Is (4, 3) a solution to x + y = 7

You have the following equation:

|n| = 8 the two vertical bras | | means absolute value of variable n

when you have an equation with an absolute value you consider that n could be negative or positive, because the absolute value of a number always results in a positive number. Then, n can be 8 or -8, because |-8| = |8| = 8. Hence, you have

n = ±8

The dimensions giving the minimum surface area are  r = 0.98 cm approx. and h = 1.998 cm .

What is surface area?

The surface area of a solid object could be a live of the full area that the surface of the article occupies.

Main body:

The surface area of the closed cylinder is given by,

S = 2πr²+2πrh

And volume is given by,

V = πr²h

Where, R is radius and h is height of cylinder.

Volume is given to be  6 cm³.

V = πr²h = 6

h = 6/πr²

Inserting this value of h in Surface area equation, we get,

S = 2πr²+ 2πr ( 6/πr²)

S = 2πr² + 12 /r

Now differentiating wrt x to find minimum, inserting ds/dr = 0 , we get,

4πr = 12/r²

r = (3/π)¹/³

r = 0.98 cm approx.

h = 6/π *(0.98)²

h = 6/3.017

h = 1.998 cm

Hence ,the dimensions giving the minimum surface area are  r = 0.98 cm approx. and h = 1.998 cm .

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Answer:

10 gallons per hour

Step-by-step explanation:

1/4x4=1. 2 1/2x4=10. Hope it helps!

Answer:

x = 4, -2

Step-by-step explanation:

x^2-2x=8

Move the constant term to the right side of the equation.

x^2 - 2x = 8

Take half of the coefficient of x and square it.

(-2/2)^2 = 1

Add the square to both sides of the equation.

x^2 - 2x + 1 = 8 + 1

Factor the perfect square trinomial.

(x - 1)^2 = 9

Take the square root of both sides of the equation.

x-1=\(\sqrt{9}\)
x-1=±3

Isolate x to find the solutions.

Taking positive

x=3+1=4

x=4

Taking negative

x=-3+1

x=-2

The solutions are:

x = 4, -2

Answer:

\(x = -2,\;\;x=4\)

Step-by-step explanation:

To solve the quadratic equation x² - 2x = 8 by factoring, subtract 8 from both sides of the equation so that it is in the form ax² + bx + c = 0:

\(x^2-2x-8=8-8\)

\(x^2-2x-8=0\)

Find two numbers whose product is equal to the product of the coefficient of the x²-term and the constant term, and whose sum is equal to the coefficient of the x-term.

The two numbers whose product is -8 and sum is -2 are -4 and 2.

Rewrite the coefficient of the middle term as the sum of these two numbers:

\(x^2-4x+2x-8=0\)

Factor the first two terms and the last two terms separately:

\(x(x-4)+2(x-4)=0\)

Factor out the common term (x - 4):

\((x+2)(x-4)=0\)

Apply the zero-product property:

\(x+2=0 \implies x=-2\)

\(x-4=0 \implies x=4\)

Therefore, the solutions to the given quadratic equation are:

\(\boxed{x = -2,\;\;x=4}\)

The measure of side length EF in the right triangle is 24.

The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c²  = a² + b²

From the diagram:

Hypotenuse DE = c = 26

Leg DF = a = 10

Leg EF = b = ?

Plug in the values and solve for b:

c²  = a² + b²

26²  = 10² + b²

676  = 100 + b²

b² = 676  - 100

b² = 576

b = +√576 ( we take the positive value since we are dealing with dimensions)

b = 24

Therefore, the length EF is 24.

Option C)24 is the correct answer.

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\(\begin{cases} 3x+5y=50\\ x+5y=31\\[-0.5em] \hrulefill\\ x+5y=31\\ x = 31-5y \end{cases}\qquad \implies \stackrel{\textit{substituting in the 1st equation}}{3(31-5y)+5y=50} \\\\\\ 93-15y+5y=50\implies 93-10y=50\implies -10y=-43 \\\\\\ y=\cfrac{-43}{10}\implies \boxed{y=\cfrac{43}{10}} \\\\[-0.35em] ~\dotfill\\\\ x = 31-5y\implies x = 31-5\left( \frac{43}{10} \right)\implies x = 31-\cfrac{43}{2}\implies \boxed{x = \cfrac{19}{2}}\)

\(\stackrel{~\hfill \textit{\large total for 7x + 5y}}{7\left( \cfrac{19}{2} \right)+5\left( \cfrac{43}{10} \right)\implies \cfrac{133}{2}+\cfrac{43}{2}\implies \cfrac{133+43}{2}\implies \cfrac{176}{2}\implies 88}\)

Given statement solution is :- Mathematical models are extremely valuable tools in various fields, including chemistry, biology, and physics. They offer several advantages: Simplification and abstraction, Prediction and simulation, Cost and time efficiency, Insight and understanding.

