Find the quotient of these complex numbers (6-7i)-(4-5i)=

The statement that every diagonal of a trapezoid divides it into two congruent triangles is false.

Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.

A trapezoid is a quadrilateral which has at least one pair of parallel sides.

The sides may or may not be equal.

Consider an isosceles trapezium, ABCD, given below which has two parallel opposite sides and the other pair of sides are equal.

If we draw a diagonal, AC, we have two triangles ABC and ADC.

AC = AC (common side)

AD = BC (given)

But AB ≠ CD

Hence the triangles cannot be congruent.

Hence the given statement is false.

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(a) Bar A: A, Bar B: O, Bar C: F

(b) One interesting feature of the graphical display is the clear difference in the percentage of individuals who are considered unfit between adolescents and adults.

(a) Bar A: Adolescents

Bar B: Overall (both adolescents and adults)

Bar C: Adult Males vs. Adult Females

(b) The percentage of unfit individuals is much higher in adolescents (33.9%) than in adults (14%). Additionally, within the adult group, the percentage of unfit individuals is higher in females (16.2%) than in males (11.2%). Another interesting feature is that there is no significant difference in the percentage of unfit individuals between male and female adolescents.

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The Emily soccer team has the higher ratio of wins to losses.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of win to loss of Emily soccer team = 9 : 12

Ratio of win to loss of Grant soccer team = 10 : 15

9 : 12 = 9 / 12 = (9 × 5) / (12 × 5) = 45 / 60

10 : 15 = 10 / 15 = (10 × 4) / (15 × 4) = 40 / 60

If 60 games are losses, then 45 games are wins for Emily soccer team.

If 60 games are losses, then 40 games are wins for Grant soccer team.

Higher ratio is for Emily soccer team.

Hence higher ratio of wins to losses is for Emily soccer team.  

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a) We cannot determine the probability

b) The mean of x - 55 is $28 - $55 = -$27, and the standard deviation of x - 55 is $0.45.

c) By the central limit theorem, the sampling distribution of x^-x will be approximately normal if the sample size is large enough.

d)  The probability that the average fee paid by the sample of households exceeds $55 is very close to 0.

a. We cannot determine the probability that the amount a randomly selected household pays for access to the internet exceeds $55 because we don't have information about the distribution of individual payments, only the mean and standard deviation of the population.

b. The mean of the sampling distribution of x is equal to the population mean, which is $28. The standard deviation of the sampling distribution of x is equal to the population standard deviation divided by the square root of the sample size, which is $10/sqrt(500) ≈ $0.45. Therefore, the mean of x - 55 is $28 - $55 = -$27, and the standard deviation of x - 55 is $0.45.

c. By the central limit theorem, the sampling distribution of x^-x will be approximately normal if the sample size is large enough. In this case, since the sample size is 500 and greater than 30, we can assume that the sampling distribution is approximately normal.

d. To find the probability that the average fee paid by the sample of households exceeds $55, we need to standardize the value of x using the sampling distribution of x^-x and then find the probability of a z-score greater than or equal to:

z = (55 - 28)/0.45 ≈ 60. The probability of a z-score greater than or equal to 60 is extremely small, as the normal distribution tails off quickly. Therefore, the probability that the average fee paid by the sample of households exceeds $55 is very close to 0.

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The system of linear equations x = 4 and y = -x -1 has a unique solution.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given is a graph of lines,

We need to find the number of solutions do the lines x = 4 and y = -x-1 have,

In the graph of the lines x = 4 and y = -x -1, intersecting at a point, we know that the lines which intersects at a single point will have only one solution.

Also,

The system of equation has the solution at the point where the line intersects,  

By observing the graph it can be concluded that the graph of x = 4 and y = - x - 1 intersect only at one point i.e (4, -5).

Therefore, the solution of the given system of equations is (4, -5)

Hence, the system of linear equations x = 4 and y = -x -1 has a unique solution.

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The value of the expression (1/2)^3 include the following: D. 1/8.

In Mathematics, an exponent can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as;

bⁿ

Where:

the variables b and n represent numerical values or an algebraic expression.

From the information provided, we can logically deduce the following as the only true statement:

Expression = (1/2)^3

Expression = 1/2 × 1/2 × 1/2

Expression = 1/8

In conclusion, the numerical value 3 represents the power of the given expression.

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Complete Question:

What is the value of the expression (1/2)^3?

Responses

19

1/9

18

1/8

16

1/6

32

The final volume of a system with initially of 2 liters if the pressure is tripled and the temperature is tripled, is 11.57 liters.

