a square has an area of 144 m². whats the length of each side?​

Answer:

If we have two figures, F and F'

Such that if we start with F, and dilate it with a scale factor K, we get F'.

We will have:

All the measures of F', are K times the correspondent measures of F.

Then if F has  s₁, s₂, ..., sₙ sides, the sides of F' will be:

K*s₁, K*s₂, ..., K*sₙ

The ratio between correspondent sides will be equal to K

The ratio between perimeters will also be equal to K (because the perimeter is the sum of all the sides of each figure, so we can just take K as a common factor)

In the case of the area, because we usually multiply a measure by another, a factor K^2 will  appear, and the quotient between the areas is K^2

And finally, for the volumes, the ratio will be K^3

a) The ratio of corresponding lengths is K, in this case is 5/2

b) The ratio of the perimeters is K, in this case is 5/2

c) The ratio of the areas is K^2, in this case is (5/2)^2 = 25/4

d) The ratio of the areas is K^3, in this case is (5/2)^3 = 125/8

e) Two figures are similar if the figures have the same shape, then the corresponding angles are exactly the same, then the ratio of corresponding angle measures is 1.

The evidence against the null hypothesis is not strong, given the observed test statistic and the sample size.

To determine how much evidence we have against the null hypothesis H0, we need to calculate the p-value. Given H0: μ = 0.68 and Ha: μ ≠ 0.68, we can perform a two-tailed t-test using the given test statistic t = 1.75. We also need to know the sample size n and the significance level α.Let's assume that α = 0.05 (which is a commonly used level of significance), and the sample size n = 10. Using these values, we can calculate the degrees of freedom (df) as follows:df = n - 1 = 10 - 1 = 9Using a t-distribution table or a calculator, we can find the p-value associated with t = 1.75 and df = 9. The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming that the null hypothesis is true. For a two-tailed test, we need to find the area in both tails beyond t = 1.75.Using a t-distribution table with df = 9, we can find that the t-value that corresponds to an area of 0.025 in the upper tail is 2.262. Similarly, the t-value that corresponds to an area of 0.025 in the lower tail is -2.262. Therefore, the p-value for the observed test statistic t = 1.75 is:p-value = P(T > 1.75 or T < -1.75)≈ 0.110Since the p-value is greater than α, we fail to reject the null hypothesis H0. That is, we don't have sufficient evidence to conclude that the population mean μ is different from 0.68.

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Answer: y = -3/5x - 6

Step-by-step explanation:

There are a few equations that can be used for this, but the simplest one would be y = mx + b

We are given:

y = -3

m = -3/5 (slope)

x = -5

b = ?

Our equation is this, we are solving for b

==> -3 = -3/5 ( -5) + b

==> -3 = -3/5 ( -5) + b ( multiply the brackets)

==> -3 = 3 + b ( subtract 3 to both sides)

==> -6 = b

Now we can make the desired equation in slope intercept form;

y = -3/5x - 6

Hope this helped! Have a great day :D

Answer:

4

Step-by-step explanation:

Calculation of the discriminant of the polynomial : x⋅2−4⋅x+5

1. Applying the formula to calculate the discriminant Δ=b2−4⋅a⋅c with : a=0, b=−2,c=5

2. Δ=(−2)2−4⋅(0)⋅(5)=4=4

3. The discriminant of the polynomial x⋅2−4⋅x+5 is equal to 4

Answer:

Your answer is Vertical.

Step-by-step explanation:

Error control, flow control, segmentation and reassembly, multiplexing, and connection setup are five tasks that a layer can perform.

Flow control: It is the efficient management of data flow between two or more devices like computers or nodes of a network.

Error control: The identification and correction of errors that occur during the transmission of data is called error control.

Segmentation and reassembly: Data to be transmitted is divided into small parts or chunks for convenience. This process is called segmentation. The combining of these chunks to reform the original data is called reassembling.

Multiplexing: The process of combination of digital data streams in one signal over a shared medium is known as multiplexing.

Connection setup: Establishing a connection between two devices that are connected to the same network is called connection setup.

All these tasks can be duplicated at different layers.