Mathematical models are extremely valuable tools in various fields, including chemistry, biology, and physics. They offer several advantages:

Simplification and abstraction: Mathematical models allow complex systems or processes to be represented using simplified mathematical equations or algorithms. This simplification helps in understanding the underlying principles and relationships of the system, making it easier to analyze and predict outcomes.

Prediction and simulation: Models enable scientists to make predictions about the behavior of a system under different conditions. They can simulate scenarios that are difficult or impossible to observe in the real world, allowing researchers to explore various hypotheses and make informed decisions.

Cost and time efficiency: Models can be used to explore different scenarios and test hypotheses in a relatively quick and cost-effective manner compared to conducting real-world experiments. They can help guide experimental design by providing insights into the most relevant variables and parameters.

Insight and understanding: Mathematical models often reveal underlying patterns and relationships that may not be immediately apparent from experimental data alone. They provide a framework for organizing and interpreting data, leading to a deeper understanding of the system being studied.

However, mathematical models also have limitations and potential disadvantages:

Simplifying assumptions: Models are based on assumptions and simplifications, which may not fully capture the complexity of the real-world system. If these assumptions are incorrect or oversimplified, the model's predictions may be inaccurate or misleading.

Uncertainty and error: Models are subject to uncertainties and errors stemming from the inherent variability of the system, limitations in data availability or quality, and simplifying assumptions. It is crucial to assess and communicate the uncertainties associated with model predictions.

Validation and verification: Models need to be validated and verified against experimental data to ensure their accuracy and reliability. This process requires rigorous testing and comparison to real-world observations, which can be challenging and time-consuming.

Mathematical models are closely linked to the fields of chemistry, biology, and physics, providing valuable insights and predictions in these disciplines. Here are some examples:

Chemistry: Mathematical models are used to study chemical reactions, reaction kinetics, and molecular dynamics. One example is the use of rate equations to model the kinetics of a chemical reaction, such as the reaction between reactants A and B to form product C.

Biology: Mathematical models play a crucial role in understanding biological systems, such as population dynamics, gene regulation, and the spread of infectious diseases. For instance, epidemiological models like the SIR (Susceptible-Infectious-Recovered) model are used to simulate and predict the spread of diseases within a population.

Physics: Mathematical models are fundamental in physics to describe physical phenomena and predict outcomes. One well-known example is Newton's laws of motion, which can be mathematically modeled to predict the motion of objects under the influence of forces.

Quantum mechanics: Mathematical models, such as Schrödinger's equation, are used to describe the behavior of particles at the quantum level, providing insights into atomic and molecular structures and the behavior of subatomic particles.

Fluid dynamics: Mathematical models, such as the Navier-Stokes equations, are employed to study the behavior of fluids, including airflow, water flow, and weather patterns.

These examples demonstrate the wide range of applications for mathematical models in understanding, predicting, and simulating various phenomena in the fields of chemistry, biology, and physics.

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Answer:

Perimeter:

= 58 m (approximate)

= 58.2066 or 58.21 m (exact)

Area:

= 208 m² (approximate)

= 210.0006 or 210 m² (exact)

Step-by-step explanation:

Given the following dimensions of a rectangle:

length (L) = \(\sqrt{252}\) meters

width (W) = \(\sqrt{175}\) meters

The formula for solving the perimeter of a rectangle is:

P  = 2(L + W) or 2L + 2W

The formula for solving the area of a rectangle is:

A = L × W

In order to determine the approximate perimeter, we must determine the perfect square that is close to the given dimensions.  

13² = 169

14² = 196

15² = 225

16² = 256

Among the perfect squares provided, 16² = 256 is close to 252 (inside the given radical for the length), and 13² = 169 (inside the given radical for the width).  We can use these values to approximate the perimeter and the area of the rectangle.

