5x+7 = 8x-71 what is the value of x

Answer:

Tn=a+(n-1)d

Tn=29+(n-1)9

Tn=29+9n-9

Tn=20+9n

Tn=20+9 (21)

T21=580

Step-by-step explanation:

a=first term

d=common difference

Tn=a+(n-1)d .....general formula for an arithmetic number pattern

Answer:

Step-by-step explanation:

I assume the 8 is the question number and the sequence is

29,38,47...

This is an arithmetic sequence as any term minus the previous term is a constant, called the common difference, which in this case is 47-38=38-29=9. An arithmetic sequence has the form

an=a+d(n-1)

Where an=nth term, a=initial term, d=common difference, and n=term number.

In this case a=29 and d=9 so

an=29+9(n-1)

an=9n+20, then the 21st term is

a(21)=9(21)+20

a(21)=189+20

a(21)=209

So the 21st term is 209.

Answer:

The ratio of the circumference of a circle to its diameter and is called π (Pi).

Step-by-step explanation:

Answer:

y = mx + b is the slope intercept form of writing the equation of a straight line. In the equation 'y = mx + b', 'b' is the point, where the line intersects the 'y axis' and 'm' denotes the slope of the line. The slope or gradient of a line describes how steep a line is. It can have either a positive or a negative value. When a standard form of a linear equation is of the form Ax + By = C, where 'x' and 'y' and 'C' are variables and 'A', 'B' are constants, the slope-intercept form is the most preferred way of expressing a straight line due to its simplicity, as it is very easy to find the slope and the 'y intercept' from the given equation.

Meaning of y = mx + b

y = mx + b is the slope-intercept form of a staight line. In the equation y = mx + b for a straight line, m is called the slope of the line and b is the y-intercept of a line. y = mx+b, where

y ⇒ how far up or down is the line,

x ⇒ how far along is the line,

b ⇒ the value of y when x = 0 and

m ⇒ how steep the line is.

This is determined by m = (difference in y coordinates)/ (difference in x coordinates). Note that difference in y coordinates is indicated as rise or fall and difference in x coordinates is indicated as run.

Step-by-step explanation:

The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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An algebraic expression which models the given context would be written as s + 0.02s = 1.05s.

Price can be define as an amount of money which is primarily set by the seller of a good (product), and it must be paid by a buyer to the seller, so as to enable the acquisition of this good (product).

An algebraic expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

Let s represent the price of a pair of shoes.

Therefore, an algebraic expression which models the given context would be written as follows:

s + 0.02s = 1.05s.

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Answer:

x = 30

Step-by-step explanation:

I'm going to assume the equation you needed help with was:

\(\frac{1}{2}(x+6) = 18\)

If not, let me know and I'll redo it.

\(\frac{1}{2} x+3 = 18\\\frac{1}{2} x = 15\\x = 30\)

Answer:

from top to bottom left to right brainliest please

Step-by-step explanation:

1. 30

2. 32

3. 270

4. 175

5. 156.75

6. 504

Answer: 4

Step-by-step explanation:

2+2=4

Answer:

2 + 2 = 4

Step-by-step explanation:

If u just started to learn how to sum, you can use sticks

II + II = IIII

Answer: n

Step-by-step explanation:

pp lol

The rectangle will form a cylinder when it rotates about the dashed line.

We have to given that;

To find plane figure which generates a cylinder when it rotates about the dashed line.

Hence, By figure we get;

When we rotate all the figure about the dashed line, we get;

The circle will form a sphere.

The rhombus (it can also be a square) will form a 2 cones attached at the bottom.

The rectangle will form a cylinder.

The triangle will form a cone.

Hence, The rectangle will form a cylinder when it rotates about the dashed line.

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Numerical integration involves approximating the definite integral of a function using numerical methods.

There are various techniques for numerical integration, including the Trapezoidal rule, Simpson's rule, and Gaussian quadrature.In general, these methods divide the integration interval into smaller sub-intervals and approximate the area under the curve within each sub-interval using mathematical formulas.

The approximations are then summed up to estimate the integral over the entire interval.The accuracy of the numerical integration depends on the number of sub-intervals used and the specific method used. Generally, increasing the number of sub-intervals leads to a more accurate approximation.

Overall, numerical integration is a useful tool for evaluating integrals that cannot be solved analytically and is commonly used in various fields such as physics, engineering, and finance.

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Answer:

The probability that A will win is 2/3 and that B will win is 1/3 so if A wins three times in a row, 2/3*2/3*2/3=8/27.

Step-by-step explanation:

Answer:

284 u^3

Step-by-step explanation:

a b c d e f g h i j k l m n o p q r s t u v w x y z

Answer: V = 1,436.03 cubic meters

Step-by-step explanation:

V = (4/3)(3.14)(r^3)

V = (4/3)(3.14)(7^3)

V = (4/3)(3.14)(343)

V = 1,436.03

hope it's helpful ❤❤❤❤❤❤❤

THANK YOU.

