Select all the statements that are true for the following systems of equations.
System A
2x-3y = 4
4x - y = 18
00
System B
3x - 4y = 5
y = 5x +3
All three systems have different solutions.
Systems B and C have the same solution.
System C simplifies to 2x-3y=4 and 4x-y=18 by dividing the second equation by three.
Systems A and B have different solutions.
Systems A and C have the same solution.
Reset
System C
2x-3y=4
12x-3y = 54
Next

The second equation results in n^2 = c^2.

Let's suppose we have two equations:

Equation 1: c^2 = a^2 + b^2

Equation 2: n^2 = a^2 + b^2

Both equations have the term a^2 + b^2. We can treat these equations as a system of equations and substitute the value of a^2 + b^2 from Equation 1 into Equation 2.

Substituting a^2 + b^2 from Equation 1 into Equation 2, we get:

n^2 = c^2

After substituting, we obtain the equation n^2 = c^2. This equation shows that the squares of the lengths of the sides n and c are equal.

It's important to note that this result holds true because both triangles have the same a and b values, leading to the same value of a^2 + b^2. Therefore, substituting that value into the second equation results in n^2 = c^2.

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The length of AB = CD and CD = AB based on the proof that :

Looking at the segments CD and AB, both segments are of equal length, hence they would be equal

Similarly , both segments are parallel and have the same end points. Hence, they are equal.

Therefore, AB = CD

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If Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

To represent the number of bags of pears, b, that Natalie sells at the Saturday market, we can use the following equation:

b = total_number_of_pears / pears_per_bag

In this equation, "total_number_of_pears" represents the total quantity of pears Natalie has, and "pears_per_bag" represents the number of pears she puts in each bag.

Given that Natalie has a total of 48 pears, we can substitute the value into the equation:

b = 48 / pears_per_bag

Now, we need to determine the number of pears she puts in each bag. The information provided states that Natalie sells bags of pears, and each bag is sold for $5. However, the specific number of pears per bag is not given. To proceed, we need this information.

Let's assume that Natalie puts 4 pears in each bag. We can substitute this value into the equation:

b = 48 / 4

Simplifying the equation gives:

b = 12

So, if Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

It's important to note that the specific value of "pears_per_bag" will affect the final result. If Natalie puts a different number of pears in each bag, the equation will yield a different number of bags sold.

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Step-by-step explanation:

To find the value(s) for x such that f(x) = 23, we can set up the equation:

x^2 - 4x + 2 = 23

To solve this quadratic equation, we need to rearrange it into the standard quadratic form:

x^2 - 4x - 21 = 0

Now, we can solve this equation by factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation x^2 - 4x - 21 = 0, the coefficients are: a = 1, b = -4, and c = -21.

Plugging these values into the quadratic formula, we get:

x = (-(-4) ± √((-4)^2 - 4(1)(-21))) / (2(1))

x = (4 ± √(16 + 84)) / 2

x = (4 ± √100) / 2

x = (4 ± 10) / 2

Now, we have two solutions:

x = (4 + 10) / 2 = 14 / 2 = 7

x = (4 - 10) / 2 = -6 / 2 = -3

Therefore, the values for x such that f(x) = 23 are x = 7 and x = -3.

Answer:

slope = - [tex]\frac{3}{2}[/tex] , y- intercept = 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

3x + 2y = 14 ( subtract 3x from both sides )

2y = - 3x + 14 ( divide through by 2 )

y = - [tex]\frac{3}{2}[/tex] x + 7 ← in slope- intercept form

with slope m = - [tex]\frac{3}{2}[/tex] and y- intercept c = 7

Answer:

7

Step-by-step explanation:

V looking shape has ends at 1 & 8

8 - 1 = 7

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The equation of the tangent line at the point (108, 6) on the curve y² = x²/(xy - 324) is: y = 6

The equation is given as:

y² = x²/(xy - 324) at (108, 6)

Differentiating implicitly with respect to x gives:

2y(dy/dx) = (2x(xy - 324) - x²(y - 324)(dy/dx)) / (xy - 324)²

Simplifying further using power rule and chain rule gives us:

[tex]\frac{dy}{dx} = \frac{x^{2}y - 648x }{2y(-324 + xy) +x^{3} }[/tex]

We can find the slope by plugging in x = 108 and y = 6 to get

[tex]\frac{dy}{dx} = \frac{(108^{2}*6) - 648(108) }{2(6)(-324 + (108*6)) + 108^{3} }[/tex]

dy/dx = 0

To find the equation of the tangent line, we use the point-slope form:

y - y₁ = m(x - x₁),

where:

(x₁, y₁) is the given point (108, 6) and m is the slope.

