gradient of line 6x+2y+9=0​

The amount of shovels that can be produced in h hours is 960 shovels

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

In the given equation,

The number of shovels produced are

C(x)=26*20+400

=520+400

=920 shovels

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Consequently, (3, 5/2) is the answer to the equations 5x+y=3 and 5x+y=2. Either conditional solutions or identities are categories for equations.

Its simplest form is thought to be the number's smallest equivalent fraction. How to determine the simplest form. Look for shared factors in the denominator and numerator. A fractional number can be checked to discover if it is a prime number. A statement having two quadrilateral and an equal sign in the middle is referred to as a mathematical equation. Every variable's degrees are listed in descending order in the general form of any equation. The formula for a linear equation is x + b = 0. The general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Either conditional solutions or identities are categories for equations. An identity holds true for whatever value of the variables.

given

5x + y = 3

5x + y = 2

x = y-3/ 5

y - 3 +y = 2

2y = 5

y = 5/2

x = 3

Consequently, (3, 5/2) is the answer to the equations 5x+y=3 and 5x+y=2.

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For all samples of 5, there is a 0.05 probability that the sample mean would be higher than 22 pounds.

The selection of bags weights, on average, 19.7 pounds.

The standard variation is 3.1 pounds.

Both the normal probability density function and the sampling distribution theorem were used.

When dealing with issues involving samples of data that are regularly distributed, the z-score algorithm is applied.

The z-score of a measure X is calculated as follows:

z = (x - μ) ÷ σ

The number of standard deviations is calculated using the Z-score. The average is the metric employed.

We examine the p-value linked with the Z-score in the z-score table after computing the Z-score.

The chance that the measure's value is less than X, or what proportion of X, is represented by this p-value.

We may calculate the likelihood that the metric exceeds X by subtracting 1.

The Central Limitation Theorem also holds for skewed variables when n is at least 30.

The sample mean will remain constant regardless of sample size.

The standard error, though, will alter.

The probability that the sample means will be higher than 22 is shown by P(a > 22).

For all samples of size 5, the possibility that they will weigh more than 22 pounds is about 0.05.

Your question is incomplete but most probably your full question was

at a certain high school, the distribution of backpack weight is approximately normal with a mean of 19.7 pounds and a standard deviation of 3.1 pounds. a random sample of 5 backpacks will be selected, and the weight, in pounds, of each backpack will be recorded. what is the probability that my next five samples will average 22 pounds?

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All the equations in which z = 5 are a solution are given as follows:

A. 8 = z + 3.

D. 12z = 60.

E. 12 + z = 17.

The first equation is defined as

8 = z + 3.

Isolating the variable z, applying the subtraction operation, which is the inverse of the addition, the solution is given as follows:

z = 8 - 3

z = 5.

The second equation is given as follows:

z - 1 = 6.

Applying the addition operation, which is the inverse of the subtraction, the solution is given as follows:

z = 7.

The third equation is given as follows:

20 = 40z

Applying the quotient operation, which is the inverse of the multiplication, the solution is given as follows:

z = 20/40

z = 0.5.

The fourth equation is given as follows:

12z = 60.

Applying the quotient operation, which is the inverse of the multiplication, the solution is given as follows:

z = 60/12

z = 5.

The fifth equation is defined as

12 + z = 17.

Isolating the variable z, applying the subtraction operation, which is the inverse of the addition, the solution is given as follows:

z = 17 - 12

z = 5.

The equations are given by the image presented at the end of the answer.

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Answer:

x=8

Step-by-step explanation:

11x+2=90

11x=88

x=8

Answer:

19. X=8

20. x=7

There are both numbers and letters in algebra. Numbers are constant, i.e. e. The unknown quantities in the algebraic formula are represented by letters or alphabets. The 9 formulas of algebra are explained further.

Algebra is a mathematical tool that we use to calculate distances, volumes, and perimeters of spaces as well as to calculate costs, rent things out, and understand time relationships.

The 9 formulas of algebra are explained as:

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The main difference between the 2D and 3D coordinate systems is that the 3D coordinate system adds a third axis (Z) to the two axes of the 2D coordinate system.

A coordinate system is a two-dimensional or three-dimensional system which is used to identify the location of a point or object in the space. It is represented by a set of axes, which are perpendicular and equally spaced from each other to form a grid-like structure. The coordinates of a point or object are determined by the intersection of the two or three axes. Common coordinate systems used in mathematics and science include the Cartesian, polar, and spherical coordinate systems.

A 2D coordinate system is a system in which two axes (X and Y) are used to define a point in a two-dimensional space. This system is used to describe the position of a point in relation to the origin, which is located at the intersection of the two axes. The two axes form a coordinate plane, which provides a visual representation of the system.

A 3D coordinate system is a system in which three axes (X, Y, and Z) are used to define a point in a three-dimensional space. This system is used to describe the position of a point in relation to the origin, which is located at the intersection of the three axes. The three axes form a coordinate space, which provides a visual representation of the system.

This third axis allows points in the 3D coordinate system to be represented in the third dimension. Additionally, the 3D coordinate system provides a more detailed representation of points, as it can represent points in all three dimensions.

