Define the variables for the situation. Then enter an equation.
Andrew's class has 5 more students than Lauren's class.
a = Andrew's class
1 = Lauren's class
Enter an equation:
+

Answer:

0

Step-by-step explanation:

−2−(−4)−2

=2−2

=0

Answer:

Step-by-step explanation:

-2 - (-4) - 2   = -2 + 4 - 2

                    = -4 + 4

                   = 0

Hint : -(-4) = 4

Answer:

Points R(4,1) S(7,3) T(6,4) after translation

R(4-3, 1) S(7-3, 3) T(6-3, 4)

R'(1, 1) S'(4, 3) T'(3, 4)

Points R'(1, 1) S'(4, 3) T'(3, 4) after reflection

R''(1, -3) S''(4, -5) T''(3, -6)

Step-by-step explanation:

Answer:Step-by-step explanation:Points R(4,1) S(7,3) T(6,4) after translation R(4-3, 1) S(7-3, 3) T(6-3, 4) R'(1, 1) S'(4, 3) T'(3, 4) Points R'(1, 1) ...

The correct option is D.

An equation to determine the area, a, of the patio that will be painted :

a = (x + 25)(x + 15) - 30

Geometric shapes are the mathematical figures that show how ordinary objects in our world are shaped. Shapes in geometry are the configurations of things with boundary lines, angles, and surfaces.

Length of the rectangular patio is (x+25).

Width of the rectangular patio is (x+15).

Length of bench is 5.

Width of the bench is 1.

Area of a rectangle is:

A = Length x Width

Area of rectangular patio is:

A\(_1\) = (x + 25)(x + 15)

Area of bench is:

A\(_2\) = 10 x 3

   = 30

The painting area is:

A = A\(_1\) - A\(_2\)

A = (x + 25)(x + 15) - 30

Therefore, the correct option is D.

An equation to determine the area, a, of the patio that will be painted :

a = (x + 25)(x + 15) - 30

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 To show that the transformation T is not linear, we need to find a counterexample that violates either T(0) = 0 or T(cu + dv) = cT(u) + dT(v), where u and v are vectors, and c and d are scalars.

Let's consider the zero vector, u = (0, 0), and a non-zero vector v = (1, 1).

According to T(0) = 0, the transformation of the zero vector should yield the zero vector. However, T(0, 0) = (4(0) - 3(0), 0 + 5, 6(0)) = (0, 5, 0) ≠ (0, 0, 0). Thus, T(0) ≠ 0, violating the condition for linearity.

Next, let's examine T(cu + dv) = cT(u) + dT(v). We choose c = 2 and d = 3 for simplicity.

T(cu + dv) = T(2(0, 0) + 3(1, 1))

          = T(0, 0 + 3, 0)

          = T(0, 3, 0)

          = (4(0) - 3(3), 0 + 5, 6(0))

          = (-9, 5, 0).

On the other hand,

cT(u) + dT(v) = 2T(0, 0) + 3T(1, 1)

            = 2(4(0) - 3(0), 0 + 5, 6(0)) + 3(4(1) - 3(1), 1 + 5, 6(1))

            = 2(0, 5, 0) + 3(1, 11, 6)

            = (0, 10, 0) + (3, 33, 18)

            = (3, 43, 18).

Since (-9, 5, 0) ≠ (3, 43, 18), T(cu + dv) ≠ cT(u) + dT(v), violating the linearity condition.

In conclusion, we have provided counterexamples that violate both T(0) = 0 and T(cu + dv) = cT(u) + dT(v). Therefore, we can conclude that the transformation T defined by T(x1, x2) = (4x1 - 3x2, x1 + 5, 6x2) is not linear.

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Answer: B

Explanation:

If the first bus is boarded at a rate of 15 people per minute, the domain of the function is; (15 ≤ x ≤ 45)

We are told that;

Total number of Juniors at Smithers High School that are taking a class trip = 130

Number of buses taking each student to their destination = 3 buses

Capacity of each bus = 45 people

Now, if the function  f(x) describes the total number of people on the first

bus, where x is the number of minutes spent loading the bus.

Then since the maximum number of people on the first bus is 45, then it means that the domain of the function is;

(15 ≤ x ≤ 45)

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Answer:

A. 18x - 3y = 6

Step-by-step explanation:

By taking 3 common from the terms 18x and 3y we get,

3 (6x-3y) = 6

or, 6x - y = 6/3

or, 6x - y = 2

And,

The equation becomes,

y = 6x - 2

The equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

By taking 3 commons from the terms 18x and 3y we get,

3 (6x-3y) = 6

6x - y = 6/3

6x - y = 2

The equation becomes,

y = 6x - 2

Therefore, the equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

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Answer:

since it is a right triangle it is 35 i think

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Use the Pythagorean theorem:

a^2 + b^2 = c^2

35^2 + b^2 = 37^2

1225 + b^2 = 1369

b^2 = 44

b = 12

Answer: 12

Answer:

So let's say if we have a function f of x. Let's say it looks like this let's call this point a and point b. Now if the function f of x if it's continuous on the closed interval a b.

