If Steve throws the football 50 m in three seconds what is the average speed of the football

patriot [66]

Answer:

Choice b.

$x^{2} + 5\, x + 6 = (x + 3)\, (x + 2)$ .

Step-by-step explanation:

The highest power of the variable $x$ in this polynomial is $2$ . In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to $0$ .)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

Apply the quadratic formula to find the two roots that would set this quadratic polynomial to $0$ . The discriminant of this polynomial is $(5^{2} - 4 \times 1 \times 6) = 1$ .

$\begin{aligned}x_{1} &= \frac{-5 + \sqrt{1}}{2\times 1} \\ &= \frac{-5 + 1}{2} \\ &= -2\end{aligned}$ .

Similarly:

$\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}$ .

By the Factor Theorem, if $x = x_{0}$ is a root of a polynomial, then $(x - x_0)$ would be a factor of that polynomial. Note the minus sign between $x$ and $x_{0}$ .

The root $x = -2$ corresponds to the factor $(x - (-2))$ , which simplifies to $(x + 2)$ .
The root $x = -3$ corresponds to the factor $(x - (-3))$ , which simplifies to $(x + 3)$ .

Verify that $(x + 2)\, (x + 3)$ indeed expands to the original polynomial:

$\begin{aligned}& (x + 2)\, (x + 3) \\ =\; & x^{2} + 2\, x + 3\, x + 6 \\ =\; & x^{2} + 5\, x + 6\end{aligned}$ .

4 0

3 years ago

Multiply the following and write your answer In scientific notation.. 3.62 × 10^-5 · 9,400.

svet-max [94.6K]

Answer:

3.4028 x 10^-1

Step-by-step explanation:

First you make the 9400 into scientific notation:

9.4x10^3

Then you combine like terms

(3.62x9.4)(10^-5x10^3)

Finally you simplify

34.028x10^-2

3.4028x10^-1

6 0

3 years ago

What is the decimal equivalent to 34 % ?

Keith_Richards [23]

Answer:

.34

Step-by-step explanation:

34% = 34/100 = .34

All percents are out of 100

3 0

3 years ago

Read 2 more answers

Are 22 42 60 a right triangle or not?

Lelechka [254]

Answer:First things first, let's explain what a right triangle is. The definition is very simple and might even seem obvious for those who already know it: a right-angled triangle is a triangle where one and only one of the angles is exactly 90°. The other two angles will clearly be smaller than the right angle because the sum of all angles in a triangle is always 180°.

In a right angled triangle the sides are defined in a special way. The side opposing the right angle is always the biggest in the triangle and receives the name of "hypotenuse". The other two sides are called catheti. The relationship between the hypotenuse and each of the cathetus is a very simple one, as we will see when we will talk about Pythagoras' theorem.

Hypotenuse calculator

If all you want to calculate is the hypotenuse of a right triangle, this page and its right triangle calculator will work just fine. However, we would also recommend to use the specific tool we have developed at Omni Calculators: the hypotenuse calculator. The hypotenuse is opposite the right angle and can be solved by using the Pythagorean theorem. In a right triangle with cathetus a and b and with hypotenuse c, Pythagoras' theorem states that: a² + b² = c².

To solve for c, take the square root of both sides to get c = √(b²+a²). This extension of the Pythagorean theorem can be considered as a "hypotenuse formula". A Pythagorean theorem calculator is also an excellent tool for calculating the hypotenuse.

Let's now solve a practical example of what it would take to calculate the hypotenuse of a right triangle without using any calculators available at Omni:

Obtain the values of a and b,

Square a and b,

Sum up both values: a² + b²,

Take the square root of the result,

The square root will yield a positive and negative result. Since we are dealing with length, disregard the negative result,

The resulting value is the value of the hypotenuse c.

Now let's see what the process would be using one of Omni's calculator, for example, the right triangle calculator on this web page:

Insert the value of a and b into the calculator

Obtain the value of c immediately

As a bonus, you will get the value of the area for such a triangle.

Step-by-step explanation:Hope this helped u also may i have brainlist plz?

4 0

3 years ago

Find the sum of a finite arithmetic sequence from n = 1 to n = 10, using the expression 3n − 8.

maw [93]

Answer:

The answer is 85

Step-by-step explanation:

The equation used to find the sum of an arithmetic series is: (n/2) * (a1 + an).

n in this case is 10 (the number of numbers in the series)

an is 22 (plug in 10 to the expression 3n-8)

and a1 is -5 (plug in 1 to the expression 3n-8)

so when you plug everything in to the final equation, you get

(10/2) * (-5 + 22)

5 * 17

85

8 0

3 years ago