need help would be apperacited .​

The factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)

The expression is given as:

x^3 + 4x^2 +5x + 20

Group the expression into two

(x^3 + 4x^2) + (5x + 20)

Factorize each group

x^2(x + 4) + 5(x + 4)

Factor out x + 4

(x^2 + 5)(x + 4)

Hence, the factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)

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Answer: x = 0

Step-by-step explanation:

Given:

   x + 4x = 0

Combine like terms:

   5x = 0

Divide both sides of the equation by 5:

   x = 0

We can also check our work by graphing. See attached, intercepts of the x-axis are solutions.

The parametric equation that represents the same path as the original equation is x = 3 + cos(2θ) and y = 2sin(2θ).

The given parametric equation can be expressed as follows;

x = 3 + cosθ

y = 2sinθ

From the given options, a plot of the various equation can be used to determine the paths of the equation.

For; x = 3 + cos(2θ) and y = 2sin(2θ), its parametric plots is same as original equation since the equation [3 + cos(2θ) and y = 2sin(2θ)] changed at equal rate of the angles.

Thus, the parametric equation that represents the same path as the original equation is x = 3 + cos(2θ) and y = 2sin(2θ).

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The complete question is

"A solid sphere is cut into 12 equal wedges. The volume of each wedge is V= 4/3πr³. Solve the formula for r."

A solid sphere is cut into 12 equal wedges. The volume of each wedge is V= 4/3πr³. The value of r is (9V/π)^1/3.

It is given that;

The  Volume of a sphere = V = 4/3πr³

Dividing into 12

4/3 x 1/12 πr³ = 1/9πr³

V = 1/9πr³

Cross multiply

9V = πr³

Divide both sides by π

9V/ π = πr³/ π

9V/ π = r³

Take the cube root of both sides

r = (9V/π)^1/3

Thus, The value of r is (9V/π)^1/3.

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The point (3, -4) lie on the line y + 4 = 4(x - 3) because the point (3,-4) satisfy the line option (A) is correct.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have an equation of a line:

y + 4 = 4(x - 3)

A (3,-4)  

Plug the above points in the equation of the line.

-4 + 4 = 4(3 -3)

0 = 0    (true)

The point lies on the line

Similarly checking for others points we will find that points (2,9), (0,0) , (1,-11), (1,11), and (-2, 3) does not lie on the line y + 4 = 4(x - 3)

Thus, the point (3, -4) lie on the line y + 4 = 4(x - 3) because the point (3,-4) satisfy the line option (A) is correct.

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Answer:

Answer: -3/2

Step-by-step explanation:

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[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve ~

We need to find volume of the given Cylinder, with information :

[tex]\qquad \sf  \dashrightarrow \:Volume_{(Cylinder)} = \pi r²h[/tex]

[tex]\qquad \sf  \dashrightarrow \:Volume_{(Cylinder)} = \pi \sdot(12) {}^{2} \sdot17[/tex]

[tex]\qquad \sf  \dashrightarrow \:Volume_{(Cylinder)} = \pi \sdot144{}^{} \sdot17[/tex]

[tex]\qquad \sf  \dashrightarrow \:Volume_{(Cylinder)} = 2448 \pi \: \: unit {}^{3} [/tex]

So, correct choice is B

The volume of the given cylinder is 2448π cubic units

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

We have to find the volume of the given cylinder

Radius is 12 units

Height is 17 units

Volume of cylinder= πr²h

Plug in the values of radius and height

Volume = π×12²×17

=π×144×17

=2448π cubic units

Hence, the volume of the given cylinder is 2448π cubic units

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After 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

We have a line of best fit:

y = 2.5 + 1.25x

Plug x = 7 weeks

y = 2.5 + 1.25(7)

y = 11.25 units

Thus, after 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.

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answer 2/3

check the attachments for more info

hope it helps :)

The functions f(x) and g(x) are equal for the x = 2/3

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given that, are two functions, f(x) = -3x + 4 and g(x) = 2, we need to find the value of x for which both are equal,

So,  

For f(x) = g(x) we should equate the two functions to get the value of x.

f(x) = g(x)

-3x + 4 =  2

-3x + 4 - 4 = 2 - 4

-3x = -2

Dividing by -3 on both sides;

(-3x)/-3 = (-2)/-3

x = 2/3

Hence, the  functions f(x) and g(x) are equal for the x = 2/3

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to get the equation of any straight line, we simply need two points off of it, let's use the ones in the table.

