The graph shows a proportional relationship. Which equation matches the graph?

Answer:

-5

Step-by-step explanation:

from graph

The width of the runway is approximately 28.3 feet. The length of the runway in feet is Length = 3.75 miles * 5,280 feet/mile

The new runway being constructed on the east side of the estate, which extends to the ranch house, is 3.75 miles long and covers a total area of 5.6 acres. To determine the width of the runway in feet, we can use the following information:

1 acre = 43,560 square feet

First, let's convert the length of the runway from miles to feet:

1 mile = 5,280 feet

Therefore, the length of the runway in feet is:

Length = 3.75 miles * 5,280 feet/mile

Next, let's calculate the width of the runway using the area and length:

Area = Length * Width

Since we are given the area in acres, we need to convert it to square feet:

Area = 5.6 acres * 43,560 square feet/acre

Now, we can solve for the width:

Width = Area / Length

Substituting the values we have:

Width = (5.6 acres * 43,560 square feet/acre) / (3.75 miles * 5,280 feet/mile)

Simplifying the expression:

Width = (5.6 * 43,560) / (3.75 * 5,280) feet

Calculating the value:

Width ≈ 560,784 / 19,800 feet

Width ≈ 28.3 feet

Therefore, the width of the runway is approximately **28.3 feet**.

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The area bounded by the graphs of y = x² + 17 and y = 0 over the interval -3 ≤ x ≤ 3 is 120 square units.

To find the area bounded by the two graphs, we need to calculate the definite integral of the difference between the upper function (y = x² + 17) and the lower function (y = 0) over the given interval.

Integrating the difference of the two functions, we have:

∫[from -3 to 3] (x² + 17 - 0) dx

Simplifying, the integral becomes:

∫[from -3 to 3] (x² + 17) dx

To evaluate this integral, we can use the power rule of integration. Integrating x² gives us (1/3)x³, and integrating the constant term 17 gives us 17x.

Applying the limits of integration, the integral becomes:

[(1/3)x³ + 17x] from -3 to 3

Evaluating the expression at the upper limit (x = 3) and subtracting the expression at the lower limit (x = -3), we get:

[(1/3)(3)³ + 17(3)] - [(1/3)(-3)³ + 17(-3)]

Simplifying further:

[(1/3)(27) + 51] - [(1/3)(-27) - 51]

= [9 + 51] - [-9 - 51]

= 60 + 60

= 120

Therefore, the area bounded by the two graphs is 120 square units.

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Answer:

6 degrees high/-10 degrees low

Step-by-step explanation:

Answer:

The distance is √58

or 7.61577...

Step-by-step explanation:

If you draw a right triangle where the given line is the hypotenuse you can use Pythagorean theorem (a²+b²=c²) to find the length.

It would be 7 units tall and 3 units wide.

7²+3²=49+9=58

The distance is √58

Answer:

x = 10

Step-by-step explanation:

Because the triangles are similar, the following equations must be solved in order to find out how much bigger or smaller the triangle is.

10 * y = 15

16 * y = 24

You'll find that

y = 1.5

Then, you are able to insert y into the following equation and solve for x

(x - 4) * y = 9

(x - 4) * 1.5 = 9

1.5x - 6 = 9

1.5x = 15

x = 10

We can plug x back into the previous equation in order to check if it is correct

(x - 4) * 1.5 = 9

(10 - 4) * 1.5 = 9

6 * 1.5 = 9

9 = 9

The maximum height of the projectile is 56.53 meters.

The height of a projectile at time t is represented by the function h (t)= −4.9 t² +18t + 40, where h(t) is the height in meters and t is the time in seconds.

This is a quadratic function of the form h(t) = at² + bt + c, where a = -4.9, b = 18, and c = 40.

To find the maximum height of the projectile, we need to find the vertex of the parabolic graph of the function h(t).

The vertex of the parabola is at the point (t, h(t)) where t = -b/2a. Substituting the values of a and b, we get t = -18/(2(-4.9)) = 1.8367 seconds.

To find the maximum height, we need to substitute t = 1.8367 seconds into the function h(t). h(1.8367) = -4.9(1.8367)^2 + 18(1.8367) + 40 = 56.53 meters.

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the area of the region. 2y =4√x ; y = 5 ; and 2y+4x = 8 is 9, using the concept of area under the curve.

The region between a curve and the -axis is referred to as the "area under a curve." This region may be wholly above the -axis, entirely below the -axis, or somewhere in between. The area under a curve in calculus is a picture of an integral.

The region enclosed by the curve, the axis, and the boundary points is referred to as the "area under the curve." Using the coordinate axes and the integration formula, the area under the curve has been determined as a two-dimensional area. The area of the asymmetric plane form in a two-dimensional array is provided by the region beneath the curve.

