Answer:
1) Yvonne buys gloves that cost $10.00. At the register, she must pay $10.80. ⇒ EXCISE TAX
2)Sasha bought a house last year. She just got a tax bill from the county showing the value of her house and the amount of tax. ⇒ PROPERTY TAX
3) Bigmart sells boots made in China and boots made in the U.S. Bigmart must pay 27% tax on each pair of boots made in China, but not on the U.S. made boots. ⇒ TARRIFF.
4)State citizens voted to add a 75-cent tax to each pack of cigarettes to pay for programs to help people quit smoking. ⇒ SALES TAX
5)Jake got his paycheck today. He worked 40 hours at $20 per hour His gross pay was $800, but the amount of his paycheck was only. ⇒ Income/Social
/Security/Medicare Taxes
X will be the speed of species b and 4x will be the speed of species a:
x + 4x = 180
5x = 180
x = 180 / 5
x = 36 m/h
If species b has a speed of 36 m/h, the speed of species a is 4 times that:
4 x 36 = 144 m/h.
Answer:
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The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².
The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines
b² = 2 • (96 cm)² - 2 (96 cm)² cos(120°) ⇒ b = 96√3 cm
Call b the base of this triangle.
The vertex angle is 120°, so the other two angles have measure θ such that
120° + 2θ = 180°
since the interior angles of any triangle sum to 180°. Solve for θ :
2θ = 60°
θ = 30°
Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find
tan(30°) = h / (b/2) ⇒ h = 48 cm
Then the area of the triangle is
1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²
and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:
3072π cm² - 2304√3 cm² ≈ 5660.3 cm²
Answer:
x = 6, x = - 6
Step-by-step explanation:
Given
y = x² - 36
To find the zeros let y = 0, that is
x² - 36 = 0 ← x² - 36 is a difference of squares and factors in general as
a² - b² = (a - b)(a + b), thus
x² - 36 = 0
x² - 6² = 0
(x - 6)(x + 6) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 6 = 0 ⇒ x = - 6