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Rasek [7]
4 years ago
5

Factor by grouping...

Mathematics
1 answer:
kupik [55]4 years ago
7 0

Answer:

x^3+9x^2-6x-54=0

Step-by-step explanation:

or, x^2(x+9)-6(x+9)=0

or,(x+9)(x^2-6)=0

Either

x+9=0

x=-9

Or

x^2-6=0

x^2=6

x=-9,x^2 =6

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If this is the given data 24, 12, 19, 26, 19, 20, 15, 17 what is the median​
MAXImum [283]

Answer:

19

Step-by-step explanation:

Rearranging the number in ascending order,

12,15,17,19,19,20,24,26

Median = The average of the 4th and 5th number

=  \frac{19 + 19}{2}  \\  = 19

4 0
3 years ago
Read 2 more answers
Which of the following represents a relation that is NOT a function? A. X 7 -5 10 -7 Y 34 32 40 34 B. X -7 -5 -7 2 Y 34 32 40 34
Nostrana [21]
The x-value of -7 shows up more than once in relation ...
  B. X -7 -5 -7 2 Y 34 32 40 34

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When there is more than one y-value for an x-value, the relation is NOT a function.
8 0
4 years ago
Find the missing side of a right triangle with leg length 5 yards and hypotenuse 13 yards.
Roman55 [17]

<em>answer =12 \: yards  \\ solution \\ hypotenuse(h) = 13 \: yards \\ perpendicular(p) = 5 \: yards \\ base(b) = ?\\ using \: pythagorus \: theorem \\  {h}^{2}  =  {p}^{2}  +  {b}^{2}  \\  {b}^{2}  =  {h}^{2}  -  {p}^{2}  \\  {b}^{2}  =  {13}^{2}  -  {5}^{2}  \\  {b}^{2}  = 169 - 25 \\  {b}^{2}  = 144 \\ b =  \sqrt{144 }  \\ b =  \sqrt{ {12}^{2} }  \\ b = 12 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment</em>

4 0
4 years ago
Read 2 more answers
A family is purchasing a house and needs to finance a $195,000 mortgage from the bank with an annual percentage rate (APR) of 5.
Airida [17]

Answer:

  a) payment: $1082.84

  b) interest: $194,822.40

Step-by-step explanation:

The monthly payment on the mortgage can be found using the given formula with the given values of principal (P=195000), interest rate (r=0.053), and time period (t=30). The value of n is 12, corresponding to the number of months in a year.

<h3>a)</h3>

The monthly payment is ...

  k=\left(1+\dfrac{r}{n}\right)^{nt}=\left(1+\dfrac{0.053}{12}\right)^{12\cdot30}\approx 4.88661119\\\\\text{monthly payment}=\dfrac{P\cdot\dfrac{r}{n}\cdot k}{k-1}=\dfrac{195000\cdot0.0044166667\cdot4.88661119}{4.88661119-1}\\\\\boxed{\text{monthly payment}=\$1082.84}

__

<h3>b) </h3>

The interest owed is the difference between the total of monthly payments and the principal of the loan:

  interest owed = (360)(1082.84) -195000 = 194,822.40

The interest owed over 30 years is $194,822.40.

3 0
2 years ago
How do you determine the area under a curve in calculus using integrals or the limit definition of integrals?
RSB [31]

Answer:

Please check the explanation.

Step-by-step explanation:

Let us consider

y = f(x)

To find the area under the curve y = f(x) between x = a and x = b, all we need is to integrate y = f(x) between the limits of a and b.

For example, the area between the curve y = x² - 4 and the x-axis on an interval [2, -2] can be calculated as:

A=\int _a^b|f\left(x\right)|dx

    = \int _{-2}^2\left|x^2-4\right|dx

\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx

   =\int _{-2}^2x^2dx-\int _{-2}^24dx

solving

\int _{-2}^2x^2dx

\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1

   =\left[\frac{x^{2+1}}{2+1}\right]^2_{-2}

    =\left[\frac{x^3}{3}\right]^2_{-2}

computing the boundaries

     =\frac{16}{3}

Thus,

\int _{-2}^2x^2dx=\frac{16}{3}

similarly solving

\int _{-2}^24dx

\mathrm{Integral\:of\:a\:constant}:\quad \int adx=ax

     =\left[4x\right]^2_{-2}

computing the boundaries

      =16

Thus,

\int _{-2}^24dx=16

Therefore, the expression becomes

A=\int _a^b|f\left(x\right)|dx=\int _{-2}^2x^2dx-\int _{-2}^24dx

  =\frac{16}{3}-16

  =-\frac{32}{3}

  =-10.67 square units

Thus, the area under a curve is -10.67 square units

The area is negative because it is below the x-axis. Please check the attached figure.

   

6 0
3 years ago
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