Explain in words the graphical transformations that f(x) undergoes to become
f(x + 9) − 1.

The largest power of 10 that is a factor of 1000! is 5^249, or 10^249.

(a) To find the largest power of 10 that is a factor of 50!, we need to count the number of factors of 5 in 50! since each factor of 5 contributes at least one factor of 10.

There are 10 multiples of 5 in 50!, namely 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Each of these contributes one factor of 5. There are also 2 multiples of 25 (25 and 50), each of which contributes an additional factor of 5. Therefore, the total number of factors of 5 in 50! is 10 + 2 = 12.

Since each factor of 10 contains one factor of 5 and one factor of 2, we also need to count the number of factors of 2. It is clear that there are more factors of 2 than factors of 5, so we only need to count the factors of 5. Therefore, the largest power of 10 that is a factor of 50! is 5^12, or 10^12.

(b) To find the largest power of 10 that is a factor of 1000!, we follow the same reasoning as in part (a). The number of factors of 5 in 1000! is:

⌊1000/5⌋ + ⌊1000/25⌋ + ⌊1000/125⌋ + ⌊1000/625⌋ = 200 + 40 + 8 + 1 = 249

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Yes, the given statement is true that any decimal that ends with a digit in the thousandths place can be written as a fraction with a denominator that is divisible by both 2 and 5.

A fraction is a part of a whole number, and a way to split up a number into equal parts.

Given that;

The statement is about the decimal that ends with a digit in the thousandths place can be written as a fraction with a denominator that is divisible by both 2 and 5.

Now, A fraction is terminating decimal as if the denominator of the fraction contains terms in the form of 2ᵃ, 5ᵇ or 2ᵃ x 5ᵇ.

Then, It is said that, there is a digit in thousandth place.

Hence, the statement given is true that any decimal that ends with a digit in the thousandths place can be written as a fraction with a denominator that is divisible by both 2 and 5.

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The linear equation that passes through the two given points is:

y = (5/8)*x + 19/8

We want to find the equation of a line that passes through (1, 3) and (9, 8).

Remember that the slope of a line that passes through two points (x₁, y₁) and (x₂, y₂) is given by the equation:

slope = (y₂ - y₁)/(x₂ - x₁)

Here we know the two points (1, 3) and (9, 8).

Then the slope is:

slope = (8 - 3)/(9 - 1) = 5/8

We can write the line as:

y = (5/8)*x + b

To  find the value of b,we can evaluate in one of the given points, for example, if we use (1, 3) then we will get:

3 = (5/8)*1 + b

3 = 5/8 + b

3 - 5/8 = b

24/8 - 5/8 = b

19/8 = b

The linear equation is:

y = (5/8)*x + 19/8

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In circle L with m/KLM = 60 and KL = 18 units, the length of arc KM is approximately 18.85 units.

What is circle?

A circle is a geometrical shape that is defined as the set of all points in a plane that are equidistant from a given point called the center of the circle. The distance between the center of the circle and any point on the circle is called the radius of the circle.

We can use the formula for the length of an arc of a circle:

L = rθ

where L is the length of the arc, r is the radius of the circle, and θ is the angle subtended by the arc at the center of the circle (in radians).

In this problem, we are given the measure of the central angle m/KLM = 60 degrees, which is equal to 60/360 = 1/6 of a full revolution (360 degrees). Therefore, the angle θ subtended by the arc KM is:

θ = (1/6) * 2π = π/3 radians

To find the length of arc KM, we need to know the radius of circle L. Since we are not given this information directly, we can use the fact that KL is a chord of the circle and the perpendicular bisector of KL passes through the center of the circle. Let O be the center of circle L, and let N be the midpoint of KL. Then ON is the radius of the circle, and KN = KL/2 = 9 units.

We can use the Pythagorean theorem to find ON:

ON² = OM² + MN²

where OM is the distance from O to the midpoint of LM. Since OM is perpendicular to LM, it is also the altitude of triangle KLM, and we can use the formula for the altitude of an equilateral triangle to find that OM = ([tex]\sqrt{3}[/tex]/2)KL = 9[tex]\sqrt{3}[/tex] units.

Since MN = KL/2 = 9 units, we have:

ON^2 = [tex](9*\sqrt{3} )^2 + 9^2[/tex] = 243 + 81 = 324

so ON = 18 units.

