Solve and describe the steps used to find x for the equation: 7x-4=-4x+18

Answer:

Scores of students:

Mean: 34.3

Mode: no mode

No. of students:

Mean: 8.3

Mode: no mode

Step-by-step explanation:

(for scores of students)

6, 30, 35, 40, 45, 50

Mean: 6 + 30 + 35 + 40 + 45 + 50 = 206/6 = 34.3

Mode: there are no mode in the set of data.

(for No. of students)

4, 5, 6, 8, 12, 15

Mean: 4 + 5 + 6 + 8 + 12 + 15 = 50/6 = 8.3

Mode: no mode

Answer:

Step-by-step explanation:

The hours that each student attend school each day is  7 hours.

The first step is to convert minutes to hours.

60 minutes = 1 hour

6300 / 60 = 105 hours

The second step is to determine the number of days the students was in school in 3 weeks: 3 x 5 = 15 days.

Now, divide 105 by 15: 105/15 = 7 hours

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Answer:

x= -0 5 or x =5

Step-by-step explanation:

Split into two equations:−4x+9=11 or −4x+9=−11

Rearrange unknown terms to the left side of the equation:−4x=11−9

Calculate the sum or difference:−4x=2

Divide both sides of the equation by the coefficient of variable:x=2÷(−4)

Remove the parentheses:x=−2÷4

Calculate the product or quotient:x=−0.5

Rearrange unknown terms to the left side of the equation:−4x=−11−9

Calculate the sum or difference:−4x=−20

Divide both sides of the equation by the coefficient of variable:x=−20÷(−4)

Remove the parentheses:x=20÷4

Calculate the product or quotient:x=5

Combine the results:x=−0.5 or x=5

:When x=−0.5

:LHS=|−4×(−0.5)+9|=11

:RHS=11

The sinusoidal function that models the situation is:

\(y = 4.5\sin{\left(\frac{\pi}{12}\right)x} + 5\)

From the function, we have that:

A sinusoidal function is a trigonometric function, and has the following format, considering no phase shift:

\(y = A\sin{(Bx)} + C\)

In which:

In this problem, the high is of 9.5 ft and the low is of 0.5 ft, hence, for the amplitude, we have that:

\(2A = 9\)

\(A = \frac{9}{2}\)

\(A = 4.5\)

With an amplitude of 4.5, the standard function would vary between -4.5 ft and 4.5 ft, while in this problem the variation is from 0.5 ft to 9.5 ft, hence the vertical shift is of:

\(C = 9.5 - 4.5 = 4.5 - (-0.5) = 5\)

Which means that the mid-line equation is of y = 5.

Period of 24 hours, hence:

\(\frac{2\pi}{B} = 24\)

\(24B = 2\pi\)

\(B = \frac{\pi}{12}\)

Hence, the function is:

\(y = 4.5\sin{\left(\frac{\pi}{12}\right)}x + 5\)

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Answer:

6=100°

8=80°

7=100°

9=80°

Step-by-step explanation:

If 6 is 100°

in a straight line theres 180 degrees

180-100=80°

8 is 80°

opposite 6 to 7 there are parallel corresponding angles meaning the angle opposite it will be the same. 8 with 9.

same with

The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).

To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,

which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).

Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.

Substituting these values into the formula for volume,

we get:11.35 = 2.6 × 1.1 × h

Simplifying this expression:

11.35 = 2.86h

Dividing both sides by 2.6 × 1.1,

we get:h ≈ 3.64 feet (rounded to two decimal places)

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The given system is

First, we multiply the second equation by -3.

Then, we combine the equations

This means the system has infinitely many solutions.

If the daughter does not want more than 2,250,000 square feet of the corn maze, hence she will choose all the portions

The formula for calculating the area of circle is expressed as;

A  = πr²

r is the radius of the circle

If r = 875ft

A = 3.14(875)²

A = 2,404,062.5squar feet

For the diameter = 1715feet

r = 1715/2

A = 3.14(1715/2)²

A =2,308,861.625 square feet

For the third portion has a 5305 feet circumference;

5305 = 2(3.14)r

r = 844.74ft

A = 3.14(844.74)^2

A = 2,240,686.70

If the daughter does not want more than 2,250,000 square feet of the corn maze, hence she will choose all the portions

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the person above has the correct work.. but the answer is  the portion with the 5305 feet circumference.

Answer:

3x² - 14x + 15

Step-by-step explanation:

Step 1: Write expression

(x - 3)(3x - 5)

Step 2: FOIL

3x² - 5x - 9x + 15

Step 3: Combine like terms

3x² - 14x + 15

To find the exact value of (7π/6) using the unit circle, locate the angle (π/6) on the unit circle in the second quadrant, determine the coordinates, and adjust the y-coordinate to be negative. The final answer is (√3/2, -1/2). This answer is obtained by understanding the reference angle and using the coordinates of the point where the angle intersects the unit circle.

To find the exact value of (7π/6) using the unit circle, follow these steps:

1. Start by understanding the reference angle. The reference angle for (7π/6) is (π/6).

2. Locate the angle (π/6) on the unit circle. This angle lies in the second quadrant.

3. Determine the coordinates of the point where the angle intersects the unit circle. For (π/6), the x-coordinate is √3/2 and the y-coordinate is 1/2.

4. Since (7π/6) lies in the second quadrant, the x-coordinate will remain the same, but the y-coordinate will be negative. Therefore, the coordinates for (7π/6) are (√3/2, -1/2).

5. The exact value of (7π/6) is (√3/2, -1/2).

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There are 15 cats in the animal shelter.

An equation in which is  the highest power of to the  variables 1 is knowns as the  linear equation. Mathematically: it is an  algebraic equations that can be also  written in the form of  ax + b = 0 or ax + by + c = 0, where a, b and c are definitely real numbers and x and y are variables with the highest power one.
In order to solve this problem, we must set up a proportion. Proportions are an equation that states that two ratios are equal. In this case, we are looking for the number of cats (c) in the animal shelter.

Let's set up the proportion.

5/3 = 25/c

We can then solve for c by multiplying both sides by c.

5c/3 = 25

c = 15

Therefore, there are 15 cats in the animal shelter.

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There are  0.09779 grams in 7.4 x 10^19 Atoms of copper.

The number of grams in a given number of atoms of an element, we need to use the concept of molar mass and Avogadro's number.

The molar mass of an element represents the mass of one mole of that element. For copper (Cu), the molar mass is approximately 63.546 grams per mole.

Avogadro's number, denoted as N_A, is the number of atoms or molecules in one mole of a substance. It is approximately 6.022 x 10^23 atoms/molecules per mole.

To calculate the mass of a given number of atoms, we can use the following steps:

Step 1: Determine the number of moles of copper atoms.

Given: 7.4 x 10^19 atoms of copper

Number of moles = (Number of atoms) / (Avogadro's number)

Number of moles = (7.4 x 10^19) / (6.022 x 10^23)

Step 2: Calculate the mass using the molar mass of copper.

Mass = (Number of moles) x (Molar mass)

Mass = (7.4 x 10^19) / (6.022 x 10^23) x 63.546

Now, we can perform the calculations:

Mass ≈ 0.09779 grams

Therefore, there are approximately 0.09779 grams in 7.4 x 10^19 atoms of copper.

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a)The value of  ∠b=64°.

b)The values of angles q, r, s, t are ∠q= 65°, ∠r=65°, ∠s=50°, ∠t=65°.

c)The value of  ∠B=72 degrees.

The same-side interior angles are additional if a transversal connects two parallel lines. Alternate interior angles are equivalent if a transversal connects two parallel lines. Corresponding angles are equal.

a) Given line PQ is parallel to ST.

   One of the theorems of parallel lines is, Corresponding angles are equal.

Here the corresponding angles are ∠a, ∠b.

so, ∠a=∠b

∴∠b=64°

b) It is given that lines B and C are parallel, according to one of the theorems of parallel lines, vertically opposite angles are equal. So, the angle opposite to 65° is also equal to 65°. Sum of the angles suspended by a line on another line is 180°. Therefore the other angle in the triangle is 180°-130°=50°.

Since the sum of interior angles in a triangle is 180°, the angle q will be:

   ∠q= 180°-(65°+50°)

    ∠q= 65°.

Vertically opposite angles are equal, therefore ∠q=∠r=65°.

∠s=180°-(65°+65°)

∠s=50°.

Corresponding angles are equal, therefore

130°=65°+∠t

∠t=65°.

c) Given lines A, and B are parallel. We know that the Corresponding angles are equal, therefore

3m=4m-24

⇒m=24

Therefore ∠B=4(24)-24

∠B=72 degrees.

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Each letter should be matched to its correct term as follows;

1. A ⇔ Efficiency.

2. B ⇔ Impossible.

3. C ⇔ Inefficiency.

In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;

Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;

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True, the given function f has an inverse.

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.  Inverse functions f and g result in f(x) = y if and only if g(y) = x.

Under the given condition, we can define the function g on the set of the images  {b | b = f(a), a belongs to A}  in a way

   g(b) = a,   if f(a) = b.

This function is defined correctly on this set and is the inverse function to f.

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Charles should hire 20 workers for each hour.

To determine the optimal number of workers to hire, Charles needs to compare the marginal cost and marginal benefit of each additional worker.

The marginal benefit of each worker is the additional number of drinks they can produce multiplied by the average selling price per drink. The marginal cost is the hourly wage of each worker multiplied by the number of hours they work.

Initially, the marginal benefit of the first worker is 20 drinks * $3/drink = $60.

The marginal cost is $15/worker * 8 hours = $120.

The second worker has a marginal benefit of 18 drinks * $3/drink = $54.

The marginal cost is still $120.

For each additional worker hired, the marginal benefit decreases by 2 drinks * $3/drink = $6, while the marginal cost remains constant at $120.

Charles should hire workers as long as the marginal benefit is greater than the marginal cost.

Once the marginal benefit is equal to or less than the marginal cost, it is no longer profitable to hire more workers.

Therefore, Charles should hire workers until the marginal benefit is equal to the marginal cost, which occurs when the marginal benefit is $120.

To find out how many workers will provide a marginal benefit of $120, we set the marginal benefit equal to $120 and solve for the number of workers:

$6 * n = $120

$n = 20

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Answer:

x = 2

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × breadth

given the rectangles have equal areas then equating the two areas gives

4x × 9 = 4(6x + 6) , that is

36x = 24x + 24 ( subtract 24x from both sides )

12x = 24 ( divide both sides by 12 )

x = 2

3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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Answer:

Step-by-step explanation:

the 2nd one!

Answer:

Your Answer should be B because you start at -1 and it decreases by -1

The solution to the differential equation \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\) is,

\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).

Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation.

The given differential equation is \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\).

Now, multiplying both sides by dx we,

\(2^{\sqrt{x}}dy = cosce(ln(y))dx\).

Dividing both sides by \(2^{\sqrt{x}}\) we have,

\(sin(ln(y))dy = \frac{dx}{2^{\sqrt{x}}}\).

\(\[ \int sin(ln(y))dy = \int \frac{dx}{2^{\sqrt{x}}}\).

\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).

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b1-h3, b2-h2, b3-h3.

Step-by-step explanation:

See the image.

Hope that helps! :)

(Can you please mark me as brainliest?)

The value of the angle ∠BAD of the given image is: 60°

The sum of angles in a triangle is 180 degrees. We know that the interior angles of an equilateral angle are equal and as such each of the angles of the equilateral triangle are 60 degrees.

Thus:

∠ADE = ∠AED = ∠DAE = 60 degrees

We know that alternate angles are angles that lie on opposite sides of the transversal line and on opposite relative sides of the other lines.

Thus:

∠BAD = ∠ADE = 60°

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The total surface area of the doghouse is 1452 ft²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The dog house has many surfaces including the roofs . The total surface area is the sum of all the area of the surfaces.

area of the roof part = 2( 13×11) + 2( 12× 10)×1/2

= 286 + 720

= 1006 ft²

surface area of the building

= 2( lb + lh + bh) -bh

= 2( 10× 11 + 10×8 + 11×8) - 10×11

= 2( 110+80+88)-110

= 2( 278) -110

= 556 -110

= 446ft²

The total surface area = 1006 + 446

= 1452 ft²

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Answer:

A

Step-by-step explanation:

is moving by 2 but there negative numbers which makes it -2

Answer:

0.5

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

you first do operation in the brackets and then multiply and then divide:

2*2*2*2*2 / 4 = 8

The difference in overall loss or gain between sell at the current day's high price or low price is found tp be the difference in overall gain as $280.10

The third option is correct.

High price value: 115 shares * $105.19 per share = $12,084.85

Low price value: 115 shares * $103.25 per share = $11,858.75

High price value: 30 shares * $145.18 per share = $4,355.40

Low price value: 30 shares * $143.28 per share = $4,298.40

The overall value at high price:

$12,084.85 + $4,355.40

= $16,440.25

The overall value at low price:

$11,858.75 + $4,298.40

= $16,157.15

In conclusion, the difference in overall gain or loss:

$16,440.25 - $16,157.15 = $280.10

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Answer:

c) 13%

Step-by-step explanation:

Given information,

→ The cost of a jacket increased from the price $75.00 to $84.75.

Now we have to,

→ find the % increase of cost of jacket.

Let's solve the problem,

→ ((84.75 - 75)/75) × 100

→ (9.75/75) × 100

→ 0.13 × 100

→ 13%

Hence, the answer is 13%.

Answer:

40% of £25.00 is 10

ypu answer should be £10

Step-by-step explanation: