The first term of a pattern is 12. The pattern follows the rule "multiply by 4." What are the next three terms?

From the information given,

Jack wants to eat 2 1/5 of his plate in 1/3 hour. The first step is to convert 2 1/5 to improper fraction. It becomes 11/5

The statement would be

Jack wants to eat 11/5 of his plate in 1/3 hour.

Let x represent how much of his plate that he will eat in 1 hour. Therefore

11/5 = 1/3

x = 1

By cross multiplying, it becomes

x * 1/3 = 1 * 11/5

x/3 = 11/5

x = 11/5 * 3

x = 33/5

Converting to mixed fraction, it becomes

6 3/5

The correct option is the first one

Answer:

-8

Step-by-step explanation:

The value that represents the variable x in the trapezoid is 108 degrees

From the question, the trapezoid represents the given parameter

We can see that the trapezoid is an isosceles triangle

This means that the angle x and y are congruent

The sum of angles is a trapezoid is 360 degrees

So, we have the following summation equation

x + x + 72+ 72 = 360

Evaluate the like terms

So, we have

2x + 144= 360

This gives

2x = 216

Divide by 2

x = 108

Hence, the value of x is 108 degrees

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The equation of the required perpendicular line is x + 3y = 24.

What is the slope relation for two perpendicular lines?
For two perpendicular lines on a plane, the product of their slopes always equals (-1).
What is the equation of line with slope 'm' and passing through the point (x₁, y₁)?
The standard equation of the line with slope 'm' and passing through the point (x₁, y₁) is y - y₁ = m(x - x₁).

Given, the required line is perpendicular to line given by y = 3x + 5 with slope, m₁ as 3, on analysis with standard equation of line; also the line passes through the point (9, 5) i.e. (x₁, y₁).
Let the slope of the required line be = m₂
As per statement established in the literature above, we have:
Slope of two perpendicular lines = -1
∴m₁ × m₂ = -1 ⇒ 3m₂ = -1 ⇒ m₂ = (-1)/3
Again, equation of the required perpendicular line is:
y - 5 = [(-1)/3][x - 9] ⇒ 3y - 15 = 9 - x ⇒ x + 3y = 24
Thus, the equation of the required perpendicular line is x + 3y = 24.

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The weight of the other person has to be the same in order for the seesaw to be balanced, then the person on the other side weighs 100 pounds as well. Now, we know that:

Then to find the mass we just multiply the weight in pounds by 0.45:

Therefore the other person has a mass of 45 kg.

The weight of the other person has to be the same in order for the seesaw to be balanced, then the person on the other side weighs 100 pounds as well. Now, we know that:

Then to find the mass we just multiply the weight in pounds by 0.45:

Therefore the other person has a mass of 45 kg.

By performing mathematical operations, the answer to the given expression (- 1.2(2/5) ÷ -2) is 0.24.

So, the values in the blank will be:

Therefore, by performing mathematical operations, the answer to the given expression (- 1.2(2/5) ÷ -2) is 0.24.

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[tex]2x = 76[/tex]

Due to alternate angles

[tex] \frac{2x}{2} = \frac{76}{2} \\ x = 38[/tex]

40°+(y-8)°+76°=180°(sum of angles in a triangle)

[tex]40 + y - 8 + 76 = 180 \\ y + 108 = 180 \\ y = 180 - 108 \\ y = 72[/tex]

ATTACHED IS THE SOLUTION.

Answer:

x = 38 ; y = 72

Step-by-step explanation:

180 = 76 + 40 + (y - 8)

180 = 108 + y

72 = y

The triangle has parallel lines, so the uppermost right angle is also 90 degrees.

90 - 76 = 14

180 = 90 + 14 + 2x

180 = 104 + 2x

76 = 2x

38 = x

The image of triangles are given .

a.

b. Find the ratio,

c.Hence the triangles are similar .

The correct option is A.

The payment for each 6 h is equal to $ 432.2 while the payment for each 30 min would be  $ 36.01.

It's a math tool for solving problems about proportion. You can relate more than 2 variables and from the proportion, it's possible to find an unknown number.

In the International System Units (SI), the standard unit for time is the second (s).  For solving any exercise, you need to know the relation between the units of the time. See below:

1h=60 min = 3600s

1 min = 60 s

Now you can solve the question from the rule of three for finding the payment in dollars.

The question gives: an each 8.33 min, the payment is 10 dollars. Thus, from this relation you can write:

First, you should convert 6h to minutes, then,

1 h ----- 60 min

6h ----- x

x=60*6=360 min

After that, you should apply the rule of three for finding the payment in dollars.

   8.33 min     -----  10 dollars.

   360 min    -------  x

8.33x=360*10

8.33x=3600

x= $ 432.2

You should apply the rule of three for finding the payment in dollars.

