Write the first six terms of the sequence.
with an explanation please! i have no idea how to solve this on my own

Answer:

x = -4

Step-by-step explanation:

4 = 2/3x - 5/3x

4 = -3/3x

4 = -x

-4 = x

[tex]\textbf{a).}\\\\r^2-12r+32\\\\=r^2 -8r-4r+32\\ \\=r(r-8) -4(r-8)\\\\=(r-8)(r-4)\\\\\textbf{b).}\\\\5a^2-7a-6\\\\=5a^2-10a+3a-6\\\\=5a(a-2)+3(a-2)\\\\=(a-2)(5a+3)\\\\\textbf{c).}\\\\16g^2+40g+25\\\\=(4g)^2 +2\cdot 5\cdot 4g+5^2\\\\=(4g+5)^2\\\\=(4g+5)(4g+5)[/tex]

Answer:

First problem:  max when x = 4

Second problem:  min when x = 1

Step-by-step explanation:

The graph of f(x) = –|x – 4| – 5 is a translation of that of g(x) = -|x|.  The vertex of the latter is (0, 0).  First this must be translated 4 units to the right and then the resulting graph 5 units downward.  The vertex of this translation is (4, -5).  Since this graph opens downward, this (4, -5) is the maximum function value, that is, when x = 4.

The graph of f(x) = x2 – 2x +­ 1, or (better yet) f(x) = x^2 – 2x +­ 1, or

f(x) = (x - 1)^2 + 0, is that of a parabola that opens upward and has its minimum at x = 1, or (1, 0).

Answer:

1. diameter=5.54m

2. radius=9.55cm

3. area=11.46feet²

Step-by-step explanation:

1. The formula of the area of a circle is: A=[tex]\pi r^{2}[/tex]

   A: area of the circle=25m²  

    [tex]\pi[/tex] : Pi≈3.14

    r: radius of the circle= unknown

   Solve the equation to find r:

   25=(3.14)r²

    r²=[tex]\frac{25}{3.14}[/tex] =7.69m²

    r= √7.69= 2.77m

   diameter d= 2 x r =2 x 2.77 =5.54m

2. The formula of the perimeter of a circle is: P=2[tex]\pi r[/tex]

   P: perimeter of the circle= 30cm

    [tex]\pi[/tex] : Pi≈3.14

   r: radius of the circle= unknown

   Solve the equation to find r:

   30=(3.14)r

   r= [tex]\frac{30}{3.14}[/tex] = 9.55cm

   radius r = 9.55cm

3. First we have to find r (radius) from  the equation of perimeter:

    P=2[tex]\pi r[/tex]

     r= [tex]\frac{P}{2\pi }[/tex] = [tex]\frac{12}{2(3.14)}[/tex] = [tex]\frac{12}{6.28}[/tex] =1.91 feet

     Substitute r in the equation of area to get the area:

     A=  [tex]\pi r^{2}[/tex] = 3.14 (1.91)² = 3.14(3.65) = 11.46 feet²

Answer: there iis none so cose zero

Step-by-step explanation:

Bob did a survey asking adults which pet they wished they had as a kid. The results are below. If 720 adults said the pet they wished they had was a dog, how many adults wished they had a rabbit?

Expansion : [tex](x+1)(x+9) = x(x+9) + 1(x+9) = x^{2} +9x + x + 9[/tex]
Simplify : [tex]x^{2} +10x + 9[/tex]

Answer:

[tex]\huge\boxed{ \bf\:x^{2} + 10x + 9}[/tex]

Step-by-step explanation:

[tex](x + 1)(x+9)[/tex]

Let's expand it at first.

[tex](x + 1)(x + 9)\\= x (x + 9) + 1 (x + 9)\\= x^{2} + 9x + x + 9[/tex]

Now, simplify it.

[tex]x^{2} + x + x + 9\\= \boxed{ x^{2} + 10x + 9}[/tex]

[tex]\rule{150pt}{2pt}[/tex]

Answer:

15 miles

Use the Pythagoras theorem

Answer: 15

Step-by-step explanation:

Let's start by stating what we are given

The perimeter is 36

One side length is 12

And the other given side is 9

Finally we have an unknown side x

The value of all the sides added together is the perimeter.

So add all the sides

12+9+x=36

21+x=36

Subtract both sides by 21

21-21+x=36-21

x=15

what's the question? Cause the pic doesn't make it clear on what we need to solve.

Answer: B is correct

Step-by-step explanation:

if you do 2 ÷ 5 you get 0.4. But that isn't an option. So, the only other possibility would be -2 ÷ 5 which gives us -0.4, and that makes sense.

I'm not the greatest at explaining this one but hopefully, this helps!

Answer:

This is a pretty tricky question but if I'm correct it might be 2

The approximate length of the actual object is 1465 ft, which is closest to option D.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

First, let's convert the length of the model from millimeters to inches:

372.5 mm = 372.5/10 cm = 37.25/2.54 in ≈ 14.65 in

Next, we can use the scale of the model to find the length of the actual object in feet:

0.5 in. = 50 ft.

So, 1 in. = 100 ft.

Therefore, the length of the actual object in feet is:

14.65 in x (100 ft/in) = 1465 ft

Therefore, the closest length is 1467 feet.

