A (4,8) and b (7,2) and let c (x,y)
A , B and C are col-linear ⇒⇒⇒ ∴ slope of AB = slope of BC
slope of AB = (2-8)/(7-4) = -2
slope of BC = (y-2)/(x-7)
∴ (y-2)/(x-7) = -2
∴ (y-2) = -2 (x-7) ⇒⇒⇒ equation (1)
<span>The distance
between two points (x₁,y₁),(x₂,y₂) = d
</span>
The ratio of AB : BC = 3:2
AB/BC = 3/2
∴ 2 AB = 3 BC

= <span>

eliminating the roots by squaring the two side and simplifying the equation
∴ 4 * 45 = (x-7)² + (y-2)² ⇒⇒⇒ equation (2)
substitute by (y-2) from equation (1) at </span><span>equation (2)
4 * 45 = 5 (x-7)²
solve for x
∴ x = 9 or x = 5
∴ y = -2 or y = 6
The point will be (9,-2) or (5,6)
the point (5,6) will be rejected because it is between A and B
So, the point C = (9,-2)
See the attached figure for more explanations
</span>
Answer:
48∛9 ft²
Step-by-step explanation:
The length (L) and width (W) are given by:
![L = 4\sqrt[3]{24}\\ W= 6\sqrt[3]{3}](https://tex.z-dn.net/?f=L%20%3D%204%5Csqrt%5B3%5D%7B24%7D%5C%5C%20W%3D%206%5Csqrt%5B3%5D%7B3%7D)
Since this is a rectangular region, the area is given by:
![A=L*W=L \\A=4\sqrt[3]{24}* 6\sqrt[3]{3}\\A=24\sqrt[3]{72}\ ft^2](https://tex.z-dn.net/?f=A%3DL%2AW%3DL%20%5C%5CA%3D4%5Csqrt%5B3%5D%7B24%7D%2A%206%5Csqrt%5B3%5D%7B3%7D%5C%5CA%3D24%5Csqrt%5B3%5D%7B72%7D%5C%20ft%5E2)
The answer can be further simplified by factoring as follows:
![A=24\sqrt[3]{72} = \\A=24\sqrt[3]{2*2*2*3*3}= 24\sqrt[3]{2^3*9}\\A=48\sqrt[3]{9}\ ft^2](https://tex.z-dn.net/?f=A%3D24%5Csqrt%5B3%5D%7B72%7D%20%3D%20%5C%5CA%3D24%5Csqrt%5B3%5D%7B2%2A2%2A2%2A3%2A3%7D%3D%2024%5Csqrt%5B3%5D%7B2%5E3%2A9%7D%5C%5CA%3D48%5Csqrt%5B3%5D%7B9%7D%5C%20ft%5E2)
The exact area is its simplest form is 48∛9 ft²
Answer:
acute base angle = 74° , obtuse base angle = 106°
Step-by-step explanation:
Since the large triangle is isosceles with vertex angle (top angle) is 32, then the bottom 2 angles would be same (let it be x):
We know angles of triangle add up to 180, so we have:
x + x + 32 = 180
2x = 180 - 32
2x = 148
x = 148/2
x = 74
This 74 degree angle is the base acute angle of the isosceles trapezoid (lower portion). We also know opposite angles of isosceles trapezoid are supplementary (add up to 180), thus
obtuse angle + 74 = 180
obtuse angle (base) = 180 - 74 = 106
Thus, acute base angle = 74° , obtuse base angle = 106°
2(2x-4) because when you multiply 2 x 2x it equals 4x. When you multiply 2 x 4 it equals 8. Leaving you with 4x-8
Answer:
Vertex form:
The vertex is 
Step-by-step explanation:
For a general quadratic function the form is:
For the function
The values of the coefficients for the function are the following:
,
,
Take the value of b and divide it by 2. Then, the result obtained squares it.
Add and subtract
Write the expression of the form
The vertex is 