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4 years ago

What are two numbers multiplied together to get 15 but add to be 12?

1 answer:

3 0

So x times y=15
x+y=12
solve
x+y=12
subtract x from both sides
y=12-x
subsitute
xy=15
x(12-x)=15
distribute
12x-x^2=15
subtract (12x-x^2) from both sides
0=x^2-12x+15
use quadratic formula which is
x= $\frac{ -b+/- \sqrt{b^{2}-4ac} }{2a}$
where you have
0=ax^2+bx+c
so
a=1
b=-12
c=15
subsitute
x= $\frac{ -(-12)+/- \sqrt{-12^{2}-4(1)(15)} }{2(1)}$
x= $\frac{ 12+/- \sqrt{144-60} }{2}$
x= $\frac{ 12+/- \sqrt{84} }{2}$
x= $\frac{ 12+/- 2\sqrt{21} }{2}$
x=6+/- $\sqrt{21}$
x=6+ $\sqrt{21}$ or 6- $\sqrt{21}$ or aprox
x=10.5826 or 1.41742
the numbers are 10.5826 and 1.41742

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If f ( x ) = 3x 2 - 6x + 2 and g ( x ) = 2x 2 + 2x - 11,<br> then find f ( x ) + g ( x ).

nikitadnepr [17]

Answer:

$5x^{2} -4x-9$

Step-by-step explanation:

f(x)+g(x)

$(3x^{2} -6x+2) + (2x^{2} +2x-11)\\3x^{2} -6x+2 + 2x^{2} +2x-11\\$
combine like terms --
$5x^{2} -4x-9$

6 0

2 years ago

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Marrrta [24]

Answer:

$f(x)=-\frac{1}{8}(x-4)^2+3$

Step-by-step explanation:

The directrix given to us has equation,

$y=5$ and the focus is $(4,1)$ .

This means that the axis of symmetry of the parabola is parallel to the y-axis and has equation $x=4$ , because it must go through the focus.

This axis of symmetry of the parabola will meet the directrix at $(4,5)$ .

The vertex of this parabola is the midpoint of the point of intersection of the axis of symmetry and the focus.

Thus,

$V(h,k)=(\frac{4+4}{2},\frac{5+1}{2})$

$V(h,k)=(4,3)$ .

The equation is given by $(x-h)^2=4p(y-k)$ .

$(x-4)^2=4p(y-3)$ .

$|p|$ is the distance between the vertex and the focus, which is 2.

This implies that,

$p=-2$ or $p=2$

But the position of the directrix and the vertex implies that the parabola opens downwards.

$\therefore p=-2$ .

The equation of the parabola now becomes;

$(x-4)^2=4(-2)(y-3)$ .

$(x-4)^2=-8(y-3)$

We solve for y to obtain,

$y=-\frac{1}{8}(x-4)^2+3$

$f(x)=-\frac{1}{8}(x-4)^2+3$

7 0

3 years ago

What is the answer need it

denis-greek [22]

Answer:

$\frac{7}{10} |$

Step-by-step explanation:

STEP 1:

2/3 + 7/10 = ?

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(2/3, 7/10) = 30

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

$(\frac{2}{3}$ * $\frac{10}{10})$ + $(\frac{7}{10} * \frac{3}{3})$ = ?

Complete the multiplication and the equation becomes

$\frac{20}{30} + \frac{21}{30}$

The two fractions now have like denominators so you can add the numerators.

Then:

$\frac{20+21}{30} = \frac{41}{30}$

This fraction cannot be reduced.

The fraction 41/30

is the same as

41 divided by 30

Convert to a mixed number using

long division for 41 ÷ 30 = 1R11, so

41/30 = 1 11/30

Therefore:

2/3+7/10= 1 11/30

STEP 2:

41/30 + -2/3

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(41/30, -2/3) = 30

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

$(\frac{41}{30} *\frac{1}{1} ) + ( \frac{-2}{3} * \frac{10}{10} )$