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On solving the provided question, we can say that by unitary method 14 more hours must she work to earn an additional 154 dollars

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

jessie worked = 22 hours last week at the auto shop

shop and earned = 242 dollars

1 hour = 242/22

154 dollars = 22/242*154 = 0.0909090909 * 154 = 13.9999999986 = 14 hours

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Answer:

200° = 10π/9 radians

Step-by-step explanation:

There are π/180 radians in 1 degree. Therefore, 200° in radians would be 200(π/180)=200π/180=10π/9 radians

Answer: Using trigonometry, we can find the length of side AC. Since we know the length of side BC and one angle, we can use the tangent function:

tan(70) = AC/6

Multiplying both sides by 6, we get:

AC = 6 * tan(70)

Using a calculator, we get:

AC ≈ 19.22

Rounding to the nearest hundredth, we get:

AC ≈ 19.22 units.

Answer:2.33

Step-by-step explanation:

Answer:

($) 60 is the profit per item when the selling price is reduced by 20%

Step-by-step explanation: 20% of 700 is 140.

The original profit is 700 - 500 = 200. The selling price is 140 less, Subtract 140 from 200. That leaves a profit of 60. (Not necessarily dollars, as the currency was not given in the question.)

Answer: B. 9

Step-by-step explanation:

First, find the median of the data set. This set has an even number of points, so find the average between the two middle points: 18 and 19. 18+19 = 37. 37/2 = 18.5. The median is 18.5.

Now, to find the lower quartile, find the median of the lower half of the data set {11, 12, 14, 15, 18}. The number in the middle is 14. The lower quartile is 14.

To find the upper quartile, find the median of the upper half of the data set {19, 21, 23, 25, 55}. The number in the middle is 23. The upper quartile is 23.

To find the interquartile range, subtract the lower quartile from the upper quartile. 23-14 = 9. The interquartile range is 9.

Answer:

8*5 = 40   8+32 = 40   21/3 = 7   21-14 = 7   21/3 = 7

Step-by-step explanation:

40/8 = 5

8 + x = 40    40-8 = x = 32

21x = 7  x = 7/21 = 1/3

21 - x = 7   21 - 7 = x = 14

21x = 7  x = 7/21 = 1/3

Answer:

blank one is 5

blank two is 32

blank three is 3

blank four is 14

blank five is 3

The temperature gradient shows the direction and rate of temperature change

The correct option that gives the temperature gradient between the two thermometers is option;

(3) 3 °C/m

Reason:

Known parameters are;

Temperature which the thermometer held at Δd = 2 meters above the floor shows, T₁ = 30°C

Temperature the thermometer on the floor shows, T₂ = 24°C

Required:

The temperature gradient between the two thermometers

Solution:

ΔT = T₁ - T₂

\(Temperature \ gradient = \dfrac{\Delta T}{\Delta d}\)

Therefore;

\(Temperature \ gradient \ between \ the \ thermometers= \dfrac{30 ^{\circ}C - 24 ^{\circ}C}{2 \, m} = 3 \, ^{\circ}C /m\)

The temperature gradient between the two thermometers = 3°C/m

Therefore, the correct option is option (3) 3°C/m

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A continuous function that has a domain of [-3, 4]  will include all the values as -3,-2,-1,-0,-1,-2,3,4

What do you mean by continuous function?

In mathematics, a continuous function is one where a continuous variation of the argument results in a continuous variation of the function's value (i.e., a change without a leap). This indicates that there aren't any discontinuities, or sudden changes in value. More specifically, a function is continuous if it is possible to guarantee that its value will not vary significantly even with arbitrarily tiny changes to its parameter. Any function that is not continuous is said to be discontinuous.

It is given that a continuous function has a domain of [-3,4]

According to the definition of closed interval,

[-3,4] will contain all the elements between them and including them.

Therefore, [-3,4] will contain elements as -3,-2,-1,-0,-1,-2,3,4

Hence, a continuous function that has a domain of [-3, 4]  will include all the values as -3,-2,-1,-0,-1,-2,3,4

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Hello,

I hope you and your family are doing well!

To solve the equation 2x + 3 for x = 3, we can substitute 3 for x in the equation:

2x + 3 = 2(3) + 3 = 6 + 3 = 9

So the solution to the equation 2x + 3 for x = 3 is 9.

Please rate this answer 5 stars and brainliest if you find it helpful since it does encourage me to continue helping others.

Happy Holidays!

Answer:

Disagree

Step-by-step explanation:

An octagon has eight sides while the shape on the right has nine sides.

Answer:

No

Step-by-step explanation:

The shape shown in the picture has 9 sides(you can count) and therefore is not an octagon because octagons only have 8 sides.

