2. (05.03 MC)In the figure below, AABC 2 ADEF. Point C is the point of intersection between AG and BF, while point E is the point of intersection between DG and BFДАBFProve AABC AGEC. (10 points)

There is no shortage of units in this market with a $5 price ceiling and the size of shortage is 0 units.

Given: On this market, the government imposes a $5 price ceiling.

We need to find the size of the shortage in this market.

From the given table, we can see that the quantity demanded for $5 price ceiling is 4 units and the quantity supplied is 8 units.

So, the demand is satisfied and an extra 4 units are also provided.

Therefore, there is no shortage of units in this market a $5 price ceiling and the size of shortage = 0 units.

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Number of cartons of cloth face masks purchased will be 19  and number of cartons of  hand-sanitizer purchased will be 5.

We had given that Maleri Designs sells cartons of cloth face masks ($10) and cartons of hand-sanitizer ($4) on eBay.

Also given that Mod World, purchased 24 cartons.

Let number of cartons of cloth face masks be x and let number of cartons of  hand-sanitizer be y.

As total carton purchased is 24.

∴ x + y = 24 --(1)

also Mod World, purchased 24 cartons for $210.

∴ Also price of cartons of cloth face masks is $10 and cartons of hand-sanitizer is $4 which is buyed at $210.

∴ 10x + 4y = 210  --(2)

Now multiplying equation (1) by 10

∴ 10x + 10y = 240 --(3)

Now subtracting (2) from (3) by simplification

∴ y = 5

∴ x = 19

Number of cartons of cloth face masks purchased will be 19  and number of cartons of  hand-sanitizer purchased will be 5.

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Answer:

(99/8)

Step-by-step explanation:

      3

12 -------

      8

8 × 12 = 96

96 + 3 = 99

 99

-------

  8

I hope this helps!

Answer:

Step-by-step explanation:

Simplifying

px + 5 = -4x + q

Reorder the terms:

5 + px = -4x + q

Reorder the terms:

5 + px = q + -4x

Solving

5 + px = q + -4x

Solving for variable 'p'.

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

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

5 + -5 + px = q + -5 + -4x

Combine like terms: 5 + -5 = 0

0 + px = q + -5 + -4x

px = q + -5 + -4x

Reorder the terms:

px = -5 + q + -4x

Divide each side by 'x'.

p = -5x-1 + qx-1 + -4

Simplifying

p = -5x-1 + qx-1 + -4

Reorder the terms:

p = -4 + qx-1 + -5x-1

Answer:

1/6

Step-by-step explanation:

1/2 1/3

lcd(least common denomitator)=6

there fore it is 1/6

In class of 34 students, 19 of them are girls, then the percentage of girls in the class is 55.9%

The total number of students in the class = 34

Number of girls in the class = 19

The percentage is defined as the ratio that can be expressed as the fraction of 100. The percentage is often represented using the percentage sign "%"

The percentage of girls in the class = (Number of girls in the class/The total number of students in the class) ×100

Substitute the values in the equation

The percentage of girls in the class = (19/34)×100

= 0.559×100

= 55.9%

Hence, in class of 34 students, 19 of them are girls, then the percentage of girls in the class is 55.9%

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Step-by-step explanation:

any linear function represents a straight line (hence the name) and is therefore of the structure

y = f(x) = ax + b

"a" is the slope of the line, and it is represented by the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another point.

"b" is the y-intercept (the y-value when x = 0).

so, let's look at the answer options :

A.

x = 0 gives us b (the y value) : 2

so, then for x = 1, y = 3 ?

3 = a×1 + 2

a = 1

now, the next point must be also on the same line for the whole function to be linear (and that means the equation has to be true for all numbers involved) :

x = 2, y = 6

6 = 1×2 + 2 = 4

6 is for sure NOT 4, so this is not a linear function.

it is actually y = x² + 2

B.

x = 0 gives us b : 1

for x = 1, y = 3 ?

3 = a×1 + 1

a = 2

again, the next point must be on the same line :

x = 2, y = 9

9 = 2×2 + 1 = 5

9 is for sure NOT 5, so this is not a linear function.

it is actuality y = 3^x.

C.

x = 0 gives us b : 0

for x = 1, y = 1 ?