Substituting the values, we have:

y - 6 = 0(x - 108)

y = 6

This is the equation of the tangent line at the point (108, 6) on the curve y² = x²/(xy - 324).

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The square root of the expression -36 is DNE

From the question, we have the following parameters that can be used in our computation:

[tex](-36)^\frac 12[/tex]

By definition, the square root of negative numbers are complex numbers

using the above as a guide, we have the following:

[tex](-36)^\frac 12[/tex] is not a real number

Hence, the solution is DNE

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Let's represent the number with the variable "x". According to the given property, we can write the following equation:

3(x + 4) < 7x

Now, let's solve this inequality to find the range of numbers that satisfy the property.

3x + 12 < 7x

Subtract 3x from both sides:

12 < 4x

Divide both sides by 4 (since the coefficient of x is 4):

3 < x

So, the range of numbers that satisfy the given property is x > 3.

Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:

The equations of the other line are:

BC: y = 2x

AD: y = 2x + 2

CD = -¹/₂x + 5.5

The formula for the equation of a line between two coordinates is expressed as:

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

Thus, for the lines we have:

BC has B(-2, 4) and C(-1, 6)

Thus:

BC: (y - 4)/(x - 2) = (6 - 4)/(-1 + 2)

BC: (y - 4)/(x - 2) =2

BC: y - 4 = 2x - 4

BC: y = 2x

AD has  A(2,2) and D(3, 4)

Thus:

AD: (y - 2)/(x - 2) = (4 - 2)/(3 - 2)

AD: y - 2 = 2x - 4

AD: y = 2x + 2

CD has C(-1, 6) and D(3, 4)

CD: (y - 6)/(x + 1) = (4 - 6)/4

CD: y - 6 = -¹/₂(x + 1)

CD = -¹/₂x + 5.5

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If sinθ = 5/13 and θ is in Quadrant II, then sin (θ/2) will be equal to  [tex]\frac{5}{\sqrt{26}}[/tex]

To find sin(θ/2), we can use the half-angle identity for sine, which states that:

sin(θ/2) = ±[tex]\sqrt{\frac{(1 - cos\theta)}{2}}[/tex]

Given that sinθ = 5/13 and θ is in Quadrant II, we can determine the value of cosθ using the Pythagorean identity

sin²θ + cos²θ = 1

sinθ = 5/13

sin²θ = (5/13)² = 25/169

cos²θ = 1 - sin²θ = 1 - 25/169 = 144/169

cosθ = ±√(144/169) = ±12/13

Since θ is in Quadrant II, the cosine is negative. Therefore, cosθ = -12/13.

Now, we can calculate sin(θ/2):

sin(θ/2) = ±√((1 - cosθ) / 2) = ±√((1 - (-12/13)) / 2) = ±√((1 + 12/13) / 2) = ±√(25/26) = ±5/√26

Since θ is in Quadrant II, sin(θ/2) will be positive.

Therefore, sin(θ/2) = 5/√26.

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The built area of 50% of the house on the rectangular piece of land measures 576 cm^2.

To find the built area of 50% of a house on a rectangular piece of land, we need to calculate the area of the rectangular piece of land and then determine 50% of that area.

The rectangular piece of land has dimensions of 64 cm by 18 cm. To calculate the area, we multiply the length by the width:

Area = Length * Width

Area = 64 cm * 18 cm

Area = 1152 cm^2

The total area of the rectangular piece of land is 1152 cm^2.

To find the built area, which is 50% of the total area, we multiply the total area by 50% (or 0.5):

Built Area = Total Area * 50%

Built Area = 1152 cm^2 * 0.5

Built Area = 576 cm^2

Therefore, the built area of 50% of the house on the rectangular piece of land measures 576 cm^2.

It's important to note that this calculation assumes that the built area is uniformly distributed on the land and represents half of the house's total area. The actual shape and distribution of the house may vary, but this calculation provides an estimate of the built area based on the given information.