Now we can find the length of arc KM using the formula:

L = rθ = 18 * (π/3) = 6π units

Rounding to the nearest hundredth, we get:

L ≈ 18.85 units.

Therefore, the length of arc KM is approximately 18.85 units.

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Answer:

Step-by-step explanation:

Generally an equation which will be true for all values of x have some statement which can be simplified into another state which will always be true.

So for example: [tex]x+4=x+4[/tex], is kind of a bit obvious to tell it's going to be true for all values as the two expressions have the same exact terms, but we can subtract "x" from both sides leading us to the statement: [tex]4=4[/tex] which is always true.

One important thing to note is you must be cautious at times, for example: [tex]\frac{x-2}{x-2}=\frac{x-2}{x-2}[/tex] may seem to be true for all values, and x-2 over x-2 is the same thing, so it simplifies to one and same thing on the right side: [tex]1=1[/tex] thus the statement should be true for all values right? Not completely, it's true for most values, except for x=2, and this is because 1=1 isn't exactly the same expression. In the original fraction the denominator has an x-2, and if we plug in x=2, we get 2-2 resulting in division by one, which of course isn't definable. So that's just one important thing to note as simplifying expressions may result in expressions that look equal, but are slightly different in a way.

On first evening she receives 19 calls and on second evening  she receives 11 calls while on 3rd evening she receives 38 calls.

A mathematical equation is a fοrmula that joins two statements and uses the equal symbol (=) tο indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is knοwn as an equation in algebra. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the twο sentences oοn either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which alsο serves as the symbol, fοr instance, 2x – 4 = 2.

X, Y, and Z represents the 1st , 2nd, and 3rd evenings

X + Y + Z = 68

⇒ X = Y + 8

⇒ Z = 2(Y + 8)

⇒ Y + Y + 8 + 2(Y + 8) = 68

Y = 11 calls

And

X = (11)+ 8 = 19 calls

Z = 2((11) + 8) = 38 calls

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Answer:

Step 1: Construct a circle through three points not on a line.

a) Points D, E, and F are not in a line. To construct a circle through points D, E, and F, begin by

drawing line segments DE and EF. Then construct the perpendicular bisectors of DE and EF, and

name the point of intersection of the perpendicular bisectors O. How do you know that point O

is the center of the circle that passes through the three points?

Answer:

Step-by-step explanation:

To show that point O is the center of the circle that passes through points D, E, and F, we can use the property of perpendicular bisectors. The perpendicular bisectors of two chords of a circle bisect the chord and pass through the center of the circle. Since the perpendicular bisectors of DE and EF intersect at point O, it follows that O must be the center of the circle that passes through points D, E, and F.

This property can also be proven using the Pythagorean theorem. Let the radius of the circle be r and let the midpoints of DE and EF be M1 and M2, respectively. Then, OM1 = OM2 = r, and the distance between M1 and M2 is equal to the distance between D and F. By the Pythagorean theorem, the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse, so we have:

OM1^2 + (M1M2)^2 = r^2 + r^2 = 2r^2

Since OM1^2 + (M1M2)^2 is equal to 2r^2, it follows that the distance between M1 and M2 is equal to the diameter of the circle. This means that M1 and M2 are the midpoints of the diameter of the circle, so they must both lie on the circumference of the circle. This, in turn, means that O is the center of the circle that passes through points D, E, and F.

Answer:3/a-6

Step-by-step explanation:

Answers

9x+6x=2600

15x=2600

x=520/3

9x=9×520/3=1560

6x=6×520/3=1040

Answer:

First side: 40in

Second side: 20in

Third side: 36in

Step-by-step explanation:

Let's call the triangle's first, second, and third sides a, b, and c respectively.

The perimeter of the triangle is 96in: a+b+c=96

The length of the first side is twice the second: a=2b

The third side is 16in more than the second: c=b+16

Now, consider the equation a+b+c=96 again, but sub '2b' in for a, and 'b+16' for c, in order to find the value of b:

a+b+c=96

2b+b+b+16=96

4b=80

b=20

Use this value for b to find a and c:

a=2b=2(20)=40

c=b+16=20+16=36

Answer:

Step-by-step explanation:

Let's call the length of the second side "x". Then, the length of the first side is 2x and the length of the third side is x + 16.