Step-by-step explanation:

The point c = 11/2 is the point in (-2, 2) such that f'(c) = (f(2) - f(-2))/(2 - (-2)).

The Mean Value Theorem states that if a function f is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) such that f'(c) = (f(b) - f(a))/(b - a). The Mean Value Theorem is a useful tool for finding the maximum and minimum values of a function on an interval.

To solve a Mean Value Theorem problem, the first step is to identify the function f, its domain of definition, and the interval [a, b]. Then, use the theorem to find the point c in the interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a).

For example, suppose we have the function f(x) = x2 + 3x + 4 defined on the interval [-2, 2]. To find the point c in the interval (-2, 2) such that f'(c) = (f(2) - f(2))/(2 - (-2)), we first calculate the derivatives of f(x). The derivative of f(x) is f'(x) = 2x + 3. Substituting x = 2 in the derivative gives f'(2) = 11. Now, we can use the Mean Value Theorem to find the point c:

f'(c) = (f(2) - f(-2))/(2 - (-2))

11 = (12 - (-2))/(2 - (-2))

11 = 14/4

c = 11/2

Therefore, the point c = 11/2 is the point in (-2, 2) such that f'(c) = (f(2) - f(-2))/(2 - (-2)).

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The expression which correctly represents the number of students studying German as required is; 3y + 2x -35.

It follows from the task content that the number of students studying German be determined from the given information.

Therefore since the total number of students is; 100.

35 students study Spanish of which y are boys, therefore, the number of girls studying Spanish is; (35 - y).

Also, since there are 3x girls in total and x of which study French, the remaining 2x study Spanish and German.

Hence, the number of girls who study German is; 2x - (35 - y).

Therefore, the total number of students (boys and girls) who study German is; 2y + 2x - (35 - y).

= 3y + 2x -35.

Ultimately, the total number of students who study German are; 3y + 2x -35.

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Answer: Jesus will have 36 dollars after 8 days

Step-by-step explanation: 8 x 8= 64

100-64=36

Answer: [b + 4 = -10]

Step-by-step explanation: We are given the equation b = -14 and told to, given this information, evaluate b + 4 = ? and find ?. Given b = -14 we can plug in -14 for b in b + 4 = ?. This gives us -14 + 4 = ?. Adding this up gives us the answer of -10. Hope that this makes sense and helps, and good afternoon to you!

-Show work-

\(b=-14\\(b)+4=?\)

\((-14)+4=?\)

\(10 = ?\\?=10\)

Answer:

A

Step-by-step explanation:

we know that xoy is 90° on every quadrant

also the origine where p start is a little bit down from x axis so A is the right answer as it is the most logical point

D and C cant be P because are a very large angle of rotation than 105.B is smaller then 105 rotation of p so A is the right one.

The distance traveled by the arrow cannot be determined from the given information. The distance traveled by the arrow depends on the speed at which it is fired, which is determined by the amount of energy released when the bowstring is released.

To prove that two functions are inverses of each other, it is necessary to show that both of the conditions f(g(x)) = x and g(f(x)) = x hold, but this does not necessarily mean that the two functions are equal.

We have,

This statement is not entirely correct.

To prove that two functions are inverses of each other, it is indeed necessary to show that both of the following conditions hold:

f(g(x)) = x for all x in the domain of g

g(f(x)) = x for all x in the domain of f

Now,

This does not necessarily mean that the two functions are equal to each other.

For example,

Consider the functions f(x) = x + 1 and g(x) = x - 1.

It can be shown that f(g(x)) = x and g(f(x)) = x for all values of x, which satisfies the conditions for being inverses of each other.

However, it is clear that f(x) and g(x) are not the same functions.

Thus,

To prove that two functions are inverses of each other, it is necessary to show that both of the conditions f(g(x)) = x and g(f(x)) = x hold, but this does not necessarily mean that the two functions are equal.

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The function g(t) is calculated to has one relative minimum and two absolute extrema over the domain [-1, 1].

To find the relative and absolute extrema of the function g(t) = \(e^{t}\) - t over the domain [-1, 1], we need to follow these steps:

Find the critical points of g(t) by setting its derivative equal to zero and solving for t.

Test the sign of the second derivative of g(t) at each critical point to determine whether it corresponds to a relative maximum, relative minimum, or an inflection point.

