Determine whether the polygons are similar, please help.

Step-by-step explanation:

you mean A = area of the rectangle ?

and p = the perimeter of the rectangle ?

the area of the rectangle is

length×width = 2y × 2x = 4xy

the perimeter is

2×length + 2×width = 2×2y + 2×2x = 4x + 4y

based on the primary circle function

x² + y² = 4

we get

y² = 4 - x²

y = sqrt(4 - x²)

1)

f(x) = 4xy = 4x×sqrt(4 - x²) = g(x)×h(x)

g(x) = 4x

h(x) = h(i(x)) = sqrt(4 - x²)

i(x) = 4 - x²

the zeros of the first derivation gives us the extreme point(s).

f'(x) = g'(x)×h(x) + g(x)×h'(x)

g'(x) = 4

(h(i(x))' = h'(i(x))×i'(x)

h'(x) = 1/(2×sqrt(x))

i'(x) = -2x

so,

f'(x) = 4×sqrt(4 - x²) + 4x×-2x/(2×sqrt(4 - x²)) =

= 4×sqrt(4 - x²) - 4x²/sqrt(4 - x²)

f'(x) = 0

4×sqrt(4 - x²) - 4x²/sqrt(4 - x²) = 0, x² < 4, -2 < x < 2

sqrt(4 - x²) - x²/sqrt(4 - x²) = 0

sqrt(4 - x²) = x²/sqrt(4 - x²)

let's multiply by sqrt(4 - x²)

4 - x² = x²

4 = 2x²

x² = 2

x = sqrt(2)

therefore, the largest A (area of the rectangle) is for

x = sqrt(2), which also makes y = sqrt(2), which makes the rectangle a square.

2)

f(x) = 4x + 4×sqrt(4 - x²)

f'(x) = 4 + 4×-2x/(2×sqrt(4 - x²)) = 0, -2 < x < 2

4 - 4x/sqrt(4 - x²) = 0

1 - x/sqrt(4 - x²) = 0

1 = x/sqrt(4 - x²)

multiply by sqrt(4 - x²)

sqrt(4 - x²) = x

square both sides

4 - x² = x²

4 = 2x²

x = sqrt(2)

so, also the perimeter of the rectangle is at maximum with

x = sqrt(2) and the rectangle is again a square.

In the question, we can draw the conclusion that, according to the formula, it will take them 10 days to get from City A to City B if they continue travelling at their current average speed of \(415 miles\)per day.

A formula is a set of mathematical signs and figures that demonstrate how to solve a problem.

Formulas for calculating the volume of \(3D\) objects and formulas for measuring the perimeter and area of \(2D\) shapes are two examples.

A formula is a fact or a rule in mathematical symbols. In most cases, an equal sign connects two or more values. If you know the value of one, you can use a formula to calculate the value of another quantity.

We need to know the average pace at which they went to figure how long it would take to get from City A to City B at the same rate.

total distance / time taken = average speed

\(415 miles\) per day \(2075/ 5\), it would take them \(10\) days to get from City A to City B because

Time taken = \(2075/415\) per days \(= 5 days\)

Therefore it will take them 10 days to get from City A to City B if they continue travelling at their current average speed of \(415 miles\)per day.

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Answer:

-18.3

Step-by-step explanation:

The claim of Carly is correct that the sum of the deviations for a data set will always be 0.

Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.

Sum of the deviations of a data set is always 0.

This is because that the sum of the positive deviations is equal to the sum of the negative deviations.

Let a data set be 3, 2, 4, 5, 1

Mean = (3 + 2 + 4 + 5 + 1) / 5 = 3

Values     Deviations

3               3 - 3 = 0

2               2 - 3 = -1

4               4 - 3 = 1

5               5 - 3 = 2

1                1 - 3 = -2

Sum of the deviations = 0 - 1 + 1 + 2 - 2 = 0

Hence the sum of the deviations for a data set will always be 0.