The perimeter of the triangle is the sum of the lengths of its sides, so we can set up an equation to solve for x:

x + 2x + (x + 16) = 96

Expanding the equation and solving for x, we get:

4x + 16 = 96

4x = 80

x = 20

So, the length of the second side is 20 inches, the length of the first side is 2 * 20 = 40 inches, and the length of the third side is 20 + 16 = 36 inches.

The required, Ask each regular customer which flavor they would like to see in his shop, would be the best method. Option C is correct.

Inductive reasoning is defined as, tempting judgments by moving from the details to the fact. It's usually determined with inferential reasoning, where you move from known information to precise conclusions.

Here,
Asking each regular customer which flavor they would like to see in the shop would be the best method because the customers are the ones who will be buying and consuming the ice cream, so their preferences are the most important. By directly asking the customers for their opinions, the owner can get a better understanding of what flavors people are interested in, and it can also help to build a relationship with the customers by showing that their input is valued.

Option A, determining the current best-selling flavor, would only provide information about the current sales and not necessarily reflect customers' interests in new flavors. Option B, visiting other ice cream shops, could provide some ideas, but it would not necessarily reflect the local market and the preferences of the shop's specific customer base. Option D, randomly generating customers to survey, may not be representative of the actual customer base and may not provide a reliable indication of which new flavor to sell.

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Answer:

x [tex]\geq[/tex] 19.75

Step-by-step explanation:

x ≥ 50 - 30.25

x ≥ 19.75

To get a free meal, he needs to spend 19.75 or more.

When x changes from 2 to 5, the average velocity (or average rate of change of y with respect to x) is 9.33 m/s. When x changes from 2 to 2 + h, the average velocity is 2 + hm/s.

Average speed is determined by dividing the total distance you travelled by the total time, whereas average velocity is determined by dividing your displacement (a vector Throughout the entire period, position to your finish position).

(A) The following formula is used to get the average velocity when x changes from 2 to 5:

value of y at x = 2

= 2²+2 = 6 m

value of y at x = 5

= 5²+5 = 30 m

displacement equals 30 – 6 = 24 m.

Time is 5 - 2 = 3 seconds.

average velocity

= displacement /Time duration

= 24/3 = m/s

B) Value of y at x = 2 = 5 for x changing from x to x plus ie for minimal change in x.

Displacement during a little change in x will be 0 because the value of y will once again be 5.

C )  

y(x) = x² + x

dy / dx = 2x + 1

dy / dx  represents instantaneous  velocity

so when x = 2

instantaneous velocity = 2 x 2 +1

= 5 m /s

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The value of x is given as follows:

x = 9.

The sum of the interior angle measures of a polygon with n sides is given by the equation presented as follows:

S(n) = 180 x (n - 2).

The figure for this problem has four sides, hence the sum of the internal angle measures is given as follows:

S(4) = 180 x (4 x 2)

S(4) = 360º.

Adding the four angle measures and equaling them to 360º, the value of x is obtained as follows:

117 + 93 + 87 + 6x + 9 = 360

306 + 6x = 360

6x = 54

x = 54/6

x = 9.

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Answer:

              Based on the measures of the following triangle's angles, the triangle can be classified as an obtuse triangle.

Step-by-step explanation:

              In order to decide which type of triangle this is, first we must understand what an acute, right, and obtuse triangle are. Acute triangles are triangles with all three of its angles less than 90°, right triangles are triangles with one angle that is exactly 90°, and obtuse triangles are triangles with one angle that is greater than 90°. Overall, we can determine the type of this triangle by looking at its angles.

             The given triangle has the angles 25°, 136°, and 19°. Now we can compare it to the rules above and see whether this triangle is acute, right, or obtuse. As the given triangle has an angle that is greater than 90°, we can conclude that the following triangle is an obtuse triangle.

Have a great day! Feel free to let me know if you have any more questions :)

The supportive statement is m∠WKT ≅ m∠TRW.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the measurement of the angle perpendicular to the parallel sides.

We know a trapezoid is isosceles if the two nonparallel sides are equal.

Therefore, In KWRT, [tex]\overline{WK}[/tex] ≅ [tex]\overline{TR}[/tex] and [tex]\overline{KR} || \overline{TW}[/tex].

The missing statement to support all other statements would be,

m∠WKT ≅ m∠TRW as the angle formed by the pair of the corresponding sides is equal.