1 = a×1 + 0 = a

a = 1

the next point :

x = 2, y = 4

4 = 1×2 = 2

4 is for sure NOT 2, so this is not a linear function.

it is actually y = x².

D.

x = 0 gives us b : 3

for x = 1, y = 9

9 = a×1 + 3

a = 6

the next point(s) must fit :

x = 2, y = 15

15 = 6×2 + 3 = 12 + 3 = 15

correct

x = 3, y = 21

21 = 6×3 + 3 = 18 + 3 = 21

correct

yes, this is a linear function.

it is y = 6x + 3

Given the standard form:

This can be expressef as a decimal by shifting the decimal point to the back 4 times (since the power is a negative 4) as shown:

Hence the equivalent value for the standard form is 0.0005. Option B is correct

Answer:

Explanation:

We are given the equation for the height:

If we differentiate this equation, we get the equation of the velocity:

The problem tells us that the object hits the ground at a velocity of -25m/s. We can write this:

Where t0 is the time when the object hits the ground, and the velocity is -25m/s

Now, we can solve for v0:

And if we use this in the height h(t) equation, we can find the value of t0. At t0, the height is 0. Thus:

And solve:

Next, we can use the quadratic formula to solve this:

Let's see which of the two solutions is the time we are looking for.

Let's go back to our solution for v0:

If we use t0 = 0.43751 s:

This means that the initial velocity is negative, thus the object goes downwards. But, the problem tells us that initially the object is thrown upwards.

The correct value of t0 = 4.66 seconds

Now we can find v0:

Thus, v0 = 20.7 m/s

The data from greatest to least is 9 3/4 > 9.5> 9 3/8> 9.125.

Any data, including numbers, alphabets, amounts, lengths, etc., are arranged in descending order from highest to lowest.

In other terms, anything is considered to be in descending order when it is arranged from a higher value to a lower value. It is possible to arrange numbers in descending order, including whole numbers, natural numbers, integers, fractions, and decimals.

For example 7, 3, 9, 2 in decreasing order, for instance. Starting with the biggest number, we'll work our way down to the lesser ones one at a time. When these numbers are listed in descending sequence, they are written as 9, 7, 3, and then 2.

Given data:

9.5, 9 3/8, 9.125, 9 3/4

Now, simplifying the mixed fraction as

9 3/8

=75/8

= 9.375

9 3/4

=39/4

= 9.75

Thus, we have the data in decimal form

9.5, 9.375, 9.125, 9.75

Hence, the data from greatest to least is 9 3/4 > 9.5> 9 3/8> 9.125.

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The simplification of the given expression would be; 4x/7 + 2y /7 + 5.

Simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.

We have been given an expression as  5/7 x + 2/7 y − 2 − 1/7 x + 7

Thus,

5/7 x + 2/7 y − 2 − 1/7 x + 7

Combine the like terms first;

5/7 x  − 1/7 x + 2/7 y − 2+ 7

Then solve the like terms;

(5 -1)x/7 + 2y /7 + 5

4x/7 + 2y /7 + 5

Therefore, the simplification of the given expression would be; 4x/7 + 2y /7 + 5.

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The value of (f·g)(x) from the given function is -2x³ - x².

The given functions are f(x) = 2x +1 and g(x) = -x².

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here,

(f·g)(x) = f(x) × g(x)

= (2x +1) × (-x²)

= 2x × (-x²) + 1 × (-x²)

= -2x³ - x²

Therefore, the value of (f·g)(x) from the given function is -2x³ - x².

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"Your question is incomplete, probably the complete question/missing part is:"

If f(x) = 2x +1 and g(x) = -x², then find (f·g)(x).

ANSWER

sin(2θ) + cos(2θ) = -31/25 = -1.24

EXPLANATION

If we do the inverse of the cosine to -3/5 we would get the angle θ. Then we can know the value of the sine:

So we have:

• sin(θ) = 4/5

• cos(θ) = -3/5

To find sin(2θ) + cos(2θ) we'll have to use the trigonometric identities:

Since we have the sine and cosine of theta, we can solve this:

The sum is:

Given,

{x : x is a letter in the word "nonintervention"}

A={x : x is a letter in the word "nonintervention"}

The roster form of the set is,

A={e, i, n, o, v, t, r}

The number of elements in the set A is,

n(A)=7

Hence, the number of elements in the set A is 7.

