Write the following number in words: 3 811 459​

The value of x in the diagram is 12.5

Two figures are considered to be "similar figures" if they have the same shape, congruent corresponding angles (meaning the angles in the same places of each shape are the same) and equal scale factors. Equal scale factors mean that the lengths of their corresponding sides have a matching ratio.

The ratio of the corresponding sides of similar shapes are equal.

Therefore;

3x/60 = 5x/8x

3x/60 = 5/8

300 = 24x

divide both sides by 24

x = 300/24

x = 12.5

therefore the value of x is 12.5

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The equivalent expression of [tex]\sqrt{36x^6z^2[/tex] is option (B) [tex]6x^3z[/tex] . The expression [tex]\sqrt{36x^6z^2[/tex]  represents the square root of the product of 36, x raised to the power of 6, and z raised to the power of 2.

What is square root ?

Square root is a mathematical operation that, when applied to a non-negative number, returns another non-negative number that, when multiplied by itself, gives the original number as a result.

The expression [tex]\sqrt{36x^6z^2[/tex]  represents the square root of the product of 36, x raised to the power of 6, and z raised to the power of 2. To simplify this expression, we can use the following rules of exponents and radicals:

[tex]\sqrt{(a * b)} = \sqrt{a} *\sqrt{b[/tex]

[tex]\sqrt{(a^2)} = a[/tex]  for all non-negative values of a

Using these rules, we can write:

[tex]\sqrt{36x^6z^2 }= \sqrt{(36 * x^6 * z^2)[/tex]

[tex]= \sqrt{(6^2 * (x^3)^2 * z^2)[/tex] (grouping factors with perfect square roots)

[tex]= 6 * x^3 * z[/tex]  (simplifying the square root of the perfect square 6^2)

Therefore, the equivalent expression of [tex]\sqrt{36x^6z^2[/tex] is [tex]6x^3z[/tex]. This means that the square root of [tex]36x^6z^2[/tex] is equal to 6 times the product of x raised to the power of 3 and z.

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The width of the canyon in the given image is 70 ft wide.

To find the width of the canyon, we can visually extend side DC and AE to form two sides of a rectangle.

Given that side DC is the same as side AE (80 ft), we can use this same reasoning to determine that the width is the sum of side AB and side BC, which is 35 + 35.

This gives us a width of 70 ft.

In a rectangle, the longer side is known as the length and the shorter side is known as the width.

Therefore, using the sum of side AB and side BC, we get a width of 70 ft for the canyon.

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Answer:

The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.

In this case, we have two similar regular hexagons. Let x be the side length of the smaller hexagon, and y be the side length of the larger hexagon. Then, we have:

Area of smaller hexagon / Area of larger hexagon = (x^2 * 6 * sqrt(3)) / (y^2 * 6 * sqrt(3)) = x^2 / y^2

We are given the areas of the two hexagons:

x^2 * 6 * sqrt(3) = 16 * sqrt(3)

y^2 * 6 * sqrt(3) = 25 * sqrt(3)

Dividing the second equation by the first equation, we get:

(y^2 * 6 * sqrt(3)) / (x^2 * 6 * sqrt(3)) = 25 * sqrt(3) / (16 * sqrt(3))

Simplifying this expression gives:

y^2 / x^2 = 25 / 16

Taking the square root of both sides, we get:

y / x = 5 / 4

Therefore, the scale factor from the smaller hexagon to the larger hexagon is 5/4.

Answer:

-16

Step-by-step explanation:

Answer: Three equivalent ratios of 8 : 5 are 16 : 10, 24 : 15 and 32 : 20.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\tt y+4+3\left(y+2\right)[/tex]

Expand by distributing terms:-

[tex]\tt y+4+3y+6[/tex]

Combine like terms:-

[tex]\boxed{\tt y+3y}+\boxed{\tt 4+6}[/tex]

[tex]\tt y+3y=\underline{\bf 4y}[/tex]

[tex]\tt 4+6=\underline{\bf 10}[/tex]

⇒ [tex]\underline{\bf 4y+10}[/tex]

Therefore, A. 4y + 10 is our answer!

