Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Solve the equation .

The solution of the equation is x =
.

Answer:

  D.  x ≈ 2.60

Step-by-step explanation:

The equation we have graphed is the one shown in the attachment. It is slightly different from the one in this problem statement.

It is often convenient to find a graphical solution to an equation by writing it in the form ...

  f(x) = 0

Then the solutions are the x-intercepts of the graph, points that most graphing calculators can readily identify.

We have done this here by defining ...

  [tex]y_1=3x^2-6x-4\\\\y_2=-\dfrac{2}{x+3}+1[/tex]

The graph is of y₁ -y₂. X-values where y₁-y₂ = 0 are solutions to the original equation, y₁ = y₂.

This equation is seen to have three solutions, approximately ...

  x = {-3.05, -0.55, 2.60}

Of these, only x ≈ 2.60 is listed among the answer choices.

__

Additional comment

The value of y₁ -y₂ expressed in standard form is ...

  [tex]3x^2-6x-4+\dfrac{2}{x+3}-1=0\\\\\dfrac{(x+3)(3x^2-6x-5)+2}{x+3}=0\\\\\dfrac{3x^3+3x^2-23x-13}{x+3}=0\\\\3x^3+3x^2-23x-13=0\quad(x\ne -3)[/tex]

The irrational solutions to this cubic can be found "exactly" by any of several applicable formulas. Numerical solutions are almost trivial to find with appropriate technology.

  x ≈ {−3.04857564747, −0.547524627423, 2.5961002749}.

Answer:

see photo

Step-by-step explanation:

Plato/Edmentum

Answer: equation y= 3/2x+ 4/3

The value of the x from the given equation is a +i and -i and +5i and -5i.

According to the statement

we have given that the equation [tex]x^4 + 6x^2 +5 =0[/tex]

and we have to find the value of x by the u substitution.

So,

The given equation is

[tex]x^4 + 6x^2 +5 =0[/tex]

Put [tex]x^2 = u[/tex] 

By substitution method

Then the equation become

[tex]u^2 +6u +5 = 0[/tex]

And solve the equation then

[tex]u^2+ u +5u +5 = 0[/tex]

Then

u(u +1) + 5(u +1) = 0

(u+5) (u +1) = 0

Then

the value of u is -1 and -5 then

The value of x is

[tex]x = \sqrt{u}[/tex]

x = √-5 And √-1

Then the value of x is +i and -i and +5i and -5i.

So, The value of the x from the given equation is a +i and -i and +5i and -5i.

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Answer:

  a.  1080

  b.  405

Step-by-step explanation:

Function evaluation is often conveniently done using a calculator. Many calculators know about the order of operations, so can be used without fear of an incorrect evaluation.

Put the value where the variable is and do the arithmetic.

  f(x) = 40(3^x)

  f(3) = 40(3^3) = 40(27) = 1080

  g(x) = 5(3^(x+1))

  g(3) = 5(3^(3+1)) = 5(3^4) = 5(81) = 405

Answer:

Step-by-step explanation:

i doont know

[tex]2 \sqrt{5} \: + \: 7 \sqrt{5} \\ \sqrt{5} \: ( \: 2 + \: 7 \: ) \\ \sqrt{5} \: ( \: 9 \: ) \\ 9 \sqrt{5} [/tex]

The simplification of the expression 2√5 + 7√5 is: 9√5.

So, Option A. is correct.

To simplify the expression 2√5 + 7√5, we can combine the like terms.

Both terms have the same radical expression, which is √5, so we can add their coefficients together.

2√5 + 7√5 = (2 + 7)√5

Now, simplify the coefficients:

2 + 7 = 9

Therefore, the simplified expression is:

2√5 + 7√5 = 9√5

So, the final answer is 9√5.

So, Option A. is correct.

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The sample space for the arrangement of a teddy bear (t), a kitten (k), and an elephant (e) is tke, tek, kte, ket, etk and ekt

The given parameters are

Stuffed toys, n = 3

Toys to arrange, r = 3 i.e. teddy bear (t), a kitten (k), and an elephant (e).

The number of arrangement is calculated as;

Ways = nPr

Substitute the known values in the above equation

Ways = 3Pr

Apply the permutation formula

Ways = 3!/0!

0! =1

So, we have

Ways = 3!/1

This gives

Ways = 3!

Expand

Ways = 3 * 2 * 1

Evaluate

Ways = 6

This means that the sample size is 6

Hence, the sample space for the arrangement of a teddy bear (t), a kitten (k), and an elephant (e) is tke, tek, kte, ket, etk and ekt

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Answer:

83in²

Step-by-step explanation:

This can also be expressed as;

Area of polygon=Area of ∆ABF +Area of rectangle BCDF + Area 0f ∆DEF

For ∆ABF;

Area of ∆ABO=∆AOF

Area of ∆ABF=2×Area of ∆ABO

Area of ∆ABO=1/2×Length×height

=1×4×7/2=28/2=14in

But area of ∆ABF=2×Area of ∆ABO

Area=2×14in=28in.

Area of rectangle;

Area=length×breadth

Area=5in×8in=40in.

Area of ∆DEF=2×Area of ∆EFG

Area=1/2× base× height

Area=1×2.5×6/2

Area=15/2=7.5in.

But area of ∆EFG=2×7.5in

=15in.

Area of polygon=28in+40in+15in=83in

The mean of the given data is 206.5.

To find the mean of the given data:

Sum of values = 211 + 226 + 186 + 221 + 181 + 228 + 207 + 215 + 203 + 203 + 204 + 196 + 226 + 212 + 212 + 201 + 219 + 191 + 191 + 185 + 193 + 231 = 4,542

Number of values = 22

Mean = 4,542 ÷ 22 = 206.5

Therefore, the mean of the given data is 206.5.

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Answer:

Step-by-step explanation:

The surface area of the larger sphere is equal to 636.365 square centimeters.

In this question we must estimate the surface area of the smaller sphere. By geometry we know that the volume of a sphere is directly proportional to the cube of its radius and the surface area is directly proportional to the square of radius, then the volume to surface area ratio is equal to:

V/A = k · r      (1)

Where:

Then, we can derive the following relationship between the two spheres by eliminating the proportionality constant:

V/(A · r) = V'/(A' · R)     (2)

Where:

First, we need to determine the radii of the spheres:

Larger radius

R = ∛(3 · V' / 4π)

R = ∛(3 · 647 / 4π)

R ≈ 5.365 cm

Smaller sphere

r = ∛(3 · V / 4π)

r = ∛(3 · 87 / 4π)

r ≈ 2.749 cm

Lastly, we find the surface area of the larger sphere:

A · r · V' = A' · R · V

A' = (A · r · V') / (R · V)

A' = (167 · 2.749 · 647) / (5.365 · 87)

A' = 636.365 cm²

The surface area of the larger sphere is equal to 636.365 square centimeters.

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In order to solve a problem that begins with a negative number and is divided by a positive number, the answer must also be negative.

Divide 21 ÷ 7

we get = 3

Mark it as negative number = -3

Hope this helps :)

Answer:

[tex]4x^{6} y^{10}[/tex]  A.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\qquad❖ \: \sf \: - 4 \: h(9) = 4[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:h(x) = - \cfrac{1}{3} x + 2[/tex]

we need to find -4 h(9) :

[tex]\qquad❖ \: \sf \: - 4 \: h(9)[/tex]

[tex]\qquad❖ \: \sf \: - 4 \bigg(- \dfrac{1}{3} \times 9 + 2 \bigg)[/tex]

[tex]\qquad❖ \: \sf \: - 4( - 3 + 2)[/tex]

[tex]\qquad❖ \: \sf \: - 4( - 1)[/tex]

[tex]\qquad❖ \: \sf \:4[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \: - 4 \: h(9) = 4[/tex]

Answer:

2

Step-by-step explanation:

slope : ( The amount y increases , when x is increased by 1 )

slope : { y2 - y1 / x2 - x1 }

slope : y2 = 2

           y1 = -4

           x2 = 5

           x1 = 2

You must minus the values in the formula to find the slope line that passes through the points:

slope : { y2 - y1 / x2 - x1 }

slope : (2) - (-4) / (5) - (2)

=> 2 + 3 / 3

=> 6/3

=> 2

Text explanation:

Difference between both y-coordinates. = 6

Difference between both x-coordinates. = 3

Divide the difference between y and x. =

y/x =2

Which means the slope of the line that passes through the points (2,-4) and (5,2) is 2.

Hope this helps! Sorry it took so long! ⸜(｡˃ ᵕ ˂ )⸝ xx

The slope of the line that passes through the points (2, -4) and (5, 2) is 2.

A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

slope = (y₂-y₁)/(x₂-x₁)

The slope of the line that passes through the points (2, -4) and (5, 2) can be calculated as shown below,

Slope = (y₂-y₁)/(x₂-x₁) =  [2 - (-4)] / (5 - 2)= 6/3 = 2

Hence, the slope of the line that passes through the points (2, -4) and (5, 2) is 2.

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The value of the firm is $50 million

The given parameters are:

EBIT = $10 million

Tax Rate, Tc = 40%

Unlevered cost of capital, RU = 12%

The value of the firm is calculated as:

Value = EBIT*(1 - Tc)/Ru

This gives

Value = 10 million *(1 - 40%)/12%

Evaluate the expression

Value = 50 million

Hence, the value of the firm is $50 million

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The value of f(3) is 147.3306

The function is given as:

[tex]f(x)=147+2e^{-0.6x[/tex]

Substitute 3 for x

[tex]f(3)=147+2e^{-0.6*3[/tex]

Evaluate the product

[tex]f(3)=147+2e^{-1.8[/tex]

Evaluate the exponent

f(3)=147 + 2* 0.1653

Evaluate the sum

f(3) = 147.3306

Hence, the value of f(3) is 147.3306

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The length of rectangle is 25 feet and the width  of rectangle is 135 feet.

According to the question,

The perimeter of a rectangle is 320 feet. The length and width if the length is an odd integer and the width is 5 times the next consecutive odd integer.

Odd integers that follow each other and they differ by 2. If x is an odd integer, then x + 2, x + 4 and x + 6 are consecutive odd integers. The perimeter of a rectangle is 320 feet. Let the length of a rectangle is x. The next consecutive odd integer is x+2.width = 5(x+2)

    =5x+10.

Let, Length - l:Width - w; l = 5w and the perimeter of a rectangle is 320 feet. Formula for perimeter of rectangle is 2(Length + Breadth). Perimeter of a rectangle is the sum of the length of all sides of the rectangle. The perimeter of a rectangle formula is,

P = 2(l + b)

In words, it is equal to the sum of two times the length and two times the breadth of the rectangle. Perimeter for any figure is defined as the length of its boundary.

2(length + width) = 320

Length+ width=160

x+5x+10=160

6x=150

x=25

Length = 25 feet

width = 5(25+2)=135 feet.

Hence, the length of rectangle is 25 feet and the width of rectangle is 135 feet..

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The volume of the composite figure is 3532.5 cubic inches

From the given figure, we have the following dimensions:

The volume of a cylinder is

V = πr^2h

So, the volume of the composite figure is

V = πR^2h - πr^2h

Substitute the known values in the above equation

V = 3.14 * 10^2 * 15 - 3.14 * 5^2 * 15

Evaluate the product

V = 3532.5

Hence, the volume of the composite figure is 3532.5 cubic inches

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The range of the function y = -x² - 3x when the domain is {-5,0,2} is:

{-10, 0}.

The range of a function is the set that contains the output values for the given domain of the function.

In this problem, the domain is:

{-5,0,2}.

Hence the output values are:

Hence the range is:

{-10, 0}.

-10 repeats, but goes only once on the range.

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Step-by-step explanation:

To find the Tth term of an arithmetic progression, you should use the formula: Tn: a + (n-1)d, whereby 'a' is the first term, you have to find 'n' and 'd' is the difference between the first 2 numbers to find out by how much the arithmetic progression is increasing or decreasing. Hence, 29/30 minus 4/5 equals to 1/6. 'a' is 4/5 and 'd' is 1/6.

Use the above formula by replace a and d then you'll get the answer. Hope this helps.

This system of equations have infinite solution.

If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.

Given that,

The system is 2x + y = 1 and 4x + 2y = 2. It is graphed below.

Solutions to a system are the intersection points. Since these two lines are the same line they intersect everywhere. There are infinitely many solutions.

2x+y = 1   ...........(1)

4x+2y = 2  .......(2)

Then from equation (2) dividing by 2 on both side

2x+y = 1

since both lines are same. They overlap to each other.it means the equation have many solution.

Hence,This system of equations have infinite solution.

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The above question is not complete.

How many solutions does this system of equations have?

(a) none

(b) exactly two

(c) infinitely many

(d) exactly one

Graph of a system of linear equations. Equation 1 is 2x plus y equals 1.. Equation 2 is 4x plus 2y equals 2. The graphs are the same line.

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.

Answer:

I hope I've finally done justice to it.

Step-by-step explanation:

[tex]y=-5x^2 \sqrt{x}[/tex]

[tex]y=-5x^2(x)^\frac{1}{2}[/tex]

[tex]y=-5( {x}^{2 + \frac{1}{2} }) = - 5 {x}^{ \frac{5}{2} } [/tex]

[tex] \frac{dy}{dx} = - 5( \frac{5}{2}) {x}^{ \frac{5}{2} - 1 } [/tex]

[tex]\frac{dy}{dx} = ( \frac{ - 25}{2}) {x}^{ \frac{3}{2} } [/tex]

[tex]\frac{dy}{dx} = ( \frac{ - 25}{2}) \sqrt[3]{ {x}^{2} } [/tex]

Answer:

a) 52  

b)115

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

given y varies directly as x² and inversely as z³ then the equation relating them is

y = [tex]\frac{kx^2}{z^3}[/tex] ← k is the constant of variation

to find k use the condition y = 12 when x = 4 and z = 2 , then

12 = [tex]\frac{k(4)^2}{2^3}[/tex] = [tex]\frac{16k}{8}[/tex] ( multiply both sides by 8 )

96 = 16k ( divide both sides by 16 )

6 = k

y = [tex]\frac{6x^2}{z^3}[/tex] ← equation of variation

when y = 1.728 and z = 5 , then

1.728 = [tex]\frac{6x^2}{5^3}[/tex] = [tex]\frac{6x^2}{125}[/tex] ( multiply both sides by 125 )

216 = 6x² ( divide both sides by 6 )

36 = x² ( take square root of both sides )

[tex]\sqrt{36}[/tex] = x , that is

x = 6

Answer:

37 child tickets / 74 adult tickets

Step-by-step explanation:

I randomly picked a number and increased or decreased whether the solution was too high or low (guess and check)

The number of child tickets sold that day is 37.

We have,

Let's assume the number of child tickets sold is "C" and the number of adult tickets sold is "A."

The cost of a child ticket: $6.80

The cost of an adult ticket: $9.90

The total sales for the day: $984.20

The number of adult tickets sold is twice the number of child tickets sold:

A = 2C

To find the number of child tickets sold, set up an equation based on the total sales:

6.80C + 9.90A = 984.20

Substituting the value of A from equation 4:

6.80C + 9.90(2C) = 984.20

Simplifying the equation:

6.80C + 19.80C = 984.20

26.60C = 984.20

C = 984.20 / 26.60

C ≈ 37

Therefore,

37 child tickets were sold that day.

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Answer:

d - 18

Step-by-step explanation:

The question said to use d as the variable. We do not know the number of dollars Paul owes. So we put d for that amount.

Then "minus" means to subtract 18.

Writing the expression is all that is being asked for. Translating the words into algebra. We aren't solving anything. Not even writing an entire equation, just an expression, so it has no equals sign.

Answer:

Since <ABC ~= <DBE and <BAC ~= <BDE, the triangle s are similar by angle-angle.

Answer:

Neither

Step-by-step explanation:

This function isn't even, because

[tex]f(x) = f( - x)[/tex]

Basically this mean for every x opposites the y value should be the same.

Here, 6 and -6 doesn't share the same y value, nor as -3,and 3.

This function isn't odd because

[tex]f( - x) = - f(x)[/tex]

Basically, this means our y values should be reflected about the orgin,

here, the y values does not switch signs for every x value and it's opposite itself , so this function isn't odd.

So The answer is neither

Answer:

[tex] {x}^{x} (1 + log(x)) [/tex]

I hope this helps you.