What two numbers add to 6 and multiply to 58

Step-by-step explanation:

Given

\(1953125=5^9\)

For a perfect square, its square root must be an integer

The square root of 1953125 i.e. \(\sqrt{1953125}=\sqrt{5^9}\)

or, \(\sqrt{5^9}=5^\frac{9}{2}\)

Clearly,  \(\frac{9}{2}\) is not an integer so, \(5^{\frac{9}{2}}\) is also not an integer

Hence, 1953125 is not a square number

The rectangle with dimensions 21 m by 21 m has the largest area among rectangles with a perimeter of 84 m.

To find the dimensions of a rectangle with a perimeter of 84 m that maximizes the area, we need to use the properties of rectangles.

Let's assume the length of the rectangle is l and the width is w.

The perimeter of a rectangle is given by the formula: 2l + 2w = P, where P is the perimeter.

In this case, the perimeter is given as 84 m, so we can write the equation as: 2l + 2w = 84.

To maximize the area, we need to find the dimensions that satisfy this equation and give the largest possible value for the area. The area of a rectangle is given by the formula: A = lw.

Now we can solve the perimeter equation for l: 2l = 84 - 2w, which simplifies to l = 42 - w.

Substituting this expression for l into the area equation, we get: A = (42 - w)w.

To maximize the area, we can find the critical points by taking the derivative of the area equation with respect to w and setting it equal to zero:

dA/dw = 42 - 2w = 0.

Solving this equation, we find w = 21.

Substituting this value of w back into the equation l = 42 - w, we get l = 42 - 21 = 21.

Therefore, the dimensions of the rectangle that maximize the area are l = 21 m and w = 21 m.

In summary, the dimensions of the rectangle are 21 m by 21 m, so the answer is A. 21, 21.

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Answer:

Student Ticket: $8

Adult $28

Step-by-step explanation:

To find out the price of each ticket create 2 equations, then solve for x & y

x = student tickets

y = adult tickets

25x + 28y = 984

25x + 25y = 900

To do this first put x on one side of the equation

25x = 900 - 25y

x = 36 - y

Now substitute this equation in x for the first equation

25(36 - y) + 28y = 984

Now distribute 25 in 36 - y, 900 - 25y + 28y = 984

After this combine like term, then subtract 900 from each side, 3y = 84

Then divide 3 on each side, y = 28

Lastly substitute 28 for y in any equation to solve for x, x = 8

x & y are the price of each ticket

Answer:

What's the question is that a good thing

Answer: 3

Step-by-step explanation:

Answer:

31 days

Step-by-step explanation:

what i did is divided it

Answer:

36- degree rotation m8

Step-by-step explanation:

mark me brainliest :)

The single transformation that took place from their starting position to their final destination is (x, y) ⇒ (x + 7, y)

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Translation is the movement of a point either up, down, left or right in the coordinate plane.

Hikers walk 3 miles east and then 2 miles north and take a water break. Hence:

(x, y) ⇒ (x + 3, y + 2)

They continue hiking 4 miles east and a final 2 miles south to their destination:

(x, y) ⇒ (x + 3 + 4, y + 2 - 2) ⇒ (x + 7, y)

The single transformation that took place from their starting position to their final destination is (x, y) ⇒ (x + 7, y)

The shape of the graph changes qualitatively at k = ± 2 and

\(k=\sqrt{(2)\).

The given function is f(x,y) = y-x²+y²+kxy.

The critical points of the function are found by taking the partial derivatives and equating them to zero:

∂f/∂x = -2x + ky = 0

y = 2x/k

∂f/∂y = 2y + kx = 0

y = -kx/2

Substituting y from the first equation into the second equation gives

x = k²x/4, so k² = 4 and k = ± 2.

Therefore, the critical points are (0,0), (2,4), and (-2,4)

We will now examine the critical points to see when the shape of the graph changes qualitatively.

There are two cases to consider:

Case 1: (0,0)At (0,0), the Hessian matrix is

H = [∂²f/∂x² ∂²f/∂x∂y;∂²f/∂y∂x ∂²f/∂y²]

=[ -2 0;0 2].

The determinant of the Hessian matrix is -4, which is negative.

Therefore, (0,0) is a saddle point and the graph changes qualitatively as k increases for all values of k.

Case 2: (±2,4)At (2,4) and (-2,4), the Hessian matrix is

H = [∂²f/∂x² ∂²f/∂x∂y;∂²f/∂y∂x ∂²f/∂y²]

=[ -2k 2k;2k 2].

