Which of the following is most likely the next step in the series?

Answer:

option E, C

Step-by-step explanation:

From the graph we will find the equation of g(x).

g(x) is a parabola with vertex ( h, k) = ( 0, 9)

Standard equation of parabola is ,  y = a (x - h)² + k

                                                     y = a (x - 0)² + 9

                                                     y = ax² + 9 ----------  ( 1 )

Now we have to find a .

To find a we will take another point through which the parabola passes .

Let it be ( 3, 0).

Substitute ( 3 , 0 ) in  ( 1 ) =>  0 = a (3 )² + 9

                                     => - 9 = 9a

                                     => a = - 1

Substitute a = - 1 in ( 1 ) => y = -1 x² + 9

                                  => y = - x² + 9

Therefore , g(x) = -x² + 9

Now using the table we will find h(x)

 [tex]h(x) = 4^{x}[/tex]

So g(x) = -x² + 9 and [tex]h(x) = 4^{x}[/tex]

Option A : both function increases on ( 0, ∞ ) - False

               [tex]\lim_{x \to \infty} g(x) = \lim_{x \to \infty} -x^2 + 9[/tex]

                                  [tex]= - \lim_{x\to \infty} x^2 + \lim_{x \to \infty} 9\\\\= - \infty + 9\\\\=- \infty[/tex]

g(x) decreases on ( 0 , ∞)

             [tex]\lim_{x\to \infty} h(x) = \lim_{x \to \infty} 4^{x}[/tex]

                                [tex]= \infty[/tex]

h(x) increases on ( 0, ∞)

option B : g(x) increasing on (- ∞, 0) - False

      g(x) = -x² + 9

       g( -2 ) = - (-2)² + 9

                 = - 4 + 9 = 5

       g ( -5) = - ( -5)² + 9

                =  - 25 + 9 = - 14

   As the value of x moves towards - ∞ , g(x) moves towards - ∞

   Therefore g(x) decreases on  (- ∞, 0)

Option C: y intercept of g(x) is greater than h(x) - True

         y intercept of g(x) = ( 0 , 9 )

         y intercept of h(x)  = ( 0 , 1 )

Option D : h(x) is a linear function - False

Option E : g(2) < h(2) - True

        g(x) =  -x² + 9

        g(2) = -(2)² + 9 = - 4 + 9 = 5

        h(x) = 4ˣ          

        h(2) = 4² = 16      

Answer:

x = 5

Step-by-step explanation:

The difference between consecutive terms will be equal , then

a₂ - a₁ = a₃ - a₂ , that is

x + 9 - (3x - 2) = 2x + 5 - (x + 9) ← distribute parenthesis on both sides

x + 9 - 3x + 2 = 2x + 5 - x - 9 , simplify both sides

- 2x + 11 = x - 4 ( subtract x from both sides )

- 3x + 11 = - 4 ( subtract 11 from both sides )

- 3x = - 15 ( divide both sides by - 3 )

x = 5

Answer:

x = 5

Step-by-step explanation:

Each new term is 1 greater than the previous term.  Therefore:

x + 9 = (3x - 2) + 1                   Equivalent to x + 9 = 3x - 2 + 1, or:

                                                                       9 + 2 - 1 = 2x, or 2x = 10

                                                Thus, x = 5

Check by substituting 5 for x as indicated:

3x - 2 becomes 13 (which means the next term must be 14)

x + 9 becomes 14, and

2x + 5 becomes 15

and these consecutive sequence terms are {13, 14, 15}

Answer:

The original price is $90.

Step-by-step explanation:

100% - 40% = 60%

[tex]\frac{54}{y} :\frac{60}{100}[/tex]

y × 60 = 54 × 100

60y = 5400

60y ÷ 60 = 5400 ÷ 60

y = 90

Answer:

90

Step-by-step explanation:

If the discount is 40%, we are still paying 100-40% or 60 %

original price * 60% = sale price

original price * .6 = 54

Divide each side by .6

original price = 54/.6

original price =90

Answer:

1. x=3/2-y-3z/2

2.x=-y/2-17/3

3.x=3-5y/2-z/2

Step-by-step explanation:

i gusse

Answer:

lol i genuinely dunno

Step-by-step explanation:

like B'(4,8) or something

Answer:

148 ft2

Step-by-step explanation:

2×(6×4 + 6×5 + 4×5) = 148 ft2

is it like this pls don't mind how I snap it

Answer:

.............soooooooooooooooerrrrrrrrrrrrryyyyyyyyyyyyyyy.......... iiiiiiiii........ doooooooonnnnnnnnntttttttt......... kkkknnnnnooooowwww

A)

Replace the letters in the given equation with the corresponding values given in the problem:

A = 10,000 x 2.718^(0.05 x 2)

A = 11,051.59 , rounded to nearest dollar = $11,052

B)20,000 = 10000 x 2.718^(0.05 x t)

Divide both sides by 10,000:

2 = 2.718^(0.05 x t)

Apply exponent rules:

0.05tln(2.718) = 2

Solve for t:

t = ln(2) / 0.05ln(2.718)

t = 13.86 years, rounded to nearest year = 14 years.

Answer:

Step-by-step explanation:

Using [tex]A=Pe^{rt[/tex] as instructed, our equation looks like this:

[tex]A=10,000e^{(.05)(2)}[/tex] which simplifies a bit to

[tex]A=10,000e^{.1[/tex] which simplifies a bit more to

A = 10,000(1.10517) so

A = 11,051.71  Easy. Now onto the second part: solving for the number of years it takes for the investment to double. Setting A equal to 20,000 since 20,000 is 10,000 doubled:

[tex]20,000=10,000e^{.05t[/tex]  Begin by dividing both sides by 10,000 to get

[tex]2=e^{.05t[/tex] and take the natural log of both sides to get that exponent down out front, keeping in mind that the natural log will "undo" the e, leaving us with:

ln(2) = .05t and

t = 14 years (that's 13.8 rounded up to the nearest year)

Answer:

The output of (-6,0) is (-9,4)

Step-by-step explanation:

Given

[tex](x,y) \to (x -3,y+4)[/tex] --- rule

Required

The output of [tex](-6,0)[/tex]

[tex](-6,0)[/tex] implies that:

[tex](x,y) = (-6,0)[/tex]

So, we have:

[tex](x,y) \to (x -3,y+4)[/tex]

[tex](-6,0) \to (-6 -3,0+4)[/tex]

[tex](-6,0) \to (-9,4)[/tex]

The output of (-6,0) is (-9,4)

Answer:

the surface area of cylinder is 75.36 inches²

hope it helps

have a nice day

Answer:

SA = 75.36

Step-by-step explanation:

So, you use the formula and replace the letters with the values.

SA = 2*3.14*2^2+2*3.14*2*4

SA = 25.12+ 50.24

SA = 75.36

your ans is here........

The percentage reduction can be written as 16.6667% of 300. 83.3333 percent decrease (%↓) or reduction from 300 is 50.

Answer:

83.33%

Step-by-step explanation:

300-50=250

250/300=83.33%

Answer:

x = 60

Step-by-step explanation:

t = [tex]\frac{k}{x}[/tex]

