Reflect triangle ABC over the line y = 2.

Translate the image by the directed line segment from (0, 0) to (3, 2).

What are the coordinates of the vertices in the final image?

Answer:

About 11.75 hours or 11 hours and 45 minutes

Step-by-step explanation:

You need to divide 376 by the base number (32) which then you get 11.75 hours/ 11 hours and 45 minutes

The equation of the parabola with vertex at the origin, axis along the x-axis, and passing through the point [3,4] is:

y = (4/9) * x^2

Since the vertex of the parabola is at the origin and the axis is along the x-axis, the equation of the parabola can be written in the form:

y = a * x^2

where 'a' is a constant that determines the shape of the parabola.

To find the value of 'a', we can use the fact that the parabola passes through the point [3,4]. Substituting these values into the equation gives:

4 = a * 3^2

4 = 9a

a = 4/9

Therefore, the equation of the parabola with vertex at the origin, axis along the x-axis, and passing through the point [3,4] is:

y = (4/9) * x^2

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Answer:

true

Step-by-step explanation:

11a - 2a

Factor out a

a(11-2)

a *9

9a

Answer:

9a is equivalent to 11a - 2a because 11a-2a=9a

Step-by-step explanation:

a. the sum of the first 200 natural numbers is 20,100. b. when the ball hits the pavement for the 6th time, it will have traveled approximately 104 feet in total (up and down).

(a) To find the sum of the first 200 natural numbers, we can use the formula for the sum of an arithmetic series.

The sum of the first n natural numbers is given by the formula: Sn = (n/2)(a + l), where Sn represents the sum, n is the number of terms, a is the first term, and l is the last term.

In this case, we want to find the sum of the first 200 natural numbers, so n = 200, a = 1 (the first natural number), and l = 200 (the last natural number).

Substituting these values into the formula, we have:

Sn = (200/2)(1 + 200)

  = 100(201)

  = 20,100

Therefore, the sum of the first 200 natural numbers is 20,100.

(b) The ball rebounds three-fourths of the distance it drops, so each time it hits the pavement, it travels a total distance of 1 + (3/4) = 1.75 times the distance it dropped.

For the 6th rebound, we need to find the distance the ball traveled when it hits the pavement.

Let's represent the initial drop distance as h (30 ft).

The total distance traveled after the 6th rebound is given by the sum of a geometric series:

Distance = h + h(3/4) + h(3/4)^2 + h(3/4)^3 + ... + h(3/4)^5 + h(3/4)^6

Using the formula for the sum of a geometric series, we can simplify this expression:

Distance = h * (1 - (3/4)^7) / (1 - 3/4)

Simplifying further:

Distance = h * (1 - (3/4)^7) / (1/4)

        = 4h * (1 - (3/4)^7)

        = 4 * 30 * (1 - (3/4)^7)

Calculating the value:

Distance ≈ 4 * 30 * (1 - 0.1335)

        ≈ 4 * 30 * 0.8665

        ≈ 104 ft

Therefore, when the ball hits the pavement for the 6th time, it will have traveled approximately 104 feet in total (up and down).

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Answer: 11

Step-by-step explanation:

\(A-B=\{2\}\).

Since there is 1 element in this set, the answer is 1.

Answer:

no sé no entiendo ingles

Check the picture below.

\(\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = \sqrt{a^2+b^2-(2ab)\cos(C)} \\\\[-0.35em] ~\dotfill\\\\ c = \sqrt{10^2+7^2~-~2(10)(7)\cos(108^o)} \implies c = \sqrt{ 149 - 140 \cos(108^o) } \\\\\\ c\approx \sqrt{149-(-43.262379)}\implies c\approx \sqrt{192.262379}\implies \boxed{c\approx 14}\)

The particular solution is xp(t) = (-1/24)cos(5t) + (1/10)sin(5t) and the general solution to the differential equation is then x(t) = c1 cos(7t) + c2 sin(7t) - (1/24)cos(5t) + (1/10)sin(5t).

The given initial value problem is a homogeneous linear differential equation of second order with constant coefficients. The characteristic equation is r^2 + 49 = 0, which has complex roots r = ±7i. Since the roots are complex, the general solution is of the form x(t) = c1 cos(7t) + c2 sin(7t).

To find the particular solution, we use the method of undetermined coefficients and assume a solution of the form xp(t) = Acos(5t) + Bsin(5t). We then find that A = -1/24 and B = 1/10. Therefore, the particular solution is xp(t) = (-1/24)cos(5t) + (1/10)sin(5t).

