Answer:
15 divided by 2 1/2
Step-by-step explanation:
$6 per yard.
Answer:
Step-by-step explanation:
Component form of a vector is given by 
, where 
represents change in x-value and 
represents change in y-value. The magnitude of a vector is correlated the Pythagorean Theorem. For vector 
, the magnitude is 
.
190 degrees counterclockwise from the positive x-axis is 10 degrees below the negative x-axis. We can then draw a right triangle 10 degrees below the horizontal with one leg being , one leg being , and the hypotenuse of the triangle being the magnitude of the vector, which is given as 9.
In any right triangle, the sine/sin of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle.
Therefore, we have:
To find the other leg, , we can also use basic trigonometry for a right triangle. In right triangles only, the cosine/cos of an angle is equal to its adjacent side divided by the hypotenuse of the triangle. We get:
Verify that 
Therefore, the component form of this vector is 
Answer:
3x2+5=11
Step-by-step explanation:
Answer:
6. r = 21 cm
7. A = 155.5 m²
Step-by-step explanation:
7: Formula for arc length is;
S = (θ/360) × 2πr
We are given;
S = 51 cm
θ = 139°
Thus;
51 = (139/360) × 2π × r
Making r the subject;
r = (51 × 360)/(2π × 139)
r ≈ 21 cm
8) Area of sector is gotten from the formula;
A = (θ/360) × πr²
A = (220/360) × (π × 9²)
A = 155.5 m²
Let the two ages be j and m, respectively. Then j+m>32.
Solving for Mary's age, we get m > 32 - j. Because j = m + 2, m > 32 - (m+2).
Continue solving for m: Adding m to both sides of this inequality results in
2m > 32 - 2. Then 2m > 30, and m > 15. Mary's age is greater than 15.