_______________________

Hope this helps! :)

Answer:

4y+10

Step-by-step explanation:

у + 4 + 3(y + 2) =

y + 4 + 3y + 6

y + 10 + 3y

4y +10

9% percent of Team B’s mean absolute deviation is the difference in the mean of the individual times of members.

The result of dividing the sum of a set of values by the total number of values in the set is mean.

The average distance between each observation and the mean is shown via a measure of variability known as the mean absolute deviation (MAD).

The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.

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The oven will heat up by 18 degrees in 1 minute at this rate.

What is the rate of change?

The term "rate of change" refers to how fast a quantity is changing with respect to time, or some other independent variable.

If the oven's temperature rose 3 degrees in 1/6 of a minute, we can find the rate of temperature increase by multiplying both sides by 6 to get:

3 degrees / (1/6 minute) = 18 degrees/minute

Hence, the oven will heat up by 18 degrees in 1 minute at this rate.

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Answer:

"B"

Add all the sides together
Step-by-step explanation:

Answer:

Step-by-step explanation:

To relate the angular motion of the hour hand (h) and the angular motion of the second hand (s), we can use the following formula:

h = (s/360) * 30

The second hand makes a full rotation of 360 degrees in one minute, so in 60 minutes (or one hour), it rotates 21,600 degrees. We know that during this time, the hour hand moves 30 degrees.

Therefore, the equation relating h and s is h = (s/360) * 30.

Answer:

When a marble is taken out from the bag and replaced, the probability of getting a red or blue marble on the first draw remains the same for the second draw. Therefore, we can use the multiplication rule of probability to calculate the probability of getting two marbles of the same color.

Let's denote the event of getting a red marble as R and the event of getting a blue marble as B. Then, the probability of getting two marbles of the same color can be calculated as follows:

Probability of getting two red marbles: P(R and R) = P(R) * P(R) = (3/7) * (3/7) = 9/49

Probability of getting two blue marbles: P(B and B) = P(B) * P(B) = (4/7) * (4/7) = 16/49

Therefore, the probability of getting two marbles of the same color is the sum of the probabilities of getting two red marbles and two blue marbles, which is:

P(same color) = P(R and R) + P(B and B) = 9/49 + 16/49 = 25/49

So the probability of getting two marbles of the same color is 25/49.

Step-by-step explanation:

Step-by-step explanation:

volume = π · r^2 · h

volume = π · 3^2 · 5

volume = π · 9 · 5

volume = π · 45

Answer : 45π

Answer:

1/9 and 1/2 one is greater then

Step-by-step explanation:

so if u look at it you will know that 1/2 is less then and 1/9 is greater then.

Answer:

The mathematical symbols used to indicate that the endpoints of an interval are not included in the graph of an inequality are "<" and ">" signs with a small circle or parenthesis next to them.

The symbol "<" with a circle or parenthesis on the right side indicates that the endpoint is not included, while the symbol ">" with a circle or parenthesis on the left side indicates that the endpoint is not included.

For example, the inequality x > 3 indicates that the variable x is greater than 3, but does not include 3 in its solution set. Similarly, the inequality y < -2 with a circle or parenthesis on the left side indicates that the variable y is less than -2, but does not include -2 in its solution set.

Step-by-step explanation:

The vector V in linear form will be v = –11i + 6j i.e. A.

In mathematics, a vector is a mathematical object that has both magnitude and direction. It is typically represented as an arrow in space, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector.

Now,

Vector RS can be represented as the difference between the coordinates of R and S:

RS = S - R

RS = (-36, 11) - (-25, 5)

RS = (-36 + 25, 11 - 5)

RS = (-11, 6)

To represent RS in linear form, we can use the components of the vector as coefficients of the basis vectors i and j:

RS = -11i + 6j

Therefore,

               the correct option is v = -11i + 6j.

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Answer:

A is right

Step-by-step explanation:

We can state this by responding to the provided question Hence, the triangle longer limb is around 351.42 in length.

A triangle is a polygon because it includes four or so additional parts. It features a simple rectangular shape. A rectangle having edges A, B, and C is referred to as a triangle. When the sides are actually not collinear, Euclidean geometry yields a single plane and cube. If a triangle contains three parts and three angles, it is a polygon. The intersections of a triangle's three sides are referred to as its corners. The sum of a triangle's sides is 180 degrees.

