What is the value of k in this table?
A.
288
B.
306
C.
324
D.
576

Answer:

x = 8

x = 1

Step-by-step explanation:

STEP 1:

Equation at the end of step 1

 (22x2 -  36x) +  32  = 0

STEP 2:

STEP 3: Pulling out like terms

3.1     Pull out like factors :

  4x2 - 36x + 32  =   4 • (x2 - 9x + 8)

Trying to factor by splitting the middle term

3.2     Factoring  x2 - 9x + 8

The first term is,  x2  its coefficient is  1 .

The middle term is,  -9x  its coefficient is  -9 .

The last term, "the constant", is  +8

Step-1 : Multiply the coefficient of the first term by the constant   1 • 8 = 8

Step-2 : Find two factors of  8  whose sum equals the coefficient of the middle term, which is   -9 .

     -8    +    -1    =    -9    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  -1

                    x2 - 8x - 1x - 8

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-8)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x-8)

Step-5 : Add up the four terms of step 4 :

                   (x-1)  •  (x-8)

            Which is the desired factorization

Equation at the end of step

3

:

 4 • (x - 1) • (x - 8)  = 0

STEP

4

:

Theory - Roots of a product

4.1    A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Equations which are never true:

4.2      Solve :    4   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

4.3      Solve  :    x-1 = 0

Add  1  to both sides of the equation :

                     x = 1

Solving a Single Variable Equation:

4.4      Solve  :    x-8 = 0

Add  8  to both sides of the equation :

                     x = 8

Supplement : Solving Quadratic Equation Directly

Solving    x2-9x+8  = 0   directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

5.1      Find the Vertex of   y = x2-9x+8

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   4.5000  

Plugging into the parabola formula   4.5000  for  x  we can calculate the  y -coordinate :

 y = 1.0 * 4.50 * 4.50 - 9.0 * 4.50 + 8.0

or   y = -12.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-9x+8

Axis of Symmetry (dashed)  {x}={ 4.50}

Vertex at  {x,y} = { 4.50,-12.25}

x -Intercepts (Roots) :

Root 1 at  {x,y} = { 1.00, 0.00}

Root 2 at  {x,y} = { 8.00, 0.00}

Solve Quadratic Equation by Completing The Square

5.2     Solving   x2-9x+8 = 0 by Completing The Square .

Subtract  8  from both side of the equation :

  x2-9x = -8

Now the clever bit: Take the coefficient of  x , which is  9 , divide by two, giving  9/2 , and finally square it giving  81/4

Add  81/4  to both sides of the equation :

 On the right hand side we have :

  -8  +  81/4    or,  (-8/1)+(81/4)

 The common denominator of the two fractions is  4   Adding  (-32/4)+(81/4)  gives  49/4

 So adding to both sides we finally get :

  x2-9x+(81/4) = 49/4

Adding  81/4  has completed the left hand side into a perfect square :

  x2-9x+(81/4)  =

  (x-(9/2)) • (x-(9/2))  =

 (x-(9/2))2

Things which are equal to the same thing are also equal to one another. Since

  x2-9x+(81/4) = 49/4 and

  x2-9x+(81/4) = (x-(9/2))2

then, according to the law of transitivity,

  (x-(9/2))2 = 49/4

We'll refer to this Equation as  Eq. #5.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-(9/2))2   is

  (x-(9/2))2/2 =

 (x-(9/2))1 =

  x-(9/2)

Now, applying the Square Root Principle to  Eq. #5.2.1  we get:

  x-(9/2) = √ 49/4

Add  9/2  to both sides to obtain:

  x = 9/2 + √ 49/4

Since a square root has two values, one positive and the other negative

  x2 - 9x + 8 = 0

  has two solutions:

 x = 9/2 + √ 49/4

  or

 x = 9/2 - √ 49/4

Note that  √ 49/4 can be written as

 √ 49  / √ 4   which is 7 / 2

Solve Quadratic Equation using the Quadratic Formula

5.3     Solving    x2-9x+8 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     1

                     B   =    -9

                     C   =   8

Accordingly,  B2  -  4AC   =

                    81 - 32 =

                    49

Applying the quadratic formula :

              9 ± √ 49

  x  =    —————

                   2

Can  √ 49 be simplified ?

Yes!   The prime factorization of  49   is

  7•7

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 49   =  √ 7•7   =

               ±  7 • √ 1   =

               ±  7

So now we are looking at:

          x  =  ( 9 ± 7) / 2

Two real solutions:

x =(9+√49)/2=(9+7)/2= 8.000

or:

x =(9-√49)/2=(9-7)/2= 1.000

Two solutions were found :

x = 8

x = 1

Answer:

Step-by-step explanation:

Given

We see that:

This is a vertical stretch by a factor of 3 and translation down 2 units

Correct choice is D

Answer: The answer is number 4

Step-by-step explanation:

The answer is the one in the right up, the first one.

Answer:

x + 6 y - 4

Step-by-step explanation:

A moved 6 units to the right so plus 6 then moved 4 units down so minus 4

Answer:

61

Step-by-step explanation:

Answer:

Step-by-step explanation:

12)

we are told that ∠ABD = 61°

then we also know that ∠ADB = 61° b/c there are the equal legs of an isosceles triangle.

and we know by inspection that the ΔBCD is identical to ΔABD so it also has 61° angles so

∠ABC = 61 + 61 =122°

:)

Answer:

Your answer is 346.36059

Step-by-step explanation:

A = pi*r²

A = pi * 10.5²

A = pi * 110.25

A = 346.36059

We can write the the area of the circle as 110.25π square centimeter.

