There were 81 people sitting in a school auditorium of which 19 were teachers, while the rest were students. How many teachers were sitting in the auditorium?

Answer:

None

Step-by-step explanation:

Answer:

x<-2

Step-by-step explanation:

17+4x<9

4x<-8

x<-2

The solution is:

Work/explanation:

Recall that the process for solving an inequality is the same as the process for solving an equation (a linear equation in one variable).

Make sure that all constants are on the right:

\(\bf{4x < 9-17}\)

\(\bf{4x < -8}\)

Divide each side by 4:

\(\bf{x < -2}\)

Answer:

12

Step-by-step explanation:

9/0.75 = 12

Answer:

4 units

Step-by-step explanation:

The measure of segment ED is 4 units.

Given In ΔCAB, point E is the midpoint of segment AC and point D is the midpoint of segment BC.

And AB is 8 units.

We have to calculate the length of segment ED.

We know that, The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side. This theorem is known as the mid point theorem.

So in  ΔCAB, E and D are the midpoint of AC and BC respectively then the length of DE is half of AB which is  \(\frac{8}{2}\) \(=4\) units.

Hence the measure of segment ED is 4 units.

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The length of a diagonal from one corner of the garden to the opposite corner is equal to the square root of the sum of the squares of the lengths of the sides of the garden. So, the length of the diagonal is about 20.2 meters.

Here's the solution:

Let d be the length of the diagonal.

We know that the length of the garden is 15 m and the width of the garden is 13.70 m.

We can use the Pythagorean theorem to find the length of the diagonal:

d^2 = 15^2 + 13.70^2

d = sqrt(15^2 + 13.70^2)

d = sqrt(225 + 187.69)

d = sqrt(412.69)

d = 20.2 m (rounded to the nearest tenth)

The simplified expression is -4mv.

We have,

To simplify the expression:

-20(m²v)(-v³) / 5(-v²)(-m^4)

We can first cancel out common factors in the numerator and denominator.

-20(m²v)(-v³) / 5(-v²)(-m^4)

= -4m²v² / vm²

Next, we can simplify further by canceling out a factor of v in the numerator and denominator:

-4m²v² / vm² = -4mv

Therefore,

The simplified expression is -4mv.

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Therefore , the solution of the given problem of equation comes out to be  option c is correct 2y = f(x) .

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation

y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given :

Every point on the graph in red is 1/2 away from the x-axis as that of the equivalent position on the graph in black.

Therefore, the vertically scale factor is equal to 1/2:

=> y = (1/2)f(x)

This problem can be solved by multiplying it by two and yields the following solution:

=> 2y = f(x)

thus , option c is correct

Therefore , the solution of the given problem of equation comes out to be  option c is correct 2y = f(x) .

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Answer:

9200

Step-by-step explanation:

9.2x10^3 is the same as saying 9.2 multiply 10 three times

Answer:

Red, Yellow, Blue

Step-by-step explanation:

They are the primary colors,

or you can use Violet, Green, And Orange

These are secondary colors

Answer:

-1

Step-by-step explanation:

I'm just good like that

Answer:

Hello!!

If Given drinks \(\frac{1}{3}\) liter of milk each day. He will drink...

a) \(2\frac{1}{3}\) liters of milk in a week.

Hope this helps

If h(x) = f(x)g(x) and h'(x) = f(x)g'(x), then f(x) = 1.

Let f and g be differentiable functions such that g(x)>0 for all x and f(0)=1.

We can then write h(x) = f(x)g(x). Taking the derivative of h(x) with respect to x, we get:

h'(x) = f'(x)g(x) + f(x)g'(x)

Since h'(x) is equal to f(x)g'(x), then we can cancel out f(x)g(x) from both sides to get:

f'(x)g(x) = 0

Since g(x) is always greater than 0, this implies f'(x) = 0. This means that f(x) is a constant function. Since f(0) = 1, then f(x) = 1 for all x.

Therefore, if h(x) = f(x)g(x) and h'(x) = f(x)g'(x), then f(x) = 1.

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Answer:

I’m pretty sure it’s A but if not then D

Step-by-step explanation:

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given expression

STEP 2: Multiply the constant with the leading term

STEP 3: Write the possible factors of the result in product form

STEP 4: Find the factors that will give the second term (-7x) when added

STEP 5: Substitute these factors for -7x in the expression in step 1

STEP 6: Factorize by grouping

Hence, the factors of the given expression are:

The break-even point is 1100 products sold. This means that if the store can sell 1100 products, it will be able to cover its costs and make a profit.

What is average ?