Evaluate g(t) at the endpoints of the domain [-1, 1] to check for absolute extrema.

Step 1: Find the critical points of g(t)

g'(t) = .\(e^{t}\) - 1

Setting g'(t) equal to zero, we get:

\(e^{t}\) - 1 = 0

\(e^{t}\) = 1

Taking the natural logarithm of both sides, we get:

t = ln(1) = 0

So, the only critical point of g(t) in the domain [-1, 1] is t = 0.

Step 2: Test the sign of the second derivative of g(t)

g''(t) = e^t

At t = 0, we have g''(0) = e⁰ = 1.

Since g''(0) is positive, the critical point t = 0 corresponds to a relative minimum.

Step 3: Evaluate g(t) at the endpoints of the domain [-1, 1]

g(-1) = e⁻¹ - (-1) = e⁻¹ + 1 ≈ 1.37

g(1) = e⁻¹ - 1 = e - 1 ≈ 1.72

Since g(t) is a continuous function over the closed interval [-1, 1], it must attain its absolute extrema at the endpoints of the interval. Therefore, the absolute minimum of g(t) over [-1, 1] occurs at t = -1, where g(-1) ≈ 1.37, and the absolute maximum occurs at t = 1, where g(1) ≈ 1.72.

To summarize:

Relative minimum: g(0) ≈ -1

Absolute minimum: g(-1) ≈ 1.37

Absolute maximum: g(1) ≈ 1.72

Therefore, the function g(t) has one relative minimum and two absolute extrema over the domain [-1, 1].

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No, a triangle cannot have two sides.

A triangle is a three-sided polygon with three edges and three vertices in geometry. The total of a triangle's internal angles equals 180 degrees, which is its most important feature. This is known as the angle sum property of a triangle.

Triangle is a closed two-dimensional shape. It is a three-sided polygon. All sides are made of straight lines.

If ABC is a triangle, it is denoted as ABC, where A, B, and C are the triangle's vertices. In Euclidean geometry, a triangle is a two-dimensional shape represented by three non-collinear points in a single plane.

Thus, No, a triangle cannot have two sides.

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Answer:

8.16666666667

Step-by-step explanation:

Answer:

7-2x=y

Step-by-step explanation:

When a point passes through a line it satisfies its equation

(X-x0 )m= y-y0

Slope = m = -2

(X-2 )(-2)=y-3

4-2x=y-3

7-2x=y

Answer:

x=2

y=16

Step-by-step explanation:

fill in y

2x+(6x+4)=20

8x+4=20

   -4.  -4

8x=16

/8. /8

x=2

Now fill in X to find y

y=6(2)+4

y=12+4

y=16

Hopes this helps please mark brainliest

Answer:

The first answer is incorrect

Step-by-step explanation:

45 divided by 9 is 5 not 40

The equation that represents the statement is j / 9 = 5.

An equation is a mathematical statement that is formed when two algebraic expressions are equated using an equal sign.

The statement j divided by 9 is 5 can be written in equation form as follows:

j / 9 = 5

j = 45

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Answer:

Step-by-step explanation:

A percentage is a way of expressing a part of a whole in terms of 100 parts. For example, 50% means 50 out of 100, or half of the whole. Sometimes, percentages can be more than 100%, which means more than the whole. For example, if you have a hot dog stand and sell 10 hot dogs in the morning and 30 hot dogs in the afternoon, you can say that you sold 300% more hot dogs in the afternoon than in the morning1.

However, in some situations, percentages more than 100% do not make sense. For example, you cannot have more than 100% of your time, money, or energy. In your question, you are given the percentages of singers in a choir who have brown hair and black hair. These percentages are based on the total number of singers in the choir, which is 100. Therefore, it is not possible for 62% of them to have brown hair and 48% of them to have black hair at the same time, because that would add up to more than 100%. The only way this could be possible is if some singers had both brown and black hair, but that is unlikely.

To illustrate this with a picture, you can use a pie chart to show the percentages of singers with different hair colors. A pie chart is a circle divided into slices that represent parts of a whole. The size of each slice is proportional to the percentage it represents. Here is an example of a pie chart for a choir with 50% brown hair and 50% black hair:

As you can see, each slice takes up half of the circle, or 180 degrees. The total angle of a circle is 360 degrees, so the sum of the angles of all the slices must be equal to 360 degrees. This means that the sum of the percentages of all the slices must be equal to 100%. If you try to make a pie chart for a choir with 62% brown hair and 48% black hair, you will end up with something like this:

As you can see, this pie chart does not make sense because the slices overlap and go beyond the circle. The angle of the brown hair slice is 223.2 degrees (62% of 360 degrees) and the angle of the black hair slice is 172.8 degrees (48% of 360 degrees). The sum of these angles is 396 degrees, which is more than 360 degrees. The sum of these percentages is 110%, which is more than 100%.

