4x + 2 – (3 + 3x) = 7

Answer:

312 m^2

Step-by-step explanation:

Start by separating the shapes.

you will get:

2 triangles with the dimensions 6m x 8m

1 rectangle with the dimensions: 9m x 8m

1 rectangle with the dimensions: 6m x 9m

1 rectangle with the dimensions: 10m x 9m

1) find the area of every shape

2 triangles with the dimensions 6m x 8m -----> 48m^2 and 48 m^2

1 rectangle with the dimensions: 9m x 8m ----> 72m^2

1 rectangle with the dimensions: 6m x 9m ----> 54 m^2

1 rectangle with the dimensions: 10m x 9m ---> 90m^2

2) add everything up

48m^2 + 48 m^2 + 72m^2 + 54 m^2 + 90m^2 =

312m^2

The value of PN is 20 in.

What are congruent triangles?

Congruent triangles are triangles in which all the sides and all the angles are congruent.

These triangles can appear identical when moved, rotated, flipped, and turned. They coincide if moved in a different direction.

In the diagram, two congruent triangles are given ΔPMN ≅ ΔQSR.

So by CPCTC (corresponding parts of congruent triangles are congruent)

In ΔPMN and ΔQSR

PN=QR=20 in.

PM=SQ=24 in.

MN=RS= 7 in.

If two triangles are said to be congruent then all corresponding parts must be equal.

So, the value of PN is 20 in.

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Answer:

C. 20 in

Step-by-step explanation:

The endpoints of the image of AB after a reflection in the line y = z are A'(2, -3) and B'(5, 2).

What is endpoints of the graph?

On a graph, an endpoint is the place where a figure comes to an end. A genuine line has no terminal because it goes on indefinitely in both directions. A ray is a figure that resembles a line and only extends in one direction infinitum. It is one type of line. The endpoint of a ray is on the side that is not extending.

(x, y) → (x, -y), x-coordinate stays as is and y-coordinate changes its sign to opposite.

We have given points:

A(2, 3) and B(5,-2).

The image of AB will have coordinates:

A'(2, -3) and B'(5, 2)

The endpoints of the image of AB after a reflection in the line y = z are A'(2, -3) and B'(5, 2).

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A table represents a relation that is also a function if it shows that every input value is assigned to exactly one output value

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Answer:

Below

Step-by-step explanation:

A   Both are the same line

****   B  If that is 4x + 6 y = 8    the lines are parallel ===> no solution***

C   Intersecting lines

D   same line

The new circle be made with double radius of the given circle.

Also,  the circumference of the new circle is double of the given circle and the Area of the new circle is Four times of the given circle.

Given, a circle

If the radius of the given circle is 'r'

then, the radius of the new circle '2r'

Now, the Circumference of the new circle be,

C' = 2π(2r)

As, the Circumference of the given circle be,

C = 2πr

On dividing, we get

C'/C = 2

C' = 2C

So, the circumference of the new circle is double of the given circle.

Now, the Area of the new circle be,

A' = π(2r)²

As, the Area of the given circle be,

A = πr²

On dividing, we get

A'/A = 4

A' = 4A

So, the Area of the new circle is Four times of the given circle.

Hence, the new circle be made with double radius of the given circle.

Also,  the circumference of the new circle is double of the given circle and the Area of the new circle is Four times of the given circle.

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The registrants would be able to see the 6 sightseeing tours in 18 ways.

Here it is given that the convention has organized the 6 sightseeing tours on 3 days each.

This implies that the 6 sightseeing tours are available on all three days.

Hence, the registrants would be able to book the tour on any of the one days.

Hence, on day 1

the registrants will be able to tour in  ways

On day 2

the registrants would again be able to tour in 6 ways,

Similarly on day 3, they will again be able to tour in 6 ways.