The combined gas law equation relates the initial and final conditions of a system of gas by considering the effect of changes in pressure, volume, and temperature:

P1 * V1 / T1 = P2 * V2 / T2

Given the initial conditions of the system:

V1 = 2 liters

P1 = 1 atm

T1 = 273 K (room temperature)

And the changes in pressure and temperature:

P2 = 3 * P1 = 3 atm

T2 = 3 * T1 = 819 K

We can calculate the final volume of the system:

V2 = (P1 * V1 / T1) * (T2 / P2) = (1 atm * 2 liters / 273 K) * (819 K / 3 atm) = approximately 11.57 liters

So the final volume of the system would be approximately 11.57 liters if the pressure is tripled and the temperature is tripled from the initial conditions.

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The car could drive approximately 293.04 miles on a full tank of gas. Drag and drop the number "293.04" into the response area to complete the statement.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that contains variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions are used to represent mathematical relationships and can be used to solve equations and perform calculations.

We can use the given information to find the car's fuel efficiency in miles per gallon (mpg) as follows:

mpg = miles driven / gallons of gas used

mpg = 249.48 miles / 12.6 gallons

mpg ≈ 19.8

This means that the car can travel approximately 19.8 miles on one gallon of gas. To find out how far the car could drive on a full tank of 14.8 gallons of gas, we can multiply the tank capacity by the car's fuel efficiency:

miles on full tank = mpg * gallons in full tank

miles on full tank = 19.8 mpg * 14.8 gallons

miles on full tank ≈ 293.04 miles

Therefore, the car could drive approximately 293.04 miles on a full tank of gas. Drag and drop the number "293.04" into the response area to complete the statement.

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The number of units manufactured at the cost of $8200 will be 95.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given that the cost, C(x), for manufacturing x units of a certain product is

C(x) = x² - 9x + 30.

The number of units will be calculated as:-

C(x) = x² - 9x + 30

8200 = x² - 9x + 30

x² - 9x - 8170 = 0

Solve the equation as below,

x² - 9x - 8170 = 0

x² - 95x + 86x - 8170 = 0

x ( x - 95 ) + 86 ( x - 95 ) = 0

( x - 95 ) ( x + 86 ) = 0

x = 95 units

Therefore, the number of units manufactured at the cost of $8200 will be 95.

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To solve this problem, we can use the formula for calculating the quarterly payment of a loan with compound interest:

Payment = (r * P) / (1 - (1 + r)^(-n))

where:

r = quarterly interest rate (12% / 4 = 0.03)

P = principal amount (remaining debt after down payment) = $150,000

n = total number of quarterly payments (10 years * 4 quarters per year = 40)

(1) Calculation of Quarterly Payment:

Payment = (0.03 * 150,000) / (1 - (1 + 0.03)^(-40)) = $2,365.87 (rounded to the nearest cent)

Therefore, the quarterly payment is $2,365.87.

(2) Calculation of Total Amount of Payment:

Total amount of payment = (number of payments) * (quarterly payment)

number of payments = 10 years * 4 quarters per year = 40

Total amount of payment = 40 * 2,365.87 = $94,634.80

Therefore, the total amount of payment is $94,634.80.

(3) Calculation of Total Amount of Interest Paid:

Total amount of interest paid = total amount of payment - principal amount

Total amount of interest paid = $94,634.80 - $150,000 = -$55,365.20

Note that the result is negative because the down payment ($50,000) exceeds the total amount of interest paid over the life of the loan. Therefore, in this case, the total amount of interest paid is $0, and the man ends up paying a total of $100,000 ($50,000 down payment + $50,000 in quarterly payments).

The cross product of two vectors v and w is explicitly defined as ijkv jwk and also transformed as a dual vector under rotation.

The cross product of two vectors v and w is defined as:

v × w = (v2w3 - v3w2)i - (v1w3 - v3w1)j + (v1w2 - v2w1)k

To show that this cross product transforms as a dual vector under rotation, consider a rotation matrix R that transforms a vector u to u'. The transformation of u can be written as:

u' = Ru

We can write the cross product of v and w in terms of their components as:

v × w = (v1, v2, v3) × (w1, w2, w3) = (v2w3 - v3w2, -(v1w3 - v3w1), v1w2 - v2w1)

To see how this changes under rotation, we can use the matrix-vector product to transform v × w:

(v × w)' = R(v × w) = (Rv × Rw)

Rotation matrix R in terms of its components:

R = (r11, r12, r13; r21, r22, r23; r31, r32, r33)

(v × w)' = (r11r12r13r21r22r23r31r32r33(v2w3 - v3w2) - (v1w3 - v3w1) + (v1w2 - v2w1))

Since the Levi-Civita symbol is a symbol and does not transform under rotation, we have:

(v × w)' = det(R)(v × w)

This shows that the cross product of two vectors v and w transforms as a dual vector under rotation, and that the transformation is proportional to the determinant of the rotation matrix R.

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According to the given information the answer is JK thus has a 10-unit length.

The measurement or size of a thing end to end is referred to as its length. In other words, it is the larger of an object's elevated two or three geometric dimensions. For instance, a rectangle's dimensions are determined by its length and width.

We must determine the separation among points J and K in order to get the length of JK. The distance formula is as follows:

d = √((x2 - x1)² + (y2 - y1)²)

Where (x1, y1) = (-5, 6) is the coordinate of J and (x2, y2) = (5, 6) is the coordinate of K.

Plugging in the values, we get:

d = √(5 - (-5))² + (6 - 6)²)

= √(10² + 0²)

= √100

= 10

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Answer:

Step-by-step explanation:

-3 1/3 goes to between -3 and -4

9/2=4 1/2 between 4 and 5

[tex]\sqrt{15}[/tex] between 3 and 4

16/5=3 1/5 between 3 and 4

\sqrt{15} between 2 and 3

Answer: the only y-intercept is 8

Step-by-step explanation:

One way I remembered equations when I was doing algebra with only an x or a y was HOY VUX.

H - horizontal
O = slope
Y = the variable in the line equation

V  =vertical
U = undefined slope
X = the variable in the line equation

As we can see this is a horizontal line so there will be no x-intercepts.

6y = 48

y = 8

the only y-intercept is 8

The required one point and two non-parallel vectors are (0, -3, 0) and (1, 0, 0), (0, 0, 1).

A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.

One point on the plane y=-3 is (0, -3, 0).

Two non-parallel vectors that are parallel to the plane y=-3 can be obtained by taking any two vectors whose y-coordinate is 0,

since any vector with a y-coordinate of 0 lies in the x-z plane, which is parallel to the y=-3 plane.

For example, the vectors (1, 0, 0) and (0, 0, 1) are non-parallel vectors that are parallel to the plane y=-3.

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To prove that ΔAED ≅ ΔCFD, we will use the two given angle equalities and the fact that D is the midpoint of AC:

Given: D is the midpoint of AC, ∠AED ≅ ∠CFD, and ∠EDA ≅ ∠FDC

To prove: ΔAED ≅ ΔCFD

Proof:

Thus, we have proved that ΔAED ≅ ΔCFD.

A and B are not independent since the result of one toss affects the second toss. Specifically, if the first toss result is a head (A), then the second toss will be more likely to result in a head (B).

A and B are conditionally independent given C since the probability of getting head(A) for the first toss does not depend on the type of coin selected (C).

P(A|C) = 1/2, P(B|C) = 1/2, P(A∩B|C) = 1/4, P(A) = 1/2, P(B) = 3/4, and P(A∩B) = 1/4. Therefore, given the information that a regular coin has been selected (C), the probability of A and B occurring independently is 1/4. This suggests that A and B are conditionally independent given C.

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If Cecily purchases a box of 100 paper clips. She puts 37 /100 of the paper clips in a jar on her desk and puts another 6 /10 in her drawer at home. The number  of the paper clips that are in Cecily's jar  is: 43.

Here is a grid to show the number of paper clips that Cecily has in her jar and drawer:

JAR | DRAWER

|

37 | 60

|

100 | 100

The fraction that the grid represents is :

37/100 + 6/100 = 43/100.

Therefore, Cecily has 43 out of 100 paper clips in her jar and drawer.

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Answer:

A) Yes, Rolle's Theorem can be applied!

Step-by-step explanation:

Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.

Here, for our continuous function [tex]f(x)=-x^2+2x[/tex] over the closed interval [tex][0,2][/tex], we can tell that the function is clearly differentiable over the interval [tex](0,2)[/tex] as [tex]f'(x)=-2x+2[/tex], so we'll need to check if [tex]f(0)=f(2)[/tex]:

[tex]f(0)=-0^2+2(0)=0\\f(2)=-(2)^2+2(2)=-4+4=0[/tex]

Next, we'll need to check if f'(x) = 0 for some x within the closed interval:

[tex]f'(x)=-2x+2=0\\-2x+2=0\\-2x=-2\\x=1[/tex]

As x=1 is contained in [0,2] and the previous conditions were met, Rolle's Theorem can be applied!

You can solve this by using the addition and multiplication properties of equality

the original equation is:

a divided by 6 - 11 = 25

then you can add 11 to both sides to get rid of it (addition property of equality)

a divided by 6 = 36

then you use the multiplication property of equality

a = 216

The measure of angle 2 from the diagram is equivalent to 111 degrees

An angle is defined as the point where two lines meet. From the diagram shown the measure of <1 and <2 lies on the same straight line.

Since the sum of angles on a straight line is 180 degrees, hence;

<1 + < 2 = 180

Substitute the given angle

69 + <2 = 180

<2 = 180 - 69

<2 = 111 degrees

Hence the measure of <2 from the given diagram is 111 degrees.

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The depreciated price of the car in the year 2022 is $148.47

Depreciation in economics is a measure of the amount of value an asset loses from influential factors affecting its market value.

Given that, in 1960 the average price of a new car was $2752. Between 1960 and 2022 car prices have decreased by an average of 4.6% per year.

We need to calculate the average price of a new car in 2022​

The question is depreciated price of the car,

Depreciated price =

A = P(1-r)ⁿ

A = final amount

P = initial amount

r = 4.6%

n = time

Here, the time = 2022 - 1960 = 62 years

Therefore,

A = 2752(1-0.046)⁶²

A = 2752(0.954)⁶²

A = 148.47

Hence, the depreciated price of the car in the year 2022 is $148.47

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Length of the sides is 54 and 54 inches.

Length is defined as the measurement of distance of an object from one end to the other.

A headboard for a bed is shaped like an isosceles trapezoid.

Since it is a isosceles trapezoid the length are equal in number.

The we have to equate the given lengths,

i.e., 6x+18 = 8x+6

Rearranging the terms we get,

6x-8x = 6-18

-2x = -12

Divide by -2 on both sides we get,

x = 6

Sub x in the given lengths we get,

6x + 18 ⇒ 6 * 6 +18 = 54

8x + 6 ⇒8 *6 +6 = 54

So, length of the sides is 54 inches.

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Answer:

20%

Step-by-step explanation:

The length of the diagonal of the rectangle is 11.70 in.

A diagonal of a polygon is a line segment that joins two vertices of the polygon which are not already joined by an edge of the polygon.

Since, there is no information about which polygon's diagonal length we are asked to find, so let us consider that the given side lengths are of a rectangle,

Now, please refer to the figure attached in the solution,

We know that, the diagonal of a rectangle divides it into two right triangles,

Here our rectangle is ABCD and the diagonal AC divides it into rt. Δ ABC and rt. Δ ADC,

Considering the rt. Δ ABC,

The diagonal AC is acting as the hypotenuse of rt. Δ ABC,

So, using Pythagoras theorem,

AC² = AB² + BC²

AC = √4²+11²

AC = √121+16

AC = 11.70

Since, the diagonals of a rectangle are congruent so, AC = BD = 11.70

Hence, the length of the diagonals of the rectangle is 11.70 in.

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The solution of the inequality is x > -2 and x < 7.

Inequality Notation: -2 < x < 7.

The graph is attached.

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4.

-5x - 7 < 3

-5x < 3 + 7

-5x < 10

x > 10/(-5)

x > -2

-5x - 7 > -42

-5x > -42 + 7

-5x > -35

x < -35/(-5)

x < 7

We have x > -2 and x < 7.

x > -2 can be written as -2 < x.

Inequality Notation: -2 < x < 7

This implies that x is in the range of -2 and 7. The graph is attached.

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The side lengths of the given squares are 11 cm and 14 cm

A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.

Given that, the sides of two squares differ by 3cm and the sum of their areas is 317cm², we need to find the length of the sides of the two squares.

Let the sides of the squares be x and y, we know that the area of a square is their side's square.

Therefore, establishing the system of equations,

x-y = 3

x = y+3.......(i)

x²+y² = 317....(ii)

Put eq(i) in eq(ii)

(y+3)²+y² = 317

y²+9+6y+y² = 317

2y²+6y-308 = 0

On factorizing, we get,

y = 11 and y = -14

Since, the length can not be negative so, ignore -14

Put y = 11 in eq(i)

x = 11+3

x = 14

Therefore, the side lengths of the given squares are 11 cm and 14 cm

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