The width of a rectangular garden is 4 meters less than 2 times the length. The area of the garden is 6 square meters. Which is the function to find the dimensions of the the garden?


a) 2l^2−4l−6=0


b) 2w^2+4w+6=0


c) 2w^2+4w−6=0


d) 2l^2−4l+6=0

Answer:

1. 12x

2. 21x

3. 14y+6x

4. 28x+20y

Step-by-step explanation:

The area of the shaded region of the circle is  1836.9 km².

Both circles have the same centre. The circumference of the inner circle is 100.48 kilometres. The circumference of a circle is the perimeter of the circle.

Therefore, the area of the shaded portion can be calculated as follows:

Hence,

circumference of the inner circle = 2πr

100.48 = 2 × 3.14 × r

100.48 = 6.28 r

r = 100.48 / 6.28

r = 16 km

Therefore,

area of the inner circle = πr²

area of the inner circle = 3.14 × 16²

area of the inner circle = 803.84 km²

area of the outside circle = πr²

area of the outside circle = 3.14 × (16 + 13)²

area of the outside circle = 3.14 × 29²

area of the outside circle = 2640.74 km²

Therefore,

area of the shaded region =  2640.74  - 803.84

area of the shaded region =  1836.9 km²

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The greatest possible length of a side of a triangle whose perimeter is 1000 and all of whose sides have integral lengths is 400.

We have to determine the greatest possible length of a side of a triangle whose perimeter is 1000 and all of whose sides have integral lengths.

The sides of a triangle have lengths ratio 5:7:8.

The perimeter of triangle is the sum of all sides. So

5x + 7x + 8x = 1000

20x = 1000

Divide by 20 on side we get

x = 50

The length of all sides:

5x = 5 × 50 = 250

7x = 7 × 50 = 350

8x = 8 × 50 = 400

Hence, the greatest possible length of triangle is 400.

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The complete question is:

The sides of a triangle have lengths ratio 5:7:8. What is the greatest possible length of a side of a triangle whose perimeter is 1000 and all of whose sides have integral lengths?

The slope of the linear line given by linear equation y= -x+20 is -1

and the slope of line perpendicular to it is 1.

what is a linear equation?

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. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now as equation of linear line is y=mx+c

where m=slope, c=constant

For y=-x+20

slope(m)= -1

also for perpendicular lines m1.m2=-1

-1.m2=-1

m=1 (slope of line perpendicular to it)

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Using Linear equations, the two equations of the given data are $10 + $250x and $4x

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Using linear Equations,

Let x be the miles covered,

Taxi company 1 charges = $10 + $250x

Taxi company 2 changes = $4x

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Helicopters would fit in either container is 1 and total weight is 4 pound.

What is Linear system of inequality?

At least two linear inequalities in the same variables make up a system of linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.

With the exception of the inequality symbol, a linear inequality is nearly identical to a linear equation.

Three basic categories of economic disparity exist:

Let 'x' represent the number of helicopters per box.

3x+14=4x+13

We move all terms to the left:

3x+14-(4x+13)=0

We get rid of parentheses

3x-4x-13+14=0

We add all the numbers together, and all the variables

-1x+1=0

We move all terms containing x to the left, all other terms to the right

-x=-1

x=-1/-1

x=1

Hence, Helicopters would fit in either container is 1 and total weight is 4 pound.

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The sketch a normal curve is attached below and in Normal Curve with mean of 50 and a Standard Deviation of 2.

The term normally curve in math is defined as a normal distribution is proper term for a Probability bell curve.

While we looking into the question we know that here from the Right of Normal standard curve we have to draw 3 vertical lines. And these lines would count up by 2 for each standard deviation 52, 54,56.

And then we have to plot from the Left of Normal standard curve, and then draw 3 vertical lines. And those lines would count up by 2 for each standard deviation 48,46,44.

Thus Normal standard curve extends indefinitely in both directions, and by approaching on the other hand it never touching the horizontal axis as it does so.

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The set builder notation for the given inequality is [tex]\left \{ {{b | b \geq 2\right \}[/tex].

The answer set of an inequality is expressed in mathematics using a set builder notation. For instance, the set builder notation is understood to mean the collection of all y, where y is bigger than 0.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than, larger than, or not equal to signs are used in place of the equal sign.

The given inequality is:

b + 2 ≥ 4

Subtract 2 on both sides of the equation:

b + 2 - 2 ≥ 4 -2

b ≥ 2

Hence, the set builder notation for the given equality is [tex]\left \{ {{b | b \geq 2\right \}[/tex].

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The percentage of the slices that were eaten will be 30%.

The percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

From the information, it should be noted that each pizza is divided into 10 slices. The total amount of slices eaten will be:

= 1 + 6 + 2

= 9

Total slices = 30

The percentage of the slices that were eaten will be:

= 9 / 30 × 100

= 30%

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Triangle ABC is the preimage and triangle A'B'C' is the image. The equation for the line of reflection is x = 4.

Reflection is a type of geometric transformation where the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.

(A) Pre image is the figure before reflection is done.

So the pre image is triangle ABC.

(B) Image is the reflected figure.

So the image is triangle A'B'C'.

(C) Coordinates of the output are :

A'(8, 9), B'(12, 4) and C'(8, 4)

(D) The line of the reflection is the parallel line to Y axis passing through 4 on the X axis.

So the equation is x = 4.

Hence triangles ABC and A'B'C' are preimage and image respectively. The coordinates for the output are A'(8, 9), B'(12, 4) and C'(8, 4).

The equation of the line of reflection is x = 4.

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I stash my allowance, birthday cash or paycheck in a bank.

The facts about Banks include the following:

The  facts about Credit union include the following:

These are non profit organizations that exist to serve their members and offer some banking services.

They accepts deposits with a higher interest rate and give loan at a lower rate which is why my decision in where to put my money will be in a credit union due to the high interest rate.

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Option (c) is the correct option.

9/10 is rational and a real no. but not an integer.

What is a rational number?

A number with the form p/q, where p and q are integers and q is not equal to 0, is said to be rational.

What is an integer?

In the category of real numbers are irrational numbers, fractions, and rational numbers like positive and negative integers.

What is a real number?

Integers, which can be both negative and positive and include zero, are numbers without a decimal or fractional component.

Our objective is to find a number which is rational and a real number but not an integer.

√2 is not rational and not a real number.

-5 is rational and a real number but It is an integer.

9/10 is rational and a real number and also not an integer.

Hence, (c) is the correct option.

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The cubic function with the zeros x = -3, x = 0 and x = 1 is given as follows:

y = x³ + 2x² - 3x.

We are given the zeros of the function, hence the function is defined using the Factor Theorem, as a product of the linear factors of the function.

The zeros of the function are given as follows:

Then the linear factors are given as follows:

Considering a leading coefficient of 1, the function is defined as follows:

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

y = x(x² + 2x - 3)

y = x³ + 2x² - 3x.

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The rounding up of each of the 12 +2 11/14 5/7 mixed number to the nearest whole number then the estimatation of the sum  can be expressed  as  A.16.

The concept here is addition of the fractions and the digits, In mathematics, summation is the process of adding a series of different types of numbers, known as addends or summands, to produce their sum or total.

The rounding up to whole number can be done as :

12 = 12.0

2 11/14 = 39/14 = 2.786= 3.0

5/7  = 0.71=1.0

Then the sum = 12+3+1=16

Therefore, option A is correct.

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Speed is calculated by dividing distance by time. Here Sam is cycling at a speed of 15 km/h and Dwight at a speed of 12km/h. So Sam cycles faster.

Speed is the rate of change in distance. so it is calculated using distance/time. Here the distance is in km and time is in minutes. The unit of distance is either m/s or km/h. So we have to do conversions first.

Lets convert the minutes to hours.

Sam cycles for 20 minutes. So 20 min = 20/60 h = 0.33 h

Dwight cycles 30 minutes. So 30 min = 30/60 h = 0.5 h

Now lets calculate the speed.

Speed Sam cycles = 5 km/ 0.33 h = 15 km/h

Speed Dwight cycles = 6 km/0.5 h = 12 km/h.

So Sam is faster than Dwight.

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The exponential function that represents the table that is given will be A. f(x) = 6(2)^x.

When when x is 6, the value of the function will be A. 384.

It should be noted that in Mathematics, the function simply shows the relationship between the variables that are given.

Based on the table, the exponential function that represents the table that is given will be A. f(x) = 6(2)^x.

In this case, when x is 6, the value of the function will be:

= 6 × 2^x

= 6 × 2^6

= 6 × 64

= 384

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Answer:

answer - x = − 12/7

According to the information in the table, the value of C is 51.

To find the value of C we must calculate the constant, for that we have to perform the following operation:

In this case, we use the values of another column to identify the constant that applies to all the values in the table and the result is the following:

Additionally, to find the value of C we must perform the following operation:

According to the above, the value of C is 51.

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Answer:

10;37°

Step-by-step explanation:

Pythagoras theorem will be used to find the length of EF and the knowledge of complementary angles will be used to solve for angle D

The diameter of a bowling ball that rolls 96 cm down the lane each time it turns once is 16.58 cm

the term called diameter is known as the length of the line through the center that touches two points on the edge of the circle.

Here we know that the ball rolls 96 cm down the lane each time it turns once.