Plot the points (0, -8), (1, -8.8) and (2, -9.6) on the graph. Therefore, the graph for the given equation is plotted below.

The given equation is 4x + 5y = -40.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

Put x=0, 1, 2, 3, 4, 5,.....in the given equation and solve for y

When x=0, 4(0)+5y=-40

⇒ 5y=-40

⇒ y=-8

When x=1, 4(1)+5y=-40

⇒ 5y=-44

⇒ y=-8.8

When x=2, 4(2)+5y=-40

⇒ 5y=-48

⇒ y=-9.6

Plot the points (0, -8), (1, -8.8) and (2, -9.6) on the graph

Therefore, the graph for the given equation is plotted below.

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we can use cross multiplication

where x is the number of fan boats

the number of fan boats to 54 sailboats is 90

The equation of the parabola for the given points is y = -3x² + 7x + 1

Equation of the parabola

The standard form of the equation of a parabola is expressed as

y = f(x) = ax² + bx + c

where a, b, and c are constants and a ≠ 0.

Given,

Here we have the points (0, 1), (1, 5), (2, 3).

Now, we have to find the equation of the parabola.

Here we are given three coordinates (0, 1), (1, 5), and (2, 3) which lie on the parabola and which means that it satisfies the parabolic equation.

In order to find the values of a, b and c we need to formulate three equations using the three given points.

Since for the three unknowns a, b, and c, we will require three equations.

For that we have to take the Point (0,1) i.e. x = 0 and y = 1

Substituting the values of x and y in the standard parabola equation, then we get,

1 = a(0)² + b(0) + c

1 = 0 +  0 + c

c = 1 -------------------(1)

Next, we have to take the Point (1, 5) i.e. x = 1 and y = 5

Substituting the values of x and y in the standard parabola equation, then we get,

5 = a(1)² + b(1) + c

5 = a +  b + c

It can be written as,

a + b + c = 5 -----------------------------(2)

Finally, we have to take the Point (2, 3) i.e. x = 2 and y = 3

Substituting the values of x and y in the standard parabola equation, then we get,

3 = a(2)² + b(2) + c

3 = 4a +  2b + c

It can be written as,

4a + 2b + c = 3 -----------------------------(2)

Apply the value of c as 1 in equation (2), then we get,

a + b + 1 = 5

a + b = 4 ---------------------(4)

Similarly, apply the value of c on the equation (3), then we get,

4a + 2b + 1 = 3

4a + 2b = 2

Divide the equation by 2 on both sides, then we get,

2a + b = 1 --------------------(5)

Subtract equation (5) from equation (4),

(2a - a) +(b - b) = 1 - 4

a = -3

Apply the value of a in the equation (4) to get the value of b,

(-3) + b = 4

b = 7

Therefore, the equation of the parabola is

y = -3x² + 7x + 1

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In statistics, there are ways of analyzing data and these include measures of "central tendency" and "measures of dispersion."

This question is focused on "measures of dispersion," that is, an analysis of how well the data set is being spread away from the centre. The centre is most commonly denoted as the mean (average), and the SPREAD is an analysis of how farther away the observed data is from the centre.

The Mean, Median and Mode are basically measures of "central tendency" and therefore, options A, B and C do not measure the SPREAD of a distribution.

The Quartiles and Standard deviation actually measure how well (either very close or very far) the data set move away from the distribution.

The Quartiles basically examine the data set from all four quarters of the entire set, the 1st, 2nd, 3rd and 4th quarters. This measure of spread measures how well the data is from the distribution depending on which quartile it falls. The Standard deviation measures how far the mean deviates (or drifts away) from the data set.

The correct answer therefore is option D.

Mrs. Richardson and Mr. Richardson have to make their hourly income 306.314 to live within their budget in Athens.

What is income?

Income is the amount of money that an individual or an organization gets in return for their services or goods offered. Depending on the context—such as taxation, financial accounting, or economic analysis—income may have a variety of definitions.

Given in the question,

The Richardson family needs 990272 per year to in their budget.

Mrs. Richardson works 22 hours a week.

Mr. Richardson works 40hours a week.

We need to calculate their hourly income.

Lets first calculate total weeks in a year.

