Find the area of shaded region?
Please help me!!!!​

If the engine with 12 gallon fuel tank uses fuel at a constant rate of 0.6 gallons per hour , then the equation to find number hours the engine has been running is "12 - 0.6x = 9.3"  .

the total capacity of the tank is = 12 gallon ;

the constant use rate of engine is = 0.6 gallons per hour ;

the amount of fuel left in the tank is = 9.3 gallons ;

let the number of hours the engine is running is = x hours  ;

the above situation can be represented as ⇒ 12 - 0.6x = 9.3 ;

⇒ 12 - 0.6x = 9.3  ;

⇒ 12 - 9.3 = 0.6x  ;

⇒ 0.6x = 2.7  ;

⇒  x = 2.7/0.6  ;

⇒ x = 4.5 hours

Therefore , the engine has been running for 4.5 hours .

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a. There are 10⁹ hertz in 1 giga hertz and 10^12 hertz in one terahertz

b. The channels frequency in hertz 6×10⁷hertz

c. The frequency of a microwave in hertz is 3× 10^10 hertz

d. The frequency of light is 10⁵ times greater than the frequency of the radio station

Frequency describes the number of waves that pass a fixed place in a given amount of time. So if the time it takes for a wave to pass is is 1/2 second, the frequency is 2 per second. If it takes 1/100 of an hour, the frequency is 100 per hour.

The S.I unit of frequency is hertz and it has other bigger unit stated as follows:

1 kilohertz = 10³hertz

1megahertz = 10⁶ hertz

1 gigahertz = 10⁹ hertz

1 tera hertz = 10^12 hertz

Therefore 60mega hertz = 60× 10⁶ = 6×10⁷

30 gigahertz = 30 × 10⁹ = 3 × 10^10

if the frequency of light is 1000 tera hertz and 100 mega hertz is the frequency of a radio station , then the frequency of light will be 1000×10^12 ÷ 100× 10⁶ = 10⁵ greater than the frequency of the radio station.

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Answer:

To solve the equation 7cos(9x)−1=1, we first need to move the 1 to the left side of the equation:

7cos(9x) = 2

To find the solutions of the equation, we can divide both sides by 7:

cos(9x) = 2/7

Now we will use the inverse cosine function, denoted as arccos, to find the angle that has a cosine value of 2/7. Since the function cos is periodic with period 2Pi, it's range is [-1,1], we will look for the solutions between 0 and 2Pi.

x = (1/9)arccos(2/7) + (2kPi)/9 for k =0,1,2,....

we can also express the solution in degrees by multiplying the radian measure with 180/Pi.

x = (20/63)arccos(2/7) + (160*k) for k =0,1,2,....

or

x = (20/63) * arccos(2/7) * (180/pi) + (160*k) for k =0,1,2,....

where k is an integer.

So, x = (20/63) * arccos(2/7) * (180/pi) + (160*k) where k =0,1,2,.... is an expression that represents all solutions to the equation in degrees.

Let a = units of A produced

Let b = units of B produced

At least 30 units of product A and 10 units of product B are required daily, and the maximum number of units per day should not exceed 80.

Therefore

a ≥ 30

b ≥ 10

a + b ≤ 80

Product A yields a profit of $15 and product B yields a profit of $8.

Therefore the objectve profit function is

P(a,b) = 15a + 8b

Answer:

The objective function is

P(a,b) = 15a + 8b, subject to

a >= 30;  b>= 10;  a+b <= 80

Create a graph that displays the constraints and calculates maximum profit at the boundary points. The solution region is shaded.

The maximum profit occurs when a=70 and b=10.

Answer:

P= 15a + 8b

Step-by-step explanation:

Answer:

..........................

The perimeter of the given figure is 79.4 units.

The perimeter of a polygon is defined as the length of the boundary around the sides of the polygon. The perimeter of a polygon can be calculated by calculating the sum of the lengths of the sides of the polygon.  

Here we have

EF = 8, FD = 10, ED = 11, IG = 24, and HG = 26.4  

As we know,

Perimeter = Sum of all sides  

The perimeter of GHI = (EF + FD + ED + IG + HG)  

=  8 + 10 + 11 + 24 + 26.4  

= 79.4 units

Therefore,

The perimeter of the given figure is 79.4 units.

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The distance between the two points R and S is √2.

The length of the line segment connecting any two points represents the distance between them. There is just one line that connects the two places.

The distance between the two points R and S can be calculated using the Pythagorean theorem. Given the coordinates (x, y) for point R and (x + 1, y + 1) for point S, the distance d between R and S is given by:

d = √((x + 1 - x)^2 + (y + 1 - y)^2) = √(1^2 + 1^2) = √2.

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A vector that is perpendicular to both of the other two non-parallel vectors is the result of their cross-product.

You can utilize methods based on the dot-product and cross-product of vectors to create a vector that is perpendicular to another supplied vector. The total of the products of the relevant components is the dot-product of the vectors A = (a1, a2, a3) and B = (b1, b2, b3):

AB = a1 b2 + a2 b2 + a3 b3. The dot product of two vectors that are perpendicular is equal to zero.

The formula for calculating the cross-product of two vectors is AB = (a2 b3 - a3 b2, a3 b1 - a1 b3, a1 b2 - a2*b1).

A vector that is perpendicular to both of the other two non-parallel vectors is the result of their cross-product.

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Answer:

answer is no

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

top: -20/(-4) = 5

bottom: -49+44 = -5

5/(-5) =-1

The value of FJ is 39 units.

See the attached figure to better understand the problem

We know that

If two triangles are similar, then the ratio of their corresponding sides is proportional and their corresponding angles are congruent.

According to this problem,

△FEG is similar to △FHJ  ( by AA Similarity Theorem)

so

[tex]\frac{FE}{FH} = \frac{FG}{FJ}[/tex]

We have,

FE = HF + EH = (26 + 14 ) units

FE= 40 units

FH = HF = 26 units

FG = 60 units

substitute the given values,

[tex]\frac{40}{26} = \frac{60}{FJ}[/tex]

[tex]FJ = \frac{26 * 60}{40}[/tex]

FJ =  39

So, the value of FJ is 39 units.

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Answer:
3(n+7) =
(3)(n) + (3)(7) =
3n + 21

Step-by-step explanation:

I hope this helps you :D

The fire station should be located at the midpoint (a/2) of the road to minimize the expected distance from the fire.

The total distance cost will be infinite if we start at one point on a given line at an infinite distance. However, as we move this point toward the given points, the total distance cost begins to decrease. After a while, it then increases once more, reaching infinite at the other infinite end of the line. Therefore, the distance cost curve resembles a U-curve, and its bottom value must be determined.

The fire station should be located at the midpoint (a/2) of the road (0,a) to minimize the expected distance from the fire.

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In the given image the triangle POR and triangle FGH are not equal or similar to each other.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

In ΔPQR, the line segment PQ measures 35 units.

In ΔPQR, the line segment PR measures 49 units.

In ΔPQR, the line segment QR measures 63 units.

In ΔFGH, the line segment FG measures 69 units.

In ΔFGH, the line segment GH measures 38 units.

In ΔFGH, the line segment HF measures 67 units.

These two triangles are not similar to each other.

Both these triangles have different measurements of line segments.

Both these triangles have no data available for their angles.

The only way the two triangles are similar is that they both are scalene triangles as they both have different measuring sides.

Therefore, the two triangles are not similar.

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The percent of error is 17.65% .

The percent of error is a way to measure the difference between the expected value and the actual value. In this case, Peter expected to earn $425 in a week but he actually earned $500.

So, the difference between the expected value and the actual value is $75. The percent of error is calculated by taking the difference between the actual value and the expected value, dividing that by the expected value, and multiplying the result by 100%.

In this case, (500-425)/425*100% = 17.65%, which means that Peter's actual earnings were 17.65% higher than what he expected to earn.

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Answer:

-7

Step-by-step explanation:

angles in a triangle add up to 180⁰

90⁰+30⁰+(x+67)=180⁰

187+x=180⁰

x=180⁰-187⁰

x=-7

In order to avoid using the variable "Vi", the equation which you should use include the following: D) Ax = Vft – 1/2at².

In Mathematics, the third equation of motion is represented by this mathematical expression:

Ax = Vit + ½at²     ......equation 1.

Where:  

From the first equation of motion, we have:

Vf = Vi + at

Making Vi the subject of formula, we have:

Vi = Vf - at    ......equation 2.

Substituting the equation, we have:

Ax = (Vf - at)t + ½at²

Ax = Vft - at² + ½at²

Ax = Vft + ½at²

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The diagonal is equal to the sum of the square roots of the width and height.[tex]\sqrt{}[/tex]14[tex]n^{2}[/tex]

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The estimated cost of tuition in 2018 using this linear function model is $726,430

What is the linear function?

A linear function is a mathematical function that describes a straight line. The general form of a linear function is:

y = f(x) = mx + b

To estimate the cost of tuition in 2018 using a linear function model, we can use the two given data points to find the slope and y-intercept of the line.

First, we can find the slope of the line by using the formula:

m = (y2 - y1) / (x2 - x1)

Where (x1, y1) is the data point for 2002 and (x2, y2) is the data point for 2012.

Substituting the values, we get:

m = (8,240 - 4,790) / (2012 - 2002) = 3,450 / 10 = 345

Next, we can use one of the data points and the slope to find the y-intercept of the line. Let's use the data point for 2002:

y = mx + b

4,790 = 345 * 2002 + b

b = 4,790 - 345 * 2002 = -1,015,290

So, the equation of the line is y = 345x - 1,015,290

To estimate the cost of tuition in 2018, we can substitute x = 2018 into the equation:

y = 345(2018) - 1,015,290 = 726,430

Hence, the estimated cost of tuition in 2018 using this linear function model is $726,430

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The value is a parameter because the class of 28 students is a population.

A statistic is a measure calculated from a sample of the population, whereas a parameter is a measure that is calculated from the entire population. It is generally a numeric value that is used to characterise a population trait. A probability distribution is defined or described by a fixed value that is typically unknown.

