Solve for x, each figure is a trapezoid

Answer:

Step-by-step explanation:

To determine the percentage increase between 2017 and 2018, we need to calculate the difference between the two years and then divide by the 2017 value and multiply by 100. So, the calculation would be:

(9960,000 - 9640,000) / 9640,000 * 100 = 3.125%

So, the number of households increased by 3.125% from 2017 to 2018.

To find the number of households in 2019, we need to find the increase from 2018 to 2019. We can do this by multiplying the number of households in 2018 by the percentage increase, and then add that to the 2018 value. So, the calculation would be:

9960,000 * (3.125 / 100) + 9960,000 = 10,298,800

Therefore, there would be approximately 10,298,800 households in 2019, rounded to the nearest ten thousand.

The simplification of the given expression would be = 210

A fraction is defined as the expression of part of a whole value in the form of a denominator and a numerator.

The above statement can be expressed above mathematically as follows:

= 7/8 × 16 × 1/2× 30

= 3360/16

= 210

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The relationship representing the amount of water remaining in the pool when using the large hose to pump out is

a. 1200 - 60x = y

The amount of water to be pumped out = 1200 gallons

The rate of pumping out using the small hose 20 gallons of water per minute. = -20x

let each minute be x, hence every minute 20x volume of water leaves the pond

The equation is represented as

water remaining = 1200 - 20x

in 2 hours, we have  120 minutes, when will the water finish

water remaining = 0 = 1200 - 20x

20x = 1200

x = 1200 / 20

x = 60 minutes hence 1 hour

For the large hose the rate of pumping out is tripled hence

water remaining = 1200 - 60x

y = 1200 - 60x

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Answer:

Step-by-step explanation:

Since the polynomial has a root of multiplicity 2 at x = 3, it can be written as (x - 3)^2 times another polynomial Q(x). Also, since it has roots of multiplicity 1 at x = 0 and x = -4, it can be written as (x - 3)^2 * (x - 0) * (x + 4) * Q(x).

Next, we can use the fact that the polynomial goes through the point (5, 144) to find the formula for Q(x). The polynomial P(x) must satisfy P(5) = 144, so we can write:

(5 - 3)^2 * (5 - 0) * (5 + 4) * Q(5) = 144

4 * 9 * 9 * Q(5) = 144

36 * Q(5) = 144

Q(5) = 4

So, the polynomial P(x) can be written as:

P(x) = (x - 3)^2 * (x - 0) * (x + 4) * 4

  = 4 * (x - 3)^2 * (x - 0) * (x + 4)

  = 4 * (x^2 - 6x + 9) * x * (x + 4)

  = 4x^4 - 84x^3 + 378x^2 - 648x + 576

This is the formula for P(x).

(A) The angular speed of the wheel in radians per minute is 3.78 radians per minute.

(B) The linear speed of a passenger in miles per hour is 4.09 miles per hour.

Angular speed is the rate at which an object rotates, measured in radians per unit of time. The unit of radians is commonly used in circular motion problems because it allows us to express angles and rotational motion in a consistent way. Linear speed, on the other hand, is the rate at which an object moves in a straight line, measured in units of distance per unit of time.

(A) To find the angular speed of the Ferris wheel in radians per minute, we first need to convert the given rate of revolutions per hour to revolutions per minute. We can do this by dividing the rate by 60 since there are 60 minutes in an hour. Therefore, the wheel completes

=> 100/60 = 5/3 revolutions per minute.

Next, we need to find the angle that the wheel turns in one minute, which we can do by dividing a full rotation (360 degrees) by the number of revolutions per minute. In this case, the angle turned in one minute is

=> (360 degrees)/(5/3 revolutions per minute) = 216 degrees per minute.

To convert this angle to radians, we multiply by (π/180) since there are π/180 radians in one degree. This gives us an angular speed of

=> (216 * π/180) = 3.78 radians per minute.

(B) Using these values, we can calculate the linear speed of the passenger as follows:

Linear speed = (distance traveled)/(time taken) = (π * 72 feet)/(1/5 minutes) = (π * 72 * 5 feet/minute) = (360 * π feet/minute)

To convert this speed to miles per hour, we divide by the number of feet per mile (5280) and multiply by the number of minutes per hour (60), giving us:

Linear speed = (360 * π feet/minute)/(5280 feet/mile) * (60 minutes/hour) = 4.09 miles per hour (rounded to two decimal places).

Therefore, the linear speed of the passenger on the Ferris wheel is approximately 4.09 miles per hour.

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The term that best describes the point W in the triangle is given by the following option:

B. Orthocenter.

The orthocenter is the point where all three altitudes of a triangle will intersect.

An altitude is a line which passing through one of the three vertices of the triangle and is perpendicular to the opposite side relative to this vertex.

Hence point W is the orthocenter of triangle XYZ.