In a triangle with three legs measuring 30, 60, and 90, the shorter leg is half as long as the hypotenuse while the larger leg is sqrt3 times as long.

Let's name the larger leg's length "x" for simplicity. Thus, we are aware of:

The shorter leg measures 203 in length.

The hypotenuse measures 406 times the length of the shorter leg.

Using the proportion of the hypotenuse and leg lengths in a 30-60-90 triangle, we may find:

x = sqrt3 times ($) 203 = 351.42$

Hence, the longer limb is around 351.42 in length.

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Answer:

The answer you are looking for is 1.5x10^1 or 0.15

Step-by-step explanation:

To find the answer I used PEMDAS. (Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction).

So I looked at the Parenthesis first, and then I looked for the exponents which were [tex]10^{-13}[/tex], also [tex]10^{11}[/tex].

When put in the calculator 0.0000000000001, and the second exponent was 100000000000.

Then having to multiply 0.0000000000001 by 6 gave me 0.00000000000006 and also multiplying 2.5 with 100000000000 gave me 250000000000.

Finally multiplying the final results with each other gave me 0.15 and in scientific notation, 1.5x10^1

I hope this was helpful!

48

The line of best fit has the following equation

y = 3.2x + 25

Since the x-values are 20 and 35, we must enter these values into the equation and subtract them to determine the difference in the y-values:

y(20) - y(35) = (3.220 + 25) - (3.235 + 25)

y(20) - y(35) = (64 + 25) - (112 + 25)

y(20) - y(35) = 89 - 137

y(20) - y(35) = -48

For x-values of 20 and 35, 48 is the most logical prediction for the difference in y-values.

Thus, Option (A) 48 is the correct answer.

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Answer:

Answer:

Step-by-step explanation:

We are given that T is the midpoint of LM, J is the midpoint of MO, and P is the midpoint of LO. This means that LT = TM, JO = OM, and LP = PO.

We can use this information to find the lengths of the sides of triangle LMO. Since T is the midpoint of LM, we have LT = TM = 9. Similarly, since J is the midpoint of MO, we have JO = OM = 12. Finally, since P is the midpoint of LO, we have LP = PO = (LO)/2 = 32/2 = 16.

Now, we can use the Pythagorean theorem to find the length of the third side, LM:

LM^2 = LT^2 + TM^2

LM^2 = 9^2 + 16^2

LM^2 = 337

LM = sqrt(337)

Therefore, the perimeter of triangle LMO is:

LM + MO + LO = sqrt(337) + 2(12) + 32

Perimeter = sqrt(337) + 56

To find the perimeter of triangle TJP, we need to find the lengths of the sides TJ, JP, and TP. Since T and J are midpoints of their respective sides, we know that TJ = 2(LT) = 18 and JP = 2(JO) = 24. To find TP, we can use the Pythagorean theorem:

TP^2 = TJ^2 + JP^2

TP^2 = 18^2 + 24^2

TP^2 = 900

TP = 30

Therefore, the perimeter of triangle TJP is:

TJ + JP + TP = 18 + 24 + 30

Perimeter = 72

Therefore, the perimeter of triangle TJP is 72.

In the polynomial function given, the value of the limit as it approached infinity is 5/3

To evaluate this limit, we need to determine the behavior of the function as x approaches infinity. To do this, we can use the fact that for any polynomial p(x) and q(x) of the same degree, the limit of p(x)/q(x) as x approaches infinity is equal to the ratio of the leading coefficients.

In this case, both the numerator and denominator are polynomials of degree 2, so we can apply this property. The leading coefficient of the numerator is 6 and the leading coefficient of the denominator is 7. Therefore, the limit as x approaches infinity of the given expression is:

lim [ (6x² - 5) / (7x² + x - 3)]

x → ∞ = 5/3

Therefore, the limit of the given expression as x approaches infinity is equal to 5/3.

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The dot notation of the recurring decimal is 51.674674674674.....

Recurrent decimal, often known as recurring decimal, is a decimal number made up only of digits that repeat after the decimal at regular intervals. As an illustration, 46.374374374, 517.338383, etc. Depending on the sort of digits that follow the decimal point—whether they are recurring, non-repeating, ending, or unending—decimals can be divided into many groups (infinite digits after the decimal point).