The average is a measure of central tendency that is calculated by adding a set of values together and dividing the sum by the number of values. It is also known as the arithmetic mean. It is a way to represent a typical value of a dataset.

The break-even point is the point at which the cost of the products equals the revenue from the sales of the products. To find the break-even point, we need to set the cost function (C(x) = 550 + 3.00x) equal to the revenue function (R(x) = 5.50x) and solve for x.

C(x) = 550 + 3.00x = R(x) = 5.50x

3.00x = 5.50x - 550

0.50x = 550

x = 1100

So the break-even point is 1100 products sold. This means that if the store can sell 1100 products, it will be able to cover its costs and make a profit.

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\(\stackrel{ x-intercept }{(\stackrel{x_1}{9}~,~\stackrel{y_1}{0})}\qquad \stackrel{ y-intercept }{(\stackrel{x_2}{0}~,~\stackrel{y_2}{-9})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-9}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{9}}} \implies \cfrac{ -9 }{ -9 } \implies \cfrac{1}{1}\implies 1\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{ 1}(x-\stackrel{x_1}{9})\implies {\Large \begin{array}{llll} y=x-9 \end{array}}\)

The area of Unnex is 7,640 square miles, and the area of Biron is 14,320 square miles.

Let's denote the area of Unnex as "U" and the area of Biron as "B."

According to the given information, Nonlief initially had an area of 36,200 square miles. After Unnex seceded, Nonlief's area reduced to 28,560 square miles. This means that the area of Unnex is the difference between the initial area of Nonlief and the area remaining after Unnex seceded:

U = Initial area of Nonlief - Area remaining after Unnex seceded

U = 36,200 - 28,560

U = 7,640 square miles

Next, we are told that after Biron seceded, Nonlief was left with an area of 21,880 square miles. To find the area of Biron, we need to subtract the remaining area from the area before Biron seceded:

B = Area before Biron seceded - Remaining area after Biron seceded

B = 36,200 - 21,880

B = 14,320 square miles

Unnex therefore has an area of 7,640 square miles, while Biron has an area of 14,320 square miles.

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The dimensions that maximize the area are 150ft × 300ft.

So, let y be the length of the side parallel to the river and x be the length of each of the two sides perpendicular to it.

The following provides the total fencing length:

The rectangular pen's surface area is:

We may determine the value of x required to maximize the area by determining the value of x for which the derivative of the area function is zero:

The value of y is: for x=150

Therefore, the dimensions that maximize the area are 150ft × 300ft.

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System state space model is: y = [1  0] x. y = 4 is an equilibrium point.  x(t) = P∧(Dt)P−1 x(0) is the state transition matrix. The system is stable. The transfer function of the system is U(s)X(s) = [(s-2)²+ 4]⁻¹ [(s-2)  -2; 2  (s-2)] [0 2].

(a) i) System state space model:

x = [y  y']T;

dx/dt = [0  2; -1  1]x + [0  2]T u;

y = [1  0] x

Here, x represents the state vector.

ii) The equilibrium point(s) of the system if u is a constant value equal to 4: dy/dt = 0

Thus, 2y = 8 or y = 4. Therefore, y = 4 is an equilibrium point.

(b) The state transition matrix for autonomous linear systems is derived as follows:

If A is diagonalizable, then there exist an invertible matrix P and diagonal matrix D such that A = PDP−1.

Thus, x(t) = P∧(Dt)P−1 x(0) is the solution where exp(Dt) is calculated from the diagonal entries of D and t is the time of propagation.

(c) i)The stability of the system is determined by the eigenvalues of the system matrix A. If all the eigenvalues have a negative real part, the system is stable. If one of the eigenvalues has a positive real part, the system is unstable. And, if one eigenvalue has a zero real part, the system is marginally stable. Since the system has two eigenvalues with negative real parts, it is stable.

ii) The transfer function of the system is given as follows:

U(s) → X(s): X(s) = (sI − A)−1 B U(s)Y(s) → X(s): Y(s) = CX(s) = C(sI − A)−1 B U(s)

Thus, substituting the values of A, B, and C we get,Y(s) = [1 -1] [(s-2)²+ 4]⁻¹ [(s-2)  -2; 2  (s-2)] [0 2]

U(s)X(s) = [(s-2)²+ 4]⁻¹ [(s-2)  -2; 2  (s-2)] [0 2]

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The given statement is not true because the actual distance between two towns is greater than 100 times the map distance since 100 miles is more than 100 times as great as 1 inch.

We are given the scale of the map as;

1 inch : 100 miles

What this means is that 1 inch on the map represents an actual distance of 100 miles.

Now, from conversion values, we know that;

1 mile = 63360 inches

Now, the question is trying to suggest that the actual distance between two towns 100 times the map distance between the two towns

The given statement is not true because as seen from the conversion above, the actual distance between two towns is greater than 100 times the map distance since 100 miles is more than 100 times as great as 1 inch.

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Daniel and Maria must babysit for 6 hours for their total fees to be the same.

To find the number of hours at which Daniel and Maria have the same total fee, we need to compare their fee structures and determine when their fees are equal.

Daniel charges a flat fee of $10 plus $6 per hour. So his total fee can be represented by the equation:

Total fee (Daniel) = $10 + $6 * Number of hours

Maria's total fee is given in the table. We can see that the total fee increases by $4 for every additional hour. So we can represent Maria's total fee by the equation:

Total fee (Maria) = $22 + $4 * Number of hours

To find the number of hours at which their fees are equal, we set the two equations equal to each other and solve for the number of hours:

$10 + $6 * Number of hours = $22 + $4 * Number of hours

Simplifying the equation, we get:

$6 * Number of hours - $4 * Number of hours = $22 - $10

$2 * Number of hours = $12

Dividing both sides by $2, we find:

Number of hours = $12 / $2

Number of hours = 6

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No , Sydney does not have enough beads to make 15 rings .

beads required for one ring = 60

total rings she have to make is = 15

total beads she has to make rings = 852 beads

now,

60 beads make ring = 1

852 beads make rings = 1/60 x 852

                                     =    14.2 rings

                             OR

                          14 total rings

So , Sydney does not have enough beads to make 15 rings . she can only make 14 beads from the given amount of beads.

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Answer:

it's 50

Step-by-step explanation:

hope this helps you !

Answer:

12.5 divided. By 0.25 is 50

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Part A: The real part of (A + B) is 9.7

Part B: The imaginary part of (A + B) is approximately 5.68

Part C: The real part of (A - B) is -3.5

Part D: The imaginary part of (A - B) is approximately -0.14.

Given that,

A = 3.1∠63.2°  

B = 6.6∠26.2°

Part A: To find the real part of (A + B), we add the real parts of A and B.

In this case,

The real part of A is 3.1 and the real part of B is 6.6.

Adding them together, we get:

Real part of (A + B) = 3.1 + 6.6 = 9.7

So, the real part of (A + B) is 9.7.

Part B: To find the imaginary part of (A + B),

Add the imaginary parts of A and B.

In this case,

The imaginary part of A can be calculated using the formula

A x sin(angle),

Which gives us:

Imaginary part of A = 3.1 x sin(63.2°)

                                ≈ 2.77

Similarly, for B:

Imaginary part of B = 6.6 x sin(26.2°) ≈ 2.91

Adding these together, we get:

Imaginary part of (A + B) ≈ 2.77 + 2.91

                                        ≈ 5.68

So, the imaginary part of (A + B) is approximately 5.68.

Part C: To find the real part of (A - B),

Subtract the real part of B from the real part of A.

In this case,

The real part of A is 3.1 and the real part of B is 6.6.

Subtracting them, we get:

Real part of (A - B) = 3.1 - 6.6

                               = -3.5

So, the real part of (A - B) is -3.5.

Part D: To find the imaginary part of (A - B),

Subtract the imaginary part of B from the imaginary part of A.

Using the previously calculated values, we have:

Imaginary part of (A - B) ≈ 2.77 - 2.91

                                        ≈ -0.14

So, the imaginary part of (A - B) is approximately -0.14.

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Answer:

line TU is parallel to line RS

Step-by-step explanation:

edg2020

Answer: line TU is parallel to line RS

Step-by-step explanation:

Answer:

No because their ratios are not the same

Step-by-step explanation:

The scalar from 5 to 10 is 2 but from 3 to 4, its 4/3.

The surface area and volume to the nearest hundredth are 276.32 square units and 351.68 cubic units respectively.

In Mathematics and Geometry, the surface area of a cylinder can be determined by using the following mathematical equation (formula):

SA = 2πrh + 2πr²

Where:

By substituting the given parameters, we have the following;

Surface area = 2πrh + 2πr²

Surface area = 2(3.14)(4)(7) + 2(3.14)(4²)

Surface area = 175.84 + 100. 48

Surface area = 276.32 square units.

Next, we would determine the volume of this cylinder by using this formula:

Volume of cylinder, V = πr²h

Volume of cylinder, V = (3.14)(4²) × 7

Volume of cylinder, V = 351.68 cubic units.

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