All categories

3 years ago

Which inequality BEST represents the situation described? The dump truck can only hold 8 tons, maximum.

Mathematics

1 answer:

Aleonysh [2.5K]3 years ago

4 0

Answer: 0 tons ≤ M ≤ 8 tons

Step-by-step explanation:

The symbols use in inequalities are such that:

a < b (a is strictly smaller than b)

a > b (a is strictly larger than b)

a ≥ b (a is smaller than or equal to b)

a ≤ b (a is larger than or equal to b)

In this case, we have the situation:

"The dump truck can only hold 8 tons, maximum"

Then if M represents the mass that the dump truck can hold, we know that the maximum possible value of M is 8 tons.

Then we would have this written as:

M is smaller than or equal to 8 tons.

or:

M ≤ 8 tons.

We also can add that M needs to be larger than zero (we can not have a negative mass) then this is written as:

0 tons ≤ M ≤ 8 tons.

You might be interested in

one leg of an isoceles right triangle measures 5 inches. round to the nearest tenth, what is the approximate length of the hypot

sergeinik [125]

Because we know the leg with the measure is not the hypotenuse, the two legs would be 5 inches each. Using the Pythagorean Theorem, 5^2 + 5^2 = C^2, when C is the length of the hypotenuse. 5^2 is 25, so 25 + 25 = 50. We need to find the square root of 50, and the closest number is 7.07 or 7.1.

7 0

3 years ago

On a baseball field, the pitcher’s mound is 60.5 feet from home plate. During practice, a batter hits a ball 195 feet at an angl

worty [1.4K]

In this problem, we can imagine that all the points connect to form a triangle. The three point or vertices are located on the pitcher mount, the home plate and where the outfielder catches the ball. So in this case we are given two sides of the triangle and the angle in between the two sides.

<span>With the following conditions, we can use the cosine law to solve for the unknown 3rd side. The formula is:</span>

c^2 = a^2 + b^2 – 2 a b cos θ

Where,

a = 60.5 ft

b = 195 ft

θ = 32°

Substituting the given values:

c^2 = (60.5)^2 + (195)^2 – 2 (60.5) (195) cos 32

c^2 = 3660.25 + 38025 – 20009.7

c^2 = 21,675.56

c = 147.23 ft

<span>Therefore the outfielder throws the ball at a distance of 147.23 ft towards the home plate.</span>

8 0

3 years ago

The function f(x) =x^3 +2x has an inverse function g. Find g’(0) and g’(3).

Dominik [7]

Step-by-step explanation:

follow the steps to get answer

7 0

3 years ago

6.2 Cool down: what are the circle coordinates?

poizon [28]

A line segment connecting two points on the circle and going through the center is called a diameter of the circle. Assume that (x,y) are the coordinates of a point on the circle shown. The equation of a circle with center (h,k) and radius r units is (x−h)2+(y−k)2=r2 .

8 0

3 years ago

Represent each of these relations on {1, 2, 3, 4} with a matrix (with the elements of this set listed in increasing order). a) {

Irina-Kira [14]

Answer:

for a a) {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}

$\left[\begin{array}{cccc}0&1&1&1\\0&0&1&1\\0&0&0&1\\0&0&0&0\end{array}\right]$

for b

b) {(1, 1), (1, 4), (2, 2), (3, 3), (4, 1)}

$\left[\begin{array}{cccc}1&0&0&1\\0&1&0&0\\0&0&1&0\\1&0&0&0\end{array}\right]$

for c) {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}

$\left[\begin{array}{cccc}0&1&1&1\\1&0&1&1\\1&1&0&1\\1&1&1&0\end{array}\right]$

for d d) {(2, 4), (3, 1), (3, 2), (3, 4)}

$\left[\begin{array}{cccc}0&0&0&0\\0&0&0&1\\1&1&0&1\\0&0&0&0\end{array}\right]$

Step-by-step explanation:

in matrix, arrays are placed in rows , which represents the horizontal sides from left to right, while arrays in the column are placed vertically from top to bottom. Here, we placed the arrays in a 4x4 matrix

for a a) {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}

$\left[\begin{array}{cccc}0&1&1&1\\0&0&1&1\\0&0&0&1\\0&0&0&0\end{array}\right]$

for b

b) {(1, 1), (1, 4), (2, 2), (3, 3), (4, 1)}

$\left[\begin{array}{cccc}1&0&0&1\\0&1&0&0\\0&0&1&0\\1&0&0&0\end{array}\right]$

for c) {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}

$\left[\begin{array}{cccc}0&1&1&1\\1&0&1&1\\1&1&0&1\\1&1&1&0\end{array}\right]$

for d d) {(2, 4), (3, 1), (3, 2), (3, 4)}

$\left[\begin{array}{cccc}0&0&0&0\\0&0&0&1\\1&1&0&1\\0&0&0&0\end{array}\right]$

7 0

4 years ago