Here the given recurring decimal is 51.674,

To write into dot notation , we need to write repeated numbers after digits. Then,

=> 51.674674674674....

Hence the dot notation of the recurring decimal is 51.674674674674.....

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It satisfies the vertical line test and represents a function.

What is function ?

Function can be defined in which it relates an input to output.

Based on the image you provided, it seems to represent a function since each input value (x-value) corresponds to a unique output value (y-value) and there is only one output value for each input value.

To verify if a graph represents a function, we can use the vertical line test. If a vertical line intersects the graph at more than one point, then the graph does not represent a function. However, in this graph, for any vertical line drawn, it only intersects the graph at one point.

Hence, it satisfies the vertical line test and represents a function.

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Answer:

See below

Step-by-step explanation:

[tex]7(6+ x)[/tex] = [tex](7)(6) + (7)(x)[/tex]
            = [tex]42 + 6x[/tex]

The triangles include:

4) To determine if a triangle is right, obtuse, or acute, we need to use the Pythagorean Theorem to determine if the square of the longest side equals the sum of the squares of the other two sides.

Here, the longest side is 9, and the other two sides are 6 and 7.

9² = 6² + 7²

81 = 36 + 49

81 = 85

Since 81 is not equal to 85, the triangle is not a right triangle. To determine if it's obtuse or acute, we need to check the cosine of the largest angle using the Law of Cosines.

cos A = (b² + c² - a²) / 2bc

Let's choose 9 as side a, since it's the largest side:

cos A = (6² + 7² - 9²) / (84)

cos A = 0.048

Since cos A is positive, angle A is acute. Therefore, the triangle is acute.

5) Using the same process as above:

16² = 10² + 12²

256 = 100 + 144

256 = 244 + 12

Since 256 is greater than 244, the triangle is obtuse.

6) Again, using the same process as above:

(8√6)² = 8² + 16²

192 = 64 + 256

192 = 320

Since 192 is less than 320, the triangle is obtuse.

7) 29² = 20² + 21²

841 = 400 + 441

841 = 841

Since 841 is equal to 841, the triangle is a right triangle.

8) √73 is greater than 8 and 3, so it must be the largest side.

(√73)² = 8² + 3²

73 = 64 + 9

73 = 73

Since 73 is equal to 73, the triangle is a right triangle.

9) 12² = 8² + 10²

144 = 64 + 100

144 = 164 - 20

Since 144 is less than 164, the triangle is obtuse.

10) 15² = 9² + (3√34)²

225 = 81 + 306

225 = 387 - 162

Since 225 is less than 387, the triangle is obtuse.

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Answer:

Step-by-step explanation:

Yes, the length and width dimensions of the two rectangular boxes are similar.

Two objects are considered similar if they have the same shape, but not necessarily the same size. The ratio of the corresponding sides of two similar objects is called the scale factor.

For the first rectangular box, the ratio of length to width is 10/8, which can be simplified to 5/4.

For the second rectangular box, the ratio of length to width is 15/12, which can be simplified to 5/4 as well.

Since the ratio of the corresponding sides of the two boxes is the same, namely 5/4, we can conclude that the length and width dimensions of the two rectangular boxes are similar.

The man's daily wage is given as follows:

$42.

The man's daily wage is obtained applying the proportions in the context of the problem.

The woman receives $24 for 8 hours of work, hence her hourly wage is given as follows:

24/8 = $3 per hour.

Their wages per hour are in the ratio 7:5, hence the man's hourly wage is obtained multiplying the woman's hourly wage by 7/5, hence:

7/5 x 3 = 21/5 = $4.2 per hour.

The man works 10 hours a day, hence the daily wage is given as follows, multiplying the hourly wage by 10:

10 x 4.2 = $42.

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The man's daily wage is $42.

We know that the woman works 8 hours per day and gets $24 per day, then her hourly pay is the quotient between these two values.

$24/8 = $3 per hour.

And we also know that their wages per hour are in the ratio 7: 5.

Then the man's hourly pay 7/5 times the hourly pay of the woman, then we just need to solve the product below:

(7/5)*$3 = x

(7/5)*$3 = $4.2

And the man works for 10 hours, then the daily wage is 10*$4.2 = $42.

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