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Note the translate question is:

On a rectangular piece of land that measures 64 cm by 18 cm, they are going to build 50% of a house. What is the built area?

Answer:

Step-by-step explanation:

waza skibidi domo dom yes yes  insanito free fire

25 quarter cups in 6 1/4 cups

answer: 61

The equation for true airspeed T in terms of altitude and differential pressure p - T = k * (1 + A/50,000) * p

To write the equation for true airspeed T in terms of altitude A and differential pressure p, we need to consider the relationship between indicated airspeed S and differential pressure.The indicated airspeed S is typically measured using a pitot tube, which measures the dynamic pressure of the air flowing around the aircraft. The differential pressure p represents the difference between the dynamic pressure measured by the pitot tube and the static pressure of the surrounding air. In other words, p = dynamic pressure - static pressure.

The equation T = (1 + A/50,000) * S, we can express S in terms of the differential pressure p. Let's assume that S is directly proportional to p:

S = k * p

where k is a constant of proportionality. By substituting this expression for S into the equation for true airspeed, we have:

T = (1 + A/50,000) * (k * p)

Simplifying, we can write the equation for true airspeed T in terms of altitude A and differential pressure p as:

T = k * (1 + A/50,000) * p

where k is the constant of proportionality relating differential pressure to indicated airspeed.

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The solution to the piecewise-defined function is shown in the attached graph.

The function g(x) is defined as follows:

g(x) = -4     if x ≠ 0

g(x) = 5       if x = 0

On the graph, when x is any value other than 0, the function takes the value of -4. This means that there will be a horizontal line at y = -4 for all x ≠ 0. The point (0, 5) will be represented by a solid dot since it's the only point where g(x) equals 5.

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The area of the parallelogram ABCD is (a) 13 square units.

Area of a parallelogram = Length × Width

Length = distance AB

Where

A = (3, 6) and B = (6, 5)

So, we have

[tex]Length = \sqrt{ {(3 - 6)}^{2} + (6 - 5) ^{2} }[/tex]

[tex] = \sqrt{ {( - 3)}^{2} + (1) ^{2} }[/tex]

[tex] = \sqrt{ 9 + 1 }[/tex]

[tex]= \sqrt{10}[/tex]

Next, we have

Width = distance AD

Where

A = (3, 6) and D = (2, 2)

So, we have

[tex]width = \sqrt{ {(3 - 2)}^{2} + (6 - 2) ^{2} }[/tex]

[tex] = \sqrt{ {( 1)}^{2} + (4) ^{2} }[/tex]

[tex]= \sqrt{ 1 + 16 }[/tex]

[tex]= \sqrt{17}[/tex]

Recall that

Area of a parallelogram = Length × Width

So, we have

= √10 × √17

Evaluate the products

√170

Take the square rppt

= 13.03840481040529

Approximately, 13 square units

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Complete question:

What is the area of parallelogram ABCD?

O 13 square units

O 14 square units

O 15 square units

O 16 square units

See attachment

For the above function describing movie rental expenses, neither the input (6.5) nor the output ($17.50) are possible or reasonable.

The solution (6.5, $17.50) does not make sense for the function g(x) representing the amount of money spent on renting movies, where x is the number of movies.

The reason is that the input value, 6.5, does not make sense in the context of renting movies. The number of movies rented should be a whole number, not a decimal or fractional value. Therefore, the input is not feasible.

In addition, the output value, $17.50, does not make sense either. Typically, the cost of renting movies is given in whole dollar amounts. It is highly unlikely to have a rental cost of $17.50 for a movie marathon involving 6.5 movies. Therefore, the output is not feasible.

In conclusion, neither the input (6.5) nor the output ($17.50) is feasible or realistic for the given function representing movie rental expenses.

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Answer:

P ≈ $12,654.89

Step-by-step explanation:

To calculate the amount of money that should be deposited today, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment ($15,000 in this case)

P = the principal amount (the amount to be deposited today)

r = the annual interest rate (4.5% or 0.045 as a decimal)

n = the number of times the interest is compounded per year (monthly compounding, so n = 12)

t = the number of years (4 years in this case)

Substituting the given values into the formula, we have:

$15,000 = P(1 + 0.045/12)^(12*4)

Simplifying the equation:

$15,000 = P(1.00375)^(48)

To solve for P, we divide both sides of the equation by (1.00375)^(48):

P = $15,000 / (1.00375)^(48)

Using a calculator, we find:

P ≈ $12,654.89

Therefore, approximately $12,654.89 should be deposited today in order to accumulate to $15,000 in 4 years with a 4.5% annual interest rate compounded monthly.

As x tends to negative one from the left, the value of f(x) tends to positive infinity. As x → -1⁻, f(x) → ∞.

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of this rational function f(x) shown below, we can logically deduce that its vertical asymptote is at x = -1 and x = 2, and its horizontal asymptote is at y = 3.

In this context, we can logically deduce that the value of f(x) tends towards positive infinity, as x tends to negative one from the left;

As x → -1⁻, f(x) → ∞.

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Savings accounts and CDs are good options for people who want to save money without taking on a lot of risk.

If Anita and Miguel do not take any money from their accounts, Anita's account will grow faster than Miguel's.

This is because the interest rate for Anita's account is 6%, while Miguel's is 5%.

The interest rate is the percentage of the principal that a bank or other financial institution pays for the use of money.

It can be thought of as a fee charged for borrowing money.

The higher the interest rate, the more money a person can earn on their investment.

Anita and Miguel's accounts are probably savings accounts or CDs, which are low-risk investments that pay a fixed interest rate.

Savings accounts and CDs are good options for people who want to save money without taking on a lot of risk.

Anita and Miguel's accounts are probably savings accounts or CDs, which are low-risk investments that pay a fixed interest rate.

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The study described is an experimental study in nature. It follows a randomized double-blind placebo-controlled trial design, where participants were randomly assigned to either a verum (onabotulinumtoxinA) or placebo (saline) group.

The researchers administered the treatment (botulinum toxin injection to the glabellar region) to the verum group while the placebo group received a saline injection. The primary end point was the change in depressive symptoms measured using the Hamilton Depression Rating Scale.

The statistical hypothesis in this study does involve a cause/effect relationship between the explanatory variable (botulinum toxin injection) and the response variable (alleviation of depression symptoms).

Potential confounding variables in this study could include factors such as participants' previous medication history, severity of depression, and other ongoing treatments or therapies for depression.

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The combinations of assembling these rectangles for which it is possible to create a rectangle with the length of 15 and the width 11 with no gaps or overlapping are:

A rectangle is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides.

Required

Which group forms a rectangle of

[tex]\text{Length}=15[/tex]

[tex]\text{Width}=11[/tex]

First, calculate the area of the big rectangle

[tex]\text{Area}=\text{Length}\times\text{Width}[/tex]

[tex]\text{A}_{\text{Big}}=15\times11[/tex]

[tex]\text{A}_{\text{Big}}=165[/tex]

Next, calculate the area of each rectangle A to E.

[tex]\text{A}_{\text{A}}=11\times7[/tex]

[tex]\text{A}_{\text{A}}=77[/tex]

[tex]\text{A}_{\text{B}}=2\times11[/tex]

[tex]\text{A}_{\text{B}}=22[/tex]

[tex]\text{A}_{\text{C}}=6\times6[/tex]

[tex]\text{A}_{\text{C}}=36[/tex]

[tex]\text{A}_{\text{D}}=6\times5[/tex]

[tex]\text{A}_{\text{D}}=30[/tex]

[tex]\text{A}_{\text{E}}=13\times4[/tex]

[tex]\text{A}_{\text{E}}=52[/tex]

Then consider each option.

(a) 2C + 2D + 2B

[tex]2\text{C}+2\text{D}+2\text{B}=(2\times36)+(2\times30)+(2\times22)[/tex]

[tex]2\text{C}+2\text{D}+2\text{B}=72+60+44[/tex]

[tex]2\text{C}+2\text{D}+2\text{B}=176[/tex]

(b) A + B + C + D

[tex]\text{A}+\text{B}+\text{C}+\text{D}=77+22+36+30[/tex]

[tex]\text{A}+\text{B}+\text{C}+\text{D}=165[/tex]

(c) A + 4B

[tex]\text{A} + 4\text{B}=77+(4\times22)[/tex]

[tex]\text{A} + 4\text{B}=77+88[/tex]

[tex]\text{A} + 4\text{B}=165[/tex]

(d) 3E + 2B

[tex]3\text{E}+2\text{B}=(3\times52)+(2\times22)[/tex]

[tex]3\text{E}+2\text{B}=156+44[/tex]

[tex]3\text{E}+2\text{B}=200[/tex]

(e) E + C + D + 3B

[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=52+36+30+(3\times22)[/tex]

[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=52+36+30+66[/tex]

[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=184[/tex]

Recall that:

[tex]\text{A}_{\text{Big}}=165[/tex]

Only options (b) and (c) match this value.

