What is 2^ + 2^? (^ means squared for those who can't math.)

Mark wants to fence 4 rectangular gardens, each with a length of 9 1/4 feet and a width of 4 1/2feet. What is the length of fenc

kolbaska11 [484]

Answer:

110 ft

Step-by-step explanation:

The length of fencing is four times the perimeter of one garden.

The formula for the perimeter of a rectangle is

P = 2l + 2w

The total perimeter for all four rectangles is

P = 4× (2l + 2w) = 8l + 8w

Data:

l = 9¼ ft

w = 4½ ft

Calculation:

P = 8l + 8w = 8×9¼ + 8×4½ = 72⁸/₄ + 32⁸/₂ =(72 + 2) + (32 + 4) = 74 + 36 = 110 ft

The total length of fencing is 110 ft.

4 0

2 years ago

51 more than y is greater than -240

svet-max [94.6K]

Answer:

y + 51 ≥ -240

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

DIscrete Math

Daniel [21]

Answer:

Step-by-step explanation:

As the statement is ‘‘if and only if’’ we need to prove two implications

$f : X \rightarrow Y$ is surjective implies there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ .
If there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ , then $f : X \rightarrow Y$ is surjective

Let us start by the first implication.

Our hypothesis is that the function $f : X \rightarrow Y$ is surjective. From this we know that for every $y\in Y$ there exist, at least, one $x\in X$ such that $y=f(x)$ .

Now, define the sets $X_y = \{x\in X: y=f(x)\}$ . Notice that the set $X_y$ is the pre-image of the element $y$ . Also, from the fact that $f$ is a function we deduce that $X_{y_1}\cap X_{y_2}=\emptyset$ , and because $f$ the sets $X_y$ are no empty.

From each set $X_y$ choose only one element $x_y$ , and notice that $f(x_y)=y$ .

So, we can define the function $h:Y\rightarrow X$ as $h(y)=x_y$ . It is no difficult to conclude that $f\circ h(y) = f(x_y)=y$ . With this we have that $f\circ h=1_Y$ , and the prove is complete.

Now, let us prove the second implication.

We have that there exists a function $h:Y\rightarrow X$ such that $f\circ h=1_Y$ .

Take an element $y\in Y$ , then $f\circ h(y)=y$ . Now, write $x=h(y)$ and notice that $x\in X$ . Also, with this we have that $f(x)=y$ .

So, for every element $y\in Y$ we have found that an element $x\in X$ (recall that $x=h(y)$ ) such that $y=f(x)$ , which is equivalent to the fact that $f$ is surjective. Therefore, the prove is complete.

3 0

2 years ago

In a class of 22 students, 15 play an instrument and 11 play a sport. There are 9

ollegr [7]

Answer:7/22

Sorry I don’t know how to explain.But here the answer.

Hope this helped!

Have a great day!

6 0

1 year ago

Which of the following are polynomial functions?

Vinil7 [7]

A polynomial function is a function involving only non-negative (positive and 0) integer powers of 'x', i.e. all terms with ' 'x' have a non-negative integer power, such as a quadratic $x^{2} x^{3}$ and so on.

Option E is the answer.

Rest all are wrong answers. they do not have positive integers.

4 0

2 years ago

Read 2 more answers