<h3>
Answer:</h3>
B. (5, -2)
<h3>
Step-by-step explanation:</h3>
Try the points in the inequalities and see what works. Here, we evaluate the point in the first inequality, and if that works, then the second inequality.
A. 2 ≤ -(-5) -5 . . . ⇒ . . . 2 ≤ 0 . . . false
B. -2 ≤ 5 -5 . . . true
... -2 ≥ -(5) -4 . . . true . . . . . . selection B is a viable choice
C. we know from A that the first inequality will be satisfied
... -2 ≥ -(-5) -4 . . . ⇒ . . . -2 ≥ 1 . . . false
D. 2 ≤ 5 -5 . . . . false
9514 1404 393
Answer:
510 cm³
Step-by-step explanation:
The overall height of the front face is 9+2 = 11 cm.
The overall width of the front face is 6+4 = 10 cm.
Out of that 11 cm by 10 cm rectangle, a cutout is made in the upper right corner. The area of that cutout (in the plane of the front face) is 2 cm high by 4 cm wide.
Then the area of the front face is ...
(11 cm)(10 cm) -(2 cm)(4 cm) = 110 cm² -8 cm² = 102 cm²
The volume of the prism can be found using the formula ...
V = Bh
where B is the area of the "base" of the prism, and h is its height. Here, the "base" is the front face, and the height is the dimension marked 5 cm. The volume is ...
V = (102 cm²)(5 cm) = 510 cm³
The volume of the prism is 510 cm³.
Answer:
see explanation
Step-by-step explanation:
a
The tangent and the radius at the point of contact form a right angle
Using Pythagoras' identity on the right triangle formed.
Let x be the distance from the centre to P, then
x² = 4² + 10² = 16 + 100 = 116 ( take the square root of both sides )
x =
≈ 10.77 cm (to 2 dec. places )
b
let the required angle be Θ, then
Using the sine or cosine ratio in the right triangle.
cosΘ =
= 
Θ =
(
) ≈ 21.8°
Answer:
Median.
Step-by-step explanation:
The median is the value separating the higher half of a data sample, a population, or a probability distribution, from the lower half. In simple terms, it may be thought of as the "middle" value of a data set. For example, in the data set {1, 3, 3, 6, 7, 8, 9}, the median is 6, the fourth number in the sample. The median is a commonly used measure of the properties of a data set in statistics and probability theory.
Answer:
x=-4
Step-by-step explanation:
Subtract x from 3x ( 2x )
2x+5=-3
Subtract 5 from -3 ( -8 )
2x=-8
Divide ( -4 )
x=-4