Can someone please help find X.

Answer:

Option A.Exponential decay, 55% decrease

Step-by-step explanation:

we have

[tex]f(x)=54(0.45)^{x}[/tex]

This is a exponential function of the form

[tex]f(x)=a(b)^{x}[/tex]

where

a is the initial value

b is the base

b=(1+r)

r is the rate of change

In this problem

a=54

b=0.45

so

0.45=1+r

r=0.45-1

r=-0.55

Convert to percentage

r=-55% ------> is negative because is a exponential decay

Answer:

Exponential decay, 55% decrease

Step-by-step explanation:

[tex]f(x) = 54(0.45)^x[/tex]

General exponential growth function is [tex]y=a(1+r)^x[/tex]

exponential growth function is [tex]y=a(1-r)^x[/tex]

The value of 1-r is less than 1 then it is exponential decay

In the given f(x) , the 1-r is 0.45 that is less than 1

So it is exponential decay.

[tex]1-r= 0.45[/tex]

Subtract 1 on both sides

[tex]r=0.55[/tex]

Multiply by 100 to get %

r= 55%

Exponential decay, 55% decrease

Answer:

  -8

Step-by-step explanation:

For roots r and s, the quadratic can be factored ...

  f(x) = (x -r)(x -s) = x^2 -(r+s)x +rs

Then the value of r^2+s^2 can be determined from the coefficient of x (-(r+s)) and the constant (rs) by ...

  r^2 +s^2 = (-(r+s))^2 -2(rs) = (r^2 +2rs +s^2) -2rs = r^2 +s^2

Comparing this to your given equation, we have the coefficient of x as (-2m) and the constant term as (m^2+2m+3). Forming the expression ...

  (x-coefficient)^2 -2(constant term)

we get ...

  r^2 +s^2 = (-2m)^2 -2(m^2 +2m +3) = 2m^2 -4m -6

  r^2 +s^2 = 2(m -1)^2 -8

The minimum value of this quadratic expression is where m=1 and the squared term is zero. That minimum value is -8.

Answer:

p = q

Step-by-step explanation:

There are 180 degrees in a triangle. If you subtract 50 and 60 from 180, you get 70. If you subtract 30 an 80 from 180, you get 70. therefore p = q.

Answer:

x=7 satisfy the equation, so it is the solution.

x=4 doesn't satisfy the equation so it is extraneous solution.

Step-by-step explanation:

The equation given is:

[tex]\sqrt{x-3}+5=x[/tex]

Adding -5 on both sides

[tex]\sqrt{x-3}=x-5[/tex]

Taking square on both sides

[tex](\sqrt{x-3})^2=(x-5)^2[/tex]

Now solving

[tex]x-3 = x^2 -10x+25\\Arranging\\x^2-10x-x+3+25=0\\x^2-11x+28=0\\Factorizingx^2-7x-4x+28=0\\\\x(x-7)-4(x-7)=0\\(x-4)(x-7)=0\\x-4=0 \,\,and\,\, x-7=0\\x=4 \,\,and\,\, x=7[/tex]

Verifying solutions:

Putting x=4 in the equation

[tex]\sqrt{x-3}+5=x[/tex]

[tex]\sqrt{4-3}+5=4[/tex]

[tex]\sqrt{1}+5=4[/tex]

[tex]1+5=4[/tex]

[tex]6\neq 4[/tex]

So, x=4 doesn't satisfy the equation so it is extraneous solution.

Now Putting x=7 and verifying

[tex]\sqrt{x-3}+5=x[/tex]

[tex]\sqrt{7-3}+5=7[/tex]

[tex]\sqrt{4}+5=7[/tex]

[tex]2+5=7[/tex]

[tex]7=7[/tex]

x=7 satisfy the equation, so it is the solution.

Answer:

= 7

Step-by-step explanation:

The inverse of the function f(x) = x + 2 is found by swapping the variables and solving for y, resulting in f^-1(x) = x - 2.

The function f(x) = x + 2 is a simple linear function in Mathematics. The inverse of any function can be found by swapping the x and the y, and then solving for y. In this case, step-by-step, it would work like this:

So the inverse of the function f(x) = x + 2 is f^-1(x) = x - 2.

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The inverse of the function f(x) = x + 2 is found by switching the roles of x and y and solving for y, resulting in the inverse function h(x) = x - 2. None of the provided options is correct.

To determine the inverse of the function f(x) = x + 2, you need to first replace f(x) with y, resulting in the equation y = x + 2. Next, swap x and y to get x = y + 2. Solve for y to find the inverse function: y = x - 2. Therefore, none of the options provided is the correct inverse of the function f(x) = x + 2. The correct inverse is h(x) = x - 2.

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Answer:

x = 9

Step-by-step explanation:

Those are chords of a circle, and the theorem to find x is, in this context:

6(3) = 2(x) so

18 = 2x and

x = 9

Answer:

C) 4,850

Step-by-step explanation:

                  No. of

LED bulbs : CFL bulbs : Total

       2        :        3         :    5

   5000     :     7500     : 12 500

Percentage of non-defective LED bulbs = 100% - 3% = 97%

No. of non-defective LED bulbs = 97% x 5000 = 4850

Answer:

The exact volume of an oblique cylinder is [tex]V=2,000\pi\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The Cavalieri's principle states that if two or more figures have the same cross-sectional area at every level and the same height, then the figures have the same volume

so

The volume of the oblique cylinder is equal to

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

we have

[tex]h=20\ cm[/tex]

[tex]r=10\ cm[/tex]

substitute

[tex]V=\pi (10)^{2} (20)[/tex]

[tex]V=2,000\pi\ cm^{3}[/tex]

Answer:

the volume of an oblique cylinder is V=2,000\pi\ cm^{3}

Hello There!

-The Numbers Ordered From Least To Greatest-

-59   -41   -23   -11

The closer the number is to zero, it is going to be a bigger number than a number far away from zero.

Answer:

The equation of the nth term is an = -621 + 42n

Step-by-step explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic sequence:

- U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

- Un = a + (n – 1)d, where a is the first term , d is the difference

  between each two consecutive terms

, n is the position of the term

* Lets solve the problem

∵ an = a + (n - 1)d

∴ a14 = a + (14 - 1)d

∴ a14 = a + 13d

∵ a14 = -33

∴ a + 13d = -33 ⇒ (1)

- Similar we can find another equation from a15

∵ a15 = a + (15 - 1)d

∴ a15 = a + 14d

∵ a15 = 9

∴ a + 14d = 9 ⇒ (2)

- We will solve equations (1) and (2) to find a and d

* Lets subtract equation (2) from equation (1)

∴ (a - a) + (13 - 14)d = (-33 - 9)

∴ -d = -42 ⇒ × both sides by -1

∴ d = 42

- Substitute this value of d in equation (1) or (2)

∵ a + 13d = -33

∵ d = 42

∴ a + 13(42) = -33

∴ a + 546 = -33 ⇒ subtract 546 from both sides

∴ a = -579

* Now lets write the equation of the nth term

∵ an = a + (n - 1)d

∵ a = -579 and d = 42

∴ an = -579 + (n - 1) 42 ⇒ open the bracket

∴ an = -579 + 42n - 42

∴ an = -621 + 42n

* The equation of the nth term is an = -621 + 42n

Answer:

B. 10.

Step-by-step explanation:

This is the number of combinations of 3 from 5.

5C3  = 5! / 3! (5-3)!

= 5*4*3*2*1 / 3*2*1 * 2*1

= 5*4/2*1

= 10.

Answer: 10 i think

Step-by-step explanation:

Answer:

  84.8 in³

Step-by-step explanation:

The formula for the volume of a cylinder is ...

  V = πr²h

The volume Mary will be filling will be 3/4 of the 9-inch height of the vase, so is ...

