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3 years ago

Not good with factoring could use a hand.

Mathematics

1 answer:

MrRa [10]3 years ago

6 0

The only factoring you need to do is already done for you:

x² + x - 12 = (x + 4) (x - 3)

What you're asked to do is decompose

(3x - 4) / (x² + x - 12)

into partial fractions, i.e. find a and b such that

(3x - 4) / (x² + x - 12) = a / (x + 4) + b / (x - 3)

Multiply both sides by x² + x - 12 :

3x - 4 = a (x - 3) + b (x + 4)

3x - 4 = (a + b) x + (-3a + 4b)

So we have

a + b = 3

-3a + 4b = -4

and solving this system gives

a = 16/7 and b = 5/7

so you should submit the numbers in bold:

(3x - 4) / (x² + x - 12) = 16 / (7 (x + 4)) + 5 / (7 (x - 3))

You might be interested in

A special discount was offered to the employees of Ryan's, a lead ing men's store. Employees were given their employee discount

Helen [10]

Answer: a) $2155, b) $1763.03.

Step-by-step explanation:

Since we have given that

Number of cable knit sweaters = 15

Cost per sweaters = $65.00

Number of pairs of khaki twill pants = 22

Cost of each pair = $50.00

Number of casual jackets = 18

Cost of each jackets = $62.00

total sale volume would be

$15\times 65+22\times 50+18\times 62\\\\=\$3191$

Employee discount = 35%

Additional discount = 15%

So, Total markdown dollars taken is given by

$3191\times \dfrac{100-35}{100}\times \dfrac{100-15}{100}\\\\=3191\times \dfrac{65}{100}\times \dfrac{85}{100}\\\\=3191\times 0.65\times 0.85\\\\=\$1763.0275$

Hence, a) $2155, b) $1763.03.

4 0

3 years ago

13....................

Mashcka [7]

13.

(a)

$y=-5x^2+21x-3$

for x = 2:

$y=-5(2)^2+21(2)-3=-20+42-3=19$

for x = 5

$y=-5(5)^2+21(5)-3=-125+105-3=-23$

(b)

The graph is:

(c)

Using the graph:

$\begin{gathered} x=1.8,y=18.6 \\ x=0.548,y=7 \\ x=3.65,y=7 \end{gathered}$ $\begin{gathered} x=1.8 \\ y=-5(1.8)^2+21(1.8)-3=-16.2+37.8-3=18.6 \end{gathered}$ $\begin{gathered} y=7 \\ -5x^2+21x-3=7 \\ -5x^2+21x-10=0 \end{gathered}$

Using the quadratic formula:

$\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-21\pm\sqrt[]{21^2-4(-5)(-10)}}{2(-5)} \\ x=\frac{-21\pm\sqrt[]{241}}{-10} \\ x=0.54758 \\ or \\ x=3.6524 \end{gathered}$

6 0

1 year ago

Circumference of a circular disc is 157 cm, find its radius

Zielflug [23.3K]

Answer:

Owwwww would be a good time

7 0

3 years ago

Read 2 more answers

Let C = C1 + C2 where C1 is the quarter circle x^2+y^2=4, z=0,from (0,2,0) to (2,0,0), and where C2 is the line segment from (2,

trapecia [35]

Not much can be done without knowing what $\mathbf F(x,y,z)$ is, but at the least we can set up the integral.

First parameterize the pieces of the contour:

$C_1:\mathbf r_1(t_1)=(2\sin t_1,2\cos t_1,0)$
$C_2:\mathbf r_2(t_2)=(1-t_2)(2,0,0)+t_2(3,3,3)=(2+t_2, 3t_2, 3t_2)$

where $0\le t_1\le\dfrac\pi2$ and $0\le t_2\le1$ . You have

$\mathrm d\mathbf r_1=(2\cos t_1,-2\sin t_1,0)\,\mathrm dt_1$
$\mathrm d\mathbf r_2=(1,3,3)\,\mathrm dt_2$

and so the work is given by the integral

$\displaystyle\int_C\mathbf F(x,y,z)\cdot\mathrm d\mathbf r$
$=\displaystyle\int_0^{\pi/2}\mathbf F(2\sin t_1,2\cos t_1,0)\cdot(2\cos t_1,-2\sin t_1,0)\,\mathrm dt_1$
${}\displaystyle\,\,\,\,\,\,\,\,+\int_0^1\mathbf F(2+t_2,3t_2,3t_2)\cdot(1,3,3)\,\mathrm dt_2$

5 0

3 years ago

Which is bigger .24 or .71

monitta

Answer:

.71

Step-by-step explanation:

7 0

3 years ago