Answer:

n=10

Step-by-step explanation:

6=3n/5

multiply both sides by 5

30=3n

divide both sides 3

10=n

Answer: 2x^2t+7xy

Step-by-step explanation:

The probability of a Type II error is represented by beta. Thus, the correct answer is option B.

Beta represents the probability of failing to reject the null hypothesis when it is false.

On the other hand, Type I error (alpha) represents the probability of rejecting the null hypothesis when it is true. A Type II error occurs when a false null hypothesis is not rejected. Hence, beta is the probability of making a Type II error.

The null hypothesis is rejected when the p-value is less than or equal to the level of significance, not exceeds it.

The p-value is the probability of obtaining a result as extreme as or more extreme than the observed result when the null hypothesis is true. If the p-value is less than the level of significance, the null hypothesis is rejected, and vice versa.

Hence, the statement "The null hypothesis is rejected when the p-value exceeds the level of significance" is false.

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The normal to the parabola\(z = x^2 + y^2\) at the point (3, 3, 18) intersects the parabola again at the point (-1/3, -1/3, 20).

To find the normal to the paraboloid\(z = x^2 + y^2\) at points (3, 3, 18), we first need to find the slope of the surface at that point. The gradient vector is given by

\(∇f(x,y,z) = < 2x, 2y, -1 >\)

So the gradient vector at points (3, 3, 18) is

∇f(3, 3, 18) = <6, 6, -1>

This gradient vector is orthogonal to the plane tangent to the surface at the point (3, 3, 18). So the surface normal at this point is parallel to the gradient vector and can be expressed as

x = 3 + 6t

y = 3 + 6t

z = 18 - t

To discover where this line converges the parabola once more, we ought to substitute the x, y, and z equations into the parabola's condition. 

\(z = x^2 + y^2\)

So it looks like this:

\(18 - t = (3 + 6t)^2 + (3 + 6t)^2\)

\(18 - t = 18t^2 + 36t + 18\)

\(0 = 18t^2 + 37t\)

t=0 or t=-37/18

The value t = 0 corresponds to the starting point (3, 3, 18), so we are interested in the second value t = -37/18. Substituting this value into the normal equation gives:

x = 3 + 6(-37/18) = -1/3

y = 3 + 6(-37/18) = -1/3

z=18-(-37/18)=360/18=20

therefore, the normal to the parabola \(z = x^2 + y^2\) at the point (3, 3, 18) intersects the parabola again at the point (-1/3, -1/3, 20). 

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Answer:

Let's call the width x and the length x + 8. Perimeter can be calculated by multiplying the sum of the length and width by 2 so we can write:

2(x + x + 8) = 80

2(2x + 8) = 80

2x + 8 = 40

2x = 32

x = 16

This means that the length is 16 cm and the width is 24 cm.

Answer:

the area of rectangle is 384 sq cm, while the length of the rectangle is 24 cm and width of rectangle is 16 cm

Step-by-step explanation:

Let the breadth of the rectangle is x cm  

Thus the length of the rectangle = (x + 8) cm

We know Perimeter = 2 (length + width)

Perimeter = 2 (x + 8 + x)

Perimeter = 2 (2x + 8)

Perimeter = 4x + 16 cm

4x + 16 = 80 cm

4x = 80 - 16

4x = 64

x = 64/4 cm

x = 16 cm

Thus the width of the rectangle is 16 cm

Length of the rectangle x + 8 = 16 + 8 = 24 cm

We know Area of rectangle = length × breadth

Area of rectangle = 24 × 16 = 384 sq cm

Answer:

So first you'll want to line your numbers in order. 0,3,4,6,6,7,7,7,

The median refers to number that is in the middle, so 6 is the median.

To find the range, you subtract the biggest number with the smallest. So 9 is the range.

And 7 is the mode because it's repeated the most.

hope this helps

median:6

range: 9

mode: 7

The conversion of decimal number directly to binary number will be faster.

The number conversion deals with the operation to change the base of the number.

Binary number - It contains only 2 numbers that are 1 and 0.

Decimal number - It contains 10 numbers that are from 0 to 9.

Hexadecimal number - It contains 16 numbers that are from 0 to F.

Convert the decimal number 431 to binary will be

431 / 2 = 215 with 1 remainder

215 / 2 = 107 with 1 remainder

107 / 2 = 53 with 1 remainder

53 / 2 = 26 with 1 remainder

26 / 2 = 13 with 0 remainder

13 / 2 = 6 with 1 remainder

6 / 2 = 3 with 0 remainder

3 / 2 = 1 with 1 remainder

1 / 2 = 0 with 1 remainder

The decimal number 431 to binary number will be 110101111.

