Ways to use coordinates to prove quadrilaterals are parallelograms, rectangles, rhombi, or squares:

Answer:

The answer is 35 yards

Step-by-step explanation:

25-19.05 = 5.95

5.95/0.17 = 35 yards

The distance d between the complex number -3 + 2i and 0 is √13.

To find the distance d between the complex number -3 + 2i and 0, you can use the formula for the distance between two complex numbers, which is:

d = √((x2 - x1)² + (y2 - y1)²)

In this case, the first complex number is -3 + 2i, so x1 = -3 and y1 = 2. The second complex number is 0, which can be represented as 0 + 0i, so x2 = 0 and y2 = 0.

Now, plug in these values into the formula:

d = √((0 - (-3))² + (0 - 2)²)

d = √((3)² + (-2)²)

d = √(9 + 4)

d = √13

So the distance d between the complex number -3 + 2i and 0 is √13.

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Answer:

6:5

Step-by-step explanation:

c = number of cats

d = number of dogs

d = c+6

Set up a ratio:

4/3 = d/c

Then replace d with c+6, so your equation only has one variable.

\(\frac{4}{3} = \frac{c+6}{c}\)

Cross multiply

4c = 3(c+6)

Multiply everything in the parentheses by 3.

4c = 3c + 18

Subtract 3c from both sides

4c - 3c = 18

c = 18

d = c + 6 = 18 + 6 = 24

If 2 more cats join, then you will have 20 cats and 24 dogs, so the ratio of dogs to cats will now be 24:20.  Divide each side by 4 for a ratio of 6:5.

Answer:

1. x = sqrt3 - 4, negative sqrt3 -4

2. x = sqrt13, negative sqrt13

3. x = sqrt7/2 , negative sqrt7/2

4. x = sqrt3/2 - 14, negative sqrt3/2 - 14

Step-by-step explanation:

sqrt = square root

The dU/dT at constant P and V is simply nR/P.

According to the ideal gas law, PV = nRT, so we can write P = nRT/V. Using this relationship, we can express the internal energy U as a function of P, V, and T:

U = f(P,V,T) = f(nRT/V, V, T)

To find dU/dP at constant V and T, we can use the chain rule:

dU/dP = (∂U/∂P)V,T + (∂U/∂V)P,T(dP/dP)V,T + (∂U/∂T)P,V(dT/dP)V,T

Since V and T are being held constant, we can simplify the second and third terms to just 0:

dU/dP = (∂U/∂P)V,T

To find (∂U/∂P)V,T, we can differentiate f(nRT/V, V, T) with respect to P, keeping V and T constant:

(∂U/∂P)V,T = (∂f/∂P)nRT/V(-nRT/V²) = -nRT/V²

So, dU/dP at constant V and T is simply -nRT/V².

To find dU/dT at constant P and V, we can again use the chain rule:

dU/dT = (∂U/∂T)P,V + (∂U/∂V)P,T(dV/dT)P,V + (∂U/∂P)V,T(dP/dT)P,V

Since P and V are being held constant, we can simplify the third term to just 0:

dU/dT = (∂U/∂T)P,V + (∂U/∂V)P,T(dV/dT)P,V

To find (∂U/∂T)P,V, we can differentiate f(nRT/V, V, T) with respect to T, keeping P and V constant:

(∂U/∂T)P,V = (∂f/∂T)nRT/V(1) = nR/V

To find (∂U/∂V)P,T, we can differentiate f(nRT/V, V, T) with respect to V, keeping P and T constant:

(∂U/∂V)P,T = (∂f/∂V)nRT/V(-nRT/V²) + (∂f/∂V)V,T = nRT/V² - nRT/V² = 0

Since the ideal gas law shows that PV = nRT, we can write V = nRT/P. Using this relationship, we can simplify the second term of dU/dT to just:

dU/dT = (∂U/∂T)P,V = nR/P

So, dU/dT at constant P and V is simply nR/P.

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a. To find dU/dPv, we need to differentiate U with respect to both P and V while treating T as a constant. Using the chain rule, we have:

dU/dPv = (∂U/∂P)v + (∂U/∂V)p * (dV/dP)v

Since U is a function of P, V, and T, we can express it as U(P,V,T). Using the ideal gas law, we substitute P = nRT/V into U:

U = f(P,V,T) = f(nRT/V, V, T)

Differentiating U with respect to P while treating V and T as constants, we get (∂U/∂P)v = -nRT/V².