P  = 2(L + W)

P = 2(13 + 16)

P = 58 m (approximate)

A = L × W

A = 13 × 16

A = 208 m² (approximate)

L = \(\sqrt{252}\) meters = 15.8745 meters

W = \(\sqrt{175}\) meters = 13.2288 meters

P  = 2(L + W)

P = 2(15.8745 + 13.2288)

P = 2(29.1033)

P = 58.2066 or 58.21 m

A = L × W

A = 15.8745 × 13.2288

A = 210.0006 or 210 m²

The degree of the polynomial is 5 and the leading coefficient is -1.

The given polynomial is f(x)

f(x) = \(-x^{5} +2x^{4} +3x^{3} +2x^{2} -8x +9\)

The degree of the polynomial is the term with the highest power,

So, in the given polynomial, the term with the highest term is \(-x^{5}\)

The highest power is 5,

So, its degree is 5.

The leading coefficient is the coefficient of the term with the degree,

So, the leading coefficient is -1.

Hence, the degree of the polynomial is 5 and the leading coefficient is -1.

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Answer:

The charges will be the same after 10 miles.

Step-by-step explanation:

Long Beach Towing Company:

Charges $40 plus $5 per mile. So after x miles, the charge will be of:

\(L(x) = 40 + 5x\)

Five-Star Towing Company:

Chargers of $70 plus $2 per mile. So after x miles, the charge will be of:

\(F(x) = 70 + 2x\)

After how many miles the charges for the two companied will be the same?

This is x for which:

\(L(x) = F(x)\)

So

\(40 + 5x = 70 + 2x\)

\(5x - 2x = 70 - 40\)

\(3x = 30\)

\(x = \frac{30}{3}\)

\(x = 10\)

The charges will be the same after 10 miles.

Answer:

42.25

Step-by-step explanation:

You multiply 6.5 by 2 by 3.25 to get the answer

Answer:

42.5 units^3

Step-by-step explanation:

VOLUME EQUATION: l x w x h

6.5 x 2 x 3.25

42.5

DON'T FORGET YOUR UNITS CUBES

Answer: 3,348 cubic inches

Step-by-step explanation:

1. Since we know that volume= length x width x height, then we can plug our values into this equation.

2. So, we would do volume= 9 x 12 x 21.

3. 9 x 12 = 108, and 108 x 21 =2,268.

4. Now that we have both of the volumes, we have to add them together.

5. 1,080 + 2,268 = 3,348

6. The combined volume is 3,348 cubic inches.

Answer:

y = 8/5x + (-4) or y = 8/5x -4

Step-by-step explanation:

Slope-intercept form is written like this:

            y = mx + b

The variable m, represents slope and b, represents the y-intercept.

To find slope, you have to find the rise/run or in other words, change of y over change of x.

From the look of the line, the slope has to be positive because the line is going up.

To go from the bottom point to the top, we have to go up 8 points and go to the right 5 points. Thus the slope is 8/5.

Now for the y-intercept. This part is easy. Just ask yourself this...

"Which of the two points is on the y-axis?"

In this case, it is the bottom point which is -4.

So your equation should look like this:

y = 8/5x + (-4)

   or y = 8/5x - 4 because when you have a plus sign and a minus sign, the result is negative.

hope this helps :)

Answer:

61 degrees

Step-by-step explanation:

==>Given ∆MNO,

MO = 18,

MN = 6

m<O = 17°

==>Required:

Measure of <N

==>SOLUTION:

Use the sine formula for finding measure of angles which is given as: Sine A/a = Sine B/b = Sine C/c

Where,

Sine A = 17°

a = 6

Sine B = N

b = 18

Thus,

sin(17)/6 = sin(N)/18

Cross multiply

sin(17)*18 = sin(N)*6

0.2924*18 = 6*sin(N)

5.2632 = 6*sin(N)

Divide both sides by 6

5.2632/6 = sin(N)

0.8772 = sin(N)

sin(N) = 0.8772

N = sin^-1(0.8772)

N ≈ 61° (approximated)

Answer:

7.5

Step-by-step explanation:

10/=3+ 5/=2.5 add them and it will be 7.5

Answer:

16 boxes

Step-by-step explanation:

16x5=80+150=230>15x16=240

Answer:

B

Step-by-step explanation:

For l1 and l2 to be parallel, these two angles need to be equal. 3x-15=2x+10, x=25

The volume of the tower is 224 in³, which is not listed among the given options.

To find the volume of the rectangular block, we need to multiply its length, width, and height. Therefore, the volume of the single block is:
8 x 3.5 x 2 = 56 cubic inches.
Since we are stacking four blocks to create a tower, we need to multiply the volume of a single block by 4.