The general solution to the differential equation is then x(t) = c1 cos(7t) + c2 sin(7t) - (1/24)cos(5t) + (1/10)sin(5t).

Using the initial conditions, we can solve for c1 and c2 to obtain x(t) = (1/5)cos(7t-1.107) + (1/24)cos(5t+0.322). Therefore, the solution to the initial value problem can be expressed as the sum of two oscillations with a phase shift of 0.322 for the cos(5t) term.

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Answer:

tim will get $4 and sam $32 if shared in the ratio 1:4

Answer:

Tim got £8 and Sam got £32

Step-by-step explanation:

Total = £40

Total Parts = 1+4 = 5

Tim got:

=> \(\frac{1}{5} * 40\)

=> £8

Sam got:

=> \(\frac{4}{5}* 40\)

=> 4 * 8

=> £32

The required answer is the  equation .

A mathematical sentence that contains an equal sign is called an equation. This is because an equation is a statement that two expressions are equal.

a. Equation: An equation is a mathematical sentence that contains an equal sign. It shows that two expressions are equal. For example, "3x + 5 = 17" is an equation because it states that the expression "3x + 5" is equal to 17.

b. Inequality: An inequality is a mathematical sentence that uses inequality symbols like greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤). Inequalities do not necessarily contain an equal sign. For example, "2x + 3 > 10" is an inequality because it shows that the expression "2x + 3" is greater than 10.

c. Expression: An expression is a mathematical phrase that can include numbers, variables, and operations. Expressions can be simplified but cannot be solved because they don't contain an equal sign. For example, "2x + 3" is an expression because it consists of numbers, a variable (x), and an operation (+).

d. Variable: A variable is a symbol, usually a letter, that represents a quantity that can vary or change. Variables are used in mathematical equations and expressions to represent unknown values. For example, in the equation "3x + 5 = 17," the variable is "x" because its value is not specified.

In summary, a mathematical sentence that contains an equal sign is an equation because it states that two expressions are equal.

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Answer:

  -7, -6, -5

Step-by-step explanation:

Let x represent the second number. Then x-1 is the first number, and x+1 is the third number.

  (x-1) +4 +2(x+1) = x -7

  3x +5 = x -7

  2x = -12

  x = -6

The integers are -7, -6, -5.

Probably not all driving scenarios can be accurately simulated by a driving simulator. Additionally, it's likely that simulator users have a different mindset than when they're actually behind the wheel.

The cited data:

Idea applied in experiment:

A driving simulator is therefore unlikely to adequately replicate all driving scenarios, which is one of our concerns about extending the outcomes of such an investigation.

Thus, users of driving simulators are also probably in a different frame of mind than they are while driving is real life.

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The charge per dozen donuts will be $18 according to the given ratio.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

As per the given,

Big bobs bakery charges $9 for 1/2 dozen donuts.

$9 for 1/2 dozen donuts

For one dozen,

$9 x 2 = $18

Hence "The above ratio will result in a fee of $18 for a dozen donuts.".

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Using translation concepts, y-coordinates greater than 38 identify a location north of the city.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Considering latitude and longitude, the coordinates of a city are given as follows:

(LON, LAT).

Hence, the given city has coordinates given by:

(25, 38)

As we move north, the latitude increases, hence, y-coordinates greater than 38 identify a location north of the city.

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Answer:

1/y^9= y^-9

1/m^15= m^-15

n^3=n^3

1/m^6=m^-6

n^4

w^12

1/32=2^-5

-6=(-6)^1

1^1

Step-by-step explanation:

Step-by-step explanation:

Use the exponent laws to identify which law to use.

1. y^-4 * y^-5 = y^-9

(add the exponents)

2. (m^-3)^5 = m^-3*5 = m^-15

(multiply the exponents)

3. n^-3 * n^6 = n^3

(add the exponents)

4. m^-12/m^-6 = m^-12-(-6) = m^-6

(subtract exponents)

5. (n^-2)^-2 = n^-2*-2 = n^4

(multiply the exponents)

6. w^5/w^-7 = w^5-(-7) = w^12

(subtract the exponents)

7. 2^-3 * 2^-2 = 2^-5

(add the exponents)

8. (-6)^4 * (-6)^-3 = -6^1

(add the exponents)

9. (4^-6)^0 = 4^-6*0 = 4^0 = 1

(multiply the exponents)

Answer: the ratio of girls to boys is 22 to 17

Answer:

8.15 miles

Step-by-step explanation:

5.95+2.2=8.15

The equation that models the shape of the monument is simply y = 25.

