Find the square root of 9 by long division method​

The coordinates of the vertices of trapezoid J'K'L'M' with its graph include the following:

J' (-3, 0).

K' (-3, -3).

L' (-8, 6).

M' (-8, 1).

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).

By applying a rotation of 90° clockwise to the vertices of trapezoid JKLM, the coordinates of the vertices of the image are as follows:

(x, y)               →                ((y - b) + a, -(x - a) + b)

J (2, 1)           →     ((1 - 3) - 1, -(2 + 1) + 3) = (-2 - 1, -3 + 3) = J' (-3, 0).

K (5, 1)           →     ((1 - 3) - 1, -(5 + 1) + 3) = (-2 - 1, -6 + 3) = K' (-3, -3).

L (8, -4)           →     ((-4 - 3) - 1, -(8 + 1) + 3) = (-7 - 1, -9 + 3) = L' (-8, 6).

M (1, -4)           →     ((-4 - 3) - 1, -(1 + 1) + 3) = (-7 - 1, -2 + 3) = M' (-8, 1).

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There are 5 chances out of 21 of picking an A, E, I, O, or U.

There are 5 vowels in the English alphabet (A, E, I, O, U) out of a total of 26 letters. So, the probability of picking a vowel is 5/26.

To find the odds in favor of picking a vowel, we divide the probability of picking a vowel by the probability of not picking a vowel:

odds in favor = probability of picking a vowel / probability of not picking a vowel

The probability of not picking a vowel is 1 - 5/26 = 21/26.

So, the odds in favor of picking an A, E, I, O, or U are:

5/26 / 21/26 = 5/21

This means that there are 5 chances out of 21 of picking an A, E, I, O, or U.

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The Modulus = 1 / √37, Argument ≈ -0.9828 radians

To find the modulus and argument of the expression (1+i)^2 / (1-√3i)^4, let's first simplify the expression.

(1+i)^2 can be expanded as follows:

[tex](1+i)^2 = (1+i)(1+i) = 1 + 2i + i^2 = 1 + 2i - 1 = 2i[/tex]

Similarly, (1-√3i)^4 can be expanded as:

(1-√3i)^4 = (1-√3i)(1-√3i)(1-√3i)(1-√3i)

Expanding this further requires using the properties of complex numbers, namely (a+b)(c+d) = ac + ad + bc + bd and i^2 = -1.

Simplifying the expression, we get:

(1-√3i)^4 = ([tex]1^4 - 4(1^3)(\sqrt{3i} ) + 6(1^2)(\sqrt{3i} )^2 - 4(1)(\sqrt{3i} )^3 + (\sqrt{3i} )^4)[/tex]

= (1 - 4√3i - 6(-3) + 4(√3i)(-√3) + (-3)^2)

= (1 - 4√3i + 18 + 4(-3) - 9)

= (10 - 4√3i)

Now, we can calculate the modulus and argument of the expression:

Modulus: The modulus of a complex number is calculated by taking the square root of the sum of the squares of its real and imaginary parts.

The modulus of (1+i)^2 / (1-√3i)^4 is the modulus of (2i) / (10 - 4√3i), which can be simplified as:

Modulus = √(([tex]2^2 + 0^2[/tex]) / (10^2 + (-4√3)^2))

= √(4 / (100 + 48))

= √(4 / 148)

= √(1 / 37)

= 1 / √37

Argument: The argument of a complex number is the angle it makes with the positive real axis in the complex plane.

The argument of (1+i)^2 / (1-√3i)^4 can be calculated as the argument of (2i) / (10 - 4√3i), which is the argument of 2i minus the argument of (10 - 4√3i).

The argument of 2i is π/2 (or 90 degrees), as it lies on the positive imaginary axis.

The argument of (10 - 4√3i) can be calculated using the inverse tangent function:

Argument = atan((-4√3) / 10)

= atan(-2√3 / 5)

≈ -0.9828 radians (or approximately -56.31 degrees)

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Answer: 4191

Step-by-step explanation: i took the quiz

The estimated average number of miles traveled per person in 1961 is approximately 4567 miles.

The given table is

Year    1915   1925   1935   1945   1955   1965   1975   1985   1995   2005

Average

miles  194     1056   1796   1788   3650   4569   6147   7460   9099  10,181

traveled

The equation for the linear regression is:

y = -211.902x² + 779.914x - 8742.14

To estimate the average number of miles traveled per person in 1961, we use the equation with the input value of 61 (1961 since 1900):

y = -211.902(61)² + 779.914(61) - 8742.14

y ≈ 4567 miles

Therefore, the estimated average number of miles traveled per person in 1961 is approximately 4567 miles.

