Write an inequality that represents 10 less than a 4 times a number more than 10,000

Which best describes the meaning of the statement if A then B

Oliga [24]

Answer:

$a => b \equiv ( \neg a \ \lor \ b )$

Step-by-step explanation:

You can understand the statement from many perspectives, but in terms of proposition logic it is best to understand it as "negation of a" or " b" in mathematical terms is written like this

$a => b \equiv ( \neg a \ \lor \ b )$

You can show that they are logically equivalent because they have the same truth table.

3 0

2 years ago

I need help with this geometry question

MArishka [77]

Answer:

Approximately 7.8 units

Step-by-step explanation:

To find the distance between any two points, we can use the distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

From the graph, we can see that A is (0,0). Let's let this be x₁ and y₁.

B is (-5,6). Let's let this be x₂ and y₂. So, substitute:

$d=\sqrt{(-5-0)^2+(6-0)^2}$

Simplify:

$d=\sqrt{(-5)^2+(6)^2}$

Square:

$d=\sqrt{25+36}$

Add:

$d=\sqrt{61}$

Take the square root. Use a calculator:

$d\approx7.8$

So, the distance between them is about 7.8 units.

And we're done!

7 0

2 years ago

What is the average rate of change of f(x) = -x2 + 3x + 6 over the interval –3

Rufina [12.5K]

Answer:

$\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3$

Step-by-step explanation:

To find the average rate of change of a function over a given interval, basically you need to find the slope. The mathematical definition of the slope is very similar to the one we use every day. In mathematics, the slope is the relationship between the vertical and horizontal changes between two points on a surface or a line. In this sense, the slope can be found using the following expression:

$Average\hspace{3}rate\hspace{3}of\hspace{3}change=Slope=\frac{y_2-y_1}{x_2-x_1} =\frac{f(x_2)-f(x_1)}{x_2-x_1}$

So, the average rate of change of:

$f(x)=-x^2+3x+6$

Over the interval $-3$

Is:

$f(x_2)=f(3)=-(3)^2+3(3)+6=-9+9+6=6\\\\f(x_1)=f(-3)=-(-3)^2+3(-3)+6=-9-9+6=-12$

$\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3$

Therefore, the average rate of change of this function over that interval is 3.

3 0

2 years ago

Please give a good answer :)

Alex

Answer:

P(4≤x≤7) = 2/3

Step-by-step explanation:

We'll begin by obtaining the sample space (S) i.e possible outcome of rolling both dice at the same time. This is illustrated below:

1,1 1,2 1,3 1,4 1,5 1,6

2,1 2,2 2,3 2,4 2,5 2,6

3,1 3,2 3,3 3,4 3,5 3,6

4,1 4,2 4,3 4,4 4,5 4,6

5,1 5,2 5,3 5,4 5,5 5,6

6,1 6,2 6,3 6,4 6,5 6,6

Adding the outcome together, the sample space (S) becomes:

2 3 4 5 6 7

3 4 5 6 7 8

4 5 6 7 8 9

5 6 7 8 9 10

6 7 8 9 10 11

7 8 9 10 11 12

Next, we shall obtain the event of 4≤x≤7. This is illustrated below:

4 5 6 7

Finally, we shall determine P(4≤x≤7). This can be obtained as follow:

Element in the sample space, n(S) = 36

Element in 4≤x≤7, n(4≤x≤7) = 24

Probability of 4≤x≤7, P(4≤x≤7) = ?

P(4≤x≤7) = n(4≤x≤7) / nS

P(4≤x≤7) = 24/36

P(4≤x≤7) = 2/3

4 0

2 years ago

A cross shaped pattern is made by arranging four identical rectangles around the sides of a square. The area of the square is 36

kipiarov [429]

Answer:

Area of a square is length * length

Area of a rectangle is length * breadth

In the question, the area of the square is 36

And the area of the rectangle is $1(1/3)$ the area of the square

To find the area of the rectangle, multiply 1(1/3) by the area of the square(36)

Area of rectangle becomes, 1(1/3) * 36 = (4/3) * 36 = 48cm2

To find the perimeter of the shape, we must find the perimeter of the rectangle - perimiter of the square

Since area of square is length * length, the length of the square is 6cm

The breadth of the rectangle is equal to the length of the square, hence, b = 6cm

Since, length * breadth = 48

l * 6 = 48

l = 8

Perimeter of the shape = 4 * perimeter of rectangle - perimter of square

Perimeter of rectangle = 2(l+b)

Perimeter of sqaure = 4l

Our answer = 4 * 2(6+8) - 4(6)

= 4 * 28 - 36

= 88cm

Step-by-step explanation:

7 0

2 years ago

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