Derive by means of the direct formulas the following functions

Using the above equation 1/i is equal to 2/(9-5j^2+3k)

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given; 2i+5j^2-3k=9

2i+5j^2-3k=9

2i=9-5j^2+3k

i=(9-5j^2+3k)/2

1/i=2/(9-5j^2+3k)

Therefore, the value of 1/i according to the given equation will be

2/(9-5j^2+3k)

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1.600 amps of current flow through resistor r3 are measured.

A resistor is a passive, two-terminal electrical component used in circuits to apply electrical resistance.

Resistors are employed in electronic circuits for a variety of purposes, including reducing current flow, adjusting signal levels, dividing voltages, biassing active devices, and terminating transmission lines.

The parameters are determined by the query:

total current = 2 amperes

Total resistance = 80 ohms

Total current = voltage * Resistance

Total current = 2* 80

= 160V.

Consequently, the current passing through resistor R3 will be

V= IR (Ohms law)

where I (current)= V/R

current = 160/ 100

Current flowing through R3 =1.600  amperes.

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Answer:

Step-by-step explanation:

The problem can be solved by using the information provided to set up a system of equations and then solving for the unknown variable, which in this case is the fixed charge.

Let x be the fixed charge.

We know that the total cost of the 11-mile trip is the fixed charge plus the charge for the distance covered, so we can write the equation:

x + 11y = 88 (1)

We also know that the total cost of the 16-mile trip is the fixed charge plus the charge for the distance covered, so we can write the equation:

x + 16y = 108 (2)

Where y is the cost per mile

We can solve for y by subtracting equation (1) from equation (2), so:

16y - 11y = 108 - 88

5y = 20

y = 4

Now we know that cost per mile is 4$, we can substitute it in equation (1)

x + 11(4) = 88

x = 24

Now we know the fixed charge is 24$ and cost per mile is 4$, we can calculate the fare for 6 miles

24 + 6(4) = $48

Therefore, Linus would have to pay $48 to travel 6 miles.

Answer: The probability that a waitress will refuse to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students from among ten students of which four are not of legal age is 0.288 or 28.8%.

Step-by-step explanation:

he probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students can be calculated using the binomial probability formula.

The binomial probability formula is: P(x) = (n choose x) * p^x * (1-p)^(n-x)

Where:

x = the number of successful outcomes (in this case, the number of minors refused service)

n = the total number of trials (in this case, the number of IDs checked)

p = the probability of a successful outcome in a single trial (in this case, the probability that a randomly chosen student is a minor)

In this case:

x = 3 (the number of minors refused service)

n = 5 (the number of IDs checked)

p = 4/10 (the probability that a randomly chosen student is a minor)

So, the probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students can be calculated as:

P(3) = (5 choose 3) * (4/10)^3 * (6/10)^2 = (10/3) * (0.16) * (0.36) = 0.288

Therefore, the probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students is 0.288 or 28.8%.

It's worth noting that this problem assumes that the waitress randomly chooses the 5 students, if the waitress doesn't pick them randomly the result may be different.

Step-by-step explanation:

For 60 muffins sold there are 3 boxes, because there are 20 muffins per box.

For 600 muffins sold there are 30 boxes, because there are 20 muffins per box.

For 6000 muffins sold there are 300 boxes, because there are 20 muffins per box.

Because 2×3=6

Answer:

7x2−4x/5

Step-by-step explanation:

7x2−4x over 5

The perimeter of the parallelogram is greater than the perimeter of the square.

What is a perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. The perimeter of a shape is obtained by adding up the length of all the sides and edges of the shape. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

Now, let's assume a geometric system of a square and a parallelogram having the same base and equivalent side of the square " a ".

Therefore, the respective two parallel sides of the Parallelogram will also be equal to " a ".

Now, let's rotate the one of the parallel lines with angle Φ clockwise then, the side lengths which aren't equal and parallel to the first set will get increased and it's incremental rate will be responsible for the increase in perimeter of the figures aslike , perimeter is the sum of the sides of the figure.

Now let's rotate alternate side length at maximum at angle θ , aslike it should touch the square at diagonally opposite angles ,

Now, let's calculate perimeters of both the figures -

Square of side length " a " = a + a + a + a = 4a

Parallelogram of two base side length " a " and two parallel set lines of length √2a

= a + a + √2a + √2a

= 2a + 2√2a

= 2a [ 1 + √2 ]

Hence, the acquired perimeter of Parallelogram is greater than that of square

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Answer:

Step-by-step explanation:

640 - 10x^2 = (4x-10)(160 + 4x)

The factors of 640-10x^2 are (4x-10) and (160 + 4x).

The cost of labor per hour is $125.

The equation that can be used to solve for the cost of labor per hour is a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.

The form of the linear equation is:

Total cost = cost of the parts + (cost per hour x total hours worked)

$585.25 = $54 + (4.25 x d)

$585.25 = $54 + 4.25d

In order to determine the value of x, take the following steps:

Combine similar terms:

$585.25 - $54 = 4.25d

Add similar terms

$531.25 = 4.25d

Divide both sides of the equation by 4.24

d = 531.25 / 4.25

d = 125

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Answer:

no

Step-by-step explanation:

An identity is an equality that is always true. An equation is an equality that is (only necessarily) conditionally true.

That is to say that for any real value inputted into a variable in an identity, an equality will result, whereas only certain values for a variable in an equation will necessarily result in an equality.

If the given equation is an identity, it should result in an equality no matter what the input for k is. So, to prove that it isn't an identity, we simply have to find one value for k that results in an inequality. To do so, we can simply plug in 0 for k and simplify.

[tex]k - 4 = 4 + k[/tex]

[tex]0 - 4 \stackrel{?}{=} 4 + 0[/tex]

[tex]-4 \ne 4[/tex]

We have found one value for k that results in an inequality. Thus, this equation is not an identity.

Answer:

yes b is a right answer hope it will help you and please make me brainlist

The plumber bought 5 pieces of copper wire and 5 pieces of plastic wire.

What is an equation?

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.

Length of each piece of copper wire = 6 m

Length of each piece of plastic wire = 1 m

Total number of pipes bought = 10

Total length of pipes = 35 m

Let the number of copper pipes be x.

Let the number of plastic pipes be y.

The equation for number of pipes will be -

x + y = 10...(1)

The equation for length of pipes will be -

6x + y = 35...(2)

Subtracting equation (1) from (2) -

5x = 25

x = 5

Substituting the value of x in equation (1) -

5 + y = 10

y = 10 - 5

y = 5

Therefore, the number of copper and plastic wires is 5 each.

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The required dilated coordinates of the quadrilateral is given as,
D'  {-4, 2}, E' (-8/3, -2), F' (10/3, -4/3), and G'  (-2, 2).

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
Initial corrdiantes

D = (-6, 3)
G = (-3, 3)
E = (-4, -3)
F = (5, -2)

Dilated coordinates of a quadrilateral with by scale factor of 2/3 is given as,
D' = (-6 × 2 / 3, 3 × 2 / 3)

D' = {-4, 2}

Similarly,

G = (-2, 2)
E = (-8/3, -2)
F = (10/3, -4/3)

Thus, the required dilated coordinates of the quadrilateral is given as,
D'  {-4, 2}, E' (-8/3, -2), F' (10/3, -4/3), and G'  (-2, 2).

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Answer: The formula for the mathematical function that takes as input an RGB color vector ⟨r,g,b⟩ and yields as output the RGB color vector that is the unique shade of gray whose total amount of light (r+g+b) is equal to that of the input is:

(r+g+b)/3, (r+g+b)/3, (r+g+b)/3

Step-by-step explanation: RGB color space is a way to represent colors digitally, where each color is represented by a combination of red, green, and blue values ranging from 0 to 255. To obtain a unique shade of gray whose total amount of light (r+g+b) is equal to that of the input color, we have to set all three color channels to the average value of the red, green and blue values.

To calculate this average value we use the formula: (r+g+b)/3

So the output of the function is ⟨(r+g+b)/3, (r+g+b)/3, (r+g+b)/3⟩ which is the unique shade of gray whose total amount of light is equal to that of the input color.

Note: This is one way to convert color to gray, other methods exist like using luminosity or other weights to RGB channels.

The total number of oranges that the trader bought is 31

A trader bought some oranges at the price of #50 each

He finds that Six of these oranges are rotten

He sells the remaining at #80

He makes a profit of #450

Therefore the number of oranges that the trader bought is

Let y represent the number of oranges that the trader bought

At a price of #50= 50x

6 oranges were rotten= x-6

Profit = 450

450= 80(x-6)-50x

450= 80x-480-50x

450= 80x-50x-480

450= 30x-480

450+480= 30x

930= 30x

x= 930/30

x= 31

Hence the trader bought 31 oranges

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Answer: To find how long it takes Kyle to reach school, we can use the formula:

Time = Distance / Speed

Given that Kyle's parents travel at a constant speed of 40 km/h and the distance from their house to school is 60 km, we can substitute these values into the formula:

Time = Distance / Speed = 60 km / 40 km/h

To convert the answer from hours to minutes we have to multiply the result by 60.

Time = (60 km / 40 km/h) * 60 = 1.5 * 60 = 90 minutes

So it takes Kyle 90 minutes to reach school from their house if their speed is constant at 40 km/h and the distance they are traveling is 60 km.

Step-by-step explanation:

The interest George Jimerson would earn by June 30 be $83368.21

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Let y represent the amount of money in Jimerson savings account after x days.

The account pays 5.5% interest compounded daily, hence:

y = 6521.37(1.055)ˣ

In June 30, the number of days from April 11 is 49. Hence;

y = 6521.37(1.055)⁴⁹ = 89889.58

The interest = 89889.58 - 6521.37 = 83368.21

The interest would be $83368.21

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Answer:

30cm

Step-by-step explanation:

it will be the root of 900cm²

=30cm

The total height of the building would be nh + 30.

Option (B) is correct.

What is a simplification in mathematics?

In mathematics, simplification refers to the process of making an expression or equation simpler or easier to understand or work with. This can involve combining like terms, removing unnecessary terms or factors, or rearranging the order of the terms.

The building's total height in feet is represented by the sum of the height of each floor plus the height of the spire.

So if the height of each floor is h, and there are n floors in the building and the building's spire is 30 feet, the total height of the building is:

= n * h + 30

=nh + 30

This is because the height of each floor is h, and there are n floors, so the total height of the floors is n * h. Adding the height of the spire, 30 feet, to the total height of the floors gives nh + 30.

Hence, the total height of the building would be nh + 30.

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Answer:

1.  Hypothesis: "All 120° angles"

    Conclusion: "are obtuse angles"

    If-then statement: If an angle measures 120°, then it is an obtuse angle.

2.  It is not raining.

Step-by-step explanation:

Conditional statement

"If this happens, then that will happen."

For the statement "All 120° angles are obtuse angles":

Therefore, the statement written in the if-then form is:

Given statement:

The definition of a negation of a statement is the opposite of the given statement.  For example, the negation of statement "p" is "not p."

Therefore, the negation of the given statement is:

Answer:

x = 4

Step-by-step explanation:

We can look at the hypotenuse of both the triangles to find the factor that we multiply by. (In similar triangles, corresponding sides are always in the same ratio)

Big triangle:little triangle

25:5

5:1

So, we have to multiply the corresponding side of the little triangle by 5 to get an equivalent value.

Solve for x:

3x+8 = 4(5) [ratio!!]

3x+8 = 20

(subtract 8 from both sides)

3x = 12

(divide both sides by 3)

x = 4

Thus, we have our answer!

The regression equation, given the line of best fit and the points on the line, would be F ( x ) = 30x + 685

To find the regression equation, you first need to find two points on the line on the graph. Those two lines would be ( 3, 775) and ( 4 , 805).

The next step would be to find the slope of the line :

= ( Y₂ - Y ₁ ) / ( X ₂ - X  ₁ )

= ( 805 - 775 ) / ( 4 - 3 )

= 30 / 1

= 30

Then use the points to find the y - intercept :

y =  mx + y- intercept

775 = 30 ( 3 ) + y - intercept

y - intercept = 775 - 90

y - intercept = 685

The regression equation is:

F ( x ) = 30x + 685

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Answer:

5/12

Step-by-step explanation:

Use associative property of addition:

2/5 + 5/12 + (-2/5) = (2/5 + (-2/5)) + 5/12  ==> switch 5/12 and -2/5

(2/5 + (-2/5)) + 5/12 =    ==> simplify

(2/5 - 2/5) + 5/12 =

0 + 5/12 = 5/12

Answer:

You can buy 17 oranges for rupee 24.

Step-by-step explanation:

3 dozen = 3 x 12 = 39 oranges

54 ÷ 39 = 1.38461538462

1 orange = rupee 1.38

1.38461538462 x 17 = 23.5384615385

17 oranges = rupee 23.54

If you add the cost of 1 more orange it would cost more than rupee 24 so you can only buy 17 oranges for rupee 24.

Hope this helps :)

The side length of the triangle AC and BC will be 72 and 31. Then the correct option is A.

The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.

The sine law in the triangle ΔABC is given as,

AB / sin C = BC / sin A = AC / sin B

In triangle ABC, ∠A = 25°, ∠C = 55° and AB = 60. Then the third angle is given as,

∠A + ∠B + ∠C = 180°

25° + ∠B + 55° = 180°

∠B = 100°

Then the length of BC is given as,

60 / sin 55° = BC / sin 25°

BC = 30.955

BC ≈ 31

Then the length of AC is given as,

60 / sin 55° = AC / sin 100°

AC = 72.134

AC ≈ 72

The side length of the triangle AC and BC will be 72 and 31. Then the correct option is A.

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Answer: 1/2 PI actually ez not gonna lie

Step-by-step explanation: We know that pi times radius squared times 45/360 equals 1/2 pi. PI*radius^2*0.125 = 1/2PI. Solve algebra to get r^2 = 4 or radius = 2. We need the diameter to find circumference. D = 2*r or D = 4. D * PI * 45/360 = answer. We get 4 * PI * 0.125 = 1/2 PI

Answer:

y = 5/4x - 8

Step-by-step explanation:

first you convert the equation to y = mx + b

then you add the the -8 into the x and the 2 into the y and solve for b

b = -8 and since it is parallel same slope.

hope this helps :)

Staff at the learning center can teach whole groups of students who need extra help or focus on working one-on-one with a specific child. They work on improving knowledge of academic subjects like biology as well as skills like reading comprehension.

Learning centre instructors work in programmes that assist at-risk students in strengthening their academic skills. Learning centre instructors can work for a private or public learning centre. Learning centre instructors work with students to teach them valuable skills and academic subjects no matter where they work.

Learning centre instructors can teach large groups of students who require extra assistance or work one-on-one with a specific child. They work on improving academic knowledge, such as biology, as well as skills, such as reading comprehension.

They are in charge of creating the overall curriculum and training programme. Learning centre instructors must also have excellent classroom management skills as well as patience in order to work with students who are experiencing difficulties.

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