Factor the quadratic trinomial x²- 9x+18
(x + ) (x+ )​

Answer:

[tex]y=\sqrt{\frac{x^{2}}{2} +34}[/tex]

Step-by-step explanation:

[tex]2y\left( x\right) y^{\prime }\left( x\right) =x[/tex]

[tex]\Longrightarrow \int 2y\left( x\right) y^{\prime }\left( x\right) dx=\int x\ dx[/tex]

[tex]\Longrightarrow y^{2}\left( x\right) =\frac{x^{2}}{2} +c\ \text{(c is a constant)}[/tex]

[tex]y\left( 2\right) =6\Longleftrightarrow y^{2}\left( 2\right) =36[/tex]

[tex]y^{2}\left( 2\right) =36\Longleftrightarrow \frac{\left( 2\right)^{2} }{2} +c=36\ \Longleftrightarrow c=34[/tex]

[tex]\Longrightarrow y\left( x\right) =\pm\sqrt{\frac{x^{2}}{2} +34}[/tex]

Answer:

=170/3 or (decimal 56.67)

Step-by-step explanation:

Steps

∫⁵ x²+3dx

⁰

Apply the Sum Rule: ∫fx) + gx) dx = ∫f(x)dx +-∫ g(x)

dx

∫⁵ x² dx +∫⁵ 3dx

⁰ ⁰

∫⁵ x² dx=125/3

⁰

∫⁵ 3dx=15

⁰

125/3+15

=170/3

Based on the calculation below, the amount that can be withdrawn each month for 10 years is a. $769.27.

First, we calculate the future value (FV) of the amount after 20 years using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:

FV = A * (((1 + r)^n – 1) / r) ................................. (1)

Where,

FV = Future value of the amount after 20 years =?

A = Monthly deposit = $235.15

r = Monthly interest rate = 3.2% / 12 = 0.00266666666666667

n = number of months = 20 * 12 = 240

Substituting the values into equation (1), we have:

FV = $235.15 * (((1 + 0.00266666666666667)^240 – 1) / 0.00266666666666667) = $78,910.41

The amount planned to be withdrawn on monthly basis can be calculated using the formula for calculating the present value (PV) of an ordinary annuity as follows:

P = PV / ((1 - (1 / (1 + r))^n) / r) …………………………………. (2)

Where;

P = Monthly withdrawal or payment = ?

PV = Present value = FV calculated above = $78,910.41

r = Monthly interest rate = 3.2% / 12 = 0.00266666666666667

n = number of months = 10 * 12 = 120

Substitute the values into equation (2), we have:

P = $78,910.41PV / ((1 - (1 / (1 + 0.00266666666666667))^120) / 0.00266666666666667) = $769.27

Therefore, the amount that can be withdrawn each month for 10 years is $769.27.

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The answer is A: $769.27

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Have a great day and God bless! :D

Answer:

[tex]f(2)=\frac{7}{4}[/tex]

Step-by-step explanation:

Step 1:  Input 2 for x and solve

[tex]f(x) = \frac{2x + 7 - x^2}{4}[/tex]

[tex]f(2) = \frac{2(2) + 7 - (2)^2}{4}[/tex]

[tex]f(2)=\frac{4+7-4}{4}[/tex]

[tex]f(2)=\frac{7}{4}[/tex]

Answer: [tex]f(2)=\frac{7}{4}[/tex]

The number of cubic centimeters that are in the volume of the cone is 12.5π cm³ OR 39.27 cm³

From the question, we are to determine the volume of the cone

The volume of a cone can be calculated by using the formula,

[tex]V = \frac{1}{3} \pi r^{2} h[/tex]

Where V is the volume

r is the radius

and h is the height

From the given information,

radius, r = 2.5 cm

slant height, l = 6.5 cm

First, we will determine the height of the cone

By Pythagoras' theorem

[tex]l^{2} = r^{2} + h^{2}[/tex]

Where [tex]l[/tex] is the slant height

r is the radius

and h is the height of the cone

Then, we can write that

[tex]6.5^{2} = 2.5^{2} + h^{2}[/tex]

[tex]42.25 = 6.25 + h^{2}[/tex]

[tex]h^{2}=42.25 - 6.25[/tex]

[tex]h^{2} =36[/tex]