Convert first to hexadecimal and then from hexadecimal to binary. Then we have

(431)₁₀ = (1AF)₁₆ = (110101111)₂

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Answer:

8.25in

Step-by-step explanation:

6×4=24in

198÷24=8.25in

hence the answer is 8.25in

Answer:

See below ~

Step-by-step explanation:

#7)

#8)

Answer:

$36.99

Step-by-step explanation:

Fabrics per yard = $7.50

Pack of buttons = $6.99

Fabrics needed = 4 yards

How much will Tanya spend at the store on her fabric and buttons?

Total cost of fabric and button = cost of 4 yards of fabric + pack of buttons

= 4(7.50) + 6.99

= 30 + 6.99

= 36.99

Total cost of fabric and button = $36.99

Answer :  1)  x = 81.3 in binary base, approximated to 3 binary places, is 101000.1010. 2) 10x in octal system is 423664. 3) the final answer in the octal system with 2 octal places accuracy is 35540. 4)x² - (1280)10x in octal system is 5113355130

1. To find the binary representation of x = 81.3 with an approximation of 3 binary places, we follow the hint:

First, multiply x by 2^k, where k is the number of binary places needed for the approximation. In this case, k = 3.

x * 2^3 = 81.3 * 8 = 650.4

Next, round the result to the nearest whole number:

Rounded value = 650

Convert the rounded value to binary:

650 = 1010001010

Finally, move the binary point k places to the left:

101000.1010

Therefore, x = 81.3 in binary base, approximated to 3 binary places, is 101000.1010.

2. Given x = (80a2)12, we need to calculate 10x in octal system (base 8).

First, convert x from duo-decimal (base 12) to decimal (base 10):

x = (80a2)12 = 8*12^3 + 0*12^2 + 10*12^1 + 2*12^0 = 8*1728 + 10*12 + 2 = 13824 + 120 + 2 = 13946

Next, multiply 10x:

10x = 10 * 13946 = 139460

Convert 139460 to octal:

139460 = 423664

Therefore, 10x in octal system is 423664.

3. We have the expression (x w - y z - 3 w^2)² and need to calculate the final answer in the octal system with 2 octal places accuracy.

Given:

x = (3E0)16

y = (111000)2

z = (8)10

w = (20)8

First, convert the values to decimal:

x = (3E0)16 = 3*16^2 + 14*16^1 + 0*16^0 = 768 + 224 + 0 = 992

y = (111000)2 = 1*2^5 + 1*2^4 + 1*2^3 + 0*2^2 + 0*2^1 + 0*2^0 = 32 + 16 + 8 + 0 + 0 + 0 = 56

z = (8)10 = 8

w = (20)8 = 2*8^1 + 0*8^0 = 16 + 0 = 16

Now substitute the values into the expression:

(x w - y z - 3 w^2)² = (992 * 16 - 56 * 8 - 3 * 16^2)²

Calculate each term:

992 * 16 = 15872

56 * 8 = 448

3 * 16^2 = 768

Substitute the calculated values back into the expression:

(15872 - 448 - 768)² = 15056²

Convert 15056 to octal:

15056 = 35540

Therefore, the final answer in the octal system with 2 octal places accuracy is 35540.

4. Given x = (92B4)16, we need to find x² - (1280)10x in octal system (base 8).

First, convert x from hexadecimal (base 16) to decimal (base 10):

x = (92B4)16 = 916^3 + 216^2 + 1116^1 + 416^0 = 36864 + 512 + 176 + 4 = 37656

Calculate x²:

x² = 37656² = 1416327936

Next, calculate (1280)10x:

(1280)10x = 1280 * 37656 = 48161280

Subtract (1280)10x from x²:

x² - (1280)10x = 1416327936 - 48161280 = 1368166656

Convert 1368166656 to octal:

1368166656 = 5113355130

Therefore, x² - (1280)10x in octal system is 5113355130.

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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

30 mens can build the house in 70 days​. The solution has been obtained by using the unitary method.

What is a unitary method?

The unitary approach is used to calculate the value of each individual unit before determining the value of the necessary number of units.

We are given that 7 men build a house in 300 days.

So, for building the house in 1 day, 2100 men will be required.

For building the house in 70 days, provided they are working at the same rate, the number of men required will be

⇒2100/70 = 30 men

Hence, 30 mens can build the house in 70 days​.

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Answer:

2/5

Step-by-step explanation:

This is because the whole wall is 5/5 (5/5 = 1 whole).

5/5 - 3/5 = 2/5

When we add or subtract like fractions, we ignore the same denominator, and just add or subtract the numerator.

Hope this helps.

Answer:

y = -3x + 7

Step-by-step explanation:

I see points (0, 7) and (1, 4).

slope = m = (4 - 7)/(1 - 0) = -3

y-intercept = 7

y = mx + b

y = -3x + 7