger triangle is 22 units
Step-by-step explanation:
The diagram of both triangles is shown in the attached photo. The isosceles triangles are triangle ABC and triangle DEF
Perimeter of triangle ABC = 11
For an isosceles triangle, the other two sides are equal. If one equal side is x, then the sum of the two equal sides is x+x = 2x
Perimeter of triangle = sum of the lengths of the 3 sides. Therefore,
11 = 5 + 2x
2x = 11-5 = 6
x = 6/2 = 3
The base of the similar triangle is 10. It means that it is 2 times the base of the smaller triangle. That means the scale factor is 2. Therefore,
If the perimeter of the small triangle is 11, the Perimeter of the larger triangle will be 2 × perimeter of the smaller triangle. This becomes
2 × 11 = 22 units.
It can also be determined by adding the length of each side
3×2 + 3×2 + 5×2 = 6+6+10 = 22 units
Answer:
y = 1/12 (x − 5)²
Step-by-step explanation:
We can solve this graphically without doing calculations.
The y component of the focus is y = 3. Since this is above the directrix, we know this is an upward facing parabola, so it must have a positive coefficient. That narrows the possible answers to A and C.
The x component of the focus is x = 5. Since this is above the vertex, we know the x component of the vertex is also x = 5.
So the answer is A. y = 1/12 (x−5)².
But let's say this wasn't a multiple choice question and we needed to do calculations. The equation of a parabola is:
y = 1/(4p) (x − h)² + k
where (h, k) is the vertex and p is the distance from the vertex to the focus.
The vertex is halfway between the focus and the directrix. So p is half the difference of the y components:
p = (3 − (-3)) / 2
p = 3
k, the y component of the vertex, is the average:
k = (3 + (-3)) / 2
k = 0
And h, the x component of the vertex, is the same as the focus:
h = 5
So:
y = 1/(4×3) (x − 5)² + 0
y = 1/12 (x − 5)²
