Find the scalar equation for the plane passing through the
points P1=(−3, 5, 3), P2=(−5, 0, 6), and P3=(−1, 10, −1).

Answer:

total salary=$20000

spend%=70%

now,

spend no=70% of $20000

=70/100 ×20000

=$14000

now,

total of spend amount of each month=

spend amount×12

=140000×12

=$168000

Answer:

Step one: The parent absolute value function will be reflected across the x-axis and translated down four units.

Step two: The vertex of the parent is (0,0). A reflection does not change the vertex, but the translation will move the vertex (plot 0,-4)

Step three: Evaluate the function at two more points on either side of the vertex. f(-1)=-5 f(1)=-5

Step-by-step explanation:

sorry if im wrong =/

The principal is 50 and the rate of interest is 0.4.

The principal (P) and the rate of interest (R) can be calculated using the following equations:
P = (400*2)/(440 - 400)
R = (440 - 400)/(P*2)
Substituting the given values in the equations we get:
P = 2000/40 = 50
R = 40/100 = 0.4

To calculate the rate and principal of the sum of money, we can use the formula for simple interest: I = Prt, where I is the interest, P is the principal, r is the rate, and t is the time in years.
Given that the yearly interest for the first year is 400 and for the second year is 440, we can set up two equations:
400 = Prt
440 = Pr( t + 1)
Since the interest is for two consecutive years, the time in the first equation is t and the time in the second equation is t + 1.

We can rearrange the first equation to solve for P:
P = 400 / rt
Substituting this value of P into the second equation gives us:
440 = (400 / rt)( t + 1)
Simplifying and rearranging gives us:
440rt = 400t + 400
40rt = 400
rt = 10

Since we are looking for the rate and principal, we can substitute the value of rt back into the first equation:
400 = P(10)
P = 40
So the principal is 40 and the rate is 10 / t. To find the rate, we can substitute the value of P back into the first equation and solve for t:
400 = 40(10 / t)
t = 10
So the rate is 10 / 10 = 1.
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Answer:

Step-by-step explanation:

So when x is translated the + means going right. With y the - means going down. So P is gonna be (-9,-1), Q(-4,0) , and R (-2,-1). See if that helps but I think it is that, but I have another idea what it could be but see if this is right.

Answer:

720m

Step-by-step explanation:

60×4 = 240

240×3 = 720

The best method to use to solve the system of equation will be Elimination method.

According to the description of the elimination approach, it involves removing a phrase that contains any of the variables from the equation in order to simplify the computations. To achieve this, multiply or divide a number by the equation(s) until all of the variable terms' coefficients are the same. The term is then eliminated or removed from the result by adding or subtracting from both equations. Because of this, the addition technique is another name for the elimination approach. For illustration, let's use the elimination approach to resolve two linear equations with two variables.

The two equations are:

3x+7y=-19

-3x+4y=12

From the above equations we can observe that the value of the coefficient of x is same, as well as, they have opposite sign.

Hence, the best method to use to solve the system of equation will be Elimination method.

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Answer:

21 times

Step-by-step explanation:

3x21=62

Answer:

Let's start by using the information given in the problem to write an equation for the perimeter of the rectangle:

Perimeter = 2(length + width)

We know that the length of the rectangle is twice its width, so we can write:

length = 2*width

Substituting this expression into the equation for the perimeter, we get:

Perimeter = 2(2*width + width)

Simplifying this expression, we get:

Perimeter = 6*width

We are given that the perimeter is 7 1/3 cm, which we can convert to a mixed number:

Perimeter = 7 + 1/3 = 22/3

Substituting this value into the equation above, we get:

22/3 = 6*width

Solving for the width, we get:

width = 22/3 ÷ 6 = 11/9

Now that we have the width, we can use the expression for the length to find its value:

length = 2*width = 2(11/9) = 22/9

Finally, we can use the formula for the area of a rectangle, A = length * width, to find the area:

A = (22/9) * (11/9) = 242/81 square cm

Therefore, the area of the rectangle is 242/81 square cm.

Answer:

1/3

Step-by-step explanation:

6/18, divide each side by 3 and you get 1/3

The determinant of the given matrix is 12.

