(Quadratic) What is the answer to this quadratic

Alex eats 2 pieces of candy. Marisol eats 3 times as many pieces of candy as Alex. Which equation can be used to determine the a

bazaltina [42]

Answer:

m = 3a

Step-by-step explanation:

The number of pieces of candy eaten by Alex is not important.

The only thing that matters is that Marisol eats 3 times as many pieces of candy.

If a is the number eaten by Andy, then 3 times a equals the number of pieces of candy eaten by Marisol, or m=3a

4 0

3 years ago

Can someone help me?

lianna [129]

Answer:

(-4,-7)

Step-by-step explanation:

7 0

3 years ago

Sketch each parabola, labeling its focus and directrix. y=(1/10)(x-1)²-2

sergiy2304 [10]

The equation of parabola is $y=\frac{1}{10}\left(x-1\right)^{2}-2$

Comparing with the vertex form of the parabola: $y=a(x-h)^2+k$

$a=\frac{1}{10},h=1,k=-2$

Hence, the vertex of the parabola is given by (h,k) = (1, -2)

Now, vertex is the midpoint of the focus and the point on the directrix.

Distance, between vertex and focus is p and that of point on the directrix is p.

Now, let us find p

$p=\frac{1}{4a}\\\\p=\frac{1}{4\cdot1/10}\\\\p=\frac{5}{2}$

Thus, the focus is given by

$(h,k+p)\\\\=(1,-2+5/2)\\\\=(1,1/2)=(1,0.5)$

And the directrix is given by

$y=k-p\\\\y=-2-5/2\\\\y=-\frac{9}{2}$

Since, a >0 hence, it is an upward parabola.

The graph is shown in the attached file.

5 0

3 years ago

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

4 years ago

A total of $12,000 is invested at two different rates: $5,000 of it is invested at 6%, and the rest is invested at 8%. How much

lesantik [10]

5000*6/100=300
7000*8/100=560
total=860

7 0

4 years ago