Suppose c is an integer. If c mod 15 = 3, what is 10c mod 15? In other words, if division of c by 15 gives a remainder of 3, what is the remainder when 10c is divided by 15?

Answer:

The set S is a vector space.

To determine if S is a vector space, we need to check if it satisfies the ten properties of a vector space.

1. The zero vector exists: In this case, the zero vector would be the function y(x) = 0, which satisfies the differential equation y'' + 2y' - y = 0, since the derivative of the zero function is also zero.

2. Closure under addition: If f(x) and g(x) are both functions satisfying the differential equation y'' + 2y' - y = sin(x), then their sum h(x) = f(x) + g(x) also satisfies the same differential equation. This can be verified by taking the second derivative of h(x), multiplying by 2, and subtracting h(x) to check if it equals sin(x).

3. Closure under scalar multiplication: If f(x) is a function satisfying the differential equation y'' + 2y' - y = sin(x), and c is a scalar, then the function g(x) = c * f(x) also satisfies the same differential equation. This can be verified by taking the second derivative of g(x), multiplying by 2, and subtracting g(x) to check if it equals sin(x).

4. Associativity of addition: (f(x) + g(x)) + h(x) = f(x) + (g(x) + h(x))

5. Commutativity of addition: f(x) + g(x) = g(x) + f(x)

6. Additive identity: There exists a function 0(x) such that f(x) + 0(x) = f(x) for all functions f(x) satisfying the differential equation.

7. Additive inverse: For every function f(x) satisfying the differential equation, there exists a function -f(x) such that f(x) + (-f(x)) = 0(x).

8. Distributivity of scalar multiplication over vector addition: c * (f(x) + g(x)) = c * f(x) + c * g(x)

9. Distributivity of scalar multiplication over scalar addition: (c + d) * f(x) = c * f(x) + d * f(x)

10. Scalar multiplication identity: 1 * f(x) = f(x)

By verifying that all these properties hold, we can conclude that the set S is indeed a vector space.

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If a water park sold 11 child tickets and 14 adult tickets then 44% of the tickets sold were child tickets

The number of child tickets = 11

The number of adult tickets = 14

The total number of tickets are 11+14

Total tickets = 25

We have to find the percentage of the tickets sold were child tickets

x/100×25 = 11

0.25x=11

Divide both sides by 0.25

x=11/0.25

x=44%

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Answer:

13y - 55

Step-by-step explanation:

Given

7(3y - 5) - 2(10 + 4y) ← distribute both parenthesis

= 21y - 35 - 20 - 8y ← collect like terms

= 13y - 55

Answer:

When using the distributive property, we can operate parenthesis:

\(a*(b+c)=ab + ac\)

So, in our case:

\(7(3y-5) -2(10+4y)\)

\(7*3y+7*(-5) - 2*10-2*4y\)

\(21y -35 - 20 - 8y\)

\(=13y - 55\)

So now we know the result is 13y - 55

SOLUTION:

=) 371/10×100

=) 371/1000

=) 0.371

The correct values of x and y for FGHJ to be a parallelogram are x=11 and y=25.

Regarding the parallelograms:

True or False – ∠D≅∠G: True. In parallelograms, opposite angles are congruent, so ∠D and ∠G are congruent.

True or False – AD¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯: False. In parallelograms, opposite sides are congruent, so AD¯¯¯¯¯¯¯¯ is not necessarily congruent to BC¯¯¯¯¯¯¯¯.

True or False – ∠A≅∠G: False. ∠A and ∠G are not necessarily congruent in parallelograms.

True or False – ∠B≅∠F: False. ∠B and ∠F are not necessarily congruent in parallelograms.

Regarding the window FGHJ:

To determine the values of x and y for FGHJ to be a parallelogram, we need opposite sides to be parallel and congruent.

Looking at the given options:

x=11, y=21: Not a parallelogram, as opposite sides are not parallel and congruent.

x=12, y=25: Not a parallelogram, as opposite sides are not parallel and congruent.

x=11, y=25: A possible parallelogram, as opposite sides FG and HJ are parallel and congruent.

x=12, y=21: Not a parallelogram, as opposite sides are not parallel and congruent.

Therefore, the correct values of x and y for FGHJ to be a parallelogram are x=11 and y=25.