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When there are two factors—a fixed element and a variable factor—the law of variable proportions is created. According to the law of variable proportions, the marginal product of a factor will gradually decrease when its quantity is raised while the other elements remain constant.

We are aware that the relationship between the number of units of a variable factor and the entire physical product is shown by the law of variable proportions.

Additionally, the TPP increases initially at a rising pace, then at a falling rate, and finally declines if we maintain other parameters constant and increase the units of the variable factor.

According to the law of variable proportions, if a producer raises the units of a variable factor while keeping other elements constant, the total product will initially increase at an increasing pace, then it will increase at a diminishing rate, and finally it will begin to decline.

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Answer:

in decimal it is 36.72, in fraction it is 918/25

Step-by-step explanation:

The system of equations is:

-2 = a + b + c

7 = 4a - 2b +c

-2 = 25a + 5b + c

The polynomial is:

y = (1/3)*x^2 - 6x - 1/3

The general polynomial of degree 2 can be written as:

y = a*x^2 + b*x +c

If we use the fact that it passes through the 3 given points, then we can write the 3 equations:

-2 = a*1^2+ b*1 + c

7 = a*(-2)^2 + b*-2 + c

-2 = a*5^2 + b*5 + c

We can simplify these to get the system of equations:

-2 = a + b + c

7 = 4a - 2b +c

-2 = 25a + 5b + c

First, isolate c on the first equation to get:

c = -2 - a- b

Replace it on the other two:

7 = 4a - 2b + (-2 - a - b)

-2 = 25a + 5b + (-2 - a - b)

9 = 3a - 3b

0 = 24a + 4b

Using the second equation we can rewrite:

-24a = 4b

-24a/4 = b

-6a = b

Ande replace that in the other equation:

9 = 3a - 3*(-6a)

9 = 3a + 18a

9/21 = a

1/3 = a

And the value of b is:

-6*(1/3) = b

-2 = b

And the value of c is:

c = -2 - (-2) - 1/3

c = -1/3

The polynomial is:

y = (1/3)*x^2 - 6x - 1/3

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The option that illustrates the truth value of the given conditional statement is; T T → T

A conditional statement is considered to be true when the antecedent and consequent statements are both true or if the antecedent is false. When the antecedent is false, it means that the truth value of the consequent does not matter; the conditional will always be true.

We are given the conditional statements at;

If 5 = 3 + 2, then 3 + 2 = 5

Now, a conditional statement, signified by t f which means true and false, is an if-then statement with t being a hypothesis and f being an inference. The statement that illustrates the truth value is T T → T because 5 = 3 + 2 which is true and 3 + 2 = 5 which is also true.

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Answer: By 40J

Step-by-step explanation:

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A line that is perpendicular to another line has a slope that is the negative reciprocal of the original line. The slope of the line y = 2/7x - 8 is 2/7. To find the slope of the line that is perpendicular to it, we take the negative reciprocal of 2/7 which is -7/2.

We know that the line we're trying to find passes through the point (-4, 2), so we can use this point and the slope to write the equation of the line in point-slope form:

y - y1 = m (x - x1)

where (x1, y1) is the point the line passes through, m is the slope, and y and x are the coordinates of any point on the line.

So the equation of the line that passes through (-4,2) and is perpendicular to the line y= 2/7x - 8 is:

y - 2 = -7/2 (x + 4)

Simplifying this, we get

y = -7/2 x - 8

Therefore the equation of the line that passes through (-4,2) and is perpendicular to the line y= 2/7x - 8 is y = -7/2 x - 8

The area of the triangle having sides 3 cm 4 cm and 5 cm is calculated to be 6 cm².

Given that,

The sides of the triangle are said to be 3 cm, 4 cm and 5 cm.

By looking at the lengths of the sides of the triangle, it is clear that they are the sides of a right angled triangle. The Pythagorean theorem can be used to verify this.

5² = 3² + 4²

25 = 25

So, 5 is said to be the hypotenuse side of the right triangle and 3, 4 are said to be the base and height of the right triangle.

The formula to find out the area of the triangle is given by,

Area A = 1/2 × Base b × Height h

A = 1/2 × b × h

From the above conclusion, b and h are found to be 3, 4.

So, A = 1/2 × b × h = 1/2 × 3 × 4 = 6 cm²

Thus, the area of the required triangle is calculated to be 6 cm².

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The original linear function is:

y = 2*x + 4   with the point (1, 6)

The translated function is:

y = 2x + 7

And the translated point is (-3, 1)

First, we want to write a random linear function, I will use:

y = 2*x + 4

To find a point on that line, we can just evaluate the function in x = 1, we will get:

y = 2*1 + 4

y = 2 + 4

y = 6

So we have the point (1, 6)

Now we want to translate it 4 units to the left and 5 units down.

To translate it 4 units to the left, we need to add 4 to the argument.

y = 2*(x + 4) + 4

And to translate it  5 units down, we just need to subtract 5, we will get:

y = 2*(x + 4) + 4 - 5

Now we can simplify this to get:

y = 2*x + 2*4 + 4 - 5

y = 2x + 8 + 4 - 5

y = 2x + 7

The new coordinates of the point are the same as the last ones, but we subtract 4 to the x-value and 5 to the y-value:

(1 - 4, 6 - 5) = (-3, 1)

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a. The equation that represents the number of inches y you have knitted after x days will be y = 4x.

b. The inches you have knitted after 7 days will be 28 inches.

c. After 30 days, you'll have knitted 100 inches.

From the information, you're You are knitting a blanket at a rate of 4 inches per day and after 4 days, you have knitted 16 inches.

The equation that represents the number of inches y you have knitted after x days will be:

y = 4 × x

y = 4x

The inches you have knitted after 7 days will be:

= 7 × 4

= 28 inches.

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Answer:

She's thinking of 19 and -7.

Step-by-step explanation:

x+y=12

x-y=26

-----------

2x=38

x=38/2

x=19

19+y=12

y=12-19=-7

The wideness of the actual balcony would be = 5.2 feet.

A scale factor is defined as the ratio between the scale of a given original object and a new object.

The actual size = scale factor × blueprint

where actual length = 9 inches

blueprint = 11.7 = 140.4 inches

scale factor = actual size/blue print

= 140.4/9 = 15.6

If the blue print width size = 4

the actual size = 4× 15.6 = 62.4 inches = 5.2 feet

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the volume of the rectangular prism is 1/2 x³.

What is rectangular prism?

The normal's length from the prism's base to its top base serves as a gauge for the structure's height. At their base, certain prisms have an angle. Prism's top end is referred to as the "base" since the word "base" can refer to either end of a prism. The area (A) of the base of a prism's base times its height (H) equals the prism's volume (V). Since A is the base area and H is the prism's height, the volume of the prism is therefore A H cubic units.

The base area is A = x*x =x²

The height is 1/2 x

The volume of the rectangular prism is A*H = 1/2 x³.

Hence the volume of the rectangular prism is 1/2 x³.

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The values of x and  y are 24 and 25 when the sum of two numbers is 49 and the difference between the numbers is 1

What is Linear equation ?

linear equation can be defined as the equation in which the highest degree is one.

Given ,

the sum of two numbers is 49 and

the difference between the numbers is 1

Let the two numbers be x and y .

so x+y = 49

x-y = 1

x = 1+y

from two equations ,

Substitute x = 1+y in x+y = 49

we get,

1+y+y = 49

2y = 49 - 1

2y = 48

y = 24

substitute y =24 in x=1+y ,

we get

x = 24+1

x = 25

Hence , the values of x and  y are 24 and 25 .

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Answer:below

Step-by-step explanation:

y=1/3x

The slope, and the y-intercepts are

A linear equation can be represented as

y = mx + c

Where

slope = m

y-intercept = c

Using the above as a guide, we have the following:

See attachment for the graph

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The margin of error of the intervals 11.13 < μ < 15.03 is 1.95

In order to get the margin of error, we would first have to find the samole mean.

The sample mean x = the upper limit + lower limit / 2

the upper limit = 15.03

The lower limit = 11.13

Then we would have: 15.03 + 11.13 / 2

= 26.16 / 2

= 13.08

Then the margin of error would be

upper limit - sample mean

= 15.03 - 13.08

= 1.95

The margin of error is given as 1.95

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After using the triangle inequality theorem, the possible values of the unknown side of the triangle is 15 < n < 25.

In this case, we are given that:

The lengths of the sides of a triangle are 20, 5, and n centimeters.

The theorem of triangle inequality stated that the lengths of any two of a triangle's sides added together must be bigger than the length of the third side. Given two sides, x and y, we can use the triangle inequality theorem to predict that the length of the third side will be between x + y and x - y.

Therefore,

x - y < n < x + y

20 - 5 < n < 20 + 5

15 < n < 25

As the result, the possible value of the unknow side of the triangle would be 15 < n < 25.

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Answer:

The power is 15 watts.

Step-by-step explanation:

It is equivalent to:

0.02012 mechanical horsepowers

0.02039 metric horsepowers

0.02011 electrical horsepowers

0.001529 boiler horsepowers

Answer:

x = 149 degree

Step-by-step explanation:

First, we have to find the missing angle of the triangle

1 triangle = 180 degree

We know 2 angles, one is 63 degrees and one is 86 degrees.

63 + 86 = 149 degree

180 - 149 = 31 degree

So, the angle of the triangle is 31 degrees. Now we know that angle add with the x to get 180 degrees, so

180 - 31 = 149 degree

So, x = 149 degree

Answer:

2x^3 -9x^2 +11x-6 divided by x-3

Step-by-step explanation:

     2x^2  - 3x  + 2

                 ------------------------------

x - 3             2x^3 - 9x^2 + 11x - 6

                  2x^3 - 6x^2

               --------------------------------------subtract

                           -3x^2    + 11x

                           -3x^2    + 9 x

               ----------------------------------------subtract

                                         2x    - 6

                                         2x    - 6

                                -----------------------------subtract

                                         0

- 2x^2 - 3x + 2

:/

Answer:

c. $350.00

Step-by-step explanation

im sorry if this didn't help i wrote everything down on paper