Similarly, differentiating U with respect to V while treating P and T as constants, we get (∂U/∂V)p = nRT/V.

Hence, dU/dPv = -nRT/V² + nRT/V * (dV/dP)v.

b. To find dU/dTv, we differentiate U with respect to both T and V while treating P as a constant. Using the chain rule:

dU/dTv = (∂U/∂T)v + (∂U/∂V)t * (dV/dT)v

Differentiating U with respect to T while treating V and P as constants, we get (∂U/∂T)v = (∂f/∂T)v.

Similarly, differentiating U with respect to V while treating T and P as constants, we get (∂U/∂V)t = (∂f/∂V)t.

Hence, dU/dTv = (∂f/∂T)v + (∂f/∂V)t * (dV/dT)v.

Note: The specific form of the function f(P,V,T) is not provided, so we cannot determine the exact values of (∂f/∂T)v, (∂f/∂V)t, and (dV/dT)v without additional information.

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Answer:

$102

Step-by-step explanation:

$85 x .2 = $17

$85 + $17 = $102

Step-by-step explanation:

100% = $85

1% = 100%/100 = 85/100 = $0.85

20% = 1%×20 = 0.85×20 = $17

so, the total cost of $85 + $17 = $102

which we could have gotten directly by multiplying

$85 by 1.2 (1.2 = 1 for the whole + 0.2 for 20%) = $102

but I wanted to show you the detailed, basic line of thinking behind the % calculations first.

whenever you have no other idea, get to 1% first and then take it from there.

The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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The push operation is called 9 times to evaluate the given postfix expression. The correct option is C) 9.

Postfix expression refers to an expression in which the operator follows the operands. It is also known as the Reverse Polish Notation (RPN). A stack data structure is used to evaluate postfix expressions.

The given postfix expression is 6 4 + 3 10 * + 2 2 - +.

To evaluate the expression, the stack data structure is used:

Step 1: Push 6 into the stack.

Step 2: Push 4 into the stack.

Step 3: Pop 4 and 6 from the stack and add them. Then push the sum (10) into the stack.

Step 4: Push 3 into the stack.

Step 5: Push 10 into the stack.

Step 6: Pop 10 and 3 from the stack and multiply them. Then push the product (30) into the stack.

Step 7: Pop 30 and 10 from the stack and add them. Then push the sum (40) into the stack.

Step 8: Push 2 into the stack.

Step 9: Push 2 into the stack.

Step 10: Pop 2 and 2 from the stack and subtract them. Then push the difference (0) into the stack.

Step 11: Pop 0 and 40 from the stack and add them. Then push the sum (40) into the stack.

Therefore, the push operation is called 9 times to evaluate the given postfix expression. The correct option is C) 9.

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Answer: The answer is a scale factor of 6

Step-by-step explanation:

5 feet is 60 inches, and on the drawing the closet is 10 inches while the real closet is 5 feet, so just divide 60 by whatever gets you 10.

See attachment for math work and answer.

Notice that 110 students out of the total number of students is the same as the number of degrees we are looking for out of 360 degrees.

Now, the total number of students is:

Then, if x is the number of degrees that we are looking for, we can set the following equation:

Multiplying the above equation by 360 we get:

Answer: 92 degrees.

Answer:ok here u go

Step-by-step explanation  the reason its no solutions is because there is no x and that makes the problem no solution

Answer:

x=1.070833

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

4(3x−2) = 4.85

(4) (3x) + (4) (−2) = 4.85 (Distribute)

12x + − 8 = 4.85

12x − 8 = 4.85

Step 2: Add 8 to both sides.

12x − 8 + 8= 4.85 + 8

12x=12.85

Step 3: Divide both sides by 12.

12x/12

=

12.85/12

x = 1.070833

Answer:

x = 277.915...

Step-by-step explanation:

\(4^{4.85} = 3x -2 \\831.746... = 3x - 2\\x = 277.915...\)

Answer:

151°

Step-by-step explanation:

angle m_3 and m_4 must add up to 180 because they both lie on a straight line. Thus, we can do 180-29 to get m_4.

Answer:

3001.6

Step-by-step explanation:

Move the decimal twice to the right

Answer:

=x^2 +4x+11

Step-by-step explanation:

f(x) = x^2 + 7,

Replace x with x+2

f(x+2) = (x+2)^2 + 7

         = (x+2)(x+2) +7

     FOIL

     = x^2 +2x+2x+4 +7

Combine like terms

    =x^2 +4x+11

Answer:

\(f(x+2)=x^2+4x+11\)

Step-by-step explanation:

In \(f(x)=x^2+7\), for all values of \(x\), we substitute \(x\) (what is in the parentheses) into \(x^2+7\) to output a \(y\) value.

In \(f(x+2)\), the term \((x+2)\) is in the parentheses. Therefore, substitute \((x+2)\) for \(x\) in \(x^2+7\) to find \(f(x+2)\):

\(f(x+2)=(x+2)^2+7\)

Expand using \((a+b)^2=a^2+2ab+b^2\),

\(f(x+2)=x^2+4x+4+7\)

Combine like terms:

\(\boxed{f(x+2)=x^2+4x+11}\)

Answer:

551.51

Step-by-step explanation:

The expression for the power delivered to a resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

According to the given information, the power delivered to a resistance R when an alternating current of frequency f and peak current I_0 passes through it is represented by the equation P = I^2_0 R sin^2 2 pi ft.

To express this equation in terms of csc^2 2 pi ft, we can use the trigonometric identity csc^2 x = 1/sin^2 x. Substituting this identity into the equation, we get P = I^2_0 R (1/sin^2 2 pi ft).

Since csc^2 x is the reciprocal of sin^2 x, we can rewrite the equation as P = I^2_0 R (csc^2 2 pi ft). This expression represents the power delivered to the resistance in terms of csc^2 2 pi ft.

Therefore, the correct expression for the power delivered to the resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

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In summary, the correct statements are 1 and 3. The conservation of momentum requires no external forces acting on a system, while the velocity of the center of mass changes only in the presence of a net external force.

To determine the validity of the given statements, let's break them down and provide a more readable explanation:

1. For the total linear momentum of a system to be conserved, there must be no external forces acting on the system.

This statement is true. According to the law of conservation of momentum, the total linear momentum of an isolated system remains constant if there are no external forces acting on it. Mathematically, this can be expressed as:

ΣP_initial = ΣP_final

where ΣP_initial is the initial total momentum of the system and ΣP_final is the final total momentum of the system.

2. The conservation of momentum depends on the conservation of energy.

This statement is false. The conservation of momentum is a separate principle from the conservation of energy. While both concepts are important in physics, they are distinct and independent of each other. Conservation of momentum is related to the balance of linear motion, while conservation of energy deals with the balance of different forms of energy in a system.

3. The velocity of the center of mass of a system changes only when there is a net external force on the system.

This statement is true. The center of mass of a system is a point that represents the average position of all the mass in the system. The velocity of the center of mass can only change if there is a net external force acting on the system. In the absence of external forces, the center of mass will continue to move with a constant velocity. This principle is derived from the conservation of momentum.

4. The correct statements are 1 and 3, because statements 1 and 3 are true.

This statement is true. Based on the explanations above, statements 1 and 3 are indeed true. Statement 2 is false because conservation of momentum does not depend on the conservation of energy. Therefore, statement 4 is also false.

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The value of x is 20

Now, According to the question:

The given equation is:

3x + 32 = 5x - 8

To solve the equation for finding the value of x .

32 + 3x = -8 + 5x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5x' to each side of the equation.

32 + 3x  -5x = -8 + 5x  -5x

Combine like terms:

3x  -5x = -2x

32  -2x = -8 + 5x  -5x

Combine like terms: 5x  -5x = 0

32  -2x = -8 + 0

32  -2x = -8

Add '-32' to each side of the equation.

32  -32 -2x = -8  -32

Combine like terms: 32  -32 = 0

0 -2x = -8  -32

-2x = -8  -32

Combine like terms: -8  -32 = -40

-2x = -40

Divide each side by '-2'.

x = 20

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The result of the integral is (10/5)sin^5(x) - (20/7)sin^7(x) + (10/9)sin^9(x) + c. To evaluate the integral ∫10cos^5(x)sin^4(x)dx, we can use a trigonometric identity and a substitution.

To simplify the integrand, we can use the trigonometric identity cos^2(x) = 1 - sin^2(x) and substitute u = sin(x).

Apply the trigonometric identity: cos^5(x) = (1 - sin^2(x))^2 * cos(x) = (1 - u^2)^2 * cos(x). Now we have the integrand as 10(1 - u^2)^2 * cos(x) * u^4.

Use the substitution: Let u = sin(x), then du = cos(x)dx. We can rewrite the integral as ∫10(1 - u^2)^2 * u^4 * du.

Expand the integrand: 10u^4 - 20u^6 + 10u^8.

Integrate each term: The integral of u^4 is u^5/5, the integral of u^6 is u^7/7, and the integral of u^8 is u^9/9.

Substitute back: Replace u with sin(x) in the antiderivative expression obtained in the previous step.

Add the constant of integration, c, to obtain the final result.

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Answer:

Step-by-step explanation:

Given question is incomplete; here is the complete question,

"Which system of equations has a solution of approximately (0.7, -1.4)?"

A). x - y = 2 and x + 2y = -2

B). x - 2y = -2 and x + y = 2

C). x - y = 2 and x - 2y = -2

D). x + y = 2 and x + 2y = -2

"If the given point (0.7, -1.4) is the solution of the system of equations, it will satisfy both the equations"

To check whether the statement given above is true or false we will substitute the values of x and y in the given equations,

A). x - y = 2

   0.7 - (-1.4) = 2.1

                    ≈ 2

    x + 2y = -2

   0.7 + 2(-1.4) = -2.1

                       ≈ -2

   True.

B). x - 2y = -2

     0.7 - 2(-1.4) = 3.5

    x + y = 2

    0.7 - 1.4 = -0.7

    False.

C). x - y = 2

    0.7 - (-1.4) = 2.1 ≈ 2

    x - 2y = -2

    0.7 - 2(-1.4) = 3.5

    False.

D). x + y = 2

    0.7 - 1.4 = -0.7

    x + 2y = -2

    0.7 + 2(1.4) = 3.5

    False.

Answer:

8 divided by 2

so NOW we do it the other way

2 divided by 8 = 0.25

Step-by-step explanation:

a = 8

b = 2

Answer:

it's 8 divided by 2? so 2 divided by 8 is .25

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.

A. No solution

y = 1/4x+5

x - 4y = 4

You can simplify the second equation into y = 1/4x - 1

Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.

The required percentage of regular grade gasoline are;

a) 34%

b) 95.5%

c)4.5%

(a) To determine the percentage of regular grade gasoline sold between $3.25 and $3.65 per gallon, we need to find the proportion of the data that falls within this range. Assuming a bell-shaped distribution, we can use the standard deviation and mean to find the z-scores for these two prices, and then look up the cumulative probability in a standard normal table.

$3.25$ is $1$ standard deviation below the mean and $3.65$ is $0.5$ standard deviation above the mean.

Using a standard normal table, we find that approximately 68% of the data falls within one standard deviation of the mean, and approximately 34% falls between $-0.5$ and $0.5$ standard deviations.

Therefore, approximately 34% of regular grade gasoline is sold between $3.25 and 3.65 per gallon.

(b) To find the percentage of regular grade gasoline sold between $3.25 and $3.85 per gallon, we need to find the cumulative probability for the range $3.25$ to $3.85$.

$3.85$ is $1.5$ standard deviations above the mean.

Using a standard normal table, we find that approximately 95.5% of the data falls within $1.5$ standard deviations of the mean.

Therefore, approximately 95.5% of regular grade gasoline is sold between $3.25 and $3.85 per gallon.

(c) To find the percentage of regular grade gasoline sold for more than $3.85 per gallon, we need to find the cumulative probability for values greater than $3.85$.

Using a standard normal table, we find that approximately 100% - 95.5% = 4.5% of the data falls above $1.5$ standard deviations from the mean.

Therefore, approximately 4.5% of regular grade gasoline is sold for more than $3.85 per gallon.

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Answer:

17%

Step-by-step explanation:

Hello!

Out of the 6 options, only 1 option will be correct. This can be represented as a ratio of 1:6.

If you randomly guess, there is an equal chance of choosing any of the 6 options.

To find the percentage of guessing the correct option, simply divide 1 by 6 (1 option is correct out of 6), and multiply the outcome by 100 (for percentage).

The probability of getting an answer correct would be 17%.

The probability of getting an answer wrong would be 83%, which can be found by subtracting 17% from 100%.

Answer:

1:23

Step-by-step explanation:

20 / 460

= 1 / 23

= 1:23

Answer:

\(c=7\)

Step-by-step explanation:

\(8=-3c+29\)

⇒ Switch sides:-

\(-3c+29=8\)

⇒ Subtract 29 from both sides:-

\(-3c+29-29=8-29\)

\(-3c=-21\)

⇒ Divde both sides by -3:-

\(\frac{-3c}{-3}=\frac{-21}{-3}\)

\(c=7\)

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