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Check the picture below.

so the parabolic path of the object is more or less like the one shown below in the picture, now this object has an initial of 1240 ft, as it gets thrown from the ski lift, so from 0 seconds is already higher than 1000 feet.

\(h=-16t^2+32t+1240\hspace{5em}\stackrel{\textit{a height of 1000 ft}}{1000=-16t^2+32t+1240} \\\\\\ 0=-16t^2+32t+240\implies 16t^2-32t-240=0\implies 16(t^2-2t-15)=0 \\\\\\ t^2-2t-15=0\implies (t-5)(t+3)=0\implies t= \begin{cases} ~~ 5 ~~ \textit{\LARGE \checkmark}\\ -3 ~~ \bigotimes \end{cases}\)

now, since the seconds can't be negative, thus the negative valid answer in this case is not applicable, so we can't use it.

So the object on its way down at some point it hit 1000 ft of height and then kept on going down, and when it was above those 1000 ft mark  happened between 0 and 5 seconds.

Solution

Since the function has at least one rational zero, we can apply fthe actor theorem

The factor theorem states that if f(x) is a polynomial of degree n greater than or equal to 1, and 'a' is any real number, then (x - a) is a factor of f(x) if f(a) = 0.

since f(1) = 0, f(-2) = 0

=> (x + 2) is a factor of f(x)

=> X - 1 IS also a factor

Solving

Answer:

The cost of a chicken shawarma wrap = $10.99

The cost of an order of spiced potatoes=$4.99

Equations needed

3x+2y =42.95

5x + 4y=74.91

Step-by-step explanation:

x = the cost of a chicken shawarma wrap

y = the cost of an order of spiced potatoes

Ms. Ironperson

3x+2y =42.95

Mr. Thoro

5x + 4y=74.91

3x+2y =42.95 (1)

5x + 4y=74.91 (2)

Multiply (1) by 2

6x + 4y=85.9 (3)

5x + 4y=74.91. (2)

Subtract (2) from (3)

6x - 5x= 85.9 - 74.91

x=$10.99

Substitute the value of x into (1)

3x+2y =42.95 (1)

3(10.99) + 2y =42.95

32.97 + 2y = 42.95

2y = 42.95 - 32.97

2y=9.98

Divide both sides by 2

y=9.98/2

=4.99

y=$4.99

Therefore,

The cost of a chicken shawarma wrap = $10.99

The cost of an order of spiced potatoes=$4.99

The equation that represents the condition is m° + 66° + m° = 120°. Then the value of m is 27°.

When two lines intersect, then their opposite angles are equal. Then the equation is given as,

m° + 66° + m° = 120°

Simplify the equation for m, then the value of 'm' is calculated as,

m° + 66° + m° = 120°

2m° = 120° - 66°

2m° = 54°

m° = 27°

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Answer:

57,000

Step-by-step explanation:

Answer:

the answer is D

Step-by-step explanation:

Answer:

The correct answer is D.

Answer:

y = -4/3x + 2

Step-by-step explanation:

Slope intercept form is y = mx + b.

Rearrange the equation into slope intercept form by isolating y:

12x + 9y = 18

9y = -12x + 18

Divide each side by 9:

y = -4/3x + 2

So, the equation is y = -4/3x + 2

Answer:

Jane used 2/5 of a scoop more of brown sugar than she did with white sugar.

Step-by-step explanation:

If you want to find how much more something is from something else, you subtract. So, subtract 9/10-1/2. If you want to subtract, they should both have the same denominator. So, 9/10-1/2 is the same as 9/10-5/10. 9/10-5/10 is equal to 4/10 which is simplified to 2/5.

Answer:

Point A'(-1,5)     ........ corrected A' instead of A

Point B'(3,-3)

Step-by-step explanation:

The current function has vertex (2,-4), and passes through (6,0).