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The equation of the line passing through the points (-2, -3) and (2, 5) is y = 2x + 1.

To find the equation of a line passing through the points (-2, -3) and (2, 5), we can use the point-slope form of a linear equation, which is:

y - y1 = m(x - x1)

where (x1, y1) represents one of the points on the line, and m represents the slope of the line.

First, let's calculate the slope (m) using the given points:

m = (y2 - y1) / (x2 - x1)

  = (5 - (-3)) / (2 - (-2))

  = 8 / 4

  = 2

Now, we have the slope (m) as 2. Let's choose one of the points, (-2, -3), and substitute its coordinates into the point-slope form equation:

y - (-3) = 2(x - (-2))

y + 3 = 2(x + 2)

Simplifying further:

y + 3 = 2x + 4

y = 2x + 4 - 3

y = 2x + 1

Therefore, the equation of the line passing through the points (-2, -3) and (2, 5) is y = 2x + 1.

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The volume of the larger cylinder is 150π.

Let's assume the ratio of the radii of the two cylinders is 3x and 5x.

We know that the volume of a cylinder is given by the formula:

V=πr²h, where r is radius and h is height.

Given that the volume of the smaller cylinder is 54π cubic centimeters  we can write the equation:

54π =π(3x)²h₁

54π =π9x²h₁

h₁=6/x²

ow, we need to find the volume of the larger cylinder. Let's denote it as V₂:

V₂=π(5x)²h₂

V₂=150π

Therefore, the volume of the larger cylinder is 150π.

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The width, in feet, of the border is,

⇒ x = 1.5 feet

We have to given that,

An artist paints a mural that measures 25 feet by 18 feet. The artist adds a border around the mural that increases the total area to 588 square feet.

Here, The area of the mural and border is modeled by the given equation,

⇒ (25 + 2x) (18 + 2x) = 588

where x represents the width of the border.

Now, WE can simplify as,

⇒ (25 + 2x) (18 + 2x) = 588

⇒ 450 + 50x + 36x + 4x² = 588

⇒ 4x² + 86x + 450 - 588 = 0

⇒ 4x² + 86x - 138 = 0

⇒ 2x² + 43x - 69 = 0

⇒ x = (- 43 ± √43² - 4×2×- 69) / 2×2

⇒ x = (- 43 ± √1849 + 552) / 4

⇒ x = (- 43 ± 49) / 4

This gives two solution,

⇒x = (- 43 + 49) / 4

⇒ x = 6/4

⇒ x = 3/2

⇒ x = ( -43 - 49) / 4

⇒ x = - 92 / 4

⇒ x = - 23

Since, Width is never negative.

Hence, the width, in feet, of the border is,

⇒ x = 1.5 width

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Answer:

-18.75

Step-by-step explanation:

Since the x is being multiplied by 4/5, we have to divide by 4/5 on both sides.

How to divide by 4/5? Take the reciprocal. The reciprocal to 4/5 is 5/4 (flip it).

Multiply both sides by 5/4.

5/4(4/5x)=5/4(-15)

x=-18.75

Answer:

[tex]x = -\frac{75}{4}[/tex]

Step-by-step explanation:

Question:

[tex]\frac{4}{5}x = -15[/tex]

Now, we multiply both sides by 5:

[tex]\frac{4}{5} x*5 = -15*5[/tex]

Simplify:

[tex]4x = -75[/tex]

Divide both sides by 4:

[tex]x = -\frac{75}{4}[/tex]

If cost price is Rs. 120, profit is Rs. 25 then the selling price is Rs.145.

We have to find the selling price

The formula for find the selling price is given below:

Selling Price = Cost Price + Profit

Given that the Cost Price (C.P.) is Rs 120 and the profit is Rs 25.

we can substitute these values into the formula:

Selling Price = 120 + 25

When one hundred twenty is added with twenty five we get One hundred twenty five.

Selling Price = 145

Therefore, the selling price is Rs 145.

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C.P. = Rs 120, profit = Rs 25​ then find the selling price?

The smallest possible number of candies Dzani bought is 11

From the question, we have the following parameters that can be used in our computation:

Represent the number of jars with x

So, we have

4x + 3 = 5x + 1

Collect the like terms

So, we have

5x - 4x = 3 - 1

Evaluate

x = 2

So, we have

Candles = 4 * 2 + 3

or

Candles = 5 * 2 + 1

Evaluate

Candles = 11

Hence, the smallest possible number of candies Dzani bought is 11

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The number of square feet tile he needs to purchase is 45.9 feet squared.