To learn more about the scale factor;

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The equation of the model h will be h = 6 × sin(2πt/8). Then the correct option is C.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

A buoy starts at a height of 0 in relation to sea level and then goes up.

Its maximum displacement in either direction is 6 feet, and the time it takes to go from its highest point to its lowest point is 4 seconds.

Then we have

[tex]h=A \times \sin \omega t, \ \ at=0, \ \ h =0[/tex]

The maximum displacement of the buoy in either direction is 6 ft, then we have

[tex]h=6 \times \sin \omega t[/tex]

The time it takes the buoy to get from the lowest to the highest point is 4 seconds then the oscillation time period will be 8 seconds.

Then we have

[tex]\omega T = 2\pi\\\\\omega = \dfrac{2\pi}{8}[/tex]

Then the h will be given as

[tex]h =6\times \sin (\dfrac{2\pi}{8}t)[/tex]

More about the function link is given below.

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Hi! To solve this problem, your first step is to:            

                                c2

              Simplify   ———

                               v27

The Equation is at the end of step 1:        c2

                                                        (v3) • ———

                                                                   v27

Now STEP 2:

Dividing exponential expressions : 

2.1    v3 divided by v27 = v(3 - 27) = v(-24) = 1/v24

After we done this, your Final result is:      c2

                                                                   ———

                                                                     v24

Answer:

I think its 22.5 or 18% if its the rate then its 22.5 I believe

Answer:

14x+c

Step-by-step explanation:

I hope it's to help

Answer: you are on your own.

Step-by-step explanation:

The equation of the linear function f(x) is f(x) = 4x - 3. So, the answer is B) 4x - 3.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
We can use the two given data points to determine the equation of the linear function f(x) using the slope-intercept form:

f(x) = mx + b

where m is the slope and b is the y-intercept.

First, we can find the slope of the function by using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (2, 5) and (x₂, y₂) = (4, 13)

m = (13 - 5) / (4 - 2) = 4

Now we can use the slope and one of the given points to solve for the y-intercept:

5 = 4(2) + b

b = -3

Therefore, the equation of the linear function f(x) is f(x) = 4x - 3.

Learn more about function here:

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Mr. Red's salary is an illustration of an arithmetic sequence

The recursive rule of the sequence is (d) an = an−1 + 500; a1 = 30000

From the complete question, we have the explicit rule of Mr. Red's salary to be

an = 500n + 29500

Where:

The above means that:

The difference between a term and the next term is 500.

So, the recursive rule is:

an = an−1 + 500

Recall that:

a1 = 30000

Hence, the recursive rule of the sequence is (d) an = an−1 + 500; a1 = 30000

Read more about arithmetic sequence at:

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Answer: C

Step-by-step explanation:

Answer:544

Step-by-step explanation:43 + 25 = 68

68 × 8 = 544

Answer:

99999

Five Digit Numbers

The smallest five-digit number is 10000 and the greatest five-digit number is 99999.

Step-by-step explanation:

Answer:

2nd option I believe

Step-by-step explanation:

subtract 2 from both sides

Answer:

The first step is to subtract from both sides

Step-by-step explanation:

if you do this it's method of balancing equations whereby you have. 3x+2-2=17

Answer:

See diagram below

Step-by-step explanation:

arctan (angle ) = 18 / (6 sqrt3)  = 60 degrees

Step-by-step explanation:

height of pole = 18m = p

length of shadow = 6[tex]\sqrt{3}[/tex] m = b

now,

tan α = p/b

        = 18/6[tex]\sqrt{3}[/tex]

        = [tex]\sqrt{3}[/tex]

or, tan α = tan 60

           α = 60

Therefore angle of elevation of the sun is 60.  

Answer:

B (cylinder)

Step-by-step explanation:

Two circular bases which are parallel and congruent :

This basically means that the shape contains a circular base (supposedly the bottom), but since it has two bases, its on the top and the bottom. Because it's congruent, the bases are both equal in shape and size. It is also parallel as well, in which the bases have the same distance between them.

The cube doesn't have any circular bases.

The sphere doesn't have any faces, nor edges.

A cone has a circular base, but it doesn't have two.

A cylinder has two circular bases, as well as they are parallel and congruent.

So, your answer is B (cylinder).

Hope this helped !

Answer:True

Step-by-step explanation:The y-axis is vertical and the x is horizontal

Answer:

32.9

Step-by-step explanation:

7*9.4/2=32.9

Answer:

t=1

Step-by-step explanation:

16-2t=5t+9

step 1 :group like term to the same side

16-9=5t+2t

step 2 : combine

7=7t

step 3: solve for t

t=7/7

t=1

length= 9.1m

area= 473.2m^2

Substitute values for length (l) and breadth (b) into the perimeter formula.

473/9.1=52

perimeter of rectangle= l+l+b+b

=52+52+9.1+9.1

P=122.2m

Answer:

Each CD was $14.1.

Step-by-step explanation:

43.50 - 1.30 = 42.2

42.2/3 = 14.1

Answer:

please the question is not clear

Answer:

(2, 4).

Step-by-step explanation:

For y = -x  the transform is:

( x, y )  reflects to (-y, - x)

So (-4, -2) reflects to (2, 4)