[tex]\begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} -1&-10\\ 3&14\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{14}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{14}-\stackrel{y1}{(-10)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{14 +10}{3 +1}\implies \cfrac{24}{4}\implies 6[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-10)}=\stackrel{m}{6}(x-\stackrel{x_1}{(-1)}) \\\\\\ y+10=6(x+1)\implies y+10=6x+6\implies y=6x-4[/tex]

Check the picture below.

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{6^2 - 4^2}=a\implies \sqrt{36-16}=a\implies \sqrt{20}=a\implies 2\sqrt{5}=a \\\\[-0.35em] ~\dotfill\\\\ sin(A )=\cfrac{\stackrel{opposite}{2\sqrt{5}}}{\underset{hypotenuse}{6}}\implies sin(A)=\cfrac{\sqrt{5}}{3} \\\\\\ cos(B )=\cfrac{\stackrel{adjacent}{2\sqrt{5}}}{\underset{hypotenuse}{6}}\implies cos(B)=\cfrac{\sqrt{5}}{3}[/tex]

We will see that f'(x) > 0, which means that f(x) is an increasing function.

For any function f(x), if f'(x) > 0, then f(x) is increasing for any value of x.

Here we have the cubic function:

f(x) = x³ + 4x

If we differentiate this, we get:

f'(x) = df(x)/dx = 3x² + 4.

And notice that x² is always positive, then f'(x) > 0, which means that f(x) is an increasing function.

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The solutions for the following system of equations will be (–1, 6) and (1, 6). Then the correct option is B.

The equations are given below.

–3x² + 4y = 21 ...1

   4x² + y = 10  ...2

Multiply equation 1 by 4 and equation 2 by 3, then we have

–12x² + 16y = 84

   12x² + 3y = 30  

Add both equations, then we have

19y = 114

   y = 6

From equation 2, we have

4x² + 6 = 10

      4x² = 4

        x² = 1

         x = ±1

         x = 1, –1

Then the correct option is B.

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Answer:

352

Step-by-step explanation:

it repeated more than once

Answer:

Step-by-step explanation:

Note

Answer: Jane's question

Howard merely asked if a visit had taken place. There isn't a number anywhere or one that can be implied.

Jane asked for a number. It requires that the responder gives a number with no embellishment. The question asks for the number of times something has occurred and there is a time frame for the answer. That usually is the characteristic of a statistical survey.

Answer:

The answer is D = 9/57

Step-by-step explanation:

Get the variable D by itself as stated to solve for D.

I got the other numbers to the other side.

70D + 6 - 9D = 35 + 4D - 20.

(70D - 9D - 4D) = (35 - 20 - 6)

57D = 9

D = 9/57

[tex]\left(\sqrt[3]{-3} \right) \left(\sqrt[3]{-5}\right)\\\\=\left( \sqrt[3]{-1}\right \sqrt[3]{3}) \left(\sqrt[3]{-1} \sqrt[3]{5} \right)\\\\=\sqrt[3]{(-1)(-1)} \cdot \sqrt[3]{(3)(5)}\\\\=\sqrt[3]{1} \cdot \sqrt[3]{15}\\\\=1\cdot \sqrt[3]{15}\\\\=\sqrt[3]{15}[/tex]

Answer:

Second option

Step-by-step explanation:

Given the following question:

We are given four choices and we need to determine which choice is a rational number. In order for any integer to be a rational number you have to be able to write it as a fraction.

In this case, options one and four are immediately excluded since they are repeating decimals. They cannot be written as a fraction which leaves us with the second option or the third option.

[tex]\sqrt{36}[/tex]
[tex]\sqrt{36} =6\times6[/tex]
[tex]=6=\frac{6}{1}[/tex]
[tex]=\frac{6}{1}[/tex]

Your answer is the second option or "sqrt36."

Hope this helps.

Answer:

324

Step-by-step explanation:

Formula: [tex]a_{n} =a_{1} +(n-1)d[/tex]

=> [tex]a_{46} =9_{1} +(n-1)7\\[/tex]

          = [tex]9_{1} +(46-1)7\\[/tex]

          = [tex]9+(45)7\\[/tex]

          = [tex]9+315[/tex]

          = [tex]324[/tex]

:D

Answer:

[tex]x=4,\:x=-2[/tex]

Step-by-step explanation:

Both equations are equal to y, so we can simply set them equal to each other and solve for x:

[tex]x^2-5=2x+3\\\\x^2-8=2x\\\\x^2-2x-8=0\\\\(x-4)(x+2)=0\\\\x=4,\:x=-2[/tex]

Answer:

an accounting metric used to represent the average number of days between a credit sale date and the date when the purchaser remits payment.