The equation that models the shape of the parabolic monument can be written in the form of a quadratic function, y = ax^2 + bx + c, where y is the height of the monument at a given distance x from the center of the base.

Since the monument has a height of 25 feet at the center of the base, we know that the vertex of the parabolic shape is located at (0, 25). Also, since the base width is 30 feet, the distance from the center of the base to either side is 15 feet.

Therefore, we can use the information about the vertex and the width to write the equation as y = -a(x-15)^2 + 25.

To determine the value of a, we need another point on the curve. Let's use one of the endpoints of the base, which is (15, 0). Plugging these values into the equation, we get:

0 = -a(15-15)^2 + 25

0 = 25

This is not possible, so we need to adjust the equation to fit the known points. We can rewrite the equation as y = a(x-15)^2 + 25, and solve for a using the other endpoint of the base, which is (-15, 0):

25 = a(-15-15)^2 + 25

0 = 900a

a = 0

This means that the equation that models the shape of the monument is simply y = 25.

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The degree measure of the largest angle is 72° in the triangle.

We have, The sum of two angles of a triangle is 6/5 of a right angle.

One of these two angles is 30° larger than the other.

Let A and B be the two angles of the triangle such that A = B + 30°.

We know that the sum of three angles in a triangle is 180°.

⇒ A + B + C = 180°

⇒ B + 30° + B + C = 180°

⇒ 2B + C = 150°

We also know that the sum of two angles of a triangle is 6/5 of a right angle.

⇒ A + B = 6/5 × 90°

⇒ B + 30° + B = 108°

⇒ 2B = 78°

⇒ B = 39°

C = 150° - 2B ⇒ 72°

A = B + 30° ⇒ 39° + 30° ⇒ 69°

Therefore, the degree measure of the largest angle in the triangle is 72°.

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C

Image for proof, dude above got it first.

Answer:

see explanation

Step-by-step explanation:

(a)

To find the first 4 terms substitute n = 1, 2, 3, 4 into the n th term formula.

a₁ = 1 + 5 = 6

a₂ = 2 + 5 = 7

a₃ = 3 + 5 = 8

a₄ = 4 + 5 = 9

For the 10 th term substitute n = 10, that is

a₁₀ = 10 + 5 = 15

The first 4 terms are 6, 7, 8, 9 and the 10 th term is 15

(b)

Substitute n = 1, 2, 3, 4 and 10 into the n th term formula

a₁ = 2(1) - 1 = 2 - 1 = 1

a₂ = 2(2) - 1 = 4 - 1 = 3

a₃ = 2(3) - 1 = 6 - 1 = 5

a₄ = 2(4) - 1 = 8 - 1 = 7

a₁₀ = 2(10) - 1 = 20 - 1 = 19

The first 4 terms are 1, 3, 5, 7 and the 10 th term is 19

The factors indicated, are classified according to whether it is associated with a movement along the aggregate demand curve or a shift of the aggregate demand curve.

Movement along the aggregate demand curve

Shift of the aggregate demand curve

An aggregate demand curve depicts the total domestic expenditure on goods and services at each price level.

The AD curve is trending higher due to rising economic prosperity. People's spending grows as their income rises, leading to an increase in AD and vice versa. As a result of the positive link between income and AD, the AD curve slopes higher.

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Full Question:

Classify each factor according to whether it is associated with a movement along the aggregate demand curve or a shift of the aggregate demand curve.

using Universal Instantiation and the Contrapositive rule, we have shown that ∀x (¬R(x) → P(x)) is true.

To show that ∀x (¬R(x) → P(x)) is true using the given premises, we can use the rule of inference called Universal Instantiation and the logical law called Contrapositive.

1. Given: ∃x (¬P(x) ∧ ¬Q(x)) is false.
2. This means that for every x in the domain, ¬P(x) ∧ ¬Q(x) is true.

3. Given: ∀x ((¬P(x) ∧ Q(x)) → R(x)) is true.
4. This means that for every x in the domain, if ¬P(x) ∧ Q(x) is true, then R(x) is also true.

Now, we want to prove: ∀x (¬R(x) → P(x)) is true.

5. Suppose we have an arbitrary element a from the domain.
6. From (2), we know that ¬P(a) ∧ ¬Q(a) is true.
7. Since (¬P(a) ∧ Q(a)) → R(a) is true (from 4), it implies that if ¬P(a) ∧ Q(a) is true, then R(a) is also true.
8. If R(a) is true, then ¬R(a) is false.
9. Thus, from 8, we have ¬R(a) → P(a).
10. This holds for any arbitrary element a in the domain, so ∀x (¬R(x) → P(x)) is true.