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Answer:

he had to go to china for the milk and while he was there he got kidnapped so it might be a while

sorry bro

Step-by-step explanation:

Answer:

Step-by-step:

he is just trying to find the best milk he can don't even worry about it just  become rich he's sure to come back then-

Answer:

7 degrees C

Step-by-step explanation:

To solve this question, we can start by ordering the temperatures from least to greatest:

4, 1, 0, -2, -1, -3, 1, -2, 3, -1  --> -3, -2, -2, -1, -1, 0, 1, 1, 3, 4

the lowest temperature would be -3 in this list, and the highest temperature in this list would be 4. We can find the difference in temperature using subtraction:

4-(-3) = 4+3=7

The difference is 7 degrees C.

Answer:

Therefore, z = 1 + i.

Step-by-step explanation:

Given that the argument of z + 1 is pi/6 and the argument of z - 1 is 2*pi/3, we can use the fact that the argument of a complex number is equal to the angle between the positive x-axis and the line connecting the origin to the complex number in the complex plane.

Let's call the complex number z = a + bi. Then, z + 1 = a + (b + 1), and z - 1 = a - (b - 1).

Using the argument values given, we have:

arg(z + 1) = pi/6, so the line connecting the origin to z + 1 makes an angle of pi/6 with the positive x-axis.

arg(z - 1) = 2pi/3, so the line connecting the origin to z - 1 makes an angle of 2pi/3 with the positive x-axis.

From the above information, we can sketch the complex plane and find the location of the complex number z. We then have two equations for a and b in terms of the argument of the complex numbers:

a = (z + 1 + z - 1)/2 = 1

b = (z + 1 - z - 1)/2 = 1

Therefore, z = 1 + i.

The perimeter of the pentagon PQRST will be equal to the perimeter of the pentagon ABCDE.

The regular polygon's edges are all identical to one another. The relationship between the number of sides to the mean distance determines the regular polygon's perimeter when it has n sides.

Then the perimeter of the pentagon ABCDE is given as,

P = AB + BC + CD + DE + EA

And the perimeter of the pentagon PQRST is given as,

P = PQ + QR + RS + ST + TP

Regular pentagons ABCDE and PQRST are congruent with each other.  Then the perimeter of the pentagons will be identical to each other.

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From given quadratic equation:

Exact Cost of 31st food processor = $15.6

Approx. cost of 31st food processor  =  $15.2

What is a quadratic equation?

The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).

It is given that the quadratic equation has two roots. Roots might have either a real or imaginary nature.

The given quadratic equation for the cost of producing x food processors is:

 C(x) = 2400 + 40x - 0.4x²

a) The exact cost of producing the 31st food PROCESSOR is:

cost of 31 food processors - cost of 30 food processors = C(31) - C(30)

= (2400 + 40*31 - 0.4*31²) - (2400 + 40*30 - 0.4*30²)

= 3255.6 - 3240 = $15.6

b) The marginal cost at x = 31

Differentiate the quadratic equation

C'(x) = 40 - 0.8x

Marginal cost = C'(31) = 40 - 0.8*31 = $15.2

So the cost of producing the 31st food processor is approx $15.2.

Therefore from the given quadratic equation:

Exact Cost of 31st food processor = $15.6

Approx. cost of 31st food processor  =  $15.2

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Answer:

Step-by-step explanation:

To prove that sin(51) + sin(81) - cos(21) = 0, we can use the trigonometric identity:

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

We can rewrite 51 and 81 as the sum of two angles:

51 = 45 + 6

81 = 90 - 9

Using the above identity, we can write:

sin(51) = sin(45 + 6) = sin(45)cos(6) + cos(45)sin(6) = (2/2)sin(6) + (2/2)cos(6) = sin(6) + cos(6)

and

sin(81) = sin(90 - 9) = sin(90)cos(9) - cos(90)sin(9) = 0 + (-1)sin(9) = -sin(9)

Finally,

sin(51) + sin(81) - cos(21) = sin(6) + cos(6) - sin(9) - cos(21) = (sin(6) + cos(6)) - (sin(9) + cos(21))

We know that sin(90 - x) = cos(x) and cos(90 - x) = sin(x), so we can rewrite the right-hand side as:

(sin(6) + cos(6)) - (cos(90 - 9) + sin(90 - 21)) = (sin(6) + cos(6)) - (cos(9) + sin(69))

We also know that sin(180 - x) = -sin(x) and cos(180 - x) = -cos(x), so we can rewrite the right-hand side as:

(sin(6) + cos(6)) - (cos(9) + -sin(111)) = (sin(6) + cos(6)) - (-sin(111) + cos(9))

Since sin(6) + cos(6) = sin(6 + 90) = sin(96) and -sin(111) + cos(9) = sin(69 - 180) = -sin(111), we can simplify the expression further to:

sin(6) + cos(6) - (-sin(111)) + cos(9) = sin(96) + cos(9)

Since sin(x + y) = sin(x)cos(y) + cos(x)sin(y), we can write:

sin(96) + cos(9) = sin(60)cos(36) + cos(60)sin(36) = (2/2)sin(36) + (√3/2)cos(36) = sin(36) + (√3/2)cos(36)

Finally, since sin(2x) = 2sin(x)cos(x), we can write:

sin(36) + (√3/2)cos(36) = 2sin(18)cos(18) + (√3/2)cos(36) = 2(√2/2)(√2/2) + (√3/2)(√2/2) = (√2 + √6)/2 + (√6/2) = (√2 + √6)

So, sin(51) + sin(81) - cos(21) = (√2 + √6) ≠ 0.

Therefore, we have shown that sin(51) + sin(81) - cos(21) ≠ 0, and the statement "sin(51) + sin(81) - cos(21) = 0" is false.

Answer:

-2x^4+4x^3+8x

Step-by-step explanation:

please check the answer given

Answer:

C.Only Maryanne's equation has the same solution as the original equation.

The solution is : 39 is the solution to Mr. Smith's equation.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

given that,

the equation is:

(16-2w)^2 + (3y÷3z)

Let w=5 y=9 and z=3

(16-2*5)^2 + (3*9÷3*3)

PEMDAS says parentheses first

Multiply and divide in the parentheses

(16-10)^2 + (27÷9)

Then add and subtract in the parentheses

(6)^2 + (3)

Now the exponent

=36 +3

=39

Hence, The solution is : 39 is the solution to Mr. Smith's equation.

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complete question:

What is the solution to Mr. Smith's equation?

Answer:

-9+3x

Step-by-step explanation:

(-3x2 + x + 5) − (4x2 − 2x)

(-6+x+5)-(8-2x)

(-1+x)-8+2x

-1+x-8+2x

-9+3x

The value of k is,

The probability distribution as a table:

r   1     2          3

P(X)   0    1/15  2/15

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

To find the value of k, we can use the fact that the sum of the probabilities for all possible values of X must equal 1.

Therefore, we have:

P(X = 1) + P(X = 2) + P(X = 3) = k(4(1)(1²) + 4(2)(2²) + 4(3)(3²))

                                              = 24k

Since we also know that P(X = 1) = 0, we have:

P(X = 1) + P(X = 2) + P(X = 3) = P(X = 2) + P(X = 3) = 0.8

Substituting this into the equation above, we get:

0.8 = 24k

k = 0.8/24 = 1/30

Therefore, the probability distribution can be written as:

r 1 2 3

P(X) 0 1/15 2/15

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Answer:

the last one

Step-by-step explanation:

first you have to distribute the 5 to all the variables.

when you do that you get

x---9x5=45

y---1x5=5

z---4x5=20

hope it helped

please mark brainliest

Answer:

Step-by-step explanation:

To find the total distance traveled by the hikers to get home, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the straight line distance) is equal to the sum of the squares of the lengths of the other two sides.

Since the hikers traveled 3 km north and 4 km east, we can consider this as the sides of a right-angled triangle, with the hypotenuse being the straight line distance traveled to get home. So, the square of the distance traveled to get home is equal to the sum of the squares of the sides, i.e., 3^2 + 4^2 = 9 + 16 = 25. Taking the square root of 25 gives us 5 km, so the distance traveled by the hikers to get home is 5 km.

The fractions greater than 5/8 are 6/8, 7/8 and 8/8

Fractions greater than 5/8

Using the number line as a guide, we have the following:

Fractions greater = 6/8, 7/8 and 8/8

Fractions less than 3/8

Using the number line as a guide, we have the following:

Fractions less = 1/8 and 2/8

Fractions greater than 3/8

Using the number line as a guide, we have the following:

Fractions greater = 4/8, 5/8, 6/8, 7/8 and 8/8

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The relation is a function only if for element x in Set X, there is only one element in Set Y so, the choice B shows the relation.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable).

When a relation will be called as a function .

Consider there be a relation R from a set X to a set Y .

Since the relation will be called a function if each element of set X is related to exactly one element in set Y.

which is, an element x in X, there is only one element in Y that x is related to.

Therefore , the correct option is B.

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The equation to represent the function is y = 6x + 10 where y is the height of the drone in meters and x is the time in seconds. so the drone rises 6 meters per second.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Let us  find the rate of change, we can divide the total change in the height of the drone by the time taken for the change.

rate of change = (change in height) / (time taken)

(40 m - 10 m/ (5 s - 0 s)= 30 m/5 s=6m/s

The drone rises 18 m every 3 s

rise per second = 18 m / 3 s = 6 m/s

This means that the initial height of the drone is 10 meters, since it takes 3 seconds for the drone to rise to a height of 28 meters

Therefore, the equation to represent the function is:

y = 6x + 10

where y is the height of the drone in meters and x is the time in seconds.