According to the formula of circumference, the total circumference is calculated by using the formula,

C = 2πr

Where the value of r is 96, then

=> c = 2 x π x 96

=> C = 192 x 3.14

=> C = 602.88

Here we have consider that the lane is 10000 cm in length , then the diameter is calculated as,

=> 10000/602.88

=> 16.58

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Answer: The correct inequality that matches the graph is 6x + y < 3.

This inequality can be graphed by plotting the points (0,3) and (1,9) as the boundary of the solution set, and shading the area above the line. The graph will be a line with a negative slope that pass through the points (0,3) and (1,9) and the shaded area will be above the line, which match the graph you have described.

We can check this by plugging the points (0,3) and (1,9) into the inequality to see if they satisfy it:

6(0) + 3 < 3 => 3 < 3 which is true

6(1) + 9 < 3 => 6 + 9 < 3 which is false

This confirms that the inequality 6x + y < 3 matches the graph.

Step-by-step explanation:

The measure of angle P is 82°.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

125° and (109° + ∠N) are alternate angles.

Alternate angles are equal.

125 = 109 + ∠N

∠N = 125 - 109

∠N = 16

Now,

The sum of the triangle ABC is 180.

∠P + ∠M + ∠N = 180

Sides opposite to equal angles are equal.

∠P = ∠M

2∠P + 16 = 180

2∠P = 180 - 16

2∠P = 164

∠P = 164/2

∠P = 82

Thus,

∠P is 82°.

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The angle that is created from the wire and the ground is 39°

Now, According to the question:

The main beam to a circus tent is 75 feet tall and is supported by 120 foot wires that extend to the ground.

We have to find the angle that is created from the wire and the ground.

Based on the given condition:

Using the definition of the sine function, we have that

[tex]sin(a) = \frac{75}{120}[/tex]

then, we can take inverse sine in both sides of the equality to clear a

a = [tex]sin^-^1\frac{75}{120}[/tex]

a = 38.68218745

and rounding to the nearest degree, the answer will be 39 degrees.

a = 39°

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The proportion of variation that the regression line can account for is indicated by the coefficient of determination.

56.44% of the variation cannot be explained by the provided regression line. The correlation coefficient for the question is R = - 0.66.

From the provided R value, the Coefficient of determination, R2, can be calculated.

R2 = - 0.662 = 0.4356.

This implies that, the percentage of variation that can be explained is equal to (0.4356) x 100%, or 43.56%.

100% - 43.566% = 56.446% is the percentage of variation that cannot be explained.

As a result, 56.44% of the variation in y cannot be explained.

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By using the point-slope form, the equation of a line that passes through the point (11, 18) with slope 3 is equal to y - 18 = 3(x - 11).

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

At data point (11, 18), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

y - 18 = 3(x - 11)

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Each numbered angle has a measurement of 109°, 109°, and 71°, respectively.

Two rays that come together at a vertex or node, also known as a common point, to produce an angle for any figure.

Angles are frequently expressed in degrees or radians.

Think about triangle

A triangle's internal angles add up to 180°.

URS, UVT, and URT add up to 180°.

35° + 36° + ∠1 = 180°

∠1 = 180° - (35° + 36°)

∠1 = 180° - 71°

∠1 = 109°

The angles 1 and 2 are now vertically opposed. This makes them equal.

∠2 = 109°.

For triangle NQO once more

∠2 + ∠3 + 35° = 180°

36° + ∠3 + 35° = 180°

∠3 = 180° - (35° + 36°)

∠3 = 180° - 109°

∠3 = 71°

As a result, 1, 2, and 3 are 109, 109, and 71 degrees, respectively.

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Here we are given a right angled triangle in which there are two unknown angles x and y . we need to find out the values of x and y. Firstly, as we know that the angle sum property of a triangle is 180° . So that,

[tex]\longrightarrow x + y +90^o = 180^o\\[/tex]

[tex]\longrightarrow x + y = 180^o -90^o = 90^o \dots \\[/tex]

[tex]\longrightarrow y = 90^o - x \dots (i) \\[/tex]

And we also have,

[tex]\longrightarrow 4x + 40 = y \\[/tex]

from equation (i) , we have ,

[tex]\longrightarrow 4x + 40 = 90 - x \\[/tex]

[tex]\longrightarrow 4x + x = 90 +40 \\[/tex]

[tex]\longrightarrow 5x = 130\\[/tex]

[tex]\longrightarrow x =\dfrac{130}{5}\\[/tex]

[tex]\longrightarrow \underline{\underline{x = 26^o}} \\[/tex]

substitute this value in equation (i) ,

[tex]\longrightarrow y = 90 - 26 \\[/tex]

[tex]\longrightarrow \underline{\underline{y = 64^o}} \\[/tex]

And we are done!

Answer: v = 33.51 cm^3

Step-by-step explanation:

Plug in radius to equation

V = 4/3 * π * 2^3

V = 4/3 * 8 * π

v = 33.51