The region bounded by the lines y = 5 and 2y + 4x = 8 and the curve

2y = 4√x

Now, finding the intersecting point between 2y + 4x = 8 and 2y = 4√x

so, 4√x + 4x = 8

or,  √x + x = 2

or, √x = (2 - x)

or, x = (2 - x)²

or, x = x² - 4x + 4

or, x² - 5x + 4 = 0

or, ( x - 4) ( x - 1) = 0

or, x = 4, 1

when x = 4 then y = 2√4 = 4

when x = 1 then y = 2 √1 = 2

when y = 4 and x = 4 then equation 2y + 4x = 8 is not satisfied.

Thus, only intersection point is: (1,2)

This is the type (II) region.

So, integrate the region with respect to y.

Now, area =

= \(\int\limits^5_2 {(y/2)^2 - ((8-2y) / 4)} \, dy\)

= \(\int\limits^5_2 {[(y^2/4) -2 + (y/2)]} \, dy\)

= \(\frac{1}{4} [y^3/3]^5_2 - 2 [y]^5_2 + \frac{1}{2} [y^2/2]^5_2\)

= \(\frac{117}{12} - 6 + \frac{21}{4}\)

= \(\frac{108}{12}\)

= 9

Thus, area = 9 of the region. 2y =4√x ; y = 5 ; and 2y+4x = 8.

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Answer:

0

Step-by-step explanation:

The sum is 0 because -30 plus 30 equals nothing. Imagine having -30 and adding 30 that would be 0. It's just kinda common sense to me.

Hope this helps :)

The sum of angles inside the sine function is simplified to obtain sin(13x) + sin(3x).

The product 2 sin(8x) cos(5x) can be rewritten as the sum of two trigonometric functions.

Using the identity for the product of sine and cosine, we have:

2 sin(8x) cos(5x) = sin(8x + 5x) + sin(8x - 5x)

Simplifying the angles inside the sine function, we get:

= sin(13x) + sin(3x)

Therefore, the product 2 sin(8x) cos(5x) can be expressed as the sum of sin(13x) and sin(3x).

The answer is provided by rewriting the given product as the sum of two trigonometric functions: sin(13x) + sin(3x). This is done by using the identity for the product of sine and cosine.

This demonstrates the process of converting the product into a sum or difference of trigonometric functions.

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Answer:

One way to find the area of a square with a side length of 12 yards is to use the formula A = s^2, where A is the area and s is the side length. Since 1 yard equals 3 feet, we can convert the side length to feet and then square it to get:

12 yards = 12 x 3 = 36 feet

A = 36^2 = 1296 square feet

Another way to find the area is to use the fact that the area of a square is equal to the length of one side squared, and the length of one side is equal to the square root of the area. So we can find the area of the square in square yards first, and then convert it to square feet:

Area in square yards = side length in yards squared

= 12 yards x 12 yards

= 144 square yards

Since 1 yard equals 3 feet, we can convert square yards to square feet by multiplying by 9:

Area in square feet = 144 square yards x 9

= 1296 square feet

Answer:

Step-by-step explanation:

we know the formula,

sin^2(0) + cos^2(0) = 1

=> cos^2(0) = 1 - sin^2(0)

=> cos^2(0) = 1 - (3/8)^2

=> cos^2(0) = 1 - 9/16

=> cos^2(0) = 7/16

=> cos(0) = square root of 7/16

Answer:

Step-by-step explanation:

\(f(x) = (x-8)(x-2)\quad\implies\quad x_1=8\,,\ \ x_2=2\\\\ h=\dfrac{x_1+x_2}2=\dfrac{8+2}2=5\\\\k=f(h)=(5-8)(5-2)=-3\cdot3=-9\)

Answer:

>

Step-by-step explanation:

because 7 is greater than 6

must be marked as brainlist

To calculate the present value of Ahmed's payments, we can use the formula for the present value of an annuity:

PV = PMT  [(1 - \((1 + r)^{(-n)\)) / r]

Where:

PV = Present Value

PMT = Payment amount per period (BD 5700)

r = Interest rate per period (8% or 0.08)

n = Number of periods (12 years)

Substituting the values into the formula, we get:

PV = 5700 * [(1 - \((1 + 0.08)^{(-12)}\))) / 0.08]

Calculating the expression within the brackets first:

(1 - \((1 + 0.08)^{(-12)\)) / 0.08 = 0.652592574

Now, multiply this value by the payment amount:

PV = 5700 * 0.652592574

PV ≈ BD 3708.349811

Rounding to two decimal places, the present value of Ahmed's payments is approximately BD 3708.35. Therefore, none of the given options (OBD 46392.10, OBD 42955.64, OBD 116823.19, BD 108169.62) are correct.