Therefore, using Universal Instantiation and the Contrapositive rule, we have shown that ∀x (¬R(x) → P(x)) is true.

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The Length of the conjugate axis is equal to 2b. The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola.

In a hyperbola, the name of the green segment is called the transverse axis. The transverse axis is the longest distance between any two points on the hyperbola, and it passes through the center of the hyperbola. It divides the hyperbola into two separate parts called branches.

The transverse axis of a hyperbola lies along the major axis, which is perpendicular to the minor axis. Therefore, it is also sometimes called the major axis.

The other axis of a hyperbola is called the conjugate axis or minor axis. It is perpendicular to the transverse axis and passes through the center of the hyperbola. The length of the conjugate axis is usually shorter than the transverse axis.In the hyperbola above, the green segment is the transverse axis, and it is represented by the letters "2a". Therefore, the length of the transverse axis is equal to 2a.

The blue segment is the conjugate axis, and it is represented by the letters "2b".

Therefore, the length of the conjugate axis is equal to 2b.The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola. In particular, the distance between the two branches of the hyperbola is determined by the length of the transverse axis.

If the transverse axis is longer, then the branches of the hyperbola will be further apart, and the hyperbola will look more stretched out. Conversely, if the transverse axis is shorter, then the branches of the hyperbola will be closer together, and the hyperbola will look more compressed.

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Answer:

150

Step-by-step explanation:

119.07 feet fence would be required.

Perimeter is a measure of the distance around the boundary of a two-dimensional shape. It is the total length of all the sides or edges of a shape. For example, if you have a rectangle with a length of 5 units and a width of 3 units, the perimeter would be:

2(5 + 3) = 2(8) = 16 units

In this case, we added up the lengths of all four sides of the rectangle to get the perimeter.

Perimeter is typically measured in units of length, such as meters, feet, or centimeters, depending on the context of the problem. It is an important concept in geometry and is used to calculate the amount of material needed for things like fencing or paving.

Now to find the total length of the fence required, we need to find the perimeter of the garden. We can break the garden into two parts: the rectangle and the semicircle.

The rectangle has a length of 30 feet and a width of 23 feet, so its perimeter is:

2(30) + 23 = 83 feet

The semicircle has a diameter equal to the width of the rectangle (23 feet), so its radius is half of the diameter, or:

r = 23/2 = 11.5 feet

The circumference of the semicircle is half of the circumference of a full circle with the same radius, so it is:

(1/2) * 2 * 3.14 * 11.5 = 36.07 feet (rounded to two decimal places)

To find the total perimeter, we add the perimeter of the rectangle and the circumference of the semicircle:

83 + 36.07 = 119.07 feet

Therefore, the gardener needs 119.07 feet of fence to surround the rose garden.

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The question is incomplete. The complete question is :

Georgia has some 4-inch cubes like the one shown below. Georgia will put the cubes in the box shown below. What is the total number of cubes that Georgia needs to exactly cover the bottom of the box with a layer one cube deep?

Solution :

It is given that :

There are small cubes that has a dimension of 4 in x  4 in x  4 in.

There is also a box which has a dimension of 24 in x 20 in x 12 in.

We need to find out how many small cubes will Georgia need to cover the bottom of the box.

So, we need to find out the surface area of the one cube and the box.

Therefore, the surface area of one cube = side x side

                                                                   = 4 inch x 4 inch

                                                                   = 16 square inches

Similarly the area of the box can be find by = length x breath

                                                                        = 24 in x 20 in

                                                                           = 480 square inches

Therefore, dividing the area of the box by the area of the cube, we get

\($=\frac{480}{16}$\)

= 30

So Georgia will require exactly 30 cubes to cover the bottom of the box with a layer of one cube deep.

Positive divisors does n2 have are 5.

If an integer n has exactly three positive divisors, including 1 and n, it means that n is a perfect square of a prime number.

The reason for this is that a prime number has only two divisors: 1 and itself. Therefore, if n has exactly three positive divisors, n must be a perfect square of a prime number, since the only divisors of a perfect square are the divisors of its square root, and its square root must be a prime number.

Let's say that n is equal to p², where p is a prime number. The positive divisors of n are 1, p, and n (which is p²).

Now, to find the number of positive divisors of n², we can use the fact that any positive divisor of n² can be expressed in the form \(p^k\), where 0 ≤ k ≤ 4 (since n² = p⁴).

Therefore, the positive divisors of n² are:

1, p, p², p³, and p⁴ (which is n²)

So, n² has 5 positive divisors: 1, p, p², p³, and n².

Hence, the answer is 5.

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