Since they need to choose either of the days given, the total number of ways to tour will be

no.of ways for day 1  +  no. of ways for day 2  +  no. of d6ays for day 3

= 6  +  6  +  6

= 18 ways

Hence, they can go on a sightseeing tour in 18 ways.

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As per the substitution method, the value of (x , y) is (-15/2, 11/2)

Substitution method:

Substitution method is the process of solve one equation for one of the variables. And substitute (plug-in) this expression into the other equation and solve. Then resubstitute the value into the original equation to find the corresponding variable.

Given,

Here we have the following expression.

3x + 5y = 5

Y = -x -2

Now, we need to find the value of x and y.

According to the substitution method, let us consider

3x + 5y = 5 -------------------(1)

Y = -x -2 ---------------------(2)

Now, we have to apply the value of y as -x - 2 in equation (1), then we get,

=> 3x + 5(-x - 2) = 5

When we expand it then we get,

=> 3x - 5x - 10 = 5

Simplify the expression,

=> -2x - 10 = 5

=> -2x = 5 + 10

=> -2x = 15

Then the value of x is,

=> x = -15/2

If the value of x is -15/2. then the value of y is calculated by using the equation (2),

=> y = -(-15/2) - 2

=> y = 15/2 - 2

=> y = (15 - 4)/2

=> y = 11/2

Therefore, the value of (x, y) is (-15/2, 11/2).

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In a farm composed of cows and chickens, there are total of 13 heads and 42 feet.

Let 'h’ represent the number of hens the farmer has.

Let 'c’ represent the number of cows the farmer has.

Assume that all hens have two legs and all cows have four.

There are a total of 42 legs. So

2h + 4c = 42 (1)

There are 13 animals in total.

h + c = 13 (2)

Now that we have our system of equations, we can solve by either substitution or elimination.

Elimination

(2) x 2

2h + 2c = 26 (3)

(2)—(3)

2c = 6

c=3

From (2):

c + h = 13

3+h = 13

h= 10

Therefore, the farmer has 3 cows and 10 hens.

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a. The the proportion that would be used is: 159/15 = 1272/x

b. See explanation for the cross product below.

c. Approximately 120 home runs will be hit.

A proportion can be defined as an equation that involves comparing two equal ratios that are equivalent to each other or set equal to each other.

a. To write a proportion that defines the situation described above, let x represent the number of runs he will hit in his career.

Therefore, we would have the following proportion:

159:15 = 1272:x

or

159/15 = 1272/x

b. Using the cross product, we can find the value of x as shown below:

159 × x = 1272 × 15

159x = 19,080

Divide both sides by 159

159x//159 = 19,080/159

x = 120

c. The number of runs he will hit in his career is: 120.

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Answer:

If the plot point was dilated by a scale factor, it would be multiplying the scale factor with each X and Y. Therefore it would be (-5,-5)

The image of (-1, -1) after the dilation by a scale factor of 5 centered at the origin is (-5, -5).

To find the image of (-1, -1) after a dilation by a scale factor of 5 centered at the origin, we can apply the formula for dilation in the coordinate plane.

The formula for dilation with a scale factor of k centered at the origin is (k * x, k * y), where (x, y) is the original point.

In this case, the original point is (-1, -1), and the scale factor is 5. Applying the dilation formula, we have:

Image = (5 * (-1), 5 * (-1))

= (-5, -5)

This means that the point (-1, -1) is dilated by a factor of 5, and its position is shifted five times farther from the origin in both the x and y directions.

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The best point estimate for the mean monthly electric bill for all residents of the local apartment complex is $69.

It is given that the mean monthly electric bill for 43 residents of the local apartment complex is $69.

That means the sample mean X for 43 residents is $69.

And we know that the sample mean, X is the best point estimate of the population mean, μ.

Therefore the best point estimate for the mean monthly electric bill for all residents of the local apartment complex is $69.

The point estimate for the population mean is the sample mean. Point estimate is the one value that is used to estimate the population parameter. It is also known as the unbiased estimate of the population mean is the sample mean.