We know that, a year has 365 days and a week has 7

So, total no. of weeks in a year = 365/7 = 52.143 weeks.

no. of weeks in a year = 52.143 weeks

Their weekly income = yearly income/no. of weeks in a year

So, weekly income = 990272/52.143

weekly income = 18991.466

Their hourly income = weekly income/working hours per week

Their weekly income is 18991.466 and,

working hours = 22 + 40 = 62 hours.

Their hourly income = 18991.466/62

Hourly income = 306.314

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Given: The information below

To Determine: How much Austine invested

Solution

Please note that the amount invested is the Principal

The formula combining principal, rate, time and interest for simple interest is

Make P the subject of the formula

Substitute for I, r and t given into the formula as shown below

Hence, the amount invested by Austine is $200

The amount which needs to be replayed if the loan is unsubsidized, as opposed to being subsidized is $59,295.86.

The monthly payment amount formula on a loan of P at rate r for t years is A = P(r ÷ 12) ÷ (1 -[tex]\frac{(1 +r)}{12} ^{-12t}[/tex])

For the normal compensation plan, T = 25. The P = $90,000 and r = 0.625, so the formula is,

A = $90,000(0.625 ÷ 12) ÷ (1 - (1 +[tex](\frac{1 +0.625}{12} )^{(-300)}[/tex])

A = $90,000(0.625) ÷ (1 - [tex](1.135)^{(-300)}[/tex])

A = $90,000(0.625) ÷ (1.832)

A = $(90,000 × 0.625) ÷ (1.832)

A = $30704.14

Payments under the extended repayment plan last for 25 years. The amount which needs to be replayed is $90,000 - $30704.14 = $59,295.86.

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If Mr. Stern charges a monthly rent of $200, we still can rent all suites. An average increase of $5 in the monthly rent imply in the addition of one suite vacant.

Therefore, the total monthly revenue r in function of the number of vacant units v can be writen in the form:

The monthly rent m is given by:

The value of v that maximize the total revenue r is the one found in the vertex of the parabola that represents r:

Therefore, the monthly rent that maximize the total revenue is m = 200 + 5*10 = $700

The monthly revenue with this monthly rent is:

SOLUTION

Define a variable for the unkwons

Then

6 dozen of doughnuts and 2 dozen of croissant cost $42, is written as

Similarly

$40 for 2 dozen of doughnuts and 5 dozen of croissant is witten as

Applying Elimination to solve the two system of equation, we have

Then, subtract the equation obtained above

Hence Y=6

Then you Eliminate Y from eqaution 1 an d 2 by

Multiplying equation 1 by 5 and equation 2 by 2

The sunbtract the equation obtained

Hence X=5

Therefore

A Dozen of doughnuts cost $5

A Dozen of Croisant cost $6

Given:

To find:

To expand the expression using binomial's theorem

To expand, we will apply the binomial theorem formula:

The expansion becomes:

Answer: you cant but here are some ways to practice:)

Find the greatest common divisor of both the numerator and the denominator. This can be done either with prime factor trees or another method.

Divide both the numerator and the denominator with the greatest common divisor.

The result is a simplified fraction. hope this helps and sorry.

if we take the black boxes as representation of negative numbers, and the white boxes as a representation of positive numbers, then we get:

after combining the similar terms we get:

therefore, the final expression is x + 1

Step 1:

What are congruences?

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.

Step 2:

JH is congruent to HI

Final answer

JH is congruent to HI

Based on the system of equations, the cost of using 19 HCF of water is $35.43

An equation is a mathematical statement that two or more values are equivalent.

Equations are stated to show that two mathematical expressions are equal using the equation sign (=).

Cost of using 17 HCF of water = $32.13

Cost of using 35 HCF of water = $61.83

Total cost of 17 HCF water = 17x + a

17x + a = 32.13 ... equation 1

Total cost of 35 HCF water = 35x + a

35x + a = 61.83 ... equation 2

35x + a = 61.83

-17x + a = 32.13

18x = 29.70

18x = 29.7

x = 29.7/18

x = 1.65

17x + a = 32.13 ... equation 1

17(1.65) + a = 32.13

28.05 + a = 32.13

a = 4.08 (32.13 - 28.05)

= 19(1.65) + 4.08

= $35.43

Thus, using the equations above, we can conclude that 19 HCF of water costs $35.43.

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Given:

(2x+5) is one of the factor.

By taking the factors equal to zero then we get the values of x.

Therefore, the zeros of the polynomial are