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The vertical asymptotes appear at x = 4 and x = -3.

From the information,

x² - x - 12 = 0

(x - 4)(x + 3) = 0

x = 4 or x = -3

The vertical asymptotes therefore appear at x = 4 and x = -3.

We must think about what happens to the function when x gets closer to infinity and negative infinity in order to locate the horizontal asymptotes.

The x² term in the numerator will predominate the x term as x increases significantly in either the positive or negative direction, while the constant term will become insignificant. As a result, the function's value will be close to that of the fraction:

f(x) = (x² + 4 x -21) / (x2- x -12) approaches negative infinity or infinity. The horizontal asymptote can be determined by polynomial long division or synthetic division and is y = 1

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Answer:

156

Step-by-step explanation:

200 minus 22 percent is 44.

200 minus 44 is 156.

Therefore the reduced version has 156 calories.

The new snack has 156 calories.

To find the number of calories in the new snack, we can start by calculating the 22% reduction in calories compared to the old version.

The old version of the snack has 200 calories.

To determine the reduction, we calculate 22% of 200 calories:

22% of 200 = (22/100) * 200 = 0.22 * 200 = 44 calories.

This means that the new snack has 44 fewer calories than the old version.

To find the number of calories in the new snack, we subtract the reduction from the old version's calories:

200 calories - 44 calories = 156 calories.

Therefore, the new snack has 156 calories.

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9514 1404 393

Answer:

  x = 10

Step-by-step explanation:

Half of the triangle makes a 30°-60°-90° "special" triangle. We know the side ratios of that are 1 : √3 : 2. The long side is 1/3 of the perimeter, so is 60/3 = 20 = 10×2. Then the altitude is 10 times the middle ratio value: 10√3 ≈ 17.32.

Comparing this with x√3, we find x = 10.

Answer:

X = 25

Step-by-step explanation:

To solve this question, we'll first of all find determine the side length of the triangle from the perimeter.

Perimeter of an equilaterial triangle = 3 * s

S = side length

Perimeter = 150cm

150 = 3s

S = 150 / 3

S = 50cm

The side lengths are 50cm each since they are all equal.

To find x,

We have to divide the triangle equally into two different part.

Check the first attachment for better illustration on how the equilaterial triangle is.

Check the second attachment for better illustration on the triangle when its divided into a right angle triangle.

From the right angle triangle, we can use pythagorean theorem to solve for x

a² = b² + c²

a = 50cm

b = 25cm

c = x√(3)

50² = [x√(3)]² + 25²

2500 = x² * 3 + 625

2500 - 625 = 3x²

1875 = 3x²

X² = 1875 / 3

X² = 625

X = √(625)

X = 25

HOPE THIS HELPS

if so please give me a brainlist

Answer:

Plot it at (4,-0.5)

Step-by-step explanation:

Answer:

-4, -0.5

Step-by-step explanation:

The length of the code words in this linear code is 4.

To find the length of code words in a linear code, we can use the formula:

Length of code words = log(base 2) of (number of code words)

In this case, the linear code contains exactly 16 code words and the transmission rate is 23.

Using the formula, we can calculate the length of code words as follows:

Length of code words = log(base 2) of 16
Length of code words = 4

Therefore, the length of the code words in this linear code is 4.

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Cost of one egg is $1.85.

Assume,

X denotes the cost of 1 egg

Y denotes the cost of 1 sausage

According to question,

Cost equation for Hannah,

3X + 2Y = 7.13   ....(i)

Cost equation for Hannah,

5X + 3Y = 11.62  ....(ii)

Subtract 3x(i) from 2x(ii) we get

X = $1.85 is the cost of one egg.

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The sum of a regular polygon's exterior angles will always equal 360 degrees.

Exterior angles are those that are parallel to a polygon's inner angles but are on the outside of it. The sum of two internal opposite angles equals the measure of an exterior angle. The Exterior Angle is the angle formed by any side of a shape and a line drawn from the opposite side. Another example: When we add up the Interior Angle and Exterior Angle we get a Straight Angle (180°), so they are "Supplementary Angles". An exterior angle of the triangle is a nonstraight angle (one that is not just an extension of a side) outside the triangle but adjacent to an interior angle (Figure 1 ).

