Hello everyone-SOLVING nonlinear system of equations- ALGEBRA 1

The area of the Shaded region, when the frame is 1 unit wide, is 20 square units.

The area of the shaded region when one rectangle is framed within another and the frame has a width of 1 unit, we need to calculate the difference between the areas of the outer rectangle and the inner rectangle.

the dimensions of the outer rectangle as length and width, and the dimensions of the inner rectangle as length' and width'. Based on the information provided, the length and width of the outer rectangle are 5 and 7 units, respectively.

The dimensions of the inner rectangle can be found by subtracting twice the width of the frame (1 unit) from the dimensions of the outer rectangle:

Length' = length - 2 * frame width = 5 - 2 * 1 = 3 units

Width' = width - 2 * frame width = 7 - 2 * 1 = 5 units

Now we can calculate the areas of the outer and inner rectangles:

Area of the outer rectangle = length * width = 5 * 7 = 35 square units

Area of the inner rectangle = length' * width' = 3 * 5 = 15 square units

Finally, to find the area of the shaded region, we subtract the area of the inner rectangle from the area of the outer rectangle:

Area of shaded region = Area of outer rectangle - Area of inner rectangle = 35 - 15 = 20 square units

Therefore, the area of the shaded region, when the frame is 1 unit wide, is 20 square units.

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To determine whether the given differential equation is exact, we need to check if it satisfies the condition:

∂M/∂y = ∂N/∂x

where M and N are the coefficients of dy and dx, respectively, in the differential equation:

(2sin(x)cos(y) − 2y^2)dy - (xsin^2(y) - 4x^2)dx = 0

Now, let's find the partial derivatives:

∂M/∂y = 2cos(x)cos(y) - 4y

∂N/∂x = -sin^2(y) - 8x

The equation is exact if ∂M/∂y = ∂N/∂x. Let's check:

2cos(x)cos(y) - 4y = -sin^2(y) - 8x

Rearranging the equation, we get:

sin^2(y) - 2cos(x)cos(y) - 8x + 4y = 0

Since ∂M/∂y = ∂N/∂x, the given differential equation is exact.

To solve the exact differential equation, we need to find a potential function φ(x, y) such that:

∂φ/∂x = M

∂φ/∂y = N

Integrating M with respect to x, we get:

φ(x, y) = ∫(2sin(x)cos(y) - 2y^2)dx

        = 2∫sin(x)cos(y)dx - 2∫y^2dx

        = -2cos(x)cos(y) - 2xy^2 + g(y)

Here, g(y) is the constant of integration with respect to x.

Next, we differentiate φ(x, y) partially with respect to y and equate it to N:

∂φ/∂y = N

-2sin(x)sin(y) - 4xy + g'(y) = -sin^2(y) - 8x

From this equation, we can equate the coefficients of the terms involving y:

-2sin(x)sin(y) - 4xy = -8x

-2sin(x)sin(y) - 4xy + 8x = 0

Comparing the coefficients, we have:

g'(y) = 0

Integrating g'(y), we obtain:

g(y) = c

Here, c is the constant of integration with respect to y.

Finally, the potential function φ(x, y) becomes:

φ(x, y) = -2cos(x)cos(y) - 2xy^2 + c

Therefore, the solution to the given exact differential equation is φ(x, y) = -2cos(x)cos(y) - 2xy^2 + c, where c is an arbitrary constant.

Answer:

Step-by-step explanation:To find the diameter of a circular field given its circumference, we can use the formula:

Circumference = π * Diameter

In this case, the circumference is given as 132m. Plugging in the values into the formula, we have:

132m = π * Diameter

To solve for the diameter, we need to isolate it on one side of the equation. We can divide both sides of the equation by π:

132m / π = Diameter

Using a calculator, we can approximate the value of π as 3.14159. Plugging in this value, we have:

132m / 3.14159 ≈ Diameter

Simplifying the division, we get:

Diameter ≈ 42m

Therefore, the diameter of the circular field is approximately 42 meters

Given statement solution is :- It  would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

To find the cost of installing tile in the dining room and carpet in the bedroom, we need to calculate the areas of both rooms first.

Given:

Every 2 centimeters on the floor plan represents 1 meter of the house.

Dining Room:

On the floor plan, the dining room is 8 cm by 10 cm.

Converting this to meters, the dimensions of the dining room are 8 cm / 2 = 4 meters by 10 cm / 2 = 5 meters.

The area of the dining room is 4 meters * 5 meters = 20 square meters.

Bedroom:

On the floor plan, the bedroom is 6 cm by 10 cm.

Converting this to meters, the dimensions of the bedroom are 6 cm / 2 = 3 meters by 10 cm / 2 = 5 meters.

The area of the bedroom is 3 meters * 5 meters = 15 square meters.

Now, let's calculate the costs.

Cost of Tile:

The cost of installing tile is $34 per square meter.

The area of the dining room is 20 square meters.

Therefore, the cost of installing tile in the dining room is 20 square meters * $34/square meter = $680.

Cost of Carpet:

The cost of installing carpet is $21 per square meter.

The area of the bedroom is 15 square meters.

Therefore, the cost of installing carpet in the bedroom is 15 square meters * $21/square meter = $315.

Therefore, it would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

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Answer:

The linear equation satisfying the given condition is,

[tex]x=t+15[/tex]

where x is Ravi's age and t is the number of years

(after 10 years (t=10) his age becomes 25)

Step-by-step explanation:

Let x be Ravi's age

Now, his  current age is unknown, but if you add 10 to it, then it becomes 25, so

x + 10 =25

so, his current age is x = 25 =10

x = 15

Now, we find the linear equation satisfying the given condition,

Let t be the number of years that have passed since the present time

so, if 0 years have passed, his age will be 15 years

after 1 year, his age will be 16 years

after 10 years, his age will be 25 years and so on

so

[tex]x = t + 15[/tex]

this satisfies the given condition, since if we add ten years i.e t = 10,

then we get 25

The equation is:

Work/explanation:

Here's the linear equation for Ravi's age.

Ravi's age is x.

If you add 10 to x you get x + 10.

That gives 25.

So the linear equation is x + 10 = 25.

Answer: Therefore, the price of a wrap is Rs 92.2 and the price of a milkshake is Rs (92.2 + 7) = 99.2.

Step-by-step explanation:

Let's assume the price of a wrap is x (in Rs).

According to the given information, a milkshake costs Rs 7 more than a wrap. So, the price of a milkshake would be x + 7 (in Rs).

The group buys 8 milkshakes and 2 wraps. Since they bought 8 milkshakes, the total cost of milkshakes would be 8 * (x + 7) = 8x + 56 (in Rs).

Similarly, the total cost of wraps would be 2x (in Rs).

The total cost for the lunch is given as Rs 978.

So, we can set up the equation:

Total cost of milkshakes + Total cost of wraps = Total cost of lunch

(8x + 56) + (2x) = 978

Combining like terms:

10x + 56 = 978

Subtracting 56 from both sides:

10x = 922

Dividing both sides by 10:

x = 92.2

Answer:

AM=Dm=6

Step-by-step explanation:

this is a simple diameter....work on it by breaking it down

The measure of the angle m∠BEC is equal to 77° using the Angles of Intersecting Chords Theorem

The Angles of Intersecting Chords Theorem states that the angle formed by the intersection of the chords is equal to half the sum of the intercepted arcs, and conversely, that the measure of an intercepted arc is half the sum of the two angles that intercept it.

m∠BEC = (arc AD + arc BC)/2

m∠BEC = (45 + 109)/2

m∠BEC = 154/2

m∠BEC = 77°

Therefore, the measure of angle m∠BEC is equal to 77° using the Angles of Intersecting Chords Theorem

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The expression that will represent each side of the equilateral triangle shapes feild is 19x + 3.

An equilateral triangle is a shape that all the side lengths are of equal, given that the perimeter which is the total sum of the triangle boundary as 30x + 9, then each side is derived as follows:

30x + 9 = 3(10x + 3) {by factorization}

each side of the shape = 3(10x + 3)/3

each side of the shape = 10x + 3

Therefore, the expression that will represent each side of the equilateral triangle shapes feild is 19x + 3.

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When it comes to medication or medical care, the person who would usually face the greatest impact from a discrepancy in dosage is the individual who is undergoing the treatment.

Insufficient dosage may result in a lack of intended therapeutic effects and failure to improve the patient's condition as anticipated. Also, if the amount administered is excessive, the individual may suffer from negative consequences or possible injury.

It should be noted that the effects of a difference in medication dosage can differ based on the type of medicine, the condition being treated, and personal characteristics like age, weight, general health, and specific reactions or sensitivities.

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Answer:

The answer is,

[tex]p(x) = \sqrt[3]{2-x}[/tex]

Step-by-step explanation:

Answer:

Example 1: Find the perimeter of a triangle with sides measuring 5 centimeters, 9 centimeters and 11 centimeters. Solution: P = 5 cm + 9 cm + 11 cm = 25 cm

Step-by-step explanation:

Answer:

b. 25 cm

Step-by-step explanation:

P = all the sides added up

= 5 cm + 9 cm + 11 cm

= 25 cm

If Paul runs at the same pace, his rate will be 7 minutes per mile.

We know that, Paul runs 4miles in 28 minutes.

To find out his rate per mile, we need to divide 28 by 4.