[tex]h = \sqrt{36}[/tex]

∴ h = 6 cm

Now, putting the parameters into the equation for the determining the volume of a cone, we get

[tex]V = \frac{1}{3}\times \pi \times 2.5^{2} \times 6[/tex]

[tex]V = \pi \times 6.25\times 2[/tex]

[tex]V = 12.5 \pi[/tex] cm³ OR 39.27 cm³

Hence, the number of cubic centimeters that are in the volume of the cone is 12.5π cm³ OR 39.27 cm³

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Answer:

∠N = 21

Step-by-step explanation:

Sum of all angles of triangle = 180°

   4x - 13 + 2x - 13 + 5x + 19 = 180

    4x + 2x + 5x  -13 - 13 + 19 = 180

Combine like terms

                       11x  - 7  = 180

                               11x = 180 + 7

                                11x = 187

                                  x = 187/11

x = 17

m∠N = 2x - 13

           = 2*17 - 13

           = 34 - 13

          = 21

Answer: Second statement is false

Step-by-step explanation: You cannot subtract 89 from 500 and get 500. You get 411.

Answer:

-5 5/6

Step-by-step explanation:

convert 2/3 into 4/6 and when u subtract a positive from a negative u add it instead  

The radius and the height of the dimension that will minimize the amount of material used in the construction are [tex]\mathbf{r = \sqrt[3]{\dfrac{1500}{\pi}} }[/tex] and [tex]\mathbf{h = \dfrac{3000}{\pi ({\dfrac{1500}{\pi}} )^{2/3}}}[/tex] respectively.

The dimension that minimizes the surface area of a cylinder can be determined by:

Given that:

The area of the cylinder = (2 πr)h + 2(πr²)

The volume of the cylinder

Let's identify the constraint equation and Optimization equation:

To minimize the surface area of the can, we have:

The constraint equation is the equation that limits us:

So, Let's solve for h in our volume equation, we have:

3000 = πr² h

h = 3000/πr²

Now, from the Area equation

[tex]\mathbf{A = 2 \pi r(\dfrac{3000}{\pi r^2}) + 2\pi r^2}[/tex]

Taking the derivate and setting it to zero, we have;

Derivative:

[tex]\mathbf{A = \dfrac{6000}{ r}+ 2\pi r^2}[/tex]

[tex]\mathbf{A = 6000 r^{-1} + 2\pi r^2}[/tex]

[tex]\mathbf{A' = -6000 r^{-2} + 4\pi r}[/tex]

[tex]\mathbf{A' = 4\pi r-\dfrac{6000}{ r^{2} }}[/tex]

Setting it to zero, we  have:

[tex]\mathbf{0=\dfrac{ 4 \pi r^3 - 6000}{r^2}}[/tex]

Factor out 4

0 = 4(πr³ - 1500)

1500 = πr³

r³ = 1500/π

[tex]\mathbf{r = \sqrt[3]{\dfrac{1500}{\pi}} }[/tex]

The above is the radius that minimizes the surface area of the cylinder;

From [tex]\mathbf{h = \dfrac{3000}{\pi r^2}}[/tex]

[tex]\mathbf{h = \dfrac{3000}{\pi ( \sqrt[3]{\dfrac{1500}{\pi}} )^2}}[/tex]

[tex]\mathbf{h = \dfrac{3000}{\pi ({\dfrac{1500}{\pi}} )^{2/3}}}[/tex]

Thus, the radius and height that minimize the amount of material to be used in its construction are [tex]\mathbf{r = \sqrt[3]{\dfrac{1500}{\pi}} }[/tex] and [tex]\mathbf{h = \dfrac{3000}{\pi ({\dfrac{1500}{\pi}} )^{2/3}}}[/tex] respectively.

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=====================================================

Explanation:

The triangular face has area of base*height/2 = 4*10/2 = 40/2 = 20 square cm.

Multiply this prism base area by the depth of the prism to get 20*2 = 40 cubic cm.

It might help to place the triangular prism so the triangular face is along the ground, so you can think of that face as the floor of this triangular room. The volume of this room is equal to the floor area times the height of the room.

volume of the room = (floor area)*(height of the room)

volume of the prism = (base area)*(height of the prism)

For any prism, the base faces are always parallel and congruent to each other.

