Answer:
The length of BC = 28 units
Step-by-step explanation:
* In triangle ABC
∵ Angles B and C are congruent
∴ m∠B = m∠C
* In any triangle if two angles are equal in measure, then the triangle is isosceles means the two sides which opposite to the congruent angles are equal in length
∴ AB = AC
∵ AB = 4x - 7
∵ AC = 2x + 7
∴ 4x - 7 = 2x + 7 ⇒ collect like terms
∴ 4x - 2x = 7 + 7
∴ 2x = 14 ⇒ divide both sides by 2
∴ x = 14 ÷ 2 = 7
* Now we can find the length of BC
∵ The length of BC = 4x ⇒ substitute the value of x
∴ The length of BC = 4 × 7 = 28 units
Answer:
It can hold up to 
of waste
<em></em>
Step-by-step explanation:
Given
-- Diameter
-- height
Required
Determine the amount of waste it can hold
This simply means that we calculate the volume of the cylindrical container.
And this is calculated using:
Where
and
So, we have:
<em>Hence, it can hold up to </em><em> of waste</em>
Answer:
y = (x-3)^2 - 17
Step-by-step explanation:
To complete the square, take the middle term bx and divide it in two. Then take the square.
x^2 - 6x - 8 has bx = -6x. Take -6/2 = -3. Square -3^2 = 9.
Now to finish completing the square add 9 and subtract 9 from one side.
y = x^2 - 6x - 8
y = (x^2 - 6x +9) -9 - 8
y = (x-3)^2 - 17
Assuming these are 4^(1/7), 4^(7/2), 7^(1/4) and 7^(1/2), the conversion process is pretty quick. the denominator, or bottom, of your fraction exponent becomes the "index" of your radical -- in ∛, "3" is your index, just for reference. the numerator, aka the top of the fraction exponent, becomes a power inside the radical.
4^(1/7) would become ⁷√4 .... the bottom of the fraction becomes the small number included in the radical and the 4 goes beneath the radical
in cases such as this one, where 1 is on top of the fraction radical, that number does technically go with the 4 beneath the radical--however, 4¹ = 4 itself, so there is no need to write the implied exponent.
4^(7/2) would become √(4⁷) ... the 7th power goes with the number under your radical and the "2" becomes a square root
7^(1/4) would become ⁴√7 ... like the first answer, the bottom of the fraction exponent becomes the index of the radical and 7 goes beneath the radical. again, the 1 exponent goes with the 7 beneath the radical, but 7¹ = 7
7^(1/2) would become, simply, √7
Answer:
vertical angles and complementary