Thus, the volume of the tower is:
56 x 4 = 224 cubic inches.
The volume of a rectangular block can be found using the formula,

V = length × width × height.

In this case, the length is 8 inches, the width is 3.5 inches, and the height is 2 inches.

V = 8 × 3.5 × 2 V

= 28 × 2 V

= 56 in³

Now that we know the volume of one block, we can find the volume of the tower created by stacking four blocks. Tower volume = block volume × number of blocks Tower volume = 56 in³ × 4 Tower volume = 224 in³

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Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

wrong its d I just did it

Answer:

the answer is should be B but im not 100% sure.

Step-by-step explanation:

The first five terms of the given sequence are:

C: 18, 30, 42, 54, 66

The formula for the nth term of an arithmetic sequence is expressed as:

aₙ = a + (n - 1)d

where:

a is first term

d is common difference

n is number of term

The formula for the sequence is 12x + 6. Thus:

First term = 12(1) + 6 = 18

Second term = 12(2) + 6 = 30

Third term = 12(3) + 6 = 42

Fourth term = 12(4) + 6 = 54

Fifth term = 12(5) + 6 = 66

Thus, the sequence is : 18, 30, 42, 54, 66

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y = 6x + 2 is the function which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

The linear function in the form y = mx + b represents the situation where y represents the cost of the babysitting job

x represents the number of hours, "m" represents the hourly rate, and "b" represents the additional fee (bus fare).

y = 3x + 2 represents an hourly rate of 3 and an additional fee of 2.

y = 3x + 1 represents an hourly rate of 3 and an additional fee of 1.

y = 6x + 2 represents an hourly rate of 6 and an additional fee of 2.

y = -6x + 2 represents a negative hourly rate of -6 and an additional fee of 2.

Hence, y = 6x + 2 is the which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

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The functions g(x) = x² - 4x + 3 and f(x) = x² - 4x are:

The functions have the same range.

The functions have the same domain.

The functions have the same x-intercepts.

Let's analyze the given functions g(x) = x² - 4x + 3 and f(x) = x² - 4x and determine which statements about them are true.

Here are the options:

The functions have the same graph.

The functions have the same range.

The functions have the same domain.

The functions have the same vertex.

The functions have the same y-intercept.

The functions have the same x-intercepts.

The functions have the same graph:

This statement is false. While both functions are quadratic functions, their additional terms make them different. g(x) has an additional constant term (+3) compared to f(x).

Their graphs will be different, with g(x) being shifted upward by 3 units compared to f(x).

The functions have the same range:

This statement is true.

Both functions are quadratic functions, and their range will be the same. The range of a quadratic function is either all real numbers (if the parabola opens upward) or the set of real numbers greater than or equal to (or less than or equal to) the vertex of the parabola.

The functions have the same domain:

This statement is true.

The domain of both functions, unless restricted by any other factors, is all real numbers.

Quadratic functions have a domain of (-∞, ∞).

The functions have the same vertex:

This statement is false.

The vertex of a quadratic function is determined by the values of "a," "b," and "c" in the general form of the quadratic function (ax^2 + bx + c).

Since g(x) has an additional constant term, its vertex will be different from the vertex of f(x).

The functions have the same y-intercept:

This statement is false.

The y-intercept of a function is the value of y when x = 0.

For f(x), when x = 0, we have f(0) = (0)² - 4(0) = 0.

For g(x), when x = 0, we have g(0) = (0)² - 4(0) + 3

= 3.

Their y-intercepts are different.

The functions have the same x-intercepts:

This statement is true.

To find the x-intercepts of both functions, we set y (or f(x) and g(x)) equal to zero and solve for x.

The quadratic equation x² - 4x + 3 = 0 can be factored as (x - 1)(x - 3) = 0, giving x = 1 and x = 3 as the x-intercepts.

Both functions have the same x-intercepts.

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Answer:

m<C = 180 - (90+32)

= 180 - 122

= 58°

Answer:

----------------------

There are various combinations of coins.

In total there are:

It is verified that the given vectors x₁ and x₂ are solutions of the given system. Using Wronskian it is shown that they are linearly independent. Then, \(W(t)=7e^{-3t}\). The general solution of the given system is written as \(x(t)=\left[\begin{array}{c}3c_1e^{2t}+c_2e^{-5t}\\2c_1e^{2t}+3c_2e^{-5t}\end{array}\right]\).