[tex]\text{A}+\text{B}+\text{C}+\text{D}=165[/tex]

[tex]\text{A} + 4\text{B}=165[/tex]

Hence, options (b) and (c) are correct.

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An output value for (fog)(x) is 55/(x² + 2x).

Domain = (-∞, 1) U (-2, 0) U (0, ∞) or {x|x ≠ 0, -2}.

In this exercise, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations in simplified form as follows;

(fog)(x) = 5/(x + 2) × 11/x

(fog)(x) = 55/x(x + 2)

(fog)(x) = 55/(x² + 2x)

For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;

x² + 2x ≠ 0

x² ≠ -2x

x ≠ -2

Domain = (-∞, 1) U (-2, 0) U (0, ∞) or {x|x ≠ 0, -2}.

In conclusion, we can reasonably infer and logically deduce that x must not be equal to 0 and -2.

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Answer:

m = -0.204

Step-by-step explanation:

Start by creating points (72, 133) and (24, 235.2+133)

You are relating the charge (as a whole number) to the total distance traveled at a respective percentage. At 72% you traveled 133 miles and at 24% you traveled a total of 368.2 miles.

Thus, you can use the slope formula [tex](y2-y1)/(x2-x1)[/tex]

Thus, (72-24)/(133-368.2) = -0.204 (approx.)

Hope this helps!

Answer: 5/ 16

explanation: total= 4x4=16

red and yellow : (r,y) or (y,r)

n= 5

p= 5 1/1 16

p = 5 over 16

Answer:

In summary, the faster cyclist cycles at a speed of 18 mi/h since they travel 36 of the 54 miles in 2 hours while cycling twice as fast as the slower cyclist.

Explanationn:

The two cyclists are 54 miles apart and heading toward each other.

One cyclist cycles 2 times as fast as the other. We will call the faster cyclist A and the slower cyclist B.

They meet 2 hours after starting. This means they travel a total distance of 54 miles in 2 hours.

Since cyclist, A cycles 2 times as fast as cyclist B, cyclist A travels 2/3 of the total distance, and cyclist B travels 1/3 of the total distance.

In two hours, cyclist A travels (2/3) * 54 miles = 36 miles.

We need to find the speed of cyclist A in miles per hour.

Speed = Distance / Time

So the speed of cyclist A is:

36 miles / 2 hours = 18 miles per hour

Therefore, the speed of the faster cyclist is 18 mi/h.

The equation of the line parallel to the line passing through (1, -2) and (-4, 3) and passing through the point (-4, -5) is y = -x - 9 in slope-intercept form.

To find the equation of a line parallel to a given line, we need to determine the slope of the given line and then use it to construct the equation of the parallel line.

First, let's calculate the slope of the given line passing through points (1, -2) and (-4, 3). The slope, denoted as m, can be found using the slope formula:

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

Substituting the coordinates, we have:

m = (3 - (-2)) / (-4 - 1) = 5 / (-5) = -1

Now that we have the slope, we can use it to construct the equation of the parallel line.

We'll use the point-slope form of a linear equation, which is:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line.

We'll use the point (-4, -5) on the parallel line:

y - (-5) = -1(x - (-4))

y + 5 = -1(x + 4)

Simplifying further:

y + 5 = -x - 4

y = -x - 9

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According to the information we can infer that it will take approximately 31 years for the wolf population to reach 500.

The given function, w(x) = 14 * 1.08^x, models the number of wolves (w) in the years since 1995 (x).

To find the number of years it will take for the population to reach 500 wolves, we can set up the equation:

Dividing both sides by 14, we get:

Taking the logarithm (base 1.08) of both sides to solve for x:

Using a calculator, we find that x ≈ 31.

According to the above it will take approximately 31 years for the wolf population to reach 500 based on the given model.

Note: This question is incomplete. Here is the complete information:
Attached image

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Answer:

πr^2 h

π(11)^2 (15)

= 1815π or = 5701