Lily has $18. Matt has twice as much of a third of the amount that Lily has, and

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

Solve for x <img src="https://tex.z-dn.net/?f=x%20%2B%2015%20%3D%208" id="TexFormula1" title="x + 15 = 8" alt="x + 15 = 8" al

Makovka662 [10]

Answer:

x = -7

Step-by-step explanation:

Subtract 15 from both sides of the equation.

x = 8 -15 = -7

8 0

3 years ago

Find the points on the lemniscate where the tangent is horizontal. 8(x2 + y2)2 = 81(x2 − y2)

slamgirl [31]

The answers to this problem are:(±5√3/8,±5/8)Here is the solution:
Step 1: x2+y2=2516[2]x2+y2=2516[2]

Step 2: Substitute:
8(25/16)^2=25(x^2−y^2)
8(25/16)^2=25(x^2−y^2)
x^2−y^2=25/32.

Add [2] and [3]:
2x^2=75/32
x^2=75/74
x=±5√3/8
Substitute into [2]:
75/64+y^2=50/32
y^2=25/64
y=±5/8

3 0

3 years ago

Read 2 more answers

Fernando will divide 0.24 by 4 to help him solve a math problem. Which model below could represent this math problem

balandron [24]

Answer:

So the model should represent either $\frac{6}{100}$ or $\frac{3}{50}$ (its equivalent and simplified form.

Step-by-step explanation:

1) Originally the question wants to represent this quotient as tiles.

So, $\frac{\frac{24}{100}}{4} =\frac{24}{100} *\frac{1}{4} =\frac{6}{100}=$

We can still simplify it, but since we're dealing with 100 x 100 squares let's keep it this way

2) So the model should represent either $\frac{6}{100}$ or $\frac{3}{50}$ (its equivalent and simplified form.

6 0

3 years ago

A number, y, is equal to twice the sum of a smaller number and 3. The larger number is also equal to 5 more than 3 times the sma

RSB [31]

Answer:

A.

Step-by-step explanation:

NOTE: The "larger number" will be referred to as y, and the "smaller number" will be referred to as x.

"A number, y, is equal to twice the sum of a smaller number and 3."

This tells us that we must add our smaller number (x) to 3 within parantheses and then multiply the entire term (x+3) by 2.

$y=2(x+3)$

"The larger number is also equal to 5 more than 3 times the smaller number."

This tells us that we must multiply 3 against our smaller number (x) and add 5 to it.

$y=3x+5$

Now, to find your answer, we can put the equations in the same form as the answer choices so as to find an equivalent equation. Lets start with the first equation.

This form calls for us to have our x term first, then our y term, then our constant.

$y=2(x+3)\\y=2x+6\\-2x+y=6$

Now that we've gotten the equation in that form, we can see that our answer choices hold that our leading co-efficient must be positive, which we can adjust for by dividing both sides by -1.

$-2x+y=6\\2x-y=-6$

This makes the only possible answer choices (A) and (C).

Now, lets do our second equation. The recipe calls for the same form, again with a positive leading coefficient.

$y=3x+5\\-3x+y=5\\3x-y=-5$

This is only represented by choices (A) and (B).

Therefore, answer choice (A) is the only one which represents both equations.

7 0

3 years ago