Area is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫F(x, y) dx dy

Given is a circle whose diameter is 21 cm​.

It is asked to find the area of a circle whose diameter is 21 cm​.

It is given that the diameter of the circle is -

d = 21 cm

r = d/2 = 21/2

r = 10.5 cm

We know that the area of the circle as -

Area = πr²

Area = π x 10.5 x 10.5

Area = 110.25π

So, it can be concluded that the area of the circle is 110.25π square centimeter.

Therefore, we can write the the area of the circle as 110.25π square centimeter.

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surface area= perimeter x height + 2b

s= pxh+2b

example: 18(8)+2(12)

explain:  18 is the perimeter and 8 is the height then you have to add the base times 2

Answer: The expected count of cake purchases is 66.67 (rounded to the hundreths).

Step-by-step explanation:  Hypothesis the bakery is trying to find is if customers are equally likely to buy each product and since the sample is 200, we would have to equally split that between the 3 categories, so the expected counts for Cakes, cookies, and pastries would all be 66.67 (rounded to the hundreths).

The expected count of cake purchases would be 66.67 (rounded to the hundredths).

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

The results are given as:

Product   Observed purchases

Cakes        65

Cookies    68

Pastries     67

To find if customers are equally likely to buy each product and since the sample is 200,

we would have to equally split that between the 3 categories,

The expected count of cake purchases = 200/3

= 66.67

Thus, the expected counts for Cakes, cookies, and pastries would be 66.67 (rounded to the hundredths).

Learn more about the unitary method;

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Answer:

d $258.50

Step-by-step explanation:

hope it helps

Answer:

[tex] \frac{1}{ \frac{ - 3}{ {6}^{x} } } \\ = 1 \times \frac{ {6}^{x} }{ - 3} \\ = - \frac{ {6}^{x} }{3} [/tex]

Answer:

52.708

Explanation:

It's 708 instead of 78 even rounded 52.708 would be more.

Answer:

52.708 is greater then 52.078

Step-by-step explanation:

Thats the answer!! Hope I could help u!! :)

Answer:

(0,0)

Step-by-step explanation:

The midpoint is (0,0) because as you can see in the graph the middle would be (0,0). However, if point A moved even one step further or closer the midpoint will also shift

Answer:

the answer is 23.........

Answer:

17/29 or 58.6%

Step-by-step explanation:

P(G or R) = 8/29 + 9/29 = 17/29

Answer:

Step-by-step explanation:

Answer:

[tex]\sf \dfrac{1}{21}[/tex]

Step-by-step explanation:

[tex]\textsf{To calculate}-\dfrac{2}{7}+\dfrac{1}{3}, \: \textsf{ first make the denominators the same}.[/tex]

[tex]\textsf{Adjust the fractions based on their lowest common multiplier}:[/tex]

[tex]\implies -\dfrac{2}{7} \cdot \dfrac{3}{3} + \dfrac{1}{3} \cdot \dfrac{7}{7}[/tex]

[tex]\implies -\dfrac{2 \cdot 3}{7 \cdot 3} + \dfrac{1 \cdot 7}{3 \cdot 7}[/tex]

[tex]\implies -\dfrac{6}{21}+\dfrac{7}{21}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]

[tex]\implies \dfrac{-6+7}{21}[/tex]

[tex]\textsf{Add the numbers of the numerator}:[/tex]

[tex]\implies \dfrac{1}{21}[/tex]

Learn more about fractions here:

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C. 700 units.

The formula for the surface area of a rectangular prism is: 2 ((Width × Length) + (Height × Length) + (Height × Width))

(14 × 12) + (7 × 12) + (7 × 14)

168 + 84 + 98 = 350

Now do 350 × 2 = 700

700 units squared.

Answer: (2,4)

Step-by-step explanation: The coordinates are 2,4

Answer:

the solution is (2, 3)

Step-by-step explanation:

Make this work easier by reducing the second equation:

-x + y = 1, or y = x + 1

Substititing x + 1 for y in the first equation, we get:

x + 1 = -5x + 13, or (after combining like terms):

6x = 12

Then x = 2, and bercause y = x + 1 (see above), y = 2 + 1 = 3

Then the solution is (2, 3)

The difference in the interest that the account will have earned at the end of 10 years is of:

D. $3.01.

The amount of interest earned, in compound interest, after t years, is given by:

[tex]I(t) = P\left(1 + \frac{r}{n}\right)^{nt} - P[/tex]

In which the variables are listed as follows:

In the context of this problem, these parameters are given as follows:

P = 250, r = 0.016, n = 12, t = 10.

Hence the interest earned by account 1 is:

[tex]I(10) = 250\left(1 + \frac{0.016}{12}\right)^{12 \times 10} - 250 = 43.35[/tex]

For simple interest, the amount of interest earned is:

I(t) = Prt.

Hence:

I(10) = 250 x 0.016 x 10 = 40.

Hence the difference is:

43.35 - 40 = $3.35.

Which is closest to option D.

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Answer:

6in

Step-by-step explanation:

Answer:

x=-4 , x=3

Step-by-step explanation:

just did it on math-ways

Step-by-step explanation:

R' = (-2,0)

E' = (-2,2)

F' = (4,4)

Answer:

step 1: x+50+4x=90

the angle of a right-angled triangle is 90 degrees, therefore if we add everything together ,we could work out what x is.

step 2: x+50+4x=90

                  x+4x=50

                      5x=50

                        x=10

then you solve the equation, x is 10

Answer:

N = -8

Hope this helps!

Mark me brainliest if I'm right :)

Answer: The Answer is D.) 16/25

Step-by-step explanation: I got it correct on Study Island