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Vika [28.1K]
3 years ago
13

What is the product?

Mathematics
1 answer:
Phoenix [80]3 years ago
3 0
(x+3)(2x-1) \\ =x(2x-1)+3(2x-1) \\ =2 x^{2} -x+6x-3 \\ =2 x^{2} +5x-3
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In the electric currect​ flow, it is found that the resistance​ (measured in the units called​ ohms) offered by a fixed length o
Morgarella [4.7K]
Let x be the resistance of the wire with the larger diameter.
x = (0.456 x (0.01)^2)/(0.0401)^2 = 0.0284 ohms
The answer is 0.0284 ohms.

7 0
2 years ago
A new cereal will be advertised in 30-second spots during a morning TV show for children. The ad will run over the next 60 days.
Arturiano [62]
The campaign will cost $216,000
7 0
2 years ago
Find the surface area of the right rectangular prism shown below. units²
faust18 [17]

Answer:

67 units^2

Step-by-step explanation:

The surface area of the prism is found by

SA = 2 ( lw+lh + wh)

     = 2 ( 5*1.5+ 4*1.5 + 5*4)

     = 2 ( 7.5+6+20)

     = 2 (33.5)

    = 67

5 0
3 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

  1. f : X \rightarrow Y is surjective implies there exists a function h : Y \rightarrow X such that  f\circ h = 1_Y.
  2. 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
Find an equation of the circle whose diameter has endpoints (1,-4) and (-3,6).
MAVERICK [17]

Answer:

(x+1)^2+(y-1)^2=58

Step-by-step explanation:

To find the equation of this circle, we must know the center and the radius.

We can find the radius by dividing the value of the distance formula by 2 (since r=\frac{d}{2}):

d=\sqrt{(-3-1)^2+(6-(-4))^2}=\sqrt{116}\\r=d/2=\frac{\sqrt{116}}{2}

We can then find the center of the circle by averaging the coordinates:

\frac{1+(-3)}{2}=-1

\frac{-4+6}{2}=1

Then, we substitute these values into the equation of a circle:

(x-(-1))^2+(y-1)^2=(\frac{\sqrt{116}}{2})^2\\(x+1)^2+(y-1)^2=58

3 0
3 years ago
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