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There will be no change in volume reducing the radius by 10%.

What is Direct Proportion?
The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation. Since the other variable is reversed in this case, the inversely proportional relationship is really represented by the same symbol.

For instance, if x and y are two quantities or variables that are intimately linked to one another, we can say x y. The ratio of x and y becomes equal to a constant when the proportionality sign is removed, for example, x/y = C, where C is a constant. In contrast, x and y are represented as x 1/y or xy = C in the case of inverse proportion.
Let the radius be r then
The volume of every sphere is,
[tex]\mathrm{V}=4 \pi \frac{\mathrm{r}^3}{3}[/tex]
In the given question, It is given:
The volume V of a sphere varies in direct proportion to the cube of its radius.

That means:[tex]\mathrm{V}[/tex] ∝ [tex]r^{3}[/tex]
That means:[tex]4 \pi \frac{\mathrm{r}^3}{3} = kr^{3}[/tex]⇒[tex]4 \pi \frac{\mathrm{1}}{3} = k[/tex]
So, The equation is independent of radius.
Hence, There will be no change in volume reducing the radius by 10%.

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The value of x and y are 45 and 48 when the system of inequality are 4x+3y≤36 and x+y≥3.

Given that,

The system of inequality are,

4x+3y≤36 and x+y≥3

We have to find the x and y values of system of inequality.

Take the system of inequality,

4x+3y≤36 ---> equation(1)

x+y≥3 ---> equation(2)

Take the equation(2)

x+y≥3

x≥3-y

Substitute in equation(1).

4x+3y≤36

4x+3y≥-36       (To get the greater than are equal to )

4(3-y)+3y≥-36

12-4y+3y≥-36

12-y≥-36

-y≥-36-12

-y≥-48

y≥48

Substitute in equation(1)

x+y≥3

x+48≥3

x≥3-48

x≥-45

Therefore, The value of x and y are 45 and 48 when the system of inequality are 4x+3y≤36 and x+y≥3.

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If a triangle whose sides length measures are consecutive integers, then the smallest possible perimeter is 9 units

If a, b and c are the sides of the triangle

Then it will be

a + b > c

b + c > a

c + a > b

Given that the side length of the measures are consecutive integer

Smallest consecutive integer is 1, 2 and 3

But

1 +2 > 3

3 = 3

Therefore it will not be the sides of the triangle

Next smallest consecutive integers are 2, 3 and 4

Then,

2+3 > 4

5 > 4

3+4 > 2

7 > 2

2+4 > 3

6 > 3

This will be the sides of the triangle

The perimeter of the triangle is the sum of sides of the triangle

The perimeter = 2 + 3 + 4

= 9 units

Hence, if a triangle whose sides length measures are consecutive integers, then the smallest possible perimeter is 9 units

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The inverse function of f(x) = 3x-4 when x = -1 will be 1.

According to the question,

We have the following function:

f(x) = 3x-4

Now, to find its inverse we will convert this function into a linear equation:

y = 3x-4

Now, we will change variable from x to y and y to x:

x = 3y-4

Now, we have to find the value of y, which will be the inverse of the given function:

Moving 4 from the right hand side to the left hand side will result in the change of signs:

x+4 = 3y

3y = x+4

Dividing by 3 on both the sides:

y = (x+4)/3

Now, we have:

[tex]f^{-1} (x)[/tex] = (x+4)/3

Putting the value of x = -1:

(-1+4)/3

3/3

1

Hence, the inverse function of f(x) = 3x-4 when x = -1 will be 1.

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Purchase consideration less fair value of net assets is goodwill (Purchase Consideration-Fair Value of Net Assets) $690,000,000

What does "goodwill" mean?

Goodwill cannot be purchased or sold on its own; rather, it is a premium over fair value that is paid during a transaction. Other intangible assets include things like licenses or patents that are independent purchases or sales. While most intangibles have a set useful life, goodwill has an unlimited lifespan.