Kyle is going to retile the bottom of his pool. He first needs to drain the pool.  

The pool hold 321 cubic feet of water and has a height of 7 feet. Therefore, the number of square feet tile he needs to purchase can be calculated as follows:

Therefore,

volume of the pool = base area × height

321 = 7b

divide both sides of the equation by 7

b = 321 / 7

b = 45.85

b =   45.9 feet squared

Therefore,

amount of square feet tiles to purchase = 45.9 feet squared

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Building an emergency fund may take time, but it can provide peace of mind and financial security in the event of an unexpected emergency.

The amount you should have in your emergency fund depends on your personal circumstances. Experts typically recommend having three to six months' worth of living expenses saved in an emergency fund.

However, if you have a high-risk job or irregular income, you may want to consider saving up to nine months' worth of expenses.

Additionally, if you have a lot of debt or dependents, you may want to have a larger emergency fund to ensure you can cover unexpected expenses or job loss.

It's important to regularly reassess your emergency fund and adjust it as needed based on changes in your financial situation

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From the data given, we do not have enough evidence to conclude that the hypothesized average production cost of P24.6 million is false.

To test the hypothesis that the average production cost in making a movie is P24.6 million, we can perform a hypothesis test using the sample data.

Let's define the null hypothesis (H₀) and the alternative hypothesis (H₁) as follows:

H₀: The average production cost is P24.6 million.

H₁: The average production cost is not P24.6 million.

We will use a t-test since we have a sample size smaller than 30 and the population standard deviation is unknown.

Given the sample information, the sample mean (x) is P28.3 million, the sample size (n) is 15, the hypothesized population mean (μ) is P24.6 million, and the sample standard deviation (s) is P9.5 million.

We can calculate the t-statistic using the formula:

t = (x - μ) / (s / √n)

Substituting the values:

t = (28.3 - 24.6) / (9.5 / √15)

t = 3.7 / (9.5 / √15)

t = 1.51

To determine whether the hypothesis is true at a 0.01 level of significance, we need to compare the calculated t-value to the critical t-value from the t-distribution table for a two-tailed test with 14 degrees of freedom (n - 1 = 15 - 1 = 14) and a significance level of 0.01.

The critical t-value for a two-tailed test with 14 degrees of freedom and a significance level of 0.01 is approximately ±2.977.

If the calculated t-value falls within the range of ±2.977, we fail to reject the null hypothesis; otherwise, we reject the null hypothesis.

Since the calculated t-value of 1.51 does not exceed the critical t-value of ±2.977 for a two-tailed test at a 0.01 level of significance, we fail to reject the null hypothesis.

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The probability of picking a white marble is 3/10

From the question, we have the following parameters that can be used in our computation:

four green marbles, six white marbles, and ten red marbles

This means that

Total = 4 + 6 + 10

Evaluate the sum

Total = 20

The probability of picking a white marble is

P = White/Total

substitute the known values in the above equation, so, we have the following representation

P = 6/20

Evaluate

P = 3/10

Hence, the probability of picking a white marble is 3/10

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Answer:

13.27 cm

Step-by-step explanation:

I am using (xy) to mean the length of the side xy

7^2 + (xy)^2 = 15^2

49 + (xy)^2 = 225

(xy)^2 = 225-49

(xy)^2 = 176

Side (xy) = sqrt(176) = 13.2664991614 = 13.27 cm

Answer: 523.8 cubic inches

Step-by-step explanation:

Volume of the sphere, V = (4/3) * π * r^3

where r is the radius of the sphere.

Given, the diameter of the sphere (d) = 10 inches

Therefore, the radius of the sphere, r = d/2 =10/2 = 5 inches

Now, substituting the value of the radius to the volume formula,

V = (4/3) * π * (5^3)

= (4/3) * (22/7) * 125

≈ 523.8 cubic inches

1. Triangle inequality theorem.

3. The missing lengths and angles are:

<B = 27.07, <C = 98 and c = 32.64.

1. According to triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

2. To determine the number of triangles that can be formed, we can use the given measurements and check if the triangle inequality theorem is satisfied.