The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

The equation for the translation of the function y = sin(x) three units up is y = sin(x) + 3.

When we translate a function, we are shifting it in a specific direction. In this case, we want to shift the function y = sin(x) three units up. To achieve this, we need to add a constant value of 3 to the original function.

The original function, y = sin(x), represents the sine of x for various angles. The sine function oscillates between -1 and 1 as x varies. By adding 3 to the function, we are effectively moving the entire graph vertically upwards by three units.

The addition of a constant value to the function affects the y-coordinate of each point on the graph. For example, if the original function had a point (0, 0), after the translation, it would become (0, 3). Similarly, a point like (π/2, 1) would be shifted to (π/2, 4).

By using the equation y = sin(x) + 3, we are indicating that the output of the sine function (y) is being modified by adding 3. This new equation represents the translation of the original function three units up.

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Answer:

28 cm, 32cm , 36cm

Step-by-step explanation:

Given:

To Find:

Solution:

Let:

As, we know that,

★ Perimeter of Triangle = Sum of all sides ★

➝ 7x + 8x + 9x = 96cm

➝ 24x = 96cm

➮ x = 96/24

➮ x = 4

So, length of the sides are:

7x = 7 × 4 ➝ 28cm

8x = 8 × 4 ➝ 32cm

9x = 9 × 4 ➝ 36cm

Given :

To Find :

Solution :

Let us assume the sides be 7x cm, 8x cm and 9x cm.

We know,

\(\qquad{ \bold{ \pmb{Sum \: of \: all \: sides \: of \: the \: triangle = Perimeter_{(Triangle)}}}}

\)

So, Substituting the values :

\(\qquad { \dashrightarrow{ \sf{7x + 8x + 9x = 96}}}\)

\(\qquad { \dashrightarrow{ \sf{24x= 96}}}\)

\(\qquad { \dashrightarrow{ \sf{ \dfrac{24x}{24} = \dfrac{96}{24} }}}\)

\(\qquad { \dashrightarrow{ \bf{ x = 4 }}}\)

Therefore,

The length of the sides of the triangle are :

\(\qquad { \dashrightarrow{ \sf{ 7x \: cm= 7 \times 4 \: cm = \bf \: 28 \: cm }}}\)

\(\qquad { \dashrightarrow{ \sf{ 8x \: cm= 8 \times 4 \: cm = \bf \: 32 \: cm }}}\)

\(\qquad { \dashrightarrow{ \sf{ 9x \: cm= 9 \times 4 \: cm = \bf \: 36 \: cm }}}\)

The largest possible value for the decimal $a. B + c. D$  us:

9.7 + 8.6 which results to 18.3.

Given that a, b, c, and d are different numbers (from 1 to 9), we are to find the largest possible value of a.b + c.d.

This problem can be answered by trial and error and with some logic. Clearly, a to d cannot be at the lower end of the values (1 to 5). Since the digits must be different, it can be a combination of digits from 6 to 9.

It is rather tempting to say that the 9.8 + 7.6 would yield the highest possible sum (=17.4) but this is incorrect. Since it is the sum of two numbers with a decimal, we have to maximize on the ones digit first before maximizing the tenths digit. Therefore: the combination of numbers must then be:

9.7 + 8.6 which results to 18.3

9.6 + 8.7 yields 18.3 as well.

Hence we get the required answer,

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The least number of integer comparisons required to find the maximum of a sequence of n integers is n-1, while the least number of item comparisons is 1. The linear search requires n comparisons for the first element, while the binary search requires n comparisons for the middle element. The search continues until the item is found or the search space is empty.

(a) The least number of integer comparisons required to find the maximum of a sequence of n integers, using the algorithm that starts by assuming that the maximum is the first list element and then runs through the list, updating the maximum each time it encounters a bigger element is n - 1. This is the best-case performance because if the list is already sorted in descending order, only one comparison would be required to find the maximum value, which is the first element. However, in the worst-case scenario, the maximum value could be at the end of the list, and in this case, n - 1 comparisons would be required.

(b) The least number of item comparisons or best-case performance used to locate an item in a list of n items with a linear search is 1. This is because if the item being searched for is the first element of the list, only one comparison would be required to find it. However, in the worst-case scenario, the item being searched for could be the last element in the list, and n comparisons would be required.

(c) The least number of item comparisons or best-case performance used to locate an item in a list of n items using a binary search, assuming that n is a power of 2, is 1. This is because the binary search algorithm always starts by checking the middle element of the list. If the item being searched for is the middle element of the list, only one comparison would be required to find it. However, in the worst-case scenario, the item being searched for could be the last element in the list, and log₂ n comparisons would be required. This is because each comparison reduces the size of the search space by half, and the search continues until the item is found or the search space is empty.

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The graph of an exponential function with an initial value of 10 and a base of 1.3z. Therefore option D is correct.

The function f(x) is an exponential function with a base of 1.3 and an initial value of 10. The graph of an exponential function with a base greater than 1 increases rapidly as x increases. Therefore, option a can be eliminated.

Option b is not a graph of an exponential function, as the function is not continuous and does not approach any asymptote.

Option c shows an exponential function with an initial value of 10 and a base of 1.3/10, which is less than 1. This means that the function would decrease over time, which is not consistent with the problem statement.

Option d shows an exponential function with an initial value of 10 and a base of 1.3, which is consistent with the problem statement. Therefore, option d is the correct answer.

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Answer:

If each student sold 6 candy bars and each candy bar is 3 bucks, then 3*6 is 18, so that means each student sold 18 dollars worth of candy bars,

Step-by-step explanation:

24* 18 = 432

432 * 0.25 = 108

They get to keep 108 dollars.

The 15th term of the geometric progression is 9,565,94.

A geometric progression can be expressed as an = a1rn-1 for some a1 and r. You are told that a2 * a4 = 2a5 and a1 + a2 + a3 + a4 = 80.

From the first equation, a2 = a1 r, a4 = a1 r3, and a5 = a1 r4. This tells us that

a1 r a1 r3 = 2 a1 r4

The r's and one a1 cancel leaving a1 = 2.

Now, plugging similarly into a1 + a2 + a3 + a4 = 80,

2 + 2r + 2r2 + 2r3 = 80

r3 + r2 + r + 1 = 40

In general, the easiest way to solve a cubic is by graphing, but here you know the answer will be a small integer, so just try a few. If we try r=3, we get 27 + 9 + 3 + 1 = 40 so r = 3.

So the geometric sequence here is an = 2 3n-1. The 15th term is then:

a15 = 2*3^14

a15 = 9,565,938.

Full question:

A G.P, the product of the 2nd and the 4th term is double the 5th term, and the sum of the first 4th terms is 80. find the 15th term.

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Answer:

it's the third one

Answer:

x = 0, 2

Step-by-step explanation:

The length of the rectangle is 6 meters longer than the width of the rectangle. Let's suppose the width is x meters. So, the length of the rectangle is (x + 6) meters.Area of rectangle is 28 square meters.Area of rectangle = length × width28 = (x + 6) × x.Solve for xx² + 6x - 28 = 0(x + 7)(x - 4) = 0x = -7 or 4

The negative value of x because it is not possible.So, the width of the rectangle is 4 meters.The length of the rectangle is (x + 6) meters= 4 + 6= 10 meters.The length of a rectangle is 6 meters longer than the width. If the area is 28 square meters, we need to find the dimensions of the rectangle. Let's suppose the width of the rectangle is x meters. We know that the length of the rectangle is 6 meters more than the width, so the length of the rectangle is (x + 6) meters.Area of a rectangle is the product of its length and width. So, the area of the rectangle is (x + 6) × x. We know that the area of the rectangle is 28 square meters. Therefore, we can write the following equation:28 = (x + 6) × x.To find the value of x, we need to solve this quadratic equation.28 = x² + 6x.Rearranging the terms, we get:

x² + 6x - 28 = 0

We can solve this equation by using the quadratic formula, but we will use the factoring method. We need to find two numbers whose product is -28 and whose sum is 6. These numbers are +7 and -4. Therefore, we can write:

x² + 7x - 4x - 28 = 0x(x + 7) - 4(x + 7) = 0(x + 7)(x - 4) = 0

Therefore, x + 7 = 0 or x - 4 = 0.If x + 7 = 0, then x = -7, which is not a valid solution because the width of the rectangle cannot be negative.If x - 4 = 0, then x = 4. Therefore, the width of the rectangle is 4 meters. The length of the rectangle is x + 6 = 4 + 6 = 10 meters. So, the dimensions of the rectangle are 4 meters by 10 meters.

Therefore, the width of the rectangle is 4 meters, and the length of the rectangle is 10 meters. The dimensions of the rectangle are 4 meters by 10 meters.

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