Rate per mile,

27÷4

=7.

Therefore, Paul's rate is 7 minutes per mile.

h = hours till they're 58 miles apart

Check the picture below.

so they're travelling in opposite directions, however the combined distances is 58 miles at say "h" hours, by the time that happend Hopi has been walking "h" hours and Brittany has also being walking "h" hours too.

Since the combined distance is 58 miles than if Hopi has covered "m" miles then Brittany covered the slack of "58 - m".

[tex]{\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Hopi&m&15&h\\ Brittany&58-m&14&h \end{array}\hspace{5em} \begin{cases} m=(15)(h)\\\\ 58-m=(14)(h) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{substituting on the 2nd equation}}{58-(\stackrel{m}{15h})=14h}\implies 58=29h\implies \cfrac{58}{29}=h\implies \boxed{2=h}[/tex]

The total surface area of the pyramid is 405.08 cm²

We have a square pyramid. First, the base has a length of 8.2 cm, then the area of the base is:

B = (8.2cm)² = 67.24 cm²

And the area of base b and height h is:

A=  b*h/2

Here b = 8.2cm and h = 10.3cm, then:

A = (8.2cm*10.3cm)/2 =  84.46 cm²

And there are 4 triangular faces, so the total area is:

area =  67.24 cm² + 4*84.46 cm² = 405.08 cm²

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Step-by-step explanation:

the base of the pyramid has an area of b × h = 10 in × 5 in = 50 in²

a triangular face with a base of

10 inches has an area of (b×h)/2 = (10in×5.6in)/2 = 28in²

a triangular face with a base of

5 inches has an area of (b×h)/2 = (5in×7.1in)/2 = 17.75in²

the total surface is the sum of the rectangle plus the four triangles

50in² + 28in² + 28in² + 17.75in² + 17.75in² = 141.50in²

-1

We can solve in this way,

-3x-5x+8=16

-8x=16-8

-8x=8

x= -8/8

x= -1

Therefore for this equation, x= -1.

The logical fallacy in the provided statement is Ad Hominem.

The speaker in the statement is attacking the character and appearance of the other person ("dirty, longhaired hippie") instead of addressing the actual issue or argument at hand.

The speaker is making assumptions and judgments about the credibility and honesty of the other person based on their appearance and the type of car they drive, rather than presenting valid evidence or reasoning.

This fallacy diverts attention from the topic being discussed and focuses on personal characteristics or attributes of the individual.

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The value of side length x and y in the right triangle is 5.7 and 9.4 respectively.

The figure in the image is a right triangle.

Angle G = 59 degree

Hypotenuse = 11

Adjacent to angle G = x

Opposite to angle G = y

To solve for the missing side length x and y, we use the trigonometric ratio.

Note that:

Sine = opposite / hypotensue

Cosine = adjacent / hypotensue

Solving for x:

cos( G ) = adjacent / hypotensue

Plug in the values:

cos( 59 ) = x / 11

Cross multiply

x = cos( 59 ) × 11

x = 5.7 units

Solving for y:

sin( G ) = opposite / hypotensue

Plug in the values:

sin( 59 ) = y / 11

Cross multiply

y = sin( 59 ) × 11

y = 9.4 units

Therefore, the value of y is approximately 9.4 units.

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Jerrica would have to win 40 additional games in a row to have an 80% winning record. This would bring her total wins to 20 + 40 = 60, and her total games played to 35 + 40 = 75.

To determine how many games Jerrica would have to win in a row in order to have an 80% winning record, we need to calculate the number of games she needs to win out of a certain total.

Let's denote the number of games she needs to win in a row as x. If she wins x additional games, her total wins would be 20 + x, and her total games played would be 35 + x.

To have an 80% winning record, she would need to win 80% of the total games played. Mathematically, this can be expressed as:

(20 + x) / (35 + x) = 80 / 100

Cross-multiplying, we get:

100(20 + x) = 80(35 + x)

Expanding and simplifying:

2000 + 100x = 2800 + 80x

Subtracting 80x from both sides:

20x = 800

Dividing by 20:

x = 40

Jerrica would have to win 40 additional games in a row to have an 80% winning record. This would bring her total wins to 20 + 40 = 60, and her total games played to 35 + 40 = 75.

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Answer:

15 is 7 more than 8.

Step-by-step explanation:

The only plausible answer.

For the given graph of f(x), find the following values-

a. lim_x→4⁺  f(x) = ∞      b. lim_ x→-3 f(x) = -2      c. lim_x→6 f(x) = DNE

d. lim_ x→4⁻ f(x) = ∞     e. lim_ x→2⁺ = 2         f. f(-3) = -2  g. lim_x→2⁻ = 1

h. lim_x→-6 = 0.5

i. The type of discontinuity at x = 4 is an infinite discontinuity

j. There is no discontinuity at x=2 because the function is defined at x=2

For the discontinuities;

a. The limit as x approaches 4 from the right side is infinity. Given that  as x approaches 4 from the right side, the y-values of the function continue to increase without bound, while the x-value remains constant at 4.

b. The limit as x approaches -3 is -2

c. The limit as x approaches 6 does not exist given that 6 has a whole and a defined spot.\

d. The limit as x approaches 4 from the left side is infinity. Similar explanation as a.

e. The limit as x approaches 2 from the right side is 2

f. The value of f(x) at x = -3 is -2

g. The limit as x approaches 2 from the left side is 1

h. the limit of the function as x approaches -6 is 0.5

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A time that an inequality was needed was when I was recently planning a trip to the beach with some friends. We wanted to make sure we had enough money to cover our expenses, so I used an equation to calculate our total cost.

The equation I used was:

Total cost > (number of people) x (cost per person)

In this case, the number of people was 4 and the cost per person was $100. So, our total cost was $400. I was able to use this equation to help me plan our trip and make sure we had enough money to cover our expenses.

I believe that by following these steps, my friend would be able to successfully plan their trip and avoid overspending.

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Adjacent sides are sides that are adjacent to a vertex (corner point) of the angle. In a right-angled triangle, the side adjacent to the angle is the side that meets the angle and forms it.

Therefore, to determine the leg adjacent to angle A, we must first determine which angle is A, then identify which side meets and creates the angle.A right-angled triangle has a right angle of 90 degrees and two legs, a and b. The hypotenuse is c. The side opposite angle A is b, and the side adjacent to angle A is a. Thus, leg a is adjacent to angle A.

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Answer:

  see attached

Step-by-step explanation:

You want a series of functions and their transformations that will develop a graph of a block capital letter "M", using trig functions.

The block letter M consists mainly of straight lines. To approximate a straight line, we have elected to use the portion of the sine function in the interval [-π/3, π/3] where it is approximately straight, but shows a hint of the sine function.

First, we created a function that moves that segment of the sine function so it is defined between the points (0, 0) and (1, 1). This makes scaling relatively easy.

Then, we created a function that draws that segment between coordinates (a, b) and (c, d).

We used this second function to draw segments between the points we chose for the outline of the left half of the letter.

Finally, we created the right half of the letter by reflecting those functions over the vertical line of symmetry (at x = 4.7). The end result is shown in the first attachment. The function and segment definitions not shown in the first attachment are shown in the second attachment. The f( ) in the Reflection section fills in the horizontal segment between the two halves of the letter.

__

Additional comment

Appending this identifier to the Desmos URL will give you the graph and function definitions we show here. This should eliminate the need to type them, if the result here is suitable.

We have used 13 function definitions that need to be changed if you desire to move the letter to different coordinates or scale it. You could combine these into two piecewise functions (one for the top, one for the bottom), so that translation or scaling could be done more easily.

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From the given options, the pair of shoes that costs $20 and is sold to the customer for $35 and the shirt that costs $12 and is sold to the customer for $20 both show a percent increase greater than 50%.

To determine which options show a percent increase greater than 50%, we need to calculate the percent increase for each option.

1)A jacket that costs $18 is sold to the customer for $25.

Percent increase = [(New Value - Old Value) / Old Value] * 100

= [(25 - 18) / 18] * 100

≈ 38.89%

2)A hat that costs $8 is sold to the customer for $12.

Percent increase = [(New Value - Old Value) / Old Value] * 100

= [(12 - 8) / 8] * 100

= 50%

3)A pair of shoes that costs $20 is sold to the customer for $35.

Percent increase = [(New Value - Old Value) / Old Value] * 100

= [(35 - 20) / 20] * 100

= 75%

4)A shirt that costs $12 is sold to the customer for $20.

Percent increase = [(New Value - Old Value) / Old Value] * 100

= [(20 - 12) / 12] * 100

= 66.67%

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The complete question is :

Which of the following show a percent increase greater than 50%? Select all that apply.?

A jacket that costs $18 is sold to the customer for $25.

A hat that costs $8 is sold to the customer for $12.

A pair of shoes that costs $20 is sold to the customer for $35.

A shirt that costs $12 is sold to the customer for $20

The rational function for this problem is defined as follows:

y = (4x + 13)/(x + 3).

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

The function has a vertical asymptote at x = -3, hence the denominator is given as follows:

x + 3.

The function has an horizontal asymptote at y = 4, with an intercept of 4.3, hence the numerator is given as follows:

4x + 13.

Thus the function is:

y = (4x + 13)/(x + 3).

The problem asks for the function rule.

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