Answer:

x^2+5x-36-7/x

Step-by-step explanation:

assuming x^3 and 5x^2

A rectangular prism is a shape that has six faces which are rectangular.

Your information is incomplete as the diagram of the rectangular prism isn't given. Therefore, an overview will be given.

It should be noted that a rectangular prism simply means a three dimensional sold shape that has six faces that are rectangles.

The formula that's used to calculate the volume of a rectangular prism will be:

= Length × Width × Height

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Answer:

Since there isn't any of the following attached, I made my wn attached below

Step-by-step explanation:

Population size: 12

Median: 28.5

Minimum: 23

Maximum: 37

First quartile: 25.5

Third quartile: 30.75

Interquartile Range: 5.25

Outliers: none

Hope this helps you a little more for your last day of finishing hmw :)

Let me know if you need anymore help !

OR have questions

The area of the reflective material is:  284 square yards.

A rectangle is a quadrilateral with four sides and four right-angles.

it has two lines of symmetry.

Analysis:

To find the area of the reflecting material we find the area of the following shapes: trapezium + rectangle + triangle

bigger base of trapezium = 2 + 6 + 2 = 10 yard

smaller base of trapezium = 6

length of rectangle = 18 yard

width of rectangle : 2+6+2 = 10 yard

base of triangle is =  10 yard

Area of reflective material = 1/2(6+10) + 18x10 + 1/2(10)(8) = 284 square yards

In conclusion, the area of reflective material is : 284 square yards.

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Answer:

  800 ft²

Step-by-step explanation:

The total surface area of a square-base pyramid is given by the formula ...

  A = s(s +2h) . . . . . . where s is the side length, h is the face slant height

In this problem, we need to find the slant height of a face in order to use this formula.

__

The distance from the middle of one edge of the base to the peak of the pyramid is the slant height of a face of the pyramid. It is the hypotenuse of a right triangle whose legs are the pyramid height, and half the width of the base. For this pyramid, that is a right triangle with legs 15 and 8.

The Pythagorean theorem is used to find the hypotenuse of that triangle:

  c² = a² +b² . . . . square of hypotenuse = sum of squares of legs

  c² = 15² +8² = 225 +64 = 289

  c = √289 = 17

The slant height of a face of the pyramid is 17 ft.

The area formula tells us the total surface area is ...

  A = s(s +2h)

  A = (16 ft)(16 ft + 2×17 ft) = (16 ft)(50 ft)

  A = 800 ft²

The total surface area is 800 square feet.

Answer:

8x4-2x2+7

Step-by-step explanation:

it's 100 percent right trust me

Answer:

[tex]a^{4}-2a^{2} -24[/tex]

Step-by-step explanation:

We do FOIL to solve this

Answer:

3.6%

Step-by-step explanation:

This is an example of dependent events. When events are dependent, you have to multiply the probability of each event that happens after each other. Probability is desired outcome over all possible outcomes. For the milk chocolate, there are 5 pieces we can pick out of 16, so it's 5/16. Next, the probability of dark chocolate is 3/15 (There is one less piece of chocolate overall now). For the white chocolate, the possibility is 8/14. So now we have to multiply:

5*3*8             120           1

______   =  _____  =  ___ = (about) 0.036

16*15*14        3360        28

So, that's 3.6%

Hope this helps!

The y-intercept of the correct graph is 185 and  y-intercept of the incorrect graph is 195. The value of average change in distance is -10 for each increase of 1 iron number.

The x-intercept is the point on the coordinate at which a line, curve or plane intersect with the y-axis.

In the graph it can be seen that the correct graph is intersect y-axis at the value 185. Thus, the y-intercept of the correct graph is 185.

c=185

For the incorrect graph this value is 195. Thus, the y-intercept of the incorrect graph is 195.

b=195

Here, the values of y-intercepts are not the same-

c≠b

185≠195

The average change in distance for each increase of 1 iron number is,

[tex]r=\dfrac{155-145}{3-4}\\r=-10[/tex]

Thus, the y-intercept of the correct graph is 185 and  y-intercept of the incorrect graph is 195. The value of average change in distance is -10 for each increase of 1 iron number.