15 = k/68

k=1020

~~~~~~~~~~~

17 = 1020/x

x = 1020/17

x = 60

The speed of car must be 60mile/hour, so that the trip will complete in 17 hours.

The rate of change of position of an object in any direction is called speed.

[tex]speed = \frac{distance}{time}[/tex]

According to the given question

At a speed of 68 miles per hour, the trip will be complete in 15 hours.

⇒ Total distance covered in 15 hours = 68 × 15 = 1,020 miles  

( because, distance = speed × time)

Therefore, the speed of car to complete the trip in 17 hours

= [tex]\frac{1020}{17} =60miles/hr[/tex]

Hence, the speed of car must be 60mile/hour, so that the trip will complete in 17 hours.

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Answer:

Solution

Height is not an example of a continuous variable.

D) The number of cheeseburgers sold yesterday at a drive-thru is not an example of continuous data.

Here, we have,

Continuous data refers to numerical data that can take on any value within a certain range or interval. It typically involves measurements or quantities that can be expressed as real numbers.

A) The time it takes to cut the grass can be measured in minutes or seconds, and it can take on any value within a range. This is an example of continuous data.

B) The lifetime (in hours) of a flashlight battery is a continuous variable. It can take on any value within a range, such as 5.3 hours, 10.7 hours, or any decimal or fractional value.

C) The weights of dogs in an animal shelter can be measured in pounds or kilograms and can take on any value within a range. This is also an example of continuous data.

D) The number of cheeseburgers sold yesterday at a drive-thru is a discrete variable. It represents a count or a whole number, such as 50 cheeseburgers, 100 cheeseburgers, etc. Discrete data involves distinct values and is not continuous.

Therefore, option D is not an example of continuous data.

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Answer:

kilogram

Step-by-step explanation:

Answer:

i. y = 4

ii. p = 45

iii. m = 5

Step-by-step explanation:

(a) In triangle PQR, PQ = QR. So that,

Perimeter = PQ + PR + QR

40 = (2y + 3) + (5y - 2) + (2y + 3)

    = 2y + 3 + 5y - 2 + 2y + 3

40 = 9y + 4

40 - 4 = 9y

36 = 9y

y = [tex]\frac{36}{9}[/tex]

y = 4

(b) The age of Rahim's father is p years. Since he is 29 years older than Rahim, we have;

p = 16 + 29

p = 45

Rahim's father is 45 years old.

(c) Cost of a chair = RM 5.90

Cost of m chairs = RM 5.90 x m

                           = RM 5.90m

Amount paid = RM 50 - RM 20.50

                      = RM 29.50

Thus,

RM 5.90m = RM 29.50

5.90m = 29.50

m = [tex]\frac{29.50}{5.90}[/tex]

   = 5

m = 5

The number of units of chairs bought is 5.

Answer:

The first one

Step-by-step explanation:

The product[tex]-4.\left[\begin{array}{c}8&-1&-5&9\end{array}\right][/tex] is equal to[tex].\left[\begin{array}{c}-32&4&20&-36\end{array}\right][/tex]. Option A is correct.

We have to find the product of[tex]-4.\left[\begin{array}{c}8&-1&-5&9\end{array}\right][/tex].

To do this we need to multiply -4 with each element in the matrix.

-4×8 = -32

-4×-1 =4

-4×-5=20

-4×9=-36

Now the matrix becomes [tex].\left[\begin{array}{c}-32&4&20&-36\end{array}\right][/tex].

Hence, the product[tex]-4.\left[\begin{array}{c}8&-1&-5&9\end{array}\right][/tex] is equal to[tex].\left[\begin{array}{c}-32&4&20&-36\end{array}\right][/tex]. Option A is correct.

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Answer:

36000cm

V= Length×Width×height

Answer:

[tex]36000 cm^{3} [/tex]

Step-by-step explanation:

Rectangular Tank is,

[tex]100cm = long[/tex]

[tex]30cm = wide[/tex]

[tex]12cm = height[/tex]

Let's Solve now

[tex]v = l \times w \times h \\ \: = 100cm \times 30cm \times 12cm \\ = 36000 {cm}^{3} [/tex]

15. 70° because a right angle is 90° and we have the angle of ADB which is 20°. So 90°-20°=70°.

16. 70° because angle PSQ is 60° and angle QSR is 10°. So 60°+10°=70°.

17. 55° because it says it in the explanation. I assume this is a typo and they meant to ask the measurement of ADC and in that case it would be 130° because angle ADB is 75° and angle BDC is 55°. 75°+55°=130°.

18. 40° because angle PSQ is a right angle which means it's 90°. So 130°-90°=40°.

19. 140° because angle ADB is 120° and angle BDC is 20° so 120°+20°=140°.

20. 125° because again it's in the explanation. But if it's a typo and they meant what is the measurement of PSQ then it is 50° because PSR is 125° and QSR is 75° so 125°-75°=50°.

Hope this helps! :)

Answer:

Step-by-step explanation:

j

Given:

A cube has square sides with area [tex]x^2+24x+144[/tex].

To find:

The expression that represents the surface area of the cube.

Solution:

It is given that,

The area of each side of cube = [tex]x^2+24x+144[/tex]

Number of sides of a cube = 6

Total surface area of the cube is the product of number of sides of the cube and the area of each side. So, the total surface area of the cube is

[tex]SA=6(x^2+24x+144)[/tex]

[tex]SA=6(x^2)+6(24x)+6(144)[/tex]

[tex]SA=6x^2+144x+864[/tex]

Therefore, the expression that represents the surface area of the cube is [tex]6x^2+144x+864[/tex].

Step-by-step explanation:

everything can be found in the picture

Answer:

दवणडतडडथवणतणलतवलडथलडद

Answer:

2,601

Step-by-step explanation:

the sum of AP = 51/2 × (1+101)

= 51/2 × 101 = 2,601

Answer:

10

Step-by-step explanation:

[tex]\sqrt{36 + 64}[/tex]

[tex]\sqrt{100}[/tex]

10

Answer:

V = 378y³

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Geometry

Volume of a Rectangular Prism: V = lwh

Step-by-step explanation:

Step 1: Define

Identify variables

l = 9y

w = 7y

h = 6y

Step 2: Find Volume

___________________________________

[tex]\quad\quad\quad\quad \boxed{\tt{v = lwh}}[/tex]

[tex]\quad\quad\quad\quad\tt{length (l)= 9y}[/tex]

[tex]\quad\quad\quad\quad\tt{width(w)= 7y}[/tex]

[tex]\quad\quad\quad\quad\tt{height(h)= 6y}[/tex]

[tex]\quad\quad\quad\quad\tt{v = lwh}[/tex]

[tex]\quad\quad\quad\quad\tt{v = (9y)(7y)(6y)}[/tex]

[tex]\quad\quad\quad\quad\tt{v = (9y)(42 {y}^{2}) }[/tex]

[tex]\quad\quad\quad\quad \underline{\tt{v = 378 {y}^{3} }}[/tex]

[tex]\quad\quad\quad\quad \underline { \boxed{\tt{ \color{magenta}v = 378 {y}^{3} }}}[/tex]

___________________________________

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