Can you work out what the
next number in the pattern
should be? 4 – 6-9-6-14 - 6
-

[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]

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:

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 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:

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

Step-by-step explanation:

assuming x^3 and 5x^2

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:

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

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]

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:

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

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:

Option 4

Step-by-step explanation:

Equating given length and width to the area :

Finding the dimensions :

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:

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

Step-by-step explanation:

cubed means to the power of 3

Answer:

12 inches.

Step-by-step explanation:

You have to use the pythagorean formula. The measurements you stated form a right angle. Therefore, a^2 + b^2 = c^2. In this equation, we know c=13, and b=5. So therefore c^2 - b^2 = 144. We have to solve for a, so square root 144 to get 12.

Answer:12 in

Step-by-step explanation:

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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Answer:

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

Step-by-step explanation:

We do FOIL to solve this

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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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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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:

8x4-2x2+7

Step-by-step explanation:

it's 100 percent right trust me

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:

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]

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

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-3+2x+3+2x = 5x

x+8+4x-3x-4 = 2x+4

4x+x-11-5X+25+4x = 4x+14

3x+5-2x-5x+9+8x = 4x+14

5+9x-7-4X-3x+6 = 2x+4

6x-9-5x+4-x+5x+5 = 5x

Step-by-step explanation:

Simplified by adding like terms

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

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:

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!