Therefore, Salvo’s statement that of the 100 singers in a children’s choir in Whitehorse, 62% have brown hair and 48% have black hair is not possible.

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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The least possible value of the area of square T is 49 i.e., the correct answer is option (C) 49, representing the least possible value of the area of square T.

The least possible value of the area of square T can be determined by analyzing the relationship between the two squares and their perimeters.

Let's denote the side length of square S as 'a'.

Since the perimeter of square S is 40, each side of the square has a length of 10 (40 divided by 4).

Square T is inscribed in square S, which means that its corners touch the sides of square S.

To find the least possible value of the area of square T, we need to consider the scenario where square T is the smallest possible square that can be inscribed in square S.

In this case, the sides of square T are parallel to the sides of square S, and the corners of square T coincide with the midpoints of the sides of square S.

Since square T is inscribed in square S, the diagonal of square T is equal to the side length of square S.

Using the expression of Pythagorean theorem, we can calculate the length of the diagonal of square T:

Diagonal of square T = √(\(10^2 + 10^2\)) = √200 = 10√2

The side length of square T can be found by dividing the diagonal length by √2:

Side length of square T = 10√2 / √2 = 10

Therefore, the area of square T is (side length)^2 = \(10^2\) = 100.

However, we are looking for the least possible value of the area of square T.

Since the answer choices are given, we can see that the smallest possible area is 49, which corresponds to option (C).

Hence, the correct answer is option (C) 49, representing the least possible value of the area of square T.

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The total number of possible 7-place license plates are 67600000.

Given: A 7-plate license plate. 2 places are for letters and 5 places are for numbers. To find how many different 7-plate license plates are possible

Let's solve the given problem:

The license plate has 7 places. 2 places are for letters and the remaining 5 places are for numbers.

Therefore, the total number of ways in which the 7-place license plate can fill are: Total possible ways in which the two letters can be filled × Total possible ways in which the 5 number places can be filled

= 676 × 100000

= 67600000 ways

Hence the total number of possible 7-place license plates are 67600000.

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Answer:

The answer is B

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Politically, governments prefer non violent resistance to something or a march thats non violent since it gets the message out and no one/thing was injured/broken while resisting non violently.

9514 1404 393

Answer:

  5.3

Step-by-step explanation:

The Pythagorean theorem applies. The square of the hypotenuse is equal to the sum of the squares of the other two sides.

  8² = x² + 6²

  64 = x² +36

  28 = x²

  √28 = x ≈ 5.3

The missing measure is 5.3.

_____

Comment on the question

The triangle isn't marked, but we must assume it is a right triangle. If it is not a right triangle, we cannot find the missing measure.

Answer:

Step-by-step explanation:

Df(P0) = Df(1, -1, 2) = 4(1) + (-1) + 7(2) = 15Therefore, the derivative of the function P0 in the direction of A is 15.

Given the function:f(x, y, z) = xy + yz + zx Also, P0(1, -1, 2) and A = 3i + 6j - 2kWe need to find the derivative of the function P0 in the direction of A. Let's solve this problem step by step.

First, we need to find the gradient of the function. Gradient of the function is defined as the vector consisting of partial derivatives of the function.The gradient of the function is given by:∇f(x, y, z) = [∂f/∂x, ∂f/∂y, ∂f/∂z]∇f(x, y, z) = [y + z, x + z, y + x]Therefore, the gradient of the function is ∇f(x, y, z) = [y + z, x + z, y + x]

Next, we need to find the directional derivative of the function in the direction of A. Directional derivative is defined as the rate of change of the function along a particular direction.The directional derivative of the function in the direction of A is given by:Df(x, y, z) = ∇f(x, y, z) .

A where " . " denotes the dot product of two vectors. Substituting the values of A and ∇f(x, y, z) in the above equation, we get:Df(x, y, z) = [y + z, x + z, y + x] . (3i + 6j - 2k)Df(x, y, z) = 3(y + z) + 6(x + z) - 2(y + x)Df(x, y, z) = 4x + y + 7zTherefore, the directional derivative of the function in the direction of A is Df(x, y, z) = 4x + y + 7z.

Finally, we need to find the derivative of the function P0 in the direction of A. Derivative of the function is defined as the directional derivative of the function at the point P0 in the direction of A.The derivative of the function P0 in the direction of A is given by:Df(P0) = Df(1, -1, 2) = 4(1) + (-1) + 7(2) = 15Therefore, the derivative of the function P0 in the direction of A is 15.

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Answer:

point A is the intersection point between XA and AC