  V = π(2 in)²(3/4·9 in) = 27π in³ ≈ 84.8 in³

_____

Comment on the answer

In more conventional units of measure, that is very nearly 3 pints of water.

Answer:

a 16

Step-by-step explanation:

16 x 12 = 192 plates

496 total plates - 192 = 304

304 packages of 8 plates

304 / 8 = 38 sets of 8 plates

38 + 16 = 54 packs of plates

Answer:

[tex]AB =3 \sqrt{5} = 6.708203932...[/tex]

Step-by-step explanation:

[tex]A( - 1,6) \:,\: B(5,3)\\ AB = \sqrt{{(x1 - x2)}^{2} + {(y1 - y2)}^{2} } \\ AB = \sqrt{ {( - 1 - 5)}^{2} + {(6 - 3)}^{2} } \\ AB = \sqrt{ {( - 6)}^{2} + {(3)}^{2} } \\ AB = \sqrt{36 + 9} \\ AB = \sqrt{45} = 3 \sqrt{5} = 6.708203932...[/tex]

The distance between A and B to 3 significant figure is 6.71

The formula for calculating the distance between two points is expressed as:

[tex]D =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Given the coordinate points (-1, 6) and (5, 3)

Substitute the given coordinates into the formula;

[tex]D =\sqrt{5+1)^2+(3-6)^2}\\D =\sqrt{(6^2+(-3)^2}\\D=\sqrt{36+9}\\D=\sqrt{45}\\D= 6.71\\[/tex]

Hence the distance between A and B to 3 significant figure is 6.71

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Answer:

There is a 1 and 6 chance (16.666...%)

Answer:

11.15 packs of paper are used in 5 days; therefore, 133.85 are left

Step-by-step explanation:

Set this up as ratio with days on top and packs of paper on the bottom.  Filling in the ratio with the info we have, keeping in mind we are looking for packs of paper left after 5 days:

[tex]\frac{days}{packs}:\frac{65}{145}=\frac{5}{x}[/tex]

Cross multiply to get 65x = 725 and x = 11.15.  This represents the number of packs used.  To get the number of packs remaining, subtract 11.15 from 145 to get 133.85 remaining after 5 days.

Answer:

Mean = 47.52 degrees

Step-by-step explanation:

We will use the following method to find the mean

Class interval     Frequency(f)     Class Mark(X)     fx

40-44                      3                              42               126

45-49                      4                              47               188

50-54                     10                             52               520

55-59                      6                              57               342

60-64                      2                              62               124

.........................................................................................................

                               25                                                1188

.........................................

The formula for mean is:

Mean = ∑fx / ∑f

= 1188/25

= 47.52 degrees

The computed mean is less than the actual mean of 51.8 degrees ..

Answer:

see below

Step-by-step explanation:

Events are independent when the probability of one of them does not depend on the other one. That is, P(A|B) = P(A) and P(B|A) = P(B).

They are not independent if the above condition is not met.

A quick assessment of the given table shows ratios of one row to the next are different between columns, and vice versa. Hence the events are not indpendent.

Answer:

C. [tex]490 \textrm{ units}^{2}[/tex]

Step-by-step explanation:

The formula for surface area is

LA + 2B

LA indicated Lateral Area and can be found multiplying perimeter of base by the height.

7 + 7 + 14 + 14 = 42 * 7 = 294

Multiply the LA from above with the area of base times 2.

98 * 2 = 196

294 + 196 = 490, so the surface area of the rectangular prism is 490 units.

To find the surface area of a rectangular prism, add up the areas of all six faces by multiplying length by width.

To find the surface area of a rectangular prism, you need to add up the areas of all six faces. Each face is a rectangle, so to find the area, you multiply the length by the width. Then, you add up the areas of all the faces to get the total surface area.