Estimating goodwill

The extra payment made as purchase consideration over the acquiree's net assets' fair market value is referred to as goodwill.

The calculation looks like this:

(Millions of Dollars)

Cost of the purchase: $ 900,000,000

Fair value of net assets is less.

True Cost of the Assets

$15,000,000 in supplies

$200,000,000 in intangible assets

$20,000,000 for property, plant, and equipment

Total $235,000,000

True Cost of Liabilities

$5,000,000 in current liabilities

$20,000,000 in Notes Payable

Total $25,000,000

Goodwill (Purchase Consideration-Fair Value of Net Assets) (Purchase Consideration-Fair Value of Net Assets) $690,000,000

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The Average Speed of car for the round trip is 346.28 km/ hr.

Average Speed is calculated by dividing the total distance that something has travelled by the total amount of time it took it to travel that distance.

If a  car travels a distance d at rate r₁ and return the same distance at rate r₂, then,

Average Speed =  total distance ÷ total time

                          = 2d ÷ d/r₁ + d/r₂

                          = 2d ÷ r₂d + r₁d / r₁r₂

                          = 2r₁r₂ / r₁ +r₂

∴ x = 2× 3030×4040/ 3030 +4040

     = 2448240 ÷ 707

     = 346.28 km/hr

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On yesterday beth walked farther. She walk 1/6 farther than the another day.

beth walked on yesterday = 1/2 of a miles

beth walked on today = 1/3 of a miles

on yesterday she walked = 1/2 of a miles = 0.5 miles

on today she walked = 1/3 of a miles = 0.3 miles

This shows she walk farther on yesterday.

and how far is calculated as :

= 1/2 - 1/3

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

= 1/6

she walked 1/6 farther on yesterday than today.

On yesterday beth walked farther. She walk 1/6 farther than the another day.

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Answer:

slope: -18+18/-2+20

slope: 0:

y = -18

Answer:

Slope = -4/3 or -1.33 in decimal form

Step-by-step explanation:

To find the slope divide the rise by the run. The rise would be the difference between the 2 y points (y2-y1) divided by the run (x2-1x)

Here the rise is (-9-3 = -12) and the run is (8-(-1) = 9) So -12/9 is -4/3 in fraction form and -1.33 in decimal form.

Answer:

Step-by-step explanation:

I believe the tax would be $ 12,150

Carrie will be paid $390 if she puts in 40 hours of work in a week.

The total amount of time of work = 40 hours.

As we are stated that the earnings for 1 hour is $9.75, so, we will perform multiplication to find the earnings for the time she worked. We are performing multiplication because the amount will increase as the number of hours increases.

Performing calculation now.

Amount earned in a week = 9.75 × 40

Performing multiplication on Right Hand Side of the equation to find the amount earned in a week

Amount earned in a week = $390

Thus, the amount paid to Carrie in a week is $390.

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Answer:   y<1

Step-by-step explanation:

Answer:

43.33%

Step-by-step explanation:

x : 100 = 520 : 1200

x = (520 * 100)/1200

x = 520/12

x = 43.333333%

From perpendicular line, we have m1

Knowing m1 * m2 = -1 for perpendicular lines gives us

-1 *m2 = -1

m2 = 1

Using y-b = m(x-a) with the point provided gives

y-1 = 1(x--5)

y = x+6

Therefore (A) is the correct answer

If the margin of error for the electoral poll is 3%, then candidate A has an advantage over candidate B of between 2 and 8 points.

Your results will deviate by how many percentage points from the actual population value, according to your margin of error.

It is considered as a very small percentage that is allowed for error in calculations.

As the question stated-

This suggests that if the margin of error for the electoral survey is 3%, candidate A is leading of candidate B by 2 to 3 percentage points.

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The complete question is-

If a national survey finds candidate A leads candidate B by 5 percent in the upcoming election and the margin of error in the survey is 3 percent, it means that-