Answer: \(\left|\begin{array}{cccc}-3 & 0 & 1 & 2 \\ -1 & 4 & 2 & 1 \\ 0 & 3 & -1 & -2 \\ 5 & -1 & 1 & 0\end{array}\right| = 12\)

The determinant of a 4x4 matrix can be calculated using the formula: \( \left|\begin{array}{cccc}a & b & c & d \\ e & f & g & h \\ i & j & k & l \\ m & n & o & p\end{array}\right| = a\left|\begin{array}{ccc}f & g & h \\ j & k & l \\ n & o & p\end{array}\right| - b\left|\begin{array}{ccc}e & g & h \\ i & k & l \\ m & o & p\end{array}\right| + c\left|\begin{array}{ccc}e & f & h \\ i & j & l \\ m & n & p\end{array}\right| - d\left|\begin{array}{ccc}e & f & g \\ i & j & k \\ m & n & o\end{array}\right|\)

Plugging in the values from the given matrix, we get: \(-3\left|\begin{array}{ccc}4 & 2 & 1 \\ 3 & -1 & -2 \\ -1 & 1 & 0\end{array}\right| - 0\left|\begin{array}{ccc}-1 & 2 & 1 \\ 0 & -1 & -2 \\ 5 & 1 & 0\end{array}\right| + 1\left|\begin{array}{ccc}-1 & 4 & 1 \\ 0 & 3 & -2 \\ 5 & -1 & 0\end{array}\right| - 2\left|\begin{array}{ccc}-1 & 4 & 2 \\ 0 & 3 & -1 \\ 5 & -1 & 1\end{array}\right|\)

Calculating the determinants of the 3x3 matrices, we get: \(-3(-4) - 0(0) + 1(-8) - 2(-4) = 12 - 8 + 8 = 12\)

Therefore, the determinant of the given matrix is 12.

Answer: \(\left|\begin{array}{cccc}-3 & 0 & 1 & 2 \\ -1 & 4 & 2 & 1 \\ 0 & 3 & -1 & -2 \\ 5 & -1 & 1 & 0\end{array}\right| = 12\)

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1. The x-intercepts are x=3 and x=1. Since 3 is greater than 1, the greatest x-intercept is x=3.

2. The y-intercept is -8.

3. g(x) has the greatest y-intercept.

1. The x-intercept of a function is found by setting f(x) = 0 and solving for x. So for f(x) = 2x²-8x+6, we have:

0 = 2x²-8x+6

0 = x²-4x+3

0 = (x-3)(x-1)

Therefore, the x-intercepts are x=3 and x=1. Since 3 is greater than 1, the greatest x-intercept is x=3.

2. The y-intercept of a function is found by setting x = 0 and evaluating f(x). So for f(x) = -x²-6x-8, we have:

f(0) = -(0)²-6(0)-8 = -8

Therefore, the y-intercept is -8.

For g(x), we have:

g(0) = 2(0)²+16(0)+31 = 31

Therefore, g(x) has the greatest y-intercept.

3. Similar to question 2, we find the y-intercept by setting x=0 and evaluating f(x):

f(0) = -(0)²-8(0)-12 = -12

Therefore, the y-intercept is -12.

4. To find the x-intercepts of f(x) = (x+8)²-4, we set f(x) = 0:

0 = (x+8)²-4

4 = (x+8)²

±2 = x+8

x = -8 ± 2

Therefore, the x-intercepts are x=-6 and x=-10. Since -6 is greater than -10, the greatest x-intercept is x=-6.

5. The axis of symmetry of a quadratic function in the form f(x) = ax²+bx+c is given by x = -b/(2a).

For f(x) = -2x²-12x-16, we have a = -2 and b = -12, so the axis of symmetry is x = -(-12)/(2*-2) = 3.

For g(x) = 2x²+16x+31, we have a = 2 and b = 16, so the axis of symmetry is x = -16/(2*2) = -4.

Therefore, f(x) has the greatest axis of symmetry.

6. To find the y-intercept, we set x=0 and evaluate the functions:

f(0) = 2(0-3)²+1 = 19

g(0) = 2(0+3)²+2 = 20

Therefore, g(x) has the greatest y-intercept.

7. To find the x-intercept, we set f(x) = 0:

0 = -(x+1)²+1

1 = (x+1)²

±1 = x+1

x = -1 ± 1

Therefore, the x-intercepts are x=-2 and x=0. Since -2 is greater than 0, g(x) has the greatest x-intercept.

8. Similar to question 6, we find the y-intercept by setting x=0 and evaluating the functions:

f(0) = -2(0+2)²+2 = -6

g(0) = 2(0+3)²-4 = 14

Therefore, g(x) has the greatest y-intercept.

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To find all the vectors that are in the subspace V of R³, we need to solve the system of equations given in the question. We can use the Gaussian elimination method to do this.

First, let's write the system of equations in matrix form:
\[ \begin{bmatrix} 1 & 2 & -3 \\ 0 & 1 & -2 \end{bmatrix} \begin{bmatrix} x_{1} \\ x_{2} \\ x_{3} \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix} \]

Now, we can use the Gaussian elimination method to find the solution:
Step 1: Subtract 2 times the second equation from the first equation to eliminate x₂:
\[ \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & -2 \end{bmatrix} \begin{bmatrix} x_{1} \\ x_{2} \\ x_{3} \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix} \]
Step 2: Solve for x₁ and x₂ in terms of x₃:
x₁ = -x₃
x₂ = 2x₃
Step 3: Write the solution in vector form:
\[ \begin{bmatrix} x_{1} \\ x_{2} \\ x_{3} \end{bmatrix} = \begin{bmatrix} -x_{3} \\ 2x_{3} \\ x_{3} \end{bmatrix} = x_{3} \begin{bmatrix} -1 \\ 2 \\ 1 \end{bmatrix} \]

So, the subspace V is the set of all scalar multiples of the vector (-1, 2, 1). In other words, V = {x₃(-1, 2, 1) | x₃ ∈ R}.

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The coefficient is 3 and, in the situation, it represents the distance covered per unit

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

M = 20 + 3d

Given an expression ax, where the variable is x

The coefficient in this variable is a

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

The coefficient in M = 20 + 3d is 3

And it represents the slope of the relation

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Answer:

33%

Step-by-step explanation:

Take the original amount and subtract to new amount.

330 -231

99

Divide this by the original amount.

99/300

.33

Change to a percent.

33%

This is the percent decrease.

The probability that a person has the disease given that his test result is positive is approximately 0.166 or 16.6%.

The Bayes theorem's assumption that the prior probabilities are known with certainty is one of its limitations. These probabilities, however, could not be known or be impossible to predict precisely in many real-world settings. Moreover, Bayes' theorem makes the assumption that each occurrence is independent, which may not necessarily be true in real-world circumstances.

Given that,

P(D) = 0.001

P(D') = 1- 0.001 = 0.999

P(T|D) = 0.99 (the test is 99% effective in detecting the disease)

P(T'|D') = 0.995

The Baye's theorem is given as follows:

P(A|B) = P(B|A) * P(A) / P(B)

Substituting the values:

P(T) = (0.99 * 0.001) + (0.005 * 0.999) = 0.00594

P(D|T) = (0.99 * 0.001) / 0.00594 ≈ 0.166

Hence, the probability that a person has the disease given that his test result is positive is approximately 0.166 or 16.6%.

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The complete question is:

Therefore, the column space C(A) in the vector space A is the set of all linear combinations of the columns of A

The column space C(A) in the vector space A can be written as the span of the columns of A. In this case, the columns of A are:

This means that any vector in the column space C(A) can be written as a linear combination of the columns of A. For example, the vector [3,2,4,3] can be written as:

Therefore, the column space C(A) in the vector space A is the set of all linear combinations of the columns of A.

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The surface area of a cylinder is approximately 240.33 square inches.

The formula for the surface area of a cylinder is A = 2πr² + 2πrh, where r is the radius and h is the height of the cylinder.

Given the 24-inch cylindrical tube and its base has a 3-inch diameter.

Here,

Radius r = 3/2 = 1.5 inches

Height h = 24 inches

To determine the surface area of the container, substitute the given values for r = 1.5 and h = 24:

A = 2π(1.5)² + 2π(1.5)(24)

A = 2π(2.25) + 72π

A = 4.5π + 72π

A = 76.5π

We can approximate π as 3.14, then

A ≈ 76.5× 3.14

Apply the multiplication operation, and we get

A = 240.33 square inches

Thus, the surface area of a cylinder is approximately 240.33 square inches.

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The y-intercept of f(x)=−3(x−2)(x+1)(x+4)  is 0,the y-intercept of f(x)=x2(x−1)3(x−4)  is 0.

f(x)=−3(x−2)(x+1)(x+4)End Behavior:  The end behavior of this function is that as x approaches negative infinity, the function approaches negative infinity, and as x approaches positive infinity, the function approaches positive infinity.

Model Degree: This is a cubic function, as the highest degree of the function is 3. Leading Coefficient: The leading coefficient of this function is -3. End Behavior (using limit notation):

lim x→-∞ f(x) = -∞
lim x→+∞ f(x) = +∞
y-intercept: The y-intercept of this function is 0.

f(x)=x2(x−1)3(x−4)End Behavior: The end behavior of this function is that as x approaches negative infinity, the function approaches negative infinity, and as x approaches positive infinity, the function approaches positive infinity.

Model Degree: This is a quartic function, as the highest degree of the function is 4. Leading Coefficient: The leading coefficient of this function is 1. End Behavior (using limit notation):
lim x→-∞ f(x) = -∞
lim x→+∞ f(x) = +∞

y-intercept: The y-intercept of this function is 0.

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The equation of the tangent line to the curve at the point (1, 3) is y = (3/2)x + 1/2.

To find the equation of the tangent line to the curve at a given point, we first need to find the slope of the tangent line at that point. We can do this by finding the derivative of the curve, which is given by y'(x) = 3x² / 2(2+x³)^(1/2).

Next, we need to find the coordinates of the point at which we want to find the equation of the tangent line. Let's say we want to find the equation of the tangent line at the point (1, 3).

Now, we can use the point-slope form of a line to find the equation of the tangent line. The point-slope form of a line is given by y - y1 = m(x - x1), where m is the slope of the line, and (x1, y1) is a point on the line.

Plugging in the values for the slope and the point, we get:

y - 3 = (3(1)²/ 2(2+(1)³)^(1/2))(x - 1)

Simplifying the equation, we get:

y - 3 = (3/2)(x - 1)

y = (3/2)x + 1/2

So, the equation of the tangent line to the curve at the point (1, 3) is y = (3/2)x + 1/2.

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Statement 1, BD ≅ SD and ED ≅ TD would not be sufficient to prove quadrilateral BEST is a parallelogram.

A quadrilateral is a parallelogram if it satisfies any of the following conditions: Opposite sides are parallel and congruent, Opposite angles are congruent, Diagonals bisect each other. If a quadrilateral satisfies any of these conditions, it is a parallelogram.

Although BD ≅ SD and ED ≅ TD indicate that the diagonals bisect each other, it does not necessarily mean that the opposite sides are parallel. For example, a kite has diagonals that bisect each other but its opposite sides are not parallel.

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Answer: $460

Step-by-step explanation:

To calculate the total amount of money you will pay back after borrowing $400 for 5 years at an annual interest rate of 3%, you can use the following formula:

Total amount = principal + interest

Principal = the amount you borrowed = $400

Interest = the amount of interest paid over the 5 years period.

To calculate the interest, we can use the formula:

Interest = Principal x Rate x Time

Rate = the annual interest rate expressed as a decimal = 0.03

Time = the time period in years = 5

So, the interest for the 5-year period is:

Interest = $400 x 0.03 x 5 = $60

Therefore, the total amount of money you will pay back is:

Total amount = $400 + $60 = $460

You will pay back $460 over five years if you borrow $400 at an annual interest rate of 3%.

Answer: To calculate the total amount of money to be paid back for borrowing $400 for 5 years at an annual interest rate of 3%, we need to use the formula for simple interest:

Simple interest = Principal x Rate x Time

where:

Principal = $400 (the amount borrowed)

Rate = 3% per year

Time = 5 years

Plugging these values into the formula, we get:

Simple interest = $400 x 0.03 x 5

= $60

Therefore, the total amount of money to be paid back is the sum of the principal and the simple interest:

Total amount = Principal + Simple interest

= $400 + $60

= $460

So, you will need to pay back a total of $460 after 5 years of borrowing $400 at an annual interest rate of 3%.

Step-by-step explanation:

The missing numbers in the expressions are:

a. x²

b. 4x²

c. 24x

d. 36x

e. 9x²

f. 1

Every combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is known as an algebraic expression (or variable expression).

Let's use the equation 5x + 7 as an example.

Now here,

We can see that by simplifying the expressions we can see that all of them are in the form of (a+b)².

So, using the same to simplify the equations we get the missing numbers.

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The simplified expression is -4x + 44/3.

An exponent is a numerical value that indicates how many times a number, variable, or expression is to be multiplied by itself. It is usually written as a superscript to the right of the base, such as in the expression 3², where 3 is the base and 2 is the exponent.

The exponent indicates that 3 is to be multiplied by itself 2 times, resulting in a value of 9. Exponents are used in many areas of mathematics, including algebra, calculus, and geometry, and are an important concept for understanding mathematical operations and functions.

To simplify the expression, we need to follow the order of operations and combine like terms where possible:

2/3(3x - 1) + 4x + 3² - 10x + 5

First, simplify the expression inside the parentheses:

2/3(3x - 1) = 2x - 2/3

Next, simplify the squared term:

3² = 9

Now, combine the like terms:

2x - 2/3 + 4x - 10x + 9 + 5 = -4x + 14 + 2/3

Finally, we can rewrite the expression with the fractional coefficient as a mixed number:

-4x + 14 + 2/3 = -4x + 44/3

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The area of triangle PTSQ with sides ST=4, TQ=20, PQ=25, PS=13 is calculated to be 260 square units.

To find the area of triangle PTSQ, we can use the formula for the area of a triangle:

Area = (1/2) × base × height

First, we need to find the height of the triangle. We can do this by drawing an altitude from point T to side PS. Let the foot of the altitude be point R. Then, triangle TRS is similar to triangle TQP by the AA similarity criterion, since angle TRS = angle TQP (both are right angles), and angle STR = angle PTQ (both are vertical angles).

Therefore, we can set up the following proportion:

TR / TS = TQ / TP

TR / 13 = 20 / (25 - TP)

Cross-multiplying, we get:

25TR - 13TQ = 260

Substituting the given values, we get:

25TR - 13(20) = 260

25TR = 520

TR = 20.8

Now, we can use the formula for the area of triangle PTSQ:

Area = (1/2) × PQ × TR

Substituting the given values, we get:

Area = (1/2) * 25 * 20.8 = 260 square units

Therefore, the area of triangle PTSQ is 260² units.

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The remainder when doing the division problem (15x^(2)+4x-37) ÷ (3x-4) is (-5).

To find the remainder, we can use polynomial long division. Here are the steps:

1. Divide the first term of the dividend (15x^(2)) by the first term of the divisor (3x) to get the first term of the quotient (5x).
2. Multiply the first term of the quotient (5x) by the divisor (3x-4) to get (15x^(2)-20x).
3. Subtract (15x^(2)-20x) from the dividend (15x^(2)+4x-37) to get the new dividend (24x-37).
4. Repeat steps 1-3 with the new dividend (24x-37) and the divisor (3x-4) to get the second term of the quotient (8) and the new dividend (-5).
5. Since the degree of the new dividend (-5) is less than the degree of the divisor (3x-4), we stop here and the new dividend (-5) is the remainder.

So, the remainder when doing the division problem (15x^(2)+4x-37) ÷ (3x-4) is (-5).

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(a) The profit function is found by subtracting the cost function from the revenue function. In this case, the profit function P(x) can be found by subtracting C(x) from R(x):

P(x) = R(x) - C(x) = (−1x^2+370x) - (5x+2400)

Simplifying the expression gives:

P(x) = -1x^2 + 370x - 5x - 2400

P(x) = -1x^2 + 365x - 2400

Therefore, the profit function is P(x) = -1x^2 + 365x - 2400.

(b) The average profit function is found by dividing the profit function by the number of items sold, x. In this case, the average profit function Pˉ(x) can be found by dividing P(x) by x:

Pˉ(x) = P(x) / x = (-1x^2 + 365x - 2400) / x

Simplifying the expression gives:

Pˉ(x) = -1x + 365 - 2400/x

Therefore, the average profit function is Pˉ(x) = -1x + 365 - 2400/x.

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Based on the given dimensions of the panel, the area of the panel is 39.6 square cm.

The panel is in the shape of a parallelogram.

A parallelogram is a convex quadrilateral in which each pair of opposite edges are parallel and of equal length.

Area of the parallelogram panel is the measure of the extent of a surface usually measured in square units.

Area of the parallelogram panel = base × height

Base = 5.5 cm

Height = 7.2 cm

Area of the parallelogram panel = base × height

= 5.5 cm × 7.2 cm

= 39.6 square cm

Therefore, the area of the parallelogram panel is 39.6 square cm

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We can start by first finding the value of 8°F, where F represents the function f(x) = x² - 8.

So, we have:

8°F = 8(f(x)) = 8(x² - 8) = 8x² - 64

Now, substituting x = -3, we get:

8°F(-3) = 8(-3)² - 64 = 8(9) - 64 = 8

Finally, substituting this value into the given expression, we have:

8°F(-3) - 4 = 8 - 4 = 4

Therefore, the statement "True" is correct.