The determinant of the Hessian matrix is 4k²+8, which is positive when k is greater than √(2).

Therefore, the critical points (2,4) and (-2,4) are local minima when

k > √(2).

Thus, the shape of the graph changes qualitatively at k = ± 2 and

k = √(2).

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Answer:

4 hours

Step-by-step explanation:

It drives 240 miles per 2 hours so then 480 will be 2+2 = 4 hours

240+240 = 480

Okay, let's solve this step-by-step:

* The box is shaped like a rectangular prism

* It has dimensions:

** 18.5 inches long

** 32 inches wide

** 12.2 inches deep

To find the volume of a rectangular prism, we use the formula:

Volume = Length x Width x Depth

So in this case:

Volume = 18.5 inches x 32 inches x 12.2 inches

= 18.5 * 32 * 12.2

= 5796 cubic inches

Therefore, the volume of the box is 5796 cubic inches.

Let me know if you need more details!

Ratio test:The ratio test is used to find out whether the given series is convergent or divergent. It is applied to series whose terms are positive. the series diverges by the Root Test because p= 1.

And if the limit is exactly equal to 1, then the test is inconclusive. The ratio test is one of the best tests that can be used for the majority of series.The ratio test can be expressed as below Root test:The root test is used to determine whether a series is convergent or divergent. It is a quick method for determining the convergence of an infinite series. This test is an application of the limit comparison test.

The test states that if the limit as n approaches infinity of the nth root of the absolute value of the nth term is less than 1, then the series converges absolutely. If the limit is greater than 1 or infinite, then the series diverges. And if the limit is exactly equal to 1, then the test is inconclusive. It is one of the most useful convergence tests.

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Answer:

40%

Step-by-step explanation:

Answer:

for converting 2/5 in percentage, we have to multiply with 100

________________________________

\( = > \: \frac{2}{5} \times 100 \\ = > \: 2 \times 20 \\ = > \: 40 \: percent\)

Answer:

Slope is -35/18

Graphed (x, y)(0, 0)(18, -35)

Step-by-step explanation:

Hope you get it right!

Answer:

Step-by-step explanation:

since its a horizontal parabola opening to the right we use a formula for the directrix

 x=h-p 4p=5/4 p=5

X= -3 v(h,k)=(2,0)

Answer:

c = 18π    exact answer

c = 56.52   decimal approximation

Step-by-step explanation:

c = 2πr

c = 2π * 9

c = 18π    exact answer

Using 3.14 for π

c = 18 * 3.14

c = 56.52   decimal approximation

To calculate the debt-equity ratio, we need to divide the total debt by the owners' equity.

The equation for the debt-equity ratio is:

Debt-equity ratio = Total debt / Owners' equity

Given the balance sheet information for 2013 and 2014:

2013:

Total debt = Long-term debt = $271,700

Owners' equity = Common stock and paid-in surplus + Accumulated retained earnings = $200,000 + $132,481 = $332,481

Debt-equity ratio (2013) = $271,700 / $332,481

2014:

Total debt = Long-term debt = $285,300

Owners' equity = Common stock and paid-in surplus + Accumulated retained earnings = $200,000 + $171,358 = $371,358

Debt-equity ratio (2014) = $285,300 / $371,358

Equity Multiplier:

The equity multiplier is a measure of how much of a company's assets are financed through debt. It is calculated by dividing total assets by owners' equity. The equation for the equity multiplier is:

Equity multiplier = Total assets / Owners' equity

2013:

Total assets = $917,617

Owners' equity = $332,481

Equity multiplier (2013) = $917,617 / $332,481

2014:

Total assets = $983,646

Owners' equity = $371,358

Equity multiplier (2014) = $983,646 / $371,358

Total Debt Ratio:

The total debt ratio is a measure of the proportion of a company's assets that are financed through debt. It is calculated by dividing total debt by total assets. The equation for the total debt ratio is:

Total debt ratio = Total debt / Total assets

2013:

Total debt = Long-term debt = $271,700

Total assets = $917,617

Total debt ratio (2013) = $271,700 / $917,617

2014:

Total debt = Long-term debt = $285,300

Total assets = $983,646

Total debt ratio (2014) = $285,300 / $983,646

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Answer:

2,100

Step-by-step explanation:

You would have to multiply 20 by 7 by 15 to find the area of the box. So when you multiply all those together you get 2,100.