Wronskian analysis helps to determine whether a solution is linearly dependent or independent.

Given the system is \(x'=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x\).

Let's differentiate x₁ concerning t, and we get,

\(\begin{aligned}x_1'&=\left[\begin{array}{c}\frac{d}{dt}(3e^{2t})&\\\frac{d}{dt}(2e^{2t})&\end{array}\right] \\&=\left[\begin{array}{c}6e^{2t}&\\4e^{2t}&\end{array}\right] \end{aligned}\)

Now,

\(\begin{aligned}\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x_1&=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]\left[\begin{array}{c}3e^{2t}\\2e^{2t}\end{array}\right]\\&=\left[\begin{array}{c}12e^{2t}-6e^{2t}\\18e^{2t}-14e^{2t}\end{array}\right]\\&=\left[\begin{array}{c}6e^{2t}\\4e^{2t}\end{array}\right]\\&=x_1'\end{aligned}\)

From this, we can write,

\(x_1'=\left[\begin{array}{cc}4&-3\\6&-7\end{array}\right]x_1\)

Therefore, we conclude that x₁ is a solution to the given system.

Let's differentiate x₂ concerning t, and we get,

\(\begin{aligned}x_2'&=\left[\begin{array}{c}\frac{d}{dt}(e^{-5t})&\\\frac{d}{dt}(3e^{-5t})&\end{array}\right] \\&=\left[\begin{array}{c}-5e^{-5t}&\\-15e^{-5t}&\end{array}\right] \end{aligned}\)

Now,

\(\begin{aligned}\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x_2&=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]\left[\begin{array}{c}e^{-5t}\\3e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}4e^{-5t}-9e^{-5t}\\6e^{-5t}-21e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}-5e^{-5t}\\-15e^{-5t}\end{array}\right]\\&=x_2'\end{aligned}\)

From this, we can write,

\(x_2'=\left[\begin{array}{cc}4&-3\\6&-7\end{array}\right]x_2\)

Therefore, we conclude that x₂ is also a solution to the given system.

Now, find the Wronskian of x₁ and x₂, we get,

\(\begin{aligned}W(t)&=\text{det}[x_1\;x_2]\\&=\text{det}\left[\begin{array}{cc}3e^{2t}&e^{-5t}\\2e^{2t}&3e^{-5t}\end{array}\right] \\&=(3e^{2t}\times3e^{-5t})-(e^{-5t}\times2e^{2t})\\&=9e^{2t-5t}-2e^{2t-5t}\\&=9e^{-3t}-2e^{-3t}\\&=7e^{-3t}\\&\neq0\end{aligned}\)

From this, we can conclude that x₁ and x₂ are independent.

Finally, we write the general solution of the system as follows,

\(\begin{aligned}x(t)&=c_1x_1+c_2x_2\\&=c_1 \left[\begin{array}{c}3e^{2t}\\2e^{2t}\end{array}\right] +c_2\left[\begin{array}{c}e^{-5t}\\3e^{-5t}\end{array}\right] \\&=\left[\begin{array}{c}3c_1e^{2t}\\2c_1e^{2t}\end{array}\right] +\left[\begin{array}{c}c_2e^{-5t}\\3c_2e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}3c_1e^{2t}+c_2e^{-5t}\\2c_1e^{2t}+3c_2e^{-5t}\end{array}\right] \end{aligned}\)

The complete question is -

First, verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearly independent. Finally, write the general solution of the system.

\(x'=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x;\; x_1=\left[\begin{array}{ccc}3e^{2t}\\2e^{2t}\end{array}\right], \;x_2=\left[\begin{array}{cc}e^{-5t}\\3e^{-5t}\end{array}\right]\)

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Answer:

f-1(x) = 1/3x would be the answer

Step-by-step explanation:

Answer:

y= 1/3x

Step-by-step explanation:

inverse function perform the opposite.

3/1 becomes 1/3

Based on the information given, the price of the zero coupon bond is $692.04.

To calculate the price of a zero coupon bond, we need to use the following formula:

\(\sf P =\dfrac{F}{1+r\div n}^{(nt)\)

Where:

Also, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.

Plugging in the values into the formula, we get:

\(\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}\)

\(\sf P = \dfrac{1000}{(1.0375)^{10}}\)

\(\sf P = \dfrac{1000}{1.4450}\)

\(\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)\)

Therefore, the price of the zero coupon bond is $692.04.

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