Answer:

0.93x

Step-by-step explanation:

the total amount is:

x(1-15%+8%)=0.93x

so the answer is 0.93x

Answer:

18.86

Step-by-step explanation:

5 ⟌94.3

90 ÷ 5 = 18

   18

5 ⟌94.3

    -90

-----------------

      4.3

cant divide by 4 so add a decimal

5 × 0.8 = 4

   18.8

5 ⟌4.3

   - 4.0

---------------

     0.3

5 × 0.06 = 0.3

  18.86

5 ⟌0.3

  - 0.3

--------------

     0

I hope this helps!

The bank which will charge a customer more in fees if she writes 18 checks per month, and by how much is Bank A by $0.30

let

Bank A = 2.50 + 0.15x

= 2.50 + 0.15(18)

= 2.50 + 2.7

= $5.20

Bank B = 4 + 0.05x

= 4 + 0.05(18)

= 4 + 0.9

= $4.9

Difference in charges = $5.20 - $4.90

= $0.30

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Answer: D (82, 84, 90, 80, 74)

Finding Range:

To find range, you must subtract the smallest number to the highest number in that number pattern.

For example, the highest in D is 90, and the smallest is 74. 90-74 is 16, which matches the range for a possible price (16 = 16).

Range is basically the most easiest to find out of median, mean, and mode. You just have to find the greatest-smallest = range.

Finding Mean:

To find mean, you must add all the numbers up then divide the sum by the QUANTITIY of all the numbers.  

For example, if we add 82, 84, 90, 80, and 74, we would get 410. Since there are 5 numbers that make up 410, we divide 410 by 5, and therefore getting 82. This matches the mean of the price of a textbook (82 = 82).

Mean is basically easy to find as you just add all the numbers and divide it by how much numbers make that sum.

Conclusion:

In conclusion, the mean and range all match a possible price of the textbook, having a range of $16 and a mean of $82. Thus, D is the right answer.

The correct option is D (82, 84, 90, 74)

Range is subtract the smallest number to the highest number in that number pattern.

Mean is addition of all the numbers up then divide the sum by the quantities of all the numbers.  

The highest in D is 90, and the smallest is 74. 90-74 is 16, which matches the range for a possible price (16 = 16).

Addition of 82, 84, 90, 80, and 74, we would get 410. Since there are 5 numbers that make up 410, we divide 410 by 5, and therefore getting 82. This matches the mean of the price of a textbook (82 = 82).

Therefore, the possible prices for the textbook is the possible prices for the textbook is  (82, 84, 90, 74).

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The linear equation that models the cost for having x additional family members added is:

c(x) = $75 + $10.99*x

Here we know that the plan has a fixed price of $75 plus $10.99 for each family member added beyond the primary account holder.

Then if there are x family members added, the cost will be:

$75 + $10.99*x

Then the linear equation that models the cost for having x additional family members added is:

c(x) = $75 + $10.99*x

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The liters of smoothies sold is 9 7/8 liters.

An equation is a statement formed when two algebraic expressions are equated by an equal sign.

The volunteer prepares 12 1/2 = 25/2 liters of smoothies

The remaining amount of smoothies is 2 5/8 = 21/8 liters of smoothies

Let the amount of smoothies sold is x liters

Then the equation formed to determine the value of x is

x = (25/2) - (21/8)

x = 79/8

x = 9 7/8 liters

Therefore, the liters of smoothies sold is 9 7/8 liters.

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Answer:

Step-by-step explanation:

If a line is parallel to another it must have the same slope

The slope/intercept form of a line is y = mx + b where m is the slope and b the y intercept

The line y = 2x + 5 has slope 2

So the slope of the line that passes through (2,3) must also have the slope 2

We have
y = 2x + b; Substituting x =2, y =3 in this equation gives us
3 = 2 (2) + b or b = -1

Hence the equation of the line is
y = 2x -1

Cross-check

Substitute for x = 2 ==> y = 2(2) - 1 = 3 which is consistent