The values of the area of the shaded region are;

1. Area = 36, perimeter = 28

2. Area = 16, perimeter = 16

3. Area = 22, perimeter = 30

4. Area = 29, perimeter = 28

6. Area = 53.9

The area of a figure is the area bounded by the line that serves as the boundary of the figure.

The areas and perimeters of the figures are found as follows;

1. The figure consists of two rectangles

The dimension of the small rectangle at the top are;

Length = 4, Width = 3

Area = 3 × 4 = 12

Dimensions of the larger rectangle are;

Width = 4, Length = 6

Area = 4 × 6 = 12

The area of the composite figure is therefore; A = 3 × 4 + 6 × 4 = 36

The sum of the length of the sides, which is the perimeter, P = 8 + 3 + 4 + 3 + 4 + 6 = 28

2. The figure consists of a right triangle at the top rectangle;

The leg lengths of the right triangle are; 3 and 4

The area of the right triangle = 0.5 × 3 × 4 = 6

The dimension of the rectangle are; Length = 5, width = 2

Area of the rectangle = 5 × 2 = 10

Area of the composite figure is therefore, A = 0.5 × 4 × 3 + 2 × 5 = 16

The perimeter of the composite figure, P = 4 + 3 + 2 + 5 + 2 = 16

3. The figure is a composite figure that is found by subtracting the area of a rectangle from the area of a right triangle as follows;

The dimensions of the triangle are;

Leg lengths; (8 + 4) = 12 and (3 + 2) = 5

Area of the right triangle = 0.5 × (8 + 4) × (3 + 2) = 30

Dimensions of the rectangle left blank are;

Length = 4, width = 2

Area of the rectangle = 4 × 2 = 8

Therefore;

Area of the composite figure = 0.5 × (8 + 4) × (3 + 2) - 4 × 2 = 22

Length of the hypotenuse side = √((8 + 4)² + (3 + 2)²) = 13

The perimeter of the composite figure = 3 + 13 + 8 + 2 + 4 = 30

4. The figure is a composite figure that consist a large rectangle and small rectangle.

Dimensions of the large rectangle are;

Length = 2 + 2 + 3 = 7

Width = 5

Area of the large rectangle = 7 × 5 = 35

Dimensions of small rectangle are;

Length = 3, width = 2

Area of the small rectangle = 3 × 2 = 6

Area of the composite figure = 35 - 6 = 29

The perimeter = 2 × (2 × 2 + 3) + 2 × 5 + 2 × 2 = 28

6. Area of the circle = π × 14²/4

Area of the square = 10 × 10 = 100

The area of the shaded region = π × 14²/4 - 100 ≈ 53.9

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Step-by-step explanation:

96/8=__________ will be the answer

Answer:  150 students

Step-by-step explanation:

Let X be the total number of students.  We are told that:

0.60X = 90 students

X = (90 students)/0.60

X = 150 students

Answer:

a. every fifth student that enters her classroom

Step-by-step explanation:

I am not for sure, it makes the most sense though because her honors class is all 3 classes, and boys in each of her classes could be biased

The factored trinomial expression is (5p + 2)(2p - 1)

From the question, we have the following parameters that can be used in our computation:

10p^2-p-2

To factor the trinomial 10p^2 - p - 2, we can use the method of finding two numbers that multiply to -20p^2 and add to -p.

We can use these numbers to write the trinomial as a product of two binomials:

So, we have

10p^2 - p - 2 = 10p^2 - 5p + 4p - 2

Factorize

10p^2 - p - 2 = 5p(2p - 1) + 2(2p - 1)

This gives

10p^2 - p - 2 = (5p + 2)(2p - 1)

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The answer will be 1374.2 m/s using root mean square.

What is  root mean square?

The root mean square formula provides the square root of the sum of all squares for each observation's data. The arithmetic mean of the squares of a set of values is known as the root mean square, or RMS, and is denoted by the abbreviation. Quadratic mean is another name for it. An integral of the squares of the instantaneous values during a cycle can be used to define the root mean square value for a function for a function that is continuously changing. The root mean square formula is used to determine the square root of the arithmetic mean of the square of the function that characterises the continuous waveform in this case.

mass of He is = 4 / 6.023*10²³

So Root mean square velocity is = √(3RT/m)

v = √(3*8.31*10³*303/4)

v = 1374.2 m/s

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Answer:

(-6, -2)

Step-by-step explanation:

The correct adjusting entry is to debit the Supplies Expense account for $1,538 and credit the Supplies account for the same amount. This entry reflects the decrease in the value of supplies used during the year.