Here,

The sum of the exterior angles of a regular polygon will always equal 360 degrees.

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Answer:

The total amount the customer would have to repay after one year is $1,007.

(2 Years = $1,067.42)  (3 Years = $1131.47)  (4 Years = $1199.36)

(5 Years = $1271.32)

Step-by-step explanation:

$950 • 6% = $57

$950 • 0.06 = $57

$950 + 6% = $1,007

I hope this helps.

Answer:

-82

Step-by-step explanation:

84/21=4

-25x4=-100

-3x-6=18

-100+18=-82

Answer:

Step-by-step explanation:

let us first model the total amount he makes

say the number of sales made us x

let the total made be y

y=2456.75+4.5x

given that the amount of sales is 32

let us put x=32 in the expression to get the total amount

y=2456.75+4.5(32)

y=2456.75+144

y=2600.75

therefore if he sale 32 new gym membership he will make $2600.75

Let n be the number of years since the population started increasing, and let p(n) the the population after n years. We'll have that:

For n = 16, we'll have that:

This way, we can conclude that:

Answer:

B) Only (-2, 9)

Step-by-step explanation:

To find out which of the given options is the solution to the linear equation, y = -2x + 5:

We can substitute the values of the given options to see whether they provide a true statement.

A) (2, -9):

y = -2x + 5

-9 = -2(2) + 5

-9 = -4 + 5

-9 = 1 (False statement. Therefore, this option is not included as a solution).

B) Only (-2, 9):

9 = -2(-2) + 5

9 = 4 + 5

9 = 9 (True statement. Thus, (-2, 9) is a solution to the given linear equation).

We no longer have to test options C and D because we already tested (2, -9) and determined that it's not a solution.

Therefore, the correct answer is option B) Only (-2, 9).

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Answer:

a) 2.5 x 10^5

b) 8.1 x 10^4

c) 9.06 x 10^8

d) 1.034 x 10^10

Answer:

The answer would be 179832 Centimeters

Step-by-step explanation:

Answer: mt rushmore is 5,725 ft

Step-by-step explanation:

Answer: Width = 4.7 meters, Length = 6.7 meters

Step-by-step explanation:

Let the width be \(w\). It follows that the length is \(w+2\).

\(w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7\)

The evidence and data support Evan's argument that plants predominantly acquire the materials they need to grow from air and water .

Evan's statement is supported by evidence and data that demonstrate how plants obtain the majority of the materials they need to grow from air and water. Here are some key points to support his argument:

Carbon Dioxide (CO2) from the air: Through the process of photosynthesis, plants take in carbon dioxide from the air. They use the carbon dioxide along with water and sunlight to produce glucose and oxygen. This glucose serves as an essential energy source for plant growth and development.

Water: Plants absorb water from the soil through their root systems. Water plays a critical role in various plant processes, including nutrient uptake, transportation, and the maintenance of cell turgidity. It is a primary component of plant cells and is necessary for photosynthesis to occur.

Essential nutrients from the soil: While air and water provide the primary materials for plant growth, plants also require certain nutrients to thrive. These essential nutrients, such as nitrogen, phosphorus, and potassium, are typically obtained from the soil. However, it's important to note that these nutrients are often dissolved in water and taken up by plant roots.

Experimentation and research: Numerous scientific experiments and studies have been conducted to investigate plant nutrient uptake. These experiments have confirmed that plants can grow and develop using only air, water, and the necessary nutrients found in these sources.

The evidence and data support Evan's argument that plants predominantly acquire the materials they need to grow from air and water. While nutrients from the soil are essential, the primary sources of plant growth materials are carbon dioxide from the air and water, which are crucial for photosynthesis and various physiological processes in plants.

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The rpm of the 10-tooth sprocket when driven by the same chain that drives a 20-tooth sprocket at 10 rpm will be 20 rpm.

The speed of a sprocket is directly proportional to the number of teeth on it. Therefore, if a 20-tooth sprocket is turning at 10 rpm, it means that it covers 200 teeth in one minute. When the same chain drives a 10-tooth sprocket, it means that the sprocket will cover half the distance or 100 teeth in one minute.
Therefore, the rpm of the 10-tooth sprocket will be double that of the 20-tooth sprocket, and it will turn at 20 rpm. This calculation is based on the fact that the chain is of the same length and is connected to the same motor, which provides the same power output. Hence, the speed of the sprocket is determined by the number of teeth on it.
In conclusion, the rpm of the 10-tooth sprocket when driven by the same chain that drives a 20-tooth sprocket at 10 rpm will be 20 rpm.