Using the standard formula

y = a(x-h)^2+k

we have

h = 2, k=-4

parabola passes through (6,0) =>

0 = a(6-2)^2 -4 = 16a -4

a = 1/4

so equation of given curve is

f(x) = (1/4)(x-2)^2-4

If the curve is compressed horizontally by a factor of 2, then the image is

g(x) = (1/4)(2(x-2))^2-4

=(x-2)^2 -4

Given A(-4,5), B(4,-3)

f(-4) = 5  

f(4) = -4

With a compression factor of 2, coordinates of y do not change.

for point A'

5 = (x-2)^2 -4

5 = (x-2)^2 -4

(x-2)^2 = 9

(x-2) = +/- 3

x-2 = -3, x = -1  (to the left of vertex, ok)

x-2 = +3, x = 5 (to the right of vertex, alternate point x)

Point A'(-1,5)     ........ corrected A' instead of A

For point B'

y = -3

-3 = (x-2)^2-4

(x-2)^2 =1

x-2 = +/- 1

x-2 = +1, x=3 (to the right of vertex, point required)

x-2 = -1, x= 1 (to the left of vertex, alternate point Y)

Point B'(3,-3)

The number of papers that Ms. Motley will grade in five days would be = 46 papers (approximately).

The number of papers Ms. Motley graded in first day = 9 papers

The number of papers Ms. Motley graded in the second day = 27 papers

The number of papers Ms. Motley graded in the third day = 31 papers

The average number of she graded for the three days is calculated as follows;

9+27+31 = 67/3 = 27.3 papers.

If in 3 days = 27.3 papers

5. days = X papers

Make X papers the subject of formula;

X papers = 5× 27.3/3

= 136.5/3

= 45.5 papers

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Answer:

The probability of getting at least one hit in 5 games is 0.772

Step-by-step explanation:

The correct question is as follows;

One interpretation of a baseball player's batting average is as the empirical probability of gettig a hit each time the player goes to bat. If a player witt a batting average of 0.256 bats 5 times in a game, and each at-bat is an independent event, what is the probability of the player getting at least one hit in the game?

We proceed with the answer as follows;

Here, we want to calculate the probability of a player with a certain batting average getting at least one hit in a game if he bats 5 times

Mathematically, Probability of getting at least one hit in 5 games = 1 - Probability of getting no hit in 5 games

Let p = probability of getting hit in a game = 0.256

q = Probability of getting no hit in a game = 1-0.256 = 0.744

So the probability of getting no hits in 5 games will be 0.744^5 = 0.228

Thus, the probability of getting at least one hit in the 5 games = 1 - 0.228 = 0.772

Answer:

Hello! answer: u = 16

Step-by-step explanation:

Its 16 Because 176 ÷ 11 = 16

Answer:

It would be 16 because when you divided 11 by 176 it would be 16

Answer:

it is 112° .. as you will solve it like this (180-44=136) and each angle down there are equal so we will divide 136÷2 so each angle is 68° ,, finally to find x you can do it in two ways 1) (68+44) =112 or you can go with (180-68=112)

Answer:

5 hours then dinner service starts

Step-by-step explanation:

Answer:

Step-by-step explanation:

From the given information:

A sandwich shop offers eight types of sandwiches, and Jamey likes all of them equally.

The probability that Jamey picks any one of them is 1/8

Suppose

X represents the number of times he chooses salami

Y represents the number of times he chooses falafel

Z represents the number of times he chooses veggie

Then  X+Y+Z ≤ 5 and;

5-X-Y-Z represents the no. of time he chooses the remaining

8 - 3 = 5 sandwiches

However, the objective is to determine the P[X=x,Y=y,Z=z] such that 0≤x,y,z≤5

So, since he chooses x no. of salami sandwiches with probability (1/8)x

and y number of falafel with probability (1/8)y

and for z (1/8)z

Therefore, the remaining sandwiches are chosen with probability \(\dfrac{5}{8} (5-x-y-z)\)

So. these x days, y days and z days can be arranged within five days in

\(= \dfrac{5!}{x!y!z!(5-x-y-z)!}\)

Thus;

\(P[X=x,Y=y,Z=z]= \dfrac{5!}{x!y!z!(5-x-y-z)} \times \dfrac{1}{8}x*\dfrac{1}{8}y* \dfrac{1}{8}z* \dfrac{5}{8}(5-x-y-z)\)

since 0 ≤ x, y, z ≤ 5 and x + y + z ≤ 5.