The adjusting entry is necessary to accurately reflect the supplies consumed during the year and the remaining supplies on hand. The Supplies Expense account is debited to recognize the expense incurred for the supplies used up during the year.

The credit to the Supplies account reduces its balance to reflect the value of supplies remaining at the end of the year. This adjustment ensures that the financial statements accurately reflect the actual supplies expense for the period and the correct value of supplies on hand.

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The weight of the astronaut with gear on the moon is 80 pounds.

The pull of gravity is different on Earth than on the Moon as gravity depends on factors such as the mass of the celestial body, the radius of the celestial body, and the density of the celestial body.

The pull of gravity on Earth = 10 m/s²

Thus, Given:

Weight of object on Earth: 25 pounds

Weight is described as the product of mass and the acceleration due to gravity

Thus, 25 = 10 * mass

mass = 2.5 unit

Weight of the object on the Moon: 4 pounds

4 = 2.5 * acceleration due to gravity on the moon

Acceleration due to gravity on the moon = 1.6 m/s²

Weight of astronaut with gear on earth = 500 pounds

500 = mass * 10

mass = 50 units

Weight of astronaut with gear on earth = 50 * 1.6

= 80 pounds

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Input data

Pocket: 8255

Iphone: 9000

Procedure

Total = Pocket - Iphone

Total = 8255 - 9000

Total = -745

Cindy would owe a total of USD 745

Answer:

100°

Step-by-step explanation:

m L 1 = (180-100) + 20 = 80+20 = 100°

(a) The critical points of the function ƒ(x, y) = (x² - 1)e^(-x² - y²) are:

1. (0, 0)

2. ((1 + √5)/2, 0)

3. ((1 - √5)/2, 0)

(b) The critical point (0, 0) is a local maximum.

To find the critical points of the function\(f\left(x,\:y\right)\:=\:\left(x^2-\:1\right)e^{-x^2-y^2}\).

we need to find the points where the partial derivatives with respect to x and y are equal to zero.

Let's start by finding the partial derivative with respect to x:

\(\frac{\partial f}{\partial x}\:=\:\left(2x\right)\left(x^2\:-\:1\right)e^{-x^2-y^2}\:+\:\left(-2x\right)e^{-x^2-y^2}\)

Setting this derivative equal to zero and simplifying, we have:

\(\:\left(2x\right)\left(x^2\:-\:1\right)e^{-x^2-y^2}\:+\:\left(-2x\right)e^{-x^2-y^2}=0\)

Factoring out \(e^{-x^2-y^2}\) and dividing by 2x, we get

\(\left(x^2-1-x\right)e^{-x^2-y^2}=0\)

Since  \(e^{-x^2-y^2}\)  is always positive and nonzero, we have:

(x² - 1 - x) = 0

x² - x - 1 = 0

Using the quadratic formula, we can solve for x:

x = (1 ± √(1 - 4(-1)))/2

x = (1 ± √5)/2

So the x-coordinates of the critical points are (1 + √5)/2 and (1 - √5)/2.

Now, let's find the partial derivative with respect to y:

\(\frac{\partial f}{\partial y}\:=\:\left(-2y\right)\left(x^2\:-\:1\right)e^{-x^2-y^2}\)

Setting this derivative equal to zero, we have:

\(\:\left(-2y\right)\left(x^2\:-\:1\right)e^{-x^2-y^2}=0\)

Since   \(e^{-x^2-y^2}\) is always positive and nonzero, we have:

y = 0

Therefore, one of the critical points occurs at (0, 0).

(b) To determine the type of critical point at (0, 0), we can use the second derivative test.

We need to calculate the second partial derivatives and evaluate them at (0, 0).

Taking the second partial derivatives, we have:

\(\frac{\partial ^2f}{\partial x^2}\:=\left(2-4x^2+4x^4\right)\:e^{-x^2-y^2}\)

\(\frac{\partial ^2f}{\partial y^2}\:=\left(x^2-1-2y^2\right)\:e^{-x^2-y^2}\)

\(\frac{\partial ^2f}{\partial x\partial \:y}\:=2xy\)

Evaluating these second partial derivatives at (0, 0), we get:

∂²ƒ/∂