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The choose ; 3i , – 3i

3x²+27=0 —> 3x² = - 27 —> x²= - 27/ 3 = - 9

x = √ - 9 = √-1 × √9 = 3 i

I hope I helped you^_^

Answer:

3rd option "The data point for player G is an outliner"

His weight is on the extreme side compared to the other players

and plus the other answers are just wrong

but the 4th option may be a possible answer

Answer:

7ab (a+b)(a-b)

Step-by-step explanation:

To find the volume of the solid obtained by rotating the region in the first quadrant bounded by y = 25, y = 1, and the y-axis around the x-axis, we can use the method of cylindrical shells.

The height of each cylindrical shell will be the difference between the two functions: y = 25 and y = 1. The radius of each cylindrical shell will be the x-coordinate of the corresponding point on the y-axis, which is 0

Let's set up the integral to find the volume:

Where a and b are the x-values that define the region (in this case, a = 0 and b = 25), f(x) is the upper function (y = 25), and g(x) is the lower function (y = 1)

\(V = ∫[0,25] 2πx * (25 - 1) dx\)Simplifying:

\(V = 2π ∫[0,25] 24x dxV = 2π * 24 * ∫[0,25] x dx\)Evaluating the integral:

\(V = 2π * 24 * [x^2/2] evaluated from 0 to 25V = 2π * 24 * [(25^2/2) - (0^2/2)]V = 2π * 24 * [(625/2) - 0]V = 2π * 24 * (625/2)V = 2π * 12 * 625V = 15000π\)Therefore, the volume of the solid obtained by rotating the region in the first quadrant bounded by y = 25, y = 1, and the y-axis around the x-axis is 15000π cubic units.

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(A) In the last congressional elections, incumbents met with a larger number of lobbyists than did challengers is true.

They were able to meet more lobbyists than their rivals because of their travel. Therefore they definitely had an advantage. As part of the 2022 American elections, which took place on November 8, 2022, while Joe Biden was still the incumbent president, the House of Representatives elections were held. In the 118th U.S. Congress, the Republican Party will hold a majority of seats in the House thanks to its electoral victory. Five non-voting members of the U.S. House of Representatives from the District of Columbia and four of the five inhabited insular areas were also elected, in addition to representatives from each of the 435 U.S. congressional districts in each of the 50 states.

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Answer:

Step-by-step explanation:

The equation of the circle,

x² + (y – 3)² = 36.

The correct option is A.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.

And the general formula of the circle,

(x – h)²+ (y - k)² = r²,

where (h, k) is the center and r is the radius of the circle.

Given:

A circle that has a diameter of 12 units and a center that lies on the y-axis.

That means, radius = 6.

And h = 0.

From the given choices:

Now, the equation of the circle,

x² + (y – 3)² = 36.

Therefore, x² + (y – 3)² = 36 is the equation.

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The correct answer is (D) If A is the given matrix, then the augmented matrix represents the equation Ax =0. The reduced echelon form of this matrix indicates that Ax =0 has only the trivial solution. Therefore, the columns of A form a linearly independent set.

A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital applications as well.

Mathematically, assume that B = {v₁, v₂, v₃, ........} is the set of vectors. Then B will be linearly independent if the vector equation

y₁v₁ + y₂v₂ + y₃v₃ + ........ = 0 possesses the trivial solution such that

y₁ = y₂ = y₃ = ........ = 0.

Let A be a matrix, then columns of A will be linearly independent if the equation Ax = 0 possesses the trivial solution. In other words, The row space of matrix A is the span of its rows. The column space denoted by

C(A) is the span of A’s columns. The dimension of the row and column spaces is always the same, which is known as the rank of A.

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Answer:

0.06 in standard form is 6.0 × 10-2

Step-by-step explanation:

Answer:

\(7^5\)

Step-by-step explanation:

When multiplying numbers with the same base (in this case the base is 7), the exponents add. So

-6+16-5=5

So the answer is \(7^5\)

We have that what the bank account hold in 2017  is mathematically given as

T=179.986

Simple interest is a simple way of forecasting and having a view of futuristic values.

Question Parameters:

An account is gaining value at a rate of 4.94% per year.

The account held $113 in 2005.

What will the bank account hold in 2017?

Generally the equation for Simple interest   is mathematically given as

S=(P*R*T)/(100)

Therefore

S=(113*4.94*12)/(100)

S=$66.986

Therefore

after 12 years

T=113+66.986

T=179.986

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Answer:

.

Step-by-step explanation:

Answer:

177 x 44 = 7788

Basically I did it with a format-

{Bottom number x every top number}

{Add 0}

{Other bottom number x every top number}

{Add it all up}

{Get your final result!}

There are a total of 14,100 tickets for 50 sold-out showings.

Let t be the number of people who bought tickets for each show.

t can be found by dividing the total tickets by the number of showings

You may also write the equation as

The equation remains the same whether you write t at the left or the right side of the equation.

Therefore, the correct option is D.

Now let us find out the exact value of t that is the number of people who bought tickets.

To each showing of the concert​, 282 people bought tickets.