The population's mean, variance, and standard deviation are just a few parameters. By employing statistical techniques like maximum likelihood estimation, these parameters are often calculated from a sample of data. In the given question, since from a class of 28, the average score was 72% of the population which is the total, this value is a parameter.

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If at local Convenience store , William buys 3 soft drinks and 2 hot dogs for $7.70, while Sarah buys 2 soft drinks and 1 hot dog at cost of $4.55 , then the cost of 1 soft drink is $1.4   and cost of 1 hot dog is $1.75  .

We will use system of equations to find cost of 1 soft drink and 1 hot dog. let the cost of 1 soft drink is = $x  ;  and

let the cost of 1 hot dog is = $y  ;

So , for William the situation is represented as ;

⇒ 3x + 2y = 7.70 .....equation(1)

and for Sarah the situation is represented as ;

⇒ 2x + y = 4.55    ....equation(2)

we first solve equation(1) for y:

⇒ y = (7.70 - 3x)/2

We can substitute this expression for y in equation (2) and solve for x:

⇒ 2x + (7.70 - 3x)/2 = 4.55

⇒ 4x + (7.70 - 3x) = 4.55×2

⇒ 4x -3x = 9.1 - 7.70

⇒ x = 1.4

So, the cost of 1 soft drink is $1.4  ,

Now , We can use this value of x to find the cost of 1 hot dog:

⇒ y = (7.70 - 3x)/2

⇒ y = (7.70 - 3×1.4)/2

⇒ y = (7.70 - 4.2)/2

⇒ y = 3.5/2  ;

⇒ y = 1.75

So, the cost of 1 hot dog is $1.75  .

Therefore, one soft drink costs $1.4  and one hot dog costs $1.75  .

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Answer:

Category A 0.75

Category B 0.25

Hope it helps !!

The area of rectangle with the given height and width is found as: Area = 5x³ + 19x² + 22x + 18.

So, from the definition of the area of the rectangle.

Area = length x width

Given:

Thus,

Area = (5x + 4)(x^2+3x+2)

Simplifying,

Area = 5x(x^2+3x+2) + 4(x^2+3x+2)

Area = 5x³ + 19x² + 22x + 18

Thus, the area of the rectangle with the given height and width is found as: Area = 5x³ + 19x² + 22x + 18.

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The complete question  is-

A rectangle has a height of x+4x+4 and a width of x^2+3x+2. Express the area of the entire rectangle.

Answer:

The formula is going to be 17 hrs

Answer:

try your best

Step-by-step explanation:

u can do it!!

The difference between the volume of the sphere and an approximation using a left sum with 16 intervals is 17.51 mm.

The term called volume in math is known as a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Here we know that the sphere has a radius of 2 mm.

Then the volume of the sphere is calculated by using the formula,

=> V = 4/3πr³

Here we know that the value of r = 2.

Then the volume is calculated as,

=> V = 4/3 x π x 2³

When we simplify this one then we get,

=> V = 10.67π = 33.51

Here we need to find the difference between the volume of the sphere and an approximation using a left sum with 16 intervals is

=> 33.51 - 16

=> 17.51

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The 12th term of the geometric sequence 7, -21, 63 is -1240029, this is determined using the Geometric progression formula.

When one term is varied by another by a common ratio, the series is referred to as a geometric progression or sequence. When we multiply the previous term by a constant (which is non-zero), we get the following term in the sequence.

The geometric progression is given by the formula:

aₙ = arⁿ⁻¹

a = first term = 7

r = common ratio = - 21 / 7 = - 3

n = number of terms = 12

Therefore, substituting the values in the GP:

a₁₂ = 7 × -3¹²⁻¹

a₁₂ = 7 × -3¹¹

a₁₂ = 7 × -177147

a₁₂ = -1240029

Therefore, the 12th term of the geometric progression is -1240029.

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If the triangles ABC and DEF are similar, then the measurement of line segment DE = 108.72 units.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

It is given that triangle ABC is similar to triangle DEF.

It can be seen in the image that ΔDEF is a dilated version of ΔABC.

In ΔABC the measurement of side AB = 23 units

In ΔABC the measurement of side BC = 11 units

In ΔDEF the measurement of side EF = 52 units

In ΔDEF the measurement of side DE = x units

Apply the formula for indirect measurement to find the measurement of side DE.

AB/DE = BC/EF

Substitute the values in the equation -

23/x = 11/52

23 × 52 = 11x

x = (23 × 52)/11

x = 1196/11

x = 108.72

Therefore, the measurement of DE is 108.72 units.

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Answer:

Solution set for x is x ≤ -3
First option

Step-by-step explanation:

We have the equation

- 4x ≥ 12

Divide both sides by 4:

- x ≥ 12/4

-x ≥ 3

Multiply by -1 to make x positive. When we multiply an inequality by a negative number the inequality sign changes:  ≥ becomes ≤

Therefore we get
x ≤ 3

On the number line this is represented by the first choice

Note that the 3rd and 4th choices are easily eliminate since they represent ≥ -3 and > -3

Choice #2 has an unfilled circle at -3. This represents a < inequality

A filled circle represents a ≤ inequality

Answer

Solution set for x is x ≤ -3
First option