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Answer:

A) 5

Explanation:

[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 - (y_2 - y_1)^2}[/tex]

Here given points:

Distance:

[tex]\rightarrow \sf \sqrt{(6 - 3)^2 - (8 - 4)^2}[/tex]

[tex]\rightarrow \sf \sqrt{9 +16}[/tex]

[tex]\rightarrow \sf \sqrt{25}[/tex]

[tex]\rightarrow \sf 5[/tex]

Answer:

[tex]t^{3}[/tex]

Step-by-step explanation:

cubed means to the power of 3

Answer:

28 m

Step-by-step explanation:

full roll length: r

Ryan bought: r/4

He trimmed 2 m: r/4 - 2

Length left: 5

r/4 - 2 = 5

r/4 = 7

r = 28

Answer: 28 m

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{10}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{4}}}\implies \cfrac{9}{3}\implies 3 \\\\\\ \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}{1}=\stackrel{m}{3}(x-\stackrel{x_1}{4}) \\\\\\ y-1=3x-12\implies y=3x-11[/tex]

The mean of the data set is 22.1

The sample proportion of numbers less than the mean is %53

To find the mean,

We would sum the numbers and then divide them by the number of data.

25.5 + 26 + 18.2 + 15.3 + 28.5 + 27 + 20.7 + 20.2 + 26.1 + 18.2 + 21.4 + 17.9 + 24.3 + 22.6 + 19.6

= 331.5

331.5/15= 22.10.

To find the proportion of numbers, we would order them:

15.3

17.9

18.2

18.2

19.6

20.2

20.7

21.4

---------

22.6

24.3

25.5

26

26.1

27

28.5

The discontinuous line shows the split of the data that are less than the mean.

Those data are 8 in number and their proportion is:

8 / 15

= 0.53

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Answer:

the answer will be

K' = -9, 5

L' = 0,5

M' = -8,3

Step-by-step explanation:

the x axis is written first and the y axis is written after that.

hope it helps!!

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Answer:

K': (9,5)

L': (0,5)

M': (8,3)

Step-by-step explanation:

Tell me if im wrong!

Answer:

First question (on left) f(x) = 5x-3. second question (on right) f)x) = 1/2*x

Step-by-step explanation:

rise(left) 4. run (left) 20.

rise(right) 8. run(right) 4.

Answer:

Write properties of function:

x intercept/zero: [tex]x_{1} =-1;x_{2} =7[/tex]

Step-by-step explanation:

x² - 6x - 7 = x² - 7x + x - 7

⇒ x(x - 7) + 1(x - 7)

⇒ (x + 1) (x - 7)

Thus, x³ - 5x² - 13x - 7 = (x + 1)(x + 1)(x - 7)

[tex]~~~~~~~~x^3 -5x^2 -13x -7=0\\\\\implies x^3 +x^2 -6x^2 -6x-7x-7=0\\\\\implies x^2(x+1) -6x(x+1) -7(x+1)=0\\\\\implies (x+1)(x^2 -6x -7) = 0\\\\\implies (x+1)(x^2 +x -7x-7)=0\\\\\implies (x+1) [x(x+1) -7(x+1)]=0\\\\\implies (x+1)(x+1)(x-7) = 0\\\\\implies (x+1)^2 (x-7) = 0\\\\\implies x = -1,~ x = 7\\\\\text{Hence, the roots are}~ -1~ \text{and}~ 7[/tex]

Answer:

Option 4

Step-by-step explanation:

Equating given length and width to the area :

Finding the dimensions :

At the end of the third year the population of beetles will be 11,576beetles

The standard form of an exponential function is given as:

y = ab^t

Given the following parameters

initial population 'a" = 10,000 beetles

Time = 3 years

rate b = 1.05

Substitute into the formula

y = 10,000(1.05)^3

y = 10,000(1.1576)
y = 11,576 beetles

Hence at the end of the third year the population of beetles will be 11,576beetles

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Given that the first term of the sequence is –1.5, the next term of the sequence would be 3

The recursive function is given as:

f(n + 1) = -2f(n)

Substitute 1 for n

f(1 + 1) = -2f(1)

Evaluate

f(2) = -2f(1)

Given that the first term is -1.5, the equation becomes

f(2) = -2 * -1.5

Evaluate

f(2) = 3

Hence, the next term of the sequence is 3

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Answer:

(D) 3

Step-by-step explanation: