Write the scale factor

Based on the fact that the rectangular plot has a length that is 10 m longer than the width, the equation that will help to find area of the rectangular plot of land is 10x + x² = 10,000

To find the area of the plot of land is the same as finding the area of a rectangle which is:

Area of a rectangle = Length x Width

Assuming the width of the rectangular plot of ground is x, then the length would be:

= 10m + x

= 10 + x

The area of the rectangular plot of ground can therefore be found by the formula:

Area of a rectangle = Length x Width

10,000 square meters = (10 + x) × x

10,000 square meters = 10x + x²

10x + x² = 10,000

In conclusion, an equation that can help you to find the dimensions of the plot of ground is 10x + x² = 10,000.

Rest of the question is:

What equation will help me find the dimensions?

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If a tire on the snowplow with a diameter of 3.2 ft turns 47 times then, the length of the street is 472.3 feet.

To clear a street the city workers use a snowplow. The diameter of the tire of the snowplow is 3.2 ft.

The tire has to turn 47 times to cover the total length of the street.

Now, we know that the circumference of a circle is given as:

C = 2πr where r is the radius of the circle. And the radius of a circle is half of its diameter.

Therefore, the circumference of the circle can be written as:

C = πD where D is the diameter of the circle.

Now, to calculate the total length of the street we will find the product of the circumference and the number of times the tire has to turn to cover the street.

Therefore,

Length of the street, L = nC

L = nπD

L = 47 × 3.14 × 3.2 ft

L = 472.256 ft

L = 472.3 ft

Hence, the length of the street is 472.3 feet.

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The point ([tex]-3\frac{1}{2}[/tex], [tex]-1\frac{1}{4}[/tex] ) on the coordinate plane is shown in the figure .

The Coordinate plane can be defined as a 2 D plane formed by the intersection of two line ,

where the horizontal line is called x axis and

the vertical line is called y axis .

In the question ,

the point is given

the point is  ([tex]-3\frac{1}{2}[/tex] , [tex]-1\frac{1}{4}[/tex] )

writing the mixed fraction  in decimal form , we get

x coordinate = [tex]-3\frac{1}{2}[/tex] ⇒ -(3*2+1)/2 = -7/2 = -3.5

y coordinate = [tex]-1\frac{1}{4}[/tex] ⇒ -(1*4+1)/4 = -5/4 = -1.25

So, the point to be plotted on the coordinate plane becomes (-3.5,-1.25)

the points plotted are shown in the figure below .

Therefore , the point ( [tex]-3\frac{1}{2}[/tex], [tex]-1\frac{1}{4}[/tex] ) on the coordinate plane is shown in the figure .

The given question is incomplete , the complete question is

Where is ([tex]-3\frac{1}{2}[/tex] , [tex]-1\frac{1}{4}[/tex]  ) on the coordinate plane?

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Answer:

3/4 - 5/6 is

0.08333333333

branliest??

The average rate of change from

3 to 5 is -16.

0 to 2 is -4

-3 to 0 is -6.

It represents the typical amount by which the function changed for each unit over that time. On the function graph, it is calculated using the slope of the line connecting the interval's ends.

Given Data

Equation = 4 -2x²

Formula-

[tex]\frac{f(a)-f(b)}{a-b}[/tex]

a)To find the average rate of change from 3 to 5

a = 5, b = 3

Equating values in the formula

[tex]\frac{4-2(5^{2} )-(4-(3)}{5-3}[/tex]²

[tex]\frac{-46+14}{2}[/tex]

-[tex]\frac{32}{2}[/tex]

-16

The average ROC 3 to 5 is -16.

b) The average ROC from 0 to 2

a = 2 b=0

Equating values in the formula

[tex]\frac{4-2(2^{2})-(4-2(0) }{2-0}[/tex]

[tex]\frac{-4-4}{2}[/tex]

[tex]\frac{-8}{2}[/tex]

-4

The average ROC from 0 to 2 is -4

c)The average ROC from -3 to 0

a= 0 b = -3

Equating values in the formula

[tex]\frac{4-2(0)-(4-2(3^{2} )}{-3-0}[/tex]

[tex]\frac{4+14}{-3}[/tex]

-[tex]\frac{18}{3}[/tex]

-6

The average ROC from -3 to 0 is -6.

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Answer:

0.000000010

Step-by-step explanation:

[tex]\displaystyle \int -\tan(\theta )\cdot \ln(3\cos(\theta )) ~~ d\theta \\\\[-0.35em] ~\dotfill\\\\ u=\ln(3\cos(\theta ))\implies \cfrac{du}{d\theta }=\cfrac{1}{3\cos(\theta )}\cdot -3\sin(\theta ) \\\\\\ \cfrac{du}{d\theta }=-\tan(\theta )\implies \cfrac{du}{-\tan(\theta )}=d\theta \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \int -\tan(\theta )\cdot u\cdot \cfrac{du}{-\tan(\theta )}\implies \int u\cdot du[/tex]

Answer:

a) 27 b) 5 c) 16 d) 7

Step-by-step explanation:

Given:

The distance travelled by the ball is, d = 40 m.

The maximum height the ball reached is, h = 3 m.

The objective is to find the distance travelled by the ball at a height of h' = 2 m.

. (vertex)

n, the

The value of x can be calculated using the general form of the equation of parabola,

Here, (p,q) stands for the vertex of the parabola (20,3).

To find the value of a, consider a coordinate (0,0) and substitute the obtained values in the general equation of parabola.

Now, consider the coordinate of the required distance x of the ball, (x,2).

Substitute the above coordinate, the value of a and the vertex in the equation of parabola.

To solve the square on RHS, take square root on both sides of the equation.

Since, the height of 2 m of ball can be obtained at either side of the vertex.

So the distance between the vertex and the required position is

Then, the other possible position of the ball is,

Hence, the height of the ball will be 2m, either at a distance of 8.5m from origin or 31.5m from the origin.

A=a+b/2×h=5+10/2×4=30. this might helpful

The force exerted by the prism on the floor = 450N

Given: height = 3m, volume = 10m³

Pressure = 75 N/m², prism

To find force

Solution:

Volume of prism = Area of base x height

= Аrеа х 3

Area = 18 = 6m²

Now,

Pressure: force / Area ⇒ 75 = force 6

force= 75×6 = 450N.

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The option that is an equivalent expression of 15x² +12x + 8 is C. 12x + 15x² + 8.

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same values for the variable, two algebraic expressions that are equivalent have the same values.

If two systems of equations have the same solution, they are equivalents. In algebra, 2(2x - 3y + 6) is equal to 4x -6y + 12 as an example of an equivalent expression.

In this case, it should be noted that 15x² +12x + 8 is the same as 12x + 15x² + 8. Therefore, the correct option is C.

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Answer:

  x = 4

Step-by-step explanation:

You want to know the value of x in the arithmetic sequence x, 2x+4, 5x.

Terms of an arithmetic sequence have a common difference. This means ...

  (2x+4) -x = 5x -(2x+4)

  x +4 = 3x -4 . . . . . . . . . . simplify

  8 = 2x . . . . . . . . add 4-x

  4 = x . . . . . . divide by 2

The value of x is 4.

__

Additional comment

The common difference is x+4 = 8. The sequence is ...

  4, 12, 20, ...

Answer:

[tex]4*10^5[/tex]

Step-by-step explanation:

So whenever sometimes says "how many is x larger than y", it just means what is x divided by y. For example 4 is 2 times as much as 2 because 4/2 = 2

With this being said we can simply divide two numbers

[tex]\frac{2*10^{12}}{5*10^6}[/tex]

Whenever you divide scientific notation you simply divide the two coefficients and subtract the exponents from the base 10

So: [tex]\frac{2*10^{12}}{5*10^6} =\frac{2}{5} * 10^{12-6}[/tex]

This gives you a result of: [tex]0.4 * 10^6[/tex]

Since we want the coefficient to be: [tex]1\le c < 10[/tex] we can take one of the 10s from the base, since 10^6 is just 6 tens being multiplied by each other and we can "borrow" one of them to get: [tex]0.4*10^6=0.4*10*10^5[/tex] which simplifies to: [tex]4*10^5[/tex]

Answer:

Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.

First find the gradient.

Formula of gradient is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2)

Gradient = (-1-(-2))÷(3-(-2))

= (-1+2)÷(3+2)

= 1/5

Equation is y = 1/5 + c

Substitute either one of the points into the equation to find c.

-2 = 1/5(-2) + c

c = -8/5

Hence equation of the line is y = 1/5x - 8/5

The points at which the graph of f(x) has a horizontal tangent line are; x = -1, x = 0.4045, x = 2.07

The horizontal tangent of a function is simply defined as the point where the slope of the function is 0.

Now, we are give the function as;

f(x) = (2x² - 2x - 1)/(x⁴ + 1)

Slope of this function is;

f'(x) = -2(2x⁵ - 3x⁴ - 2x³ - 2x + 1)/(x⁴ + 1)²

Now, when the slope is zero, we will have that;

-2(2x⁵ - 3x⁴ - 2x³ - 2x + 1) = 0

Using an online polynomial root calculator, the roots of this slope are;

x = -1, x = 0.4045, x = 2.07

These values are the points where there is a horizontal tangent line.

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ANSWER:

64 square inches.

STEP-BY-STEP EXPLANATION:

The first thing is to calculate the ratio between the corresponding sides of the triangles:

We must bear in mind that the area of the larger t triangle is equal to the area of the small triangle multiplied by the ratio of the square, since the area is a quadratic unit, therefore:

The area of the larger triangle is 64 square inches.

Answer:

Step-by-step explanation:

you have a 1/6 of rolling a certain number on a regular die.

if you try to get 5 or 6 you have a 2/6 chance of rolling either of them

if you try to evens you have a 3/6 chance of rolling 2,6, or 4

hello! it would help if you gave more information so we could better answer the question ^^

A. Yes; lines n and p are parallel because corresponding angles are congruent.

According to the reverse of the comparable angles theorem, lines n and p are parallel if angles 1 and 2 are congruent.

The converse of the corresponding angles theorem is what?

According to the corresponding angles theorem, the corresponding angles on each line that a transversal cuts are congruent if the two lines are parallel to one another.

In contrast, lines that fall on those angles are parallel to one another if two corresponding angles are congruent to one another.

The diagram's angles 1 and 2 relate to one another.

In light of the converse of the equivalent angles theorem, lines n and p are parallel if angles 1 and 2 are congruent.

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The system of linear equations and their solutions are:

1. (51, 26):  x - y = 25; 2x + 3y = 180

2. (-17, -36): x - y = 19; -2x + y/6 = 28

3. (47, 33): 2x - 3y = -5; x + y/11 = 50

4. (-31, -56): 2x - y = -6; x - 305/3 = 2y.

We can solve a system using the substitution method by finding the value of one of the variables, followed by substitution.

1. x - y = 25 -- eqn. 1

2x + 3y = 180 -- eqn. 2

Rewrite eqn. 1:

x = 25 + y

Substitute x = 25 + y into eqn. 2:

2(25 + y) + 3y = 180

50 + 2y + 3y = 180

5y = 180 - 50

5y = 130

y = 26

Substitute y = 26 into eqn. 1:

x - 26 = 25

x = 25 + 26

x = 51

The solution is: (51, 26).

2. x - y = 19 -- eqn. 1

-2x + y/6 = 28 -- eqn. 2

Rewrite eqn. 1:

x - y = 19

x = 19 + y

Substitute x = 19 + y into eqn. 2:

-2(19 + y) + y/6 = 28

-38 - 2y + y/6 = 28

-11y/6 = 28 + 38

-11y/6 = 66

-11y/6 (-6/11)= 66(-6/11)

y = -36

Substitute y = 36 into eqn. 1:

x - y = 19

x - (-36) = 19

x + 36 = 19

x = 19 - 36

x = -17

The solution is: (-17, -36).

3. 2x - 3y = -5 -- eqn. 1

x + y/11 = 50 -- eqn. 2

x + y/11 = 50

x = 50 - y/11

Substitute x = 50 - y/11 into eqn. 1

2(50 - y/11) - 3y = -5

100 - 2y/11 - 3y = -5

-35y/11 = -5 - 100

-35y/11 = -105

-35y/11(-11/35) = -105(-11/35) (multiplication property)

y = 33

Substitute y = 33 into eqn. 2:

x + 33/11 = 50

x + 3 = 50

x + 3 - 3 = 50 - 3

x = 47

The solution is (47, 33).

4. Solving the last one, we will definitely have the solution, (-31, -56).

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NSWER

C. C = 5/9(F - 32); 59°F =

EXPLANATION

irst, we have to solve the formula for cC. Subtract 32 from both sides,

Then, multiply both sides by 5,

And divide both sides by 9,

Hence, the formula to convert from degrees Fahrenheit to degrees Celsius is C = 5/9(F - 32).

So, 59°F is equal to,

Hence, 59°F is equivalent to 15°C.

The transformation is a reflection across the y-axis (the line x = 0).

On the image we can see two triangles, both are at the same distance of the vertical axis.

We also can notice that the figure is reflected, this is, the longest point of the triangle points to opposite ways.

With this we can conclude that we had some kind of reflection. Particularly, because both triangles are a the same distance of the vertical axis, we can conclude that the reflection was across the line x = 0.

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Percentage - The amount to pay for the policy $596,774.19

What is Percent ?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.

Given that,

Investment policy pay
PV = $37,000 year;
investment return: 6.2%
r = 6.2%
r = 6.2/100
r = 0.062

We must use one year as the number of periods even if we just need to calculate the value for one year. We employ: to determine the FV of a lump sum.

FV=PV/r
FV=37,000/0.062
FV= $596774.1935
to 2 decimal point
FV=$596,774.19

Hence, $596,774.19 is to pay for the policy

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Answer:

B. 5a² + 3b + 6a

Step-By-Step Explanation:

First, see what has like terms. 7a² and -2a² both have the exponent 2 and the letter a, so you can combine those to get 5a². 3b and 6a cannot be combined because they have a different letter. So, 5a² + 3b + 6a is your answer.

The scale factor of model of Eiffel tower is 3:1640.

The scale factor is the ratio of measure of small length to large length. The base of both actual tower and scale down model is mentioned in question. Keep the values in ratio to find the scale factor.

Scale factor = 0.75 : 410

Removing decimal to get the whole number

Scale factor = 75:41000

Dividing the both parts of ratio by 25 to find the scale factor of mentioned model

Scale factor = 3:1640

As the Eiffel tower is scaled down in the model, the scale factor is 3:1640.

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For the marching bands vary from 18 to 48 player, the numbers of players  arranged in the greatest number of rectangles is 48 players.

As given in the question,

Number of players in the given marching bands vary from 18 to 48 players

To form a rectangles in the marching bands minimum two rows are required.

Greatest length and width of the rectangles formed by 18 to 48 players

19,23,29,....,47 are prime numbers

18 = 2 ×9 , 3×6

20 = 2×10 ,4×5

21= 3×7

22 = 2× 11

24=2×12, 3×8, 4×6

and so on

48 = 2 ×24 , 3×16, 4×12, 6×8,

48 players represents greatest number of rectangles

Therefore, for the marching bands vary from 18 to 48 player, the numbers of players  arranged in the greatest number of rectangles is 48 players.

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Answer:

The slope is -5/2

Step-by-step explanation

I tried to show how I solved this problem in the image, but its not too great, so I hope this helps. :)

Bertha's dive is 5 times farther than the end of Vernon's dive

A ratio can defined mathematical as an ordered pair of numbers, like variables b and c, when written form b / c with the denominator greater than the value zero.

It explains how many times a particular number is composed of another number in a given proportion.

It is also seen as the comparison of two quantities, elements or numbers having the same unit measure. It goes further to explain how much of one of the element or quantity contains another.

This is done on the basis of  their magnitude or sizes.

Given that;

Bertha's dive ended = -25 m

Vernon's dive ended = -5 m

Divide the values

= -25/-5

= 5 times

Hence, the value is 5 times

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1) given

2) base angles theorem

3) PN=QN

4) [tex]\angle 3=\angle 4[/tex]

5) MP=OQ

7) PQ, QP

8) MQ=PO

9) ASA