3. We have,

a = 27, b = 15, and A = 55°,

Using the Law of Sines,

sin A/ a = sin B/ b

sin 55 /27 = sin B / 15

0.81915204428 / 27 = sin B /15

0.4550844690444 = sin B

<B = 27.07

Now, <C = 180 - <A - <B = 180 - 55 - 27.07 = 98

Now, Using the Law of Sines

sin A/ a = sin C/ C

0.81915204428 / 27 = sin 98 / c

0.030338964602963 = 0.99026807 /c

c = 32.64

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The correct answer is:

A. Real, irrational

Given is a number √7, we need to identify the category of the number.

The number √7 is a real number because it exists on the number line.

We see that the imaginary numbers are those which can not be drawn on number line.

It is also an irrational number because it cannot be expressed as a ratio of two integers.

The number √7 cannot be written as a fraction or a terminating or repeating decimal.

It is a non-repeating, non-terminating decimal that goes on forever without a pattern.

Hence, it is considered irrational.

Therefore, the correct answer is:

A. Real, irrational

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There is no quantity that can be added to 1⅔ gross to make 15 cm scores, as it would result in a negative value.

To solve the problem, we need to determine the quantity that needs to be added to 1⅔ gross to make a total of 15 cm scores.

First, let's convert 1⅔ gross to a more manageable unit. One gross is equal to 144 units, so 1⅔ gross can be expressed as:

1⅔ gross = 1 gross + ⅔ gross = 144 + (2/3) * 144 = 144 + 96 = 240 units.

Now, let's denote the quantity that needs to be added as "x" units.

Therefore, we can set up an equation to represent the given situation:

240 + x = 15.

To solve for x, we subtract 240 from both sides of the equation:

x = 15 - 240 = -225.

The result, x = -225, indicates that we need to add -225 units to 1⅔ gross to make a total of 15 cm scores. However, since quantities cannot be negative in this context, it means that it is not possible to add a negative value to the given quantity.

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The quadratic function for the path of the basketball as it is thrown indicates;

The path of the basketball will not make the shot

The height reached is about 5.24 meters

A quadratic function is a function of the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, c, are numbers.

The function for the path of the basketball is; b(x) = (-1/7)·x² + 1.36·x + 2

The function for the location of the basketball net is; n(x) = 3 and (8 < x < 8.5), where;

n(x) = The vertical height of the basketball

Plugging in the value of the n(x) = b(x), to check if equations have a common solution, we get;

b(x) = n(x) = 3 = (-1/7)·x² + 1.36·x + 2

(-1/7)·x² + 1.36·x + 2 - 3 = 0

(-1/7)·x² + 1.36·x - 1 = 0

(1/7)·x² - 1.36·x + 1 = 0

Solving the above equation, we get;

x = (119 - √(9786))/(25) ≈ 0.803, and x = (119 + √(9786))/(25) ≈ 8.717

Therefore, the x-coordinates of the height of the path of the basketball when the height is 3 meters are 0.803 and 8.717, neither of which are within the range (8 < x < 8.5), therefore, the baseketball will not go through the net and the path will not make the shot.

Bonus; The x-coordinates of the highest point of a quadratic function, f(x) = a·x² + b·x + c is; -b/(2·a)

Therefore, the x-value at the highest point of the equation, b(x) = (-1/7)·x² + 1.36·x + 2 is; x = -1.36/(2 × (-1/7)) = 1.36 × 7/2 = 9.52/2 = 4.76

The height of the highest point is; b(9.52) = (-1/7)·(4.76)² + 1.36·(4.76) + 2 ≈ 5.24 meters

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To find the area of the front of the podium add the area of two triangle and one rectangle.

To find the area of the front of the podium by decomposing it into two triangles and a rectangle, you can follow these steps:

Measure the dimensions: Measure the necessary dimensions of the triangles and rectangle. Typically, you would need to measure the base and height of each triangle and the length and width of the rectangle.

Calculate the area of each shape: Use the appropriate formulas to calculate the area of each shape.

The formula for the area of a triangle is (1/2) x base x height,

and for a rectangle, it is length x width.

Sum up the areas: Add up the areas of the two triangles and the rectangle to find the total area of the front of the podium.

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The solutions are x = 29° and y = 27°.

In the given quadrilateral, the angles are mentioned.

So,

Q = 79°

R = 109°

S = (6y - 61)°

T = (4x - 45)°

A quadrilateral is a polygon with four vertices, four sides, and four angles with a total angle of 360 degrees.

The quadrilateral makes two triangles when its diagonals are drawn. These two triangles have an angle total of 180 degrees. The quadrilateral's total angle sum is hence 360°.

So,

T + R = 180°

(4x - 45) + 109 = 180

4x + 64 = 180

4x = 180 - 64

4x = 116

Therefore, x = 116/4

x = 29°

S + Q = 180°

(6y - 61) + 79 = 180

6y + 18 = 180

6y = 180 - 18

6y = 162

Therefore,

y = 162/6

y = 27°

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The solution for y is y = log(N - (4^y))/log(8y).

The given expression is (8y + 4) ° y = N. To solve for y, we can simplify the expression first. We will use the exponent rules to solve this. According to the exponent rules, if we have a power raised to another power, we can multiply the exponents.

Therefore, we can write (8y + 4) ° y as (8y + 4)^(y).Now we can distribute the exponent to both terms inside the parentheses, giving us (8^y)(y^y) + (4^y) = N. We can simplify this expression further by multiplying the coefficients, which gives us (8^y)(y^y) + (4^y) = N.

We can then solve for y by rearranging the terms. We can subtract (4^y) from both sides, giving us (8^y)(y^y) = N - (4^y).

We can then take the logarithm of both sides, giving us y log(8y) = log(N - (4^y)).

Finally, we can solve for y by dividing both sides by log(8y), giving us y = log(N - (4^y))/log(8y).

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Then , if KL is 45 units long, then KM will be the angle bisector of LKN.

To find the value of X that makes KM the angle bisector of LKN, we need to use the angle bisector theorem. According to the theorem, if a line bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides of the triangle.

Let's apply this theorem to triangle LKN. Suppose that KM bisects angle LKN, and let X be the length of KL. Then, according to the angle bisector theorem:

LK / KN = KL / KN
LK = KL * (KN / KN)
LK = KL

This tells us that LK and KL have the same length, which means that triangle LKN is isosceles. Therefore, we can write:

LK = KN

Now, we can use the fact that the sum of the angles of a triangle is 180 degrees to find the measure of angle LKN. We know that angle LKN is bisected by KM, so we can write:

angle LKM = angle MKN

Let's call this angle x. Then, we have:

angle LKN = 2x

And since triangle LKN is isosceles, we also have:

angle LNK = angle KLN = (180 - angle LKN) / 2
angle LNK = (180 - 2x) / 2
angle LNK = 90 - x

Now, we can use the fact that the sum of the angles of a triangle is 180 degrees to write:

angle LKM + angle LKN + angle LNK = 180

Substituting the values we found earlier, we get:

x + 2x + (90 - x) = 180

Simplifying, we get:

x = 45
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Answer:

The answer is 32°

Step-by-step explanation:

TC is perpendicular to CD.

90 + 3x + 8 + 7x + 2 = 180

x = 8

/_TDC = 3x + 8 = 32

To assure the random selection of a sample population for determining the percentage of students who bring their lunch to school, a method known as simple random sampling can be employed.

Simple random sampling is a technique that provides each member of the population an equal chance of being selected for the sample. Here's an explanation of how simple random sampling can be implemented in this scenario:

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The 5 × 10⁻³ cm radius of one spherical cancerous cell indicates that the number of cells in the initial volume of 0.3 cm³ of the tumor is; 572,958 cells

The volume, V, of a sphere is the product of the cube of the radius of the sphere, pi, and (4/3); V =  (4/3) × Pi × (The radius of the sphere, r)³

The volume of each cancerous cell can be calculated as follows;

The shape of each cancerous cell = A sphere

Volume of a sphere = (4/3) × π × r³

Where;

r = The radius of the sphere

The radius of the cancerous sphere, r = 5 × 10⁻³ cm

The volume of each cancerous cell = (4/3) × π × (5 × 10⁻³)³

The number of cancerous cells = The initial volume of the tumor ÷ The volume of one cancerous cell

The number of cancerous cells = 0.3/((4/3) × π × (5 × 10⁻³)³) ≈ 572958

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Answer:

Hi

Please mark brainliest ❣️

Thanks

Step-by-step explanation:

The answer is NO

Reason

x= 2 y= 1

Now input in the first inequality

y≤ -x + 4

1 ≤ -2 +4

1≤ 2 i.e 1 is less than two

Next inequality

y≤ x +1

1 ≤ 2 + 1

1≤ 3 i.e 1 is less than 3

But 1 is not equal to 3 and also not equal to 2

Hence our answer is NO

Answer:

Hi

Please mark brainliest ❣️

Thanks

Step-by-step explanation:

True

Reason

Use the last person time to minus the first person time which is

53.3 - 51.3