find equation of the line that contains the point (4,-2) and is perpendicular to the line y= _2x+8

Answer:

B

Step-by-step explanation:

Do 115000/100x6.5    You get 7.475k

The polynomials completely factorized have the following expressions;

50). x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

51). x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

52). x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

53). x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

For the polynomial x³ - 3x² - 26x - 12 divisible by x - 6;

(x³ - 3x² - 26x - 12)/(x - 6) = x² + 3x + 2

x² + 3x + 2 = (x + 1)(x + 2)

so;

x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

For the polynomial x³ - 12x² + 12x + 80 divisible by x - 10;

(x³ - 12x² + 12x + 80)/(x - 10) = x² - 2x - 8

x² - 2x - 8 = (x + 2)(x - 4)

so;

x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

For the polynomial x³ - 18x² + 95x + 126 divisible by x - 9;

(x³ - 12x² + 12x + 80)/(x - 9) = x² - 9x + 14

x² - 9x + 14 = (x - 2)(x - 7)

so;

x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

For the polynomial x³ - x² + 21x + 45 divisible by x + 5;

(x³ - x² + 21x + 45)/(x + 5) = x² - 6x + 9

x² - 6x + 9 = (x - 3)(x - 3)

so;

x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

Therefore, by complete factorization the expressions (x - 6)(x + 1)(x + 2), (x - 10)(x + 2)(x - 4), (x - 9)(x - 2)(x - 7), and (x + 5)(x - 3)(x - 3) are the factors of their respective polynomial.

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(i) Use the formula for the determinant of a 2×2 matrix.

\(\begin{vmatrix}a&b\\c&d\end{vmatrix} = ad-bc\)

\(\implies \det(A) = \begin{vmatrix}4 & -3 \\ 2 & 5\end{vmatrix} = 4\times5 - (-3)\times2 = \boxed{26}\)

(ii) The adjugate matrix is the transpose of the cofactor matrix of A. (These days, the "adjoint" of a matrix X is more commonly used to refer to the conjugate transpose of X, which is not the same.)

The cofactor of the (i, j)-th entry of A is the determinant of the matrix you get after deleting the i-th row and j-th column of A, multiplied by \((-1)^{i+j}\). If C is the cofactor matrix of A, then

\(C = \begin{pmatrix}5&-2\\3&4\end{pmatrix}\)

Then the adjugate of A is the transpose of C,

\(\mathrm{adj}(A) = C^\top = \boxed{\begin{pmatrix}5&3\\-2&4\end{pmatrix}}\)

(iii) The inverse of A is equal to 1/det(A) times the adjugate:

\(A^{-1} = \dfrac1{\det(A)} \mathrm{adj}(A) = \boxed{\begin{pmatrix}\frac5{26}&\frac3{26}\\\\-\frac1{13}&\frac2{13}\end{pmatrix}}\)

(iv) The system of equations translates to the matrix equation

\(A\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}6\\16\end{pmatrix}\)

Multiplying both sides on the left by the inverse of A gives

\(A^{-1}\left(A\begin{pmatrix}x\\y\end{pmatrix}\right)=A^{-1} \begin{pmatrix}6\\16\end{pmatrix}\)

\(\left(A^{-1}A\right)\begin{pmatrix}x\\y\end{pmatrix}=A^{-1} \begin{pmatrix}6\\16\end{pmatrix}\)

\(\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}\frac5{26}&\frac3{26}\\\\-\frac1{13}&\frac2{13}\end{pmatrix} \begin{pmatrix}6\\16\end{pmatrix}\)

\(\begin{pmatrix}x\\y\end{pmatrix}=\boxed{\begin{pmatrix}3\\2\end{pmatrix}}\)

Answer:

Step-by-step explanation:

\(y=(\frac{1}{g} )x\)

Constant up a proportionally is  \(\frac{1}{g}\).

Answer:

11x+6

Step-by-step explanation:

Using FOIL

(x+1)-(-2x-5)-original

F-first=(x+2x)=3x

O-outside=(x+5)=5x

I-inside=(1+2x)=3x

L-last=(1+5)=6

11x+6

Answer:

560   should be your answer

Step-by-step explanation:

hope it helped

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=3\\ y=18 \end{cases} \\\\\\ 18=a(3-0)^2+0\implies 18=9a\implies \cfrac{18}{9}=a\implies 2=a \\\\\\ y=2(~~x-0~~)^2 + 0\implies \boxed{y=2x^2}\)

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer: 23.76 sq yds

Step-by-step explanation:

0.5*9.9*4.7=23.76

Area of triangle: 0.5*b*h

Solution :

Given :

\($n_1=388$\) , \($x_1 = 294, \ n_2 = 566, \ x_2 = 38$\)

Sample proportion, \($(\hat p_1)=\frac{x_1}{n_1}$\)

                                        \($=\frac{294}{388}$\)

                                       = 0.7577

Sample proportion, \($(\hat p_2)=\frac{x_2}{n_2}$\)

                                        \($=\frac{38}{566}$\)

                                       = 0.0671

For 95 % CI, z = 1.96

The confidence interval for the population proportion,

\($p_1-p_2=(\hat p_1-\hat p_2)\pm z \left\{\sqrt{\frac{\hat p_1 \times (1- \hat p_1)}{n_1}+\frac{\hat p_2 \times (1- \hat p_2)}{n_2}}\right\}$\)

           \($=(0.7577-0.0671)\pm 1.96 \left\{\sqrt{\frac{0.7577 \times (1- 0.7577)}{388}+\frac{0.0671 \times (1- 0.0671)}{566}}\right\}$\)

\($=0.6906 \pm 1.96 \times \left 0.0241$\)

= \($0.6906 \pm 0.0472 $\)

Lower limit : 0.6906 - 0.0472 = 0.6434

Upper limit : 0.6906 + 0.0472 = 0.7378

Answer:

160 units²

Step-by-step explanation:

Surface area of the square pyramid = a² + 2al

Where,

a = side length of the square = 8

l = slant height of the triangular face = 6

Plug in the values

Surface area of the square pyramid = 8² + 2*8*6

= 64 + 96

= 160 units²

Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

3/5 or 60% of the prism's volume will be filled with sand.

The volume of each cube is e³ = 5³ = 125 cubic centimeters.

Since the rectangular prism is made up of two cubes, its volume is 2e³ = 2(125) = 250 cubic centimeters.

If Arusha fills the prism with 150 cubic centimeters of sand, the fraction of the prism's volume that will be filled with sand is:

150/250 = 3/5

Therefore, 3/5 or 60% of the prism's volume will be filled with sand.

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Answer:

tobe specific, it is 53.33%, but if you want just a whole #, it is 53%

Answer:

53.33%

Step-by-step explanation:

or 53% if rounded to the nearest whole

The correct option is B: The result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.

Once kids have a firm grasp on right fractions, they are exposed to mixed numbers and improper fractions.

Divide the numerator and denominator to create a mixed fractions from an incorrect fraction. The solution to this problem is the whole number portion; the leftover portion is the numerator; its denominator stays the same.

We can convert the two fractions to decimal form in order to compare them.

7.375 is equivalent to 7 3/8, and

4/5 is equivalent to 0.8.

7.375 multiplied by 0.8 results in:

7.375 × 0.8 = 5.9

Since the result is 5.9, which is less than 7.375, it follows that 7 3/8 multiplied by 4/5 is less than 7 3/8.

Thus, the result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.

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Answer:

asd

Step-by-step explanation:

sadasdasdasdasnst465557

Answer:

Step-by-step explanation:

Answer:

58 inches

Step-by-step explanation:

In order to find the perimeter of a shape, you must add up the total length of all the sides. 15 inches + 12 inches + 8 inches + 9 inches + 14 inches = 58 inches.

Given the polynomial Q(x)=2x^3+3x^2+3x+1, and knowing the only real zero is x= -1/2, the complex zeros are:

z1 = -3/4 + (√(3) / 2)i

z2 = -3/4 - (√(3) / 2)i

Since the polynomial Q(x) has degree 3 and only one real zero, we know that it must have two complex zeros in the form of a complex conjugate pair, let's call them z1 and z2.

From Vieta's Formulas, we know that the sum of the zeros of a polynomial is equal to the negation of the coefficient of the linear term divided by the leading coefficient. So, in this case:

z1 + z2 = -3/2

Also, the product of the zeros of a polynomial is equal to the negation of the constant term divided by the leading coefficient. So, in this case:

z1 * z2 = -1/2

Since z1 and z2 are complex conjugates, they have the same magnitude and opposite phases. Hence, we can represent them in the form:

z1 = a + bi

z2 = a - bi

where a and b are real numbers and "i" is the imaginary unit.

Using the two equations above, we can find the value of "a" and "b":

a = -3/4

b = √(1/4 - (-1/2)) = √(3/4) = √(3) / 2

So, the complex zeros are:

z1 = -3/4 + (√(3) / 2)i

z2 = -3/4 - (√(3) / 2)i

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Answer:

Step-by-step explanation:

Given the polynomial Q(x)=2x^3+3x^2+3x+1, and knowing the only real zero is x= -1/2, the complex zeros are:

z1 = -3/4 + (√(3) / 2)i

z2 = -3/4 - (√(3) / 2)i

The value of the fraction expression -2 1/2 - (-4 3/5) is 2 1/10

From the question, we have the following parameters that can be used in our computation:

−2 /2/1 −(−4 3/5)

Express properly

So, we have the following representation

-2 1/2 - (-4 3/5)

Remove the brackets

This gives

-2 1/2 - (-4 3/5) = -2 1/2 + 4 3/5

Express the denominator as 10

So, we have

-2 1/2 - (-4 3/5) = -2 5/10 + 4 6/10

Evaluate the difference

-2 1/2 - (-4 3/5) = 2 1/10

Hence, the solution is 2 1/10

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Answer:

10.2

Step-by-step explanation:

if u write is down with the decimals tgat and count that is what u would get also 2 plus 8 is ten and two pluse two is 41

The expression that represent the perimeter of the triangle is 3d² - 4d + 1.

The perimeter of any two-dimensional figure is simply the distance around the figure.

Hence, the perimeter of the triangle is the sum of all its 3 side lengths.

From the diagram:

Side length 1 = ( d² + 3 )

Side length 2 = ( 4d² + 3d - 2 )

Side length 3 = ( -2d² - 7d )

Hence, the perimeter of the triangle will be:

Perimeter = side length 1 + side length 2 + side length 3

Plug in the expressions

Perimeter = ( d² + 3 ) + ( 4d² + 3d - 2 ) + ( -2d² - 7d )

Collect and add like terms:

Perimeter = d² + 3 + 4d² + 3d - 2 + -2d² - 7d

Perimeter = d² + 4d² - 2d² + 3d - 7d + 3 - 2

Perimeter = 3d² - 4d + 1

Therefore, the perimeter is 3d² - 4d + 1.

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Answer:

m= -1

y intercept= 1

y= - x + 1

Step-by-step explanation:

Answer: 60

Step-by-step explanation:

Formula to find sample size :\(n=(\dfrac{z^c\times\sigma}{E})^2\), where \(z^c\) = critical z value , E -= Margin of error, \(\sigma\) = population standard deviation.

Given: E= 2.3

Critical z-value for 99% confidence level = 2.576

\(\sigma=6.9\)

Then, required sample size :

\(n=(\dfrac{6.9\times2.576}{2.3})^2=(7.728)^2\\\\=59.72\approx60\)

Hence, the required sample size = 60

Answer:

18. 4/12

Step-by-step explanation

1/6 x 6/3 = 6/18= 1/3

1/3 x 4/4 = 4/12

Answer:

First Answer: 5.5

Second Answer: 12

Step-by-step explanation: Hope this helps

Answer:

D. its a two dimensional object

Answer:

A. It is a polygon

C. It is a one-dimensional object

The shape is a polygon in two dimensions since a polygon must have at least three straight sides.

Answer:

5 ≤ L ≤ 35

Step-by-step explanation:

Let w represent the width of the rectangle.

The perimeter (P) of the rectangle is given by:

P = 2w + 2L

Where L is the length of the rectangle.

We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:

100 ≤ 2(30) + 2L ≤ 160

100 ≤ 90 + 2L ≤ 160

10 ≤ 2L ≤ 70

We can now divide both sides by 2 to solve for L:

5 ≤ L ≤ 35

Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is:  5 ≤ L ≤ 35

Answer:

8x-4

Step-by-step explanation:

4 is less meaning it is subtraction and product of 8 and x is 8x

Answer:

4x² + 24x + 36

Step-by-step explanation:

(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36

Answer:

I'm think its parallel ||