Answer:
64 square yards
Step-by-step explanation:
If the room is a square, then all sides of the room should be equal. To find the area of the room, we would need to multiply 2 adjacent sides of the room, meaning 24 x 24 = 576. Since we need yards of carpet, not feet, and we know that 1 square yard is 9 square feet, we divide our total area in feet by 9. This gives us 64sq yards of carpet
<u>Answer</u>
2. 40
<u>Explanation</u>
The angle subtended by the diameter to the circumference is equal to 90°.
∴ angle ABC = 90°
Angles in a triangle = 180°
50 + 90 + x = 180
90 + x = 180
x = 180 - 90
= 90°
Answer:
Height= 8341.6 feet
Step-by-step explanation:
A surveyor determined the height of the new summit by measuring the angle of elevation to the top to be 37°46'. She then moved 1000 feet closer to the volcano and measured the angle of elevation to be 40°30'.
40°30'= 40.5°
37°46'= 37.767°
b = 180-40.5
b= 139.5°
a= 180-139.5-37.767
a= 2.733°
Using sine method
1000/Sina= y/sinB
1000/sin 2.733= y/sin 139.5
(1000*sin 139.5)/sin 2.733= y
(1000*0.6494)/0.04768= y
13619.96= y
Y= 13620 feet
Height/sin 37.767= 13620
Height=13620*sin37.767
Height= 8341.59
Height= 8341.6 feet
Answer:
–9(3x³ – 8x + 9)
Step-by-step explanation:
–27x³ + 72x – 81
The above equation can be factorised as follow:
–27x³ = –3 * 3 * 3 * x * x * x
72x = 2 * 2 * 2 * 3 * 3 * x
–81 = –3 * 3 * 3 * 3
Common factor = 3 * 3
Greatest common factor = 9
Thus,
–27x³ + 72x – 81 = 9(–3x³ + 8x – 9)
–27x³ + 72x – 81 = –9(3x³ – 8x + 9)
Answer:
1. = 3√10 2. = 5 3. = 6√2
Step-by-step explanation:
Use <u>Intersecting Secant-Tangent Theorem</u>:
If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
1. In this circle, DB is a tangent and DA is a secant. They intersect at point D.
So DB² = DC x DA
² = 5 x (5 + 13)
² = 90
= √90 = 3√10
2. In this circle, FE is a tangent and FH is a secant. They intersect at point F.
So FE² = FG x FH
10² = x 20
100 = 20
= 5
3. In this circle, NM is a tangent and NP is a secant. They intersect at point N.
So NM² = NO x NP
² = 4 x (4 + 14)
² = 72
= √72 = 6√2