Select the correct answer What is the sum of -6 4/5 and 6 4/5?

If p(x) = x 2 + 7x + 3 is divided by x + 4, the remainder is

igor_vitrenko [27]

tep 1 : 3 Simplify — x Equation at the end of step 1 : 3 px - ((9x + —) + 4) = 0 x Step 2 :Rewriting the whole as an Equivalent Fraction :

2.1 Adding a fraction to a whole

Rewrite the whole as a fraction using x as the denominator :

9x 9x • x 9x = —— = —————— 1 x

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

9x • x + 3 9x2 + 3 —————————— = ——————— x x Equation at the end of step 2 : (9x2 + 3) px - (————————— + 4) = 0 x Step 3 :Rewriting the whole as an Equivalent Fraction :

3.1 Adding a whole to a fraction

Rewrite the whole as a fraction using x as the denominator :

4 4 • x 4 = — = ————— 1 x Step 4 :Pulling out like terms :

4.1 Pull out like factors :

 9x2 + 3 = 3 • (3x2 + 1)

Polynomial Roots Calculator :

4.2 Find roots (zeroes) of : F(x) = 3x2 + 1
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 3 and the Trailing Constant is 1.

The factor(s) are:

of the Leading Coefficient : 1,3
of the Trailing Constant : 1

Let us test ....

P Q P/Q F(P/Q) Divisor -1 1 -1.00 4.00 -1 3 -0.33 1.33 1 1 1.00 4.00 1 3 0.33 1.33

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

4.3 Adding up the two equivalent fractions

3 • (3x2+1) + 4 • x 9x2 + 4x + 3 ——————————————————— = ———————————— x x Equation at the end of step 4 : (9x2 + 4x + 3) px - —————————————— = 0 x Step 5 :Rewriting the whole as an Equivalent Fraction :

5.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using x as the denominator :

px px • x px = —— = —————— 1 x Trying to factor by splitting the middle term

5.2 Factoring 9x2 + 4x + 3

The first term is, 9x2 its coefficient is 9 .
The middle term is, +4x its coefficient is 4 .
The last term, "the constant", is +3 

Step-1 : Multiply the coefficient of the first term by the constant 9 • 3 = 27

Step-2 : Find two factors of 27 whose sum equals the coefficient of the middle term, which is 4 .

-27 + -1 = -28 -9 + -3 = -12 -3 + -9 = -12 -1 + -27 = -28 1 + 27 = 28 3 + 9 = 12 9 + 3 = 12 27 + 1 = 28

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Adding fractions that have a common denominator :

5.3 Adding up the two equivalent fractions

px • x - ((9x2+4x+3)) px2 - 9x2 - 4x - 3 ————————————————————— = —————————————————— x x Equation at the end of step 5 : px2 - 9x2 - 4x - 3 —————————————————— = 0 x Step 6 :When a fraction equals zero : 6.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

px2-9x2-4x-3 ———————————— • x = 0 • x x

Now, on the left hand side, the x cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
 px2-9x2-4x-3 = 0

Solving a Single Variable Equation :

6.2 Solve px2-9x2-4x-3 = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

6 0

3 years ago

A.118 B.242 C.180 D.149

Scrat [10]

Answer:

Step-by-step explanation: First find angle 2. 180-59= 121 angle 1 and 2 are equal so their sum must be

242

5 0

3 years ago

I need help with #11

Troyanec [42]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\

\begin{array}{rllll} 
% left side templates
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}$

$\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}
\\\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\end{array}$

$\bf \begin{array}{llll}


\bullet \textit{ vertical shift by }{{ D}}\\
\qquad if\ {{ D}}\textit{ is negative, downwards}\\\\
\qquad if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}
\end{array}$

now, with that template in mind, let's take a peek at this function

$\bf \begin{array}{lllcclll}
y=&2(&1x&-2)^2&-4\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}\\\\
-----------------------------\\\\
A\cdot B=2\impliedby \textit{shrunk by a factor of 2, of half-size}\\\\
\cfrac{C}{B}= \cfrac{-2}{1}\implies -2\impliedby \textit{horizontal right shift of 2 units}\\\\
D=-4\impliedby \textit{vertical down shift of 4 units}$

so, the graph of y=2(x-2)²-4, is really the same graph of y=x², BUT, narrower, and moved about horizontally and vertically

8 0

3 years ago

Read 2 more answers

Which expression corresponds to this graph?

Elodia [21]

Answer: Choice A

The number line graph is visually showing every number that is 19 or smaller; hence $x \le 19$

Note the use of a closed or filled in circle at the endpoint (in contrast to an open circle). This indicates we are including the endpoint 19 as part of the solution set, and that's why we go for "or equal to" as part of the inequality sign.

5 0

2 years ago

50 US states for the namethat start with the letter W what percent of US states have the names that start with the letter W

Vanyuwa [196]

Washington, West Virginia, Wisconsin, Wyoming
Four states out of 50
4 / 50 * 100 = 8 per cent.

3 0

3 years ago