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Answer:

(4,-2)

Step-by-step explanation:

coordinate of midpoint(x1+x2)/2, (y1+y2)/2

x1=6, x2=2 , y1=-7, y2=3

x=6+2/2 ⇒8/2=4

y=-7+3/2 ⇒ y=-4/2=-2

(4,-2)

The polynomial function in which p has four zeros at -4,-1,0, and 9 are:

--x(x + 4)(x + 1)(x-9) , -3x(x+4)(2x + 2)(x-9) and  -3x(x + 4)(x + 1)(x − 9)²

Here given polynomial function,

a. 3x(x-4)(x - 1)(x + 9)

if x = 0

then the function becomes 0

but -4 , -9 , -1 does not satisfy.

Therefore the function does not have four zeroes

b. --x(x + 4)(x + 1)(x-9)

Here the function will have four zeroes,

x = 0

(x + 4 ) = 0 when x = -4

(x + 1 ) = 0 when x = -1

(x - 9) = 0 when x = 9

Therefore the function has four zeroes.

c. -3x(x+4)(2x + 2)(x-9)

Here the function will have four zeroes,

x = 0

(x + 4 ) = 0 when x = -4

(2x + 2 ) = 0 when x = -1

(x - 9) = 0 when x = 9

d. 3x(x+4)(x-1)(x-9)

Here the function will have four zeroes,

x = 0

(x + 4 ) = 0 when x = -4

(x - 1 ) = 0 when x = 1

(x - 9) = 0 when x = 9

Here x = -1 does not satisfy, So the function does not have four zeroes.

e. -3x(x + 4)(x + 1)(x − 9)²

Here the function will have four zeroes,

x = 0

(x + 4 ) = 0 when x = -4

(x - 1 ) = 0 when x = 1

(x - 9)² = 0 when x = 9

Therefore the function has four zeroes.

Therefore the polynomial functions with four zeros at -4,-1,0, and 9 are as follows: —x(x + 4)(x + 1)(x-9), -3x(x+4)(2x + 2)(x-9) and

-3x(x + 4)(x + 1)(x-9) ²

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(a) The function rule for Big Wave Waterpark, f(x) = 2.5x + 5. where f(x) is total cost and x is number of slides ridden.

b) The function rule for Coaster City is, f(x) = 5x + 7.50, where x is the number of roller coaster ridden and f(x) is total cost.

c) The function rule for Virtual Reality Lan is, f(x) = 3x + 10, where f(x) is total cost and x is the number reality rides ridden.

(a) Let f(x) = ax +b be the function which represents the total cost of Big Wave Park where x represents the number of taken ride.

We can see that f(2) = 10; f(4) = 15 and f(6) = 20.

Therefore, 2a + b = 10 and 4a + b = 15

So, 2(2a + b) - (4a + b) = 2*10 - 15

4a + 2b - 4a - b = 20 - 15

b = 5

Now, f(6) = 20

6a + b = 20

6a + 5 = 20 [putting the value of 'b']

6a = 20 - 5 = 15

a = 15/6 = 5/2 = 2.5

Hence, the function rule for Big Wave Waterpark is, f(x) = 2.5x + 5.

(b) The function rule for Coaster city is, f(x) = 5x + 7.50, where x is the number of roller coaster ridden.

(c) Let the total cost for Virtual Reality Lan is, f(x) = cx + d, where x is the number reality rides ridden.

From the given graph we can see that, f(10) = 40; f(20) = 70; f(30) = 100.

So, 10c + d= 40 ........... (i)

20c + d = 70 ............... (ii)

Solving (i) and (ii) we get,

2(10c + d) - (20c + d) = 2*40 - 70

20c + 2d - 20c - d = 80 - 70

d = 10

So putting the value d = 10 in f(30) = 100 we get,

30c + 10 = 100

30c = 100 - 10 = 90

c = 90/30 = 3

So the function rule is, f(x) = 3x + 10.

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