The distribution is said to be Multinomial distribution.

Answer:

49

Step-by-step explanation:

They all added up to 49

Answer:

x = 6.73

Step-by-step explanation:

tan17 = x / 22

x = 22 * tan17

x = 6.73

sin17 = 0.2924

cos17 = 0.9563

tan17 = 0.3057

Answer: A

Step-by-step explanation:

\(-\frac{4}{x}+1=0\\\\1=\frac{4}{x}\\\\x=4\)

Answer:

false

Step-by-step explanation:

I dont think I need to explain,

The girl which is correct between kate and her friend Margo is Margo.

The correct answer option is option B

If each friend gets the same number of pens;

Number of pens each friend get = Number of pens Kate has / Number of Kate's friends

= 63 / 9

= 7

Check:

Number of pens each friend get × Number of Kate's friends = Number of pens Kate has

7 × 9 = 63

Therefore, Kate's friend, Margo is correct.

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The graph of the function f(x) = 5(2)^x is an upward-sloping exponential curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing the x-axis.

The function f(x) = 5(2)^x represents exponential growth. Let's analyze its graph.

As x increases, the value of 2^x grows exponentially. Multiplying it by 5 further amplifies the growth. Here are a few key points to consider:

When x = 0, 2^0 = 1, so f(0) = 5(1) = 5. This is the y-intercept of the graph, meaning the function passes through the point (0, 5).

As x increases, 2^x grows rapidly. For positive values of x, the function will increase quickly. As x approaches positive infinity, 2^x grows without bound, resulting in the function also growing without bound.

For negative values of x, 2^x approaches zero. However, the function is multiplied by 5, so it will not reach zero. Instead, it will approach y = 0, but the graph will never touch or cross the x-axis.

The function is always positive since 2^x is positive for any value of x, and multiplying by 5 does not change the sign.

Based on these observations, we can conclude that the graph of f(x) = 5(2)^x will be an exponential growth curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing or touching the x-axis.

The graph will have a smooth curve that rises steeply as x increases. The rate of growth will be determined by the base, in this case, 2. The larger the base, the steeper the curve. The function will approach but never reach the x-axis as x approaches negative infinity.

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In total, the number of greetings will be 1159.

Mathematical symbols used to represent quantities or values include numbers. They are employed in the measurement, comparison, addition, subtraction, multiplication, and division processes in mathematics. According to their qualities and properties, numbers can be categorized into a variety of groups, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers. There are specific properties and guidelines for mathematical operations for each group of numbers. Mathematics depends on numbers, which are also utilized in many other disciplines, including science, engineering, economics, and statistics.

The number of greetings exchanged between the host and the other mothers and daughters must be counted first. Since there is only one host, the number of mother-daughter pairs is 20 - 1 = 19. There are thus a total of 38 greetings, 19 between the host and the other moms, and 19 between the host and the other daughters.

The number of pleasantries exchanged between the guest mums and everyone else must next be tallied. The host, the other mothers, and the daughters must all be greeted, making a total of 20 - 1 = 19 guest mothers. Thus, each host mother must extend 1 + 19 + 20 = 40 greetings. There will be 760 greetings exchanged between the guest mothers and everyone, or 19 x 40.

The number of pleasantries exchanged between the mothers and the invited girls must also be tallied. Moreover, there are 20 guest girls, so 19 of them must welcome the mothers. As a result, there will be 361 pleasantries exchanged between the mothers and the guest daughters.

In total, the number of greetings will be 38 + 760 + 361 = 1159.

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Answer:

volume=60cm3, surface area=96cm2

Step-by-step explanation:

volume=1/3×(6×6)×5

=60cm3

surface area= 4(1/2×6×5)+(6×6)

=96cm2