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Answer: 6.38

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

The requried graph with the x-axis labeled a number of side dishes and the y-axis labeled cost in dollars and a line going from point [0,5.25] through point [3, 9.75]. Option C is correct.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
Calculate the slope of the given relation in the table, using any two of the ordered pair,
m = 11.25 - 8.25 / 4 - 2
m = 3/2
m = 1.5

Now calculate the slope in each option, the slope of any option matches with m = 1.5 then that will be the required graph, so the slope of the graph mentioned in option C matches with m = 1.5.

Thus, Option C is the required answer.

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Solving a quadratic equation, we will see that the object will hit the ground after 5.9 seconds.

The equation for the vertical movement of an object will be:

H(t) = -16*t^2 + v0*t + h0

Where v0 is the initial velicity, in this case 85ft/s, and h0 is the initial height,  55ft.

Then the height equation is:

H(t) = -16*t^2 + 85*t + 55

The object will hit the ground when the height is equal to zero, then we need to solve:

-16*t^2 + 85*t + 55 = 0

Using the quadratic formula we will get:

[tex]t = \frac{-85 \pm \sqrt{(85)^2 - 4*(-16)*55} }{2*-16} \\\\t = \frac{-85 \pm 103.7 }{-32}[/tex]

We only care for the positive solution, which is:

t = (-85 - 103.7)/-32 = 5.9

So it will take 5.9 seconds for the object to hit the ground.

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Answer:

what is that maybe l can be of help to u

Answer: 2: 56 degrees

4: 56 degrees

(Number 6 is not in the image)

Step-by-step explanation:

So for #2 we know the whole angle is 90 degrees, so all we have to do is 90-34 = 56

And for #4, we know the angle is 180 so all we have to do is 180-124=56

Regarding the pattern, we have that:

Regarding subtraction by even numbers, we have that:

Hence the pattern cannot be subtract 4, as the sequence would be composed either by all even numbers or all odd numbers.

Regarding subtraction by odd numbers, we have that:

We can see that the results alternate, hence the pattern can be subtract 5.

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The solution to the equation 16^{2x - 3} · 4^{-2x} = 4^2 include the following: C. x = 4.

In Mathematics, laws of indices can be defined as the standard principles or rules that are used for simplifying an equation or expression that involves powers (exponents) of the same base.

By rewriting the mathematical expression and applying the multiplication law of indices, we have the following:

16^{2x - 3} · 4^{-2x} = 4^2

4^2{2x - 3} · 4^{-2x} = 4^2

2{2x - 3} + {-2x} = 2

4x - 6 - 2x = 2

2x = 2 + 6

2x = 8

x = 8/2

x = 4.

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Answer:

The island is 728 feet off the coast.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the percent of the people who attended the Baybridge Middle School Winter Formal who are not students at Baybridge, we can use the following steps:

Find the fraction of non-student attendees: 18 attendees out of 90 total attendees can be represented as 18/90.

Convert the fraction to a decimal: 18/90 = 0.20, which can be rounded to 0.2.

Convert the decimal to a percentage: 0.2 * 100 = 20%.

So, 20% of the people who attended the Baybridge Middle School Winter Formal are not students at Baybridge.

Step-by-step explanation:

we need to remember 2 things for right-angled triangles (which we need to use to find the sides of the rectangle, so that we then can calculate the area) :

1. Pythagoras

a² + b² = c²

with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs.

2. geometric mean theorem

height = sqrt(p×q)

with p and q being the segments of the baseline the height is splitting it into. in our case MA and AL.

so, to get the length of the rectangle (PL) we use Pythagoras :

PL² = 6² + 8² = 36 + 64 = 100

PL = 10 units

to get PM we first need to get ML. and for that we need to get MA.

6 = sqrt(MA × 8)

36 = MA × 8

MA = 36/8 = 4.5 units

that means ML = 8 + 4.5 = 12.5 units

and again Pythagoras

ML² = PL² + PM²

12.5² = 10² + PM²

156.25 = 100 + PM²

56.25 = PM²

PM = 7.5 = 7.5 units

so, the area of the rectangle is

10 × 7.5 = 75 = 75.00 units²

to "round" to the nearest hundredth.

Answer:

Alright, so we want to know how much that can be earned in one year. So that's going to be 3000. And this is simple interest. So this is one plus 0.011, which equals $3,033. And that's the solution to this exercise.

Answer:

$3,036

Step-by-step explanation:

The new customer can open a money market account. The bank will deposit $3,000 into the account.

The bank will pay 1.2% (0.012) in interest every year. This interest will increase the original amount to $3,036.