   8.33 min     -----  10 dollars.

   30 min    -------  x

8.33x=30*10

8.33x=300

x= $ 36.01

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The length of the incline of the ramp will be [h] = 12.0415 ft

According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the base and perpendicular. Mathematically, we can write -

h² = p² + b²

Given is the installation of wheelchair ramp such that the ramp should have a base of 12 ft and height of 1 ft long.

From the data given, we can consider the ramp construction as right angled triangle. We can write -

base [b] = 12 ft

height [p] = 1 ft

Using the Pythagoras theorem -

h² = (12 x 12) + (1 x 1)

h² = 144 + 1

h = √145

h = 12.0415

Therefore, the length of the incline of the ramp will be [h] = 12.0415 ft

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[This question also has part B. Visit the following link for part B -

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the answer is in the photo I took of solving it

The relation between the events Y and W prevents us from completing the analysis.

The relation between the events Y and W prevents us from completing the analysis.

Case 1: W is more likely than Y then we have the following analysis:

Z, X, Y, and W are arranged in ascending order of more likeliness.

Case 2: Y is more likely than W then we have the following analysis:

Z, X, W, and Y are arranged in ascending order of more likeliness.

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Answer:

correct me if im wrong but my answer is x=7, or in other words, 7.

Step-by-step explanation:

Answer:

7 years old

Step-by-step explanation:

You would start by going backward. If 13 is 8 less, then you would first add 8. You would have 21. Now all you have to do is divide by three. So your answer would be 7. If you would want to check you could plug it back in. 7 multiplied by 3 is 21. 21 - 8=13

The Answer, 7 years old

The lower value of the perimeter is 140 inches .

Width of the rectangle is 20 inches .

The length of the rectangle is calculated as ,

Rearranging the terms ,

The higher value of perimeter is 220 inches .

Width of the rectangle is 20 inches .

The length is calculated as,

Therefore,

Thus the range of values for the length of the given rectangle are 50 and 90 .

The vertical component of the force is 69.28  N and the horizontal component of the force is 40 N.

Resolution of forces is the process of separating a force into two or more pieces so that the combined effect on the body is the same as if it had been a single force. We can analyze motion individually in different directions thanks to the resolution of forces.

Given that a heavy box is pulled across a wooden floor with a rope. The rope forms an angle of 60.0° with the floor. A tension of 80.0 N is maintained on the rope.

The vertical component and the horizontal component will be calculated as:-

Vertical component = 80sin60=69.28 N

Horizontal component = 80cos60 = 40 N

Therefore, the vertical component of the force is 69.28  N and the horizontal component of the force is 40 N.

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SOLUTION

Given the question in the question tab, the following are the solution step to get the number of books they have altogether.

Step 1: Write the notations for Joseph's and Mike's books

Step 2: Write the statements in a mathematical form

Step 3: Solve to get the value of j by using substitution method

Therefore, Joseph had 84 books initially.

Step 4: Get the number of books they had altogether by summing the number of books for the each of them initially

Hence, they both had 112 books altogether.

The rate of interest on the given principal is 7.5%.

Given that, simple interest = $56.25, principal = $300 and time period = [tex]2\frac{1}{2}[/tex] years.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.

Now, 56.26 = (300 × R × 2.5)/100

⇒ 5625 = 750R

⇒ R = 7.5%

Therefore, the rate of interest on the given principal is 7.5%.

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The distance between the two cyclists changing exists 38.4 meters per second.

A differential equation in mathematics exists an equation that links the derivatives of one or more unknown functions. Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.

A differential equation in mathematics is an equation that includes one or more functions and their derivatives. The rate of change of a function at a place is determined by the derivatives of the function. It is mostly employed in disciplines like physics, engineering, biology, and others.

There exists at least a couple of ways to work this. One exists to write the equation for the distance between the cyclists and differentiate it.

d² = (3900 + 32t)² + (5200 + 24t)²

simplifying the above equation, we get

(2d)d/dt = 2(3900 + 32t)(32) +2(5200 + 24t)(24)

At t = 0,

dd/dt = (32·3900 + 24·5200)/√(3900² + 5200²)

simplifying the above equation, we get

= (124800 + 124800)/√(15210000 + 27040000)

= 249600/6500 = 38.4 meters per second

Therefore, the distance between the two cyclists changing exists 38.4 meters per second.

The complete question is:

A road running north to south crosses a road going east to west at the point P. Cyclist A is riding north along the first road, and cyclist B is riding east along the second road. At a particular time, cyclist A is 39 hundred meters to the north of P and traveling at 32 meters per second, while cyclist B is 52 hundred meters to the east of P and traveling at 24 meters per second. How fast is the distance between the two cyclists changing?

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Answer: [tex]x=15[/tex]

Step-by-step explanation:

By the consecutive interior angles theorem,

[tex]150+3x-15=180\\\\3x-15=30\\\\3x=45\\\\x=15[/tex]

Step 1: redraw the figure given

Step 2: State the relationship between the lines

It can be observed that

(i) line XY is perpendicular to line PS

(ii) line XY is perpendicular to line QT

(iii) line PS is parallel to line QT

Hence, XY⊥PS, XY ⊥ QT, PS ║ QT, The Second option.

The vertex of a parabola is the extreme point (maximum or minimum, depending on the the sign of the quadratic coefficient).

In the graph, we can see that the x-coordinate of the vertex is x=-1 and the y-coordinate is y=3.

Then, we can write the coordinates of the vertex as (h,k) = (-1,3)

Answer: The coordinates of the vertex are (-1,3)

486lb of grass seed is required to cover the field on the right.

The area of Rectangle is length times of width

Let us find the areas of two rectangle larger and smaller.

Area of the larger rectangle:

60×90=5400 square feet.

Now divide the larger square area by the smaller square area:

Area of the smaller rectangle

40×50=200 square feet.

Now divide larger rectangle with smaller

5400/200 =27

27 is the ratio of the difference

27×18=486 lb.

Hence 486lb of grass seed is required to cover the field on the right.

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The true statements about the constraints in this situation are:

In order to determine the true statements, we would substitute the value of x and y into the given linear equation and then evaluate. From the information provided, the constraints in this situation are modeled or represented by this linear equation:

2x + 0.50y = 120

Where:

When x = 40 and y = 60, we have:

2x + 0.50y = 120

2(40) + 0.50(60) = 120

80 + 30 = 120

110 ≠ 120 (Not a solution).

When x = 30 and y = 120, we have:

2x + 0.50y = 120

2(30) + 0.50(120) = 120

60 + 60 = 120

120 = 120 (True solution).

Therefore, if we buy 30 pounds of beans we can buy with 120 pounds of rice.

When x = 0 and y = 240, we have:

2x + 0.50y = 120

2(0) + 0.50(240) = 120

0 + 120 = 120

120 = 120 (True solution).

Therefore, if we buy no beans we can buy 240 pounds of rice.

When x = 0 - 5 and y = 240 + 20, we have:

2x + 0.50y = 120

2(0 - 5) + 0.50(240 + 20) = 120

-10 + 130 = 120

120 = 120 (True solution).

Therefore, if we buy 20 more pounds of rice, we would have to buy 5 less pounds of beans.

When x = 0 + 10 and y = 240 - 60, we have:

2x + 0.50y = 120

2(0 + 10) + 0.50(240 - 60) = 120

20 + 90 = 120

110 = 120 (Not a solution).

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Answer:

12r^3

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

it doesn't seem to be correct question

x=3

Approximately 34% of people sleep more than 8.5 hours per night.

According to the Empirical Rule states for a normally distributed random variable: 68% of the measures are within 1 standard deviation of the mean, 95% of the measures are within 2 standard deviations of the mean and 99.7% of the measures are within 3 standard deviations of the mean. According to the question, Mean = 7 and Standard deviation = 1.5. Also, in the question the normal distribution is symmetric, which means that 50% of the measures are below the mean and the rest 50% are above the mean. Now, the mean is 7 and 8.5 is 1 one standard deviation above the mean. So, by the Empirical Rule, of the 50% of the measures that are above the mean, 68% are within 1 standard deviation of the mean (more than 8.5 hours). So, we get

0.5*0.68 = 0.34 which is equal to 34%.

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The possible values of x that satisfies the given dimensions and the condition that the volume must be no more than 280 cubic feet is x = [1,5]

The dimensions of the aquarium is: 2x ft , (x -1) ft, and (x + 2) ft. Since the volume must be no more than 280 ft³, it means:

V = 2x (x - 1) (x + 2) ≤ 280

Divide both sides by 2:

x (x - 1) (x + 2) ≤ 140

x³ + x² - 2x - 140 ≤ 0

(x - 5) (x² + 6x + 28) ≤ 0

Since x² + 6x + 28 is always greater than zero then x that satisfies the above inequality is:

x - 5  ≤ 0

or x  ≤ 5

Using the interval notation, x = (-∞, 5]

However, remember that the dimension is always a positive number.

Hence,

x - 1 ≥ 0

or x  ≥ 1

Therefore, the solution is [1, 5]

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To solve this problem, we need to use the Law of Cosines. The law states that given any triangle ABC:

Then;

Since we want to find the measure of angle x, we can use:

c = 175 mi

a = 200 mi

b = 50 mi

C = x

Now, by the Law of Cosines:

And solve:

To the nearest whole number, x = 54°