For example, if the length of one side is 4 units, the width is 2 units, and the height is 3 units, the surface area would be:
Face 1: 4 units x 2 units = 8 square units
Face 2: 4 units x 2 units = 8 square units
Face 3: 4 units x 3 units = 12 square units
Face 4: 4 units x 3 units = 12 square units
Face 5: 2 units x 3 units = 6 square units
Face 6: 2 units x 3 units = 6 square units
Total surface area: 8 + 8 + 12 + 12 + 6 + 6 = 52 square units.

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Answer: Option D

phase

Step-by-step explanation:

By definition, the cosine function has the following form

[tex]y = cos (x - \phi)[/tex]

Where [tex]\phi[/tex] is known as the phase angle

By definition the sinx function is equal to the cosx function with a phase shift of [tex]\frac{\pi}{2}[/tex]

So if we have the function

[tex]y = cos (x - \phi)[/tex] and we want to transform it into the function [tex]y=sin(x)[/tex] then [tex]\phi = \frac{\pi}{2}[/tex]

Finally

[tex]y = cos(x - \frac{\pi}{2})=sin(x)[/tex]

the answer is the option D

Final answer:

The cosine function aligns with the sine function by introducing a phase shift, typically represented by phi (φ), indicating that D. phase is the correct answer.

Explanation:

The cosine function can be made to have the same values as the sine function for each angle by including a shifted phase in the calculation. This shift is referred to as a phase shift and is typically represented by the Greek letter phi (φ).

In the context of trigonometric functions, a phase shift will slide one function over to match that of another.

Specifically, when the sine function is shifted left by 90 degrees (π/2 radians), it aligns perfectly with the cosine function, indicating that the sine and cosine are out of phase by 90 degrees.

Thus, the correct answer is D. phase.

Answer:

The vertex of the parabola is (2 , 2) ⇒ answer B

Step-by-step explanation:

* Lets revise the equation of a parabola

- The equation is in the form (x − h)² = 4p (y − k), where h and k are the

 vertex of the parabola

- If  p > 0, the parabola opens up  

- If p < 0, the parabola opens down

* Lets solve the problem

∵ The equation of the parabola is (x - h)² = 4p (y - k)

∵ The equation of the parabola is (x - 2)² = -12 (y - 2)

- By comparing the two equations

∴ 4p = -12 ⇒ divide both sides by 4

∴ p = -3 ⇒ -3 < 0

∵ p < 0

∴ The parabola opens down

- From the two equations

∴ h = 2 ⇒ the x-coordinate of the vertex

∴ k = 2 ⇒ the y-coordinate of the vertex

∴ The vertex of the parabola is (2 , 2)

The vertex of the given parabola (x - 2)^2 = -12(y - 2) is at the point (2, 2), which corresponds to Option B.

The vertex of the parabola defined by the equation (x - 2)^2 = -12(y - 2) can be found by identifying the point (h, k), where the equation fits the general form (x \\- h)^2 = 4p(y \\- k). Here, h and k represent the coordinates of the vertex, and p indicates the distance from the vertex to the focus or directrix. The given equation can be rearranged to match the general form with h = 2 and k = 2, making the vertex (2, 2). Hence, the correct answer is Option B.

Step-by-step explanation:

59 mi/hr × (5280 ft/mi) × (1 hr / 3600 s) = 86.53 ft/s

Rounded to the nearest whole number, the speed is approximately 87 ft/s.

Answer:

8x^2+3x

Step-by-step explanation:

What I read is 2x+8x^2-4x+5x

combining like terms means putting the terms that have the same variable part together

8x^2 is the only one that doesn't have any terms like it as far as the variable part

so 8x^2+2x-4x+5x

We just need to figure out 2-4+5 which is -2+5=3

So the answer is 8x^2+3x

Answer:

Step-by-step explanation:

the translation (x,y) --> (x+6,y-4):

(1, 5)--> (1+6,5-4)=(7,1)

(2, 2)--> (2+6,2-4)=(8,- 2)

(6, 3)--> (6+6,3-4)=(12,- 1)

the image of A triangle has vertices of (1, 5), (2, 2), and (6, 3) is :

the triangle has vertices of (7, 1), (8,- 2), and (12, -1)

Answer:

5.5% per year

Step-by-step explanation:

Using Formula A = P (1 + rt)

Where

A = Final amount = $10,000 + $6,600  = $16,600

P = Principal = Beginning Amount = $10,000

t = time = 12 years

r = rate in $/year (which we need to find)

Assembling the formula

A = P (1 + rt)

16,600 = 10,000 (1 + 12r)

[tex]\frac{16,600}{10,000}[/tex] = 1 + 12r

1.66 = 1 + 12r

1.66 - 1 = 12r

0.66 = 12 r

r = 0.055 = 5.5%

Answer:

Yellow Paint: 0.44736842105%

Red Paint: 0.19736842105%

Water: 0.35526315789%

Step-by-step explanation:

Yelow:

30 x 0.3 = 9

8 + 9 = 17

30 + 8 = 38

17/38 = 0.44736842105%

Red:

30 x 0.25 = 7.5

7.5/38 = 0.19736842105%

Water:

30 x 0.45 = 13.5

13.5/38 = 0.35526315789%

Answer:

h = 2 and k = 6

Step-by-step explanation:

Since the lines intersect at (- 3, 1) then this is the solution to the system of equations.

That is x = - 3 and y = 1

Substitute these values into the equations and solve for h and k

hx - 4y = - 10

- 3h - 4 = - 10 ( add 4 to both sides )

- 3h = - 6 ( divide both sides by - 3 )

h = 2

Similarly

kx + 3y = - 15

- 3k + 3 = - 15 ( subtract 3 from both sides )

- 3k = - 18 ( divide both sides by - 3 )

k = 6

Answer:

  16.5 ft by 25.5 ft

Step-by-step explanation:

Let w represent the width of the garden in feet. Then w+9 is the garden's length, and w(w+9) represents its area.

The surrounding walkway adds 8 feet to each dimension, so the total area of the garden with the walkway is ...

  (w+8)(w+9+8) = w^2 +25w +136

If we subtract the area of the garden itself, then the remaining area is that of the walkway:

  (w^2 +25w +136) - (w(w+9)) = 400

  16w + 136 = 400 . . .simplify

  16w = 264 . . . . . . . . subtract 136

  264/16 = w = 16.5 . . . . . width of the garden in feet

  w+9 = 25.5 . . . . . . . . . . .length of the garden in feet

Answer:

  A.  8, 10, 14

Step-by-step explanation:

As a rough cut, a triangle will be obtuse if the longest side is about 1.4 or more times the length of the second-longest side. This derives from the relationship in an isosceles right triangle, where the hypotenuse is √2 ≈ 1.414 times the length of the two equal-length sides. If one side is shorter than the other, and the hypotenuse is still 1.414 times the length of the second-longest side, then the triangle is no longer a right triangle, but is an obtuse triangle.

Here, the first selection has a middle-length side of 10 and a longest side of 14, about 1.4 times 10. It is an obtuse triangle.

_____

More rigorously, you can see if the sum of the squares of the short sides is less than the square of the longest side. If so, the triangle is obtuse. (The Law of Cosines will tell you the angle opposite the longest side must have a negative cosine, so must be greater than 90°.)

Our answer choices are ...

  A. 8^2 + 10^2 = 164 < 14^2 = 196 . . . . . obtuse

  B. 9^2 + 12^2 = 225 = 15^2 . . . . . . . . . . right

  C. 10^2 +14^2 = 296 > 17^2 = 289 . . . . . acute

  D. 12^2 +15^2 = 369 > 19^2 = 361 . . . . . acute

Answer:

A) 8, 10 and 14

correct on edg2020 :)

Answer:

10x

Step-by-step explanation:

Note the place values of the value 3 in both of the decimals.

The value of the 3 in 46.132 is in the hundredths place.

The value of the 3 in 8.553 is in the thousandths place.

Divide thousands with hundreds: 1000/100 = 10

The value of the 3 in 46.132 is 10x larger than the value of 3 in 8.553

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