Therefore, the drone rises 6 meters per second.

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Answer:

been a while, so I'd check w someone else too, but hope this helps

Step-by-step explanation:

The total area of the figure is 258cm². Thus, option 3 is corect.

Given:

shorter side: 18 centimeters

perpendicular height : 4 centimeters

portion from a point to a vertical line created by two vertices : 3centimeters

height : 12 centimeters

from figure we know that,  it is the vertex's height as well as the length of the sides to multiply together and we also have to divide since there is 5 sides

So , after multiplying the vertex height and sides and dividing it by the 5 , we get 258 cm²

Hence , the total area of the figure is 258cm².

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The volume of the solid obtained by rotating about the x-axis the region enclosed by the curves is 32π/5 cubic units.

In this problem, we are asked to find the volume of a solid obtained by rotating a region enclosed by curves about the x-axis. We will use integration to calculate the volume.

First, let's sketch the region and the solid we need to find the volume of.

The region is enclosed by the curves

=> y = 16 /(x² + 16), y = 0, x = 0, and x = 4.

When we rotate this region about the x-axis, we get a solid with a hole in the center, shaped like a donut.

To find the volume of this solid, we can use the method of cylindrical shells.

We start by taking a thin strip of the region, parallel to the y-axis, and of width dy. This strip has height y, and we rotate it about the x-axis to get a cylindrical shell of thickness dy and radius x.

The volume of this cylindrical shell is given by the formula V = 2πxy dy, where x is the distance from the y-axis to the edge of the shell.

To express x in terms of y, we can solve for x in the equation

y = 16 /(x² + 16).

y(x² + 16) = 16

x² = 16/y - 16

x = √(16/y - 16)

Now we can substitute x into the formula for V to get:

V = 2πx(16/(x² + 16)) dy

[tex]= 2\pi(16/y - 16)^{1/2}(16/y) dy \\\\= 32\pi(y - y^{3/2}) dy[/tex]

To find the total volume, we integrate this expression from y = 0 to y = 1 (since the maximum value of y is 16/16 = 1):

[tex]\int_0^1 32\pi(y - y{(3/2)}) dy = 32\pi/5[/tex]

Therefore, the volume of the solid obtained by rotating the region about the x-axis is 32π/5 cubic units.

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Answer:

f(-7) = 15

Step-by-step explanation:

Subsitute x = - 7 into f (X) = - 3 (x+2)

f(-7) = -3 x (-7+2)

calculate the sum or difference

f(-7) =-3 x (-5)

determine the sign for multiplication or division

f(-7)=3x5

calculate the product or quotient

f(-7)=15

final awnser f(-7)=15

The height of each elevator at this time is, -2.5 m, negative means below ground level.

The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.

Distance = Time × Speed

To find how long it would take each elevator to reach ground level, we can set h = 0 in the given expressions for their travel times:

Elevator A:  

= 0.8h + 16

= 0.8(0) + 16

= 16 seconds

Elevator B:  

= -0.8h + 12

= -0.8(0) + 12
= 12 seconds

Therefore, elevator A would take 16 seconds and elevator B would take 12 seconds to reach ground level at this time.

To find at what height the elevators pass each other, we can set their travel times equal to each other and solve for h:

0.8h + 16 = -0.8h + 12

1.6h = -4

h = -2.5

Now, we can substitute value of h in the expression

Elevator A:

= 0.8(-2.5) + 16

= 14 seconds

Elevator B:

= -0.8(-2.5) + 12

= 14 seconds

Therefore, the elevators would pass each other 14 seconds after they both start moving towards each other.

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The complete question:

Elevators A building has two elevators that both go above and below ground.

At a certain time of day, the travel time it takes elevator A to reach height h in meters is 0.8h+16 seconds.

The travel time it takes elevator B to reach height h in meters is -0.8h+12 seconds.

How long would it take each elevator to reach ground level at this time? If the two elevators travel toward one another, at what height do they pass each other? How long would it take?

On solving the provided question, we can say that  inches if a cylinder's enlarged capacity is 45 in3, its compressed volume is 6 in cubic .

One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.

In a certain engine, the compression ratio is 7.5: 1.

A cylinder's enlarged volume is 45 in3 in.

We must determine the cylinder's compressed volume.

Let v represent the cylinder's compressed volume.

The aforementioned circumstance can be described as

7.5 : 1 = expanded volume : compressed volume

7.5/1 = 45/v

7.5 = 45/v

v = 45/7.5

v = 6 cubic inches .

Therefore, if a cylinder's enlarged capacity is 45 in3, its compressed volume is 6 in cubic .

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Answer:

The question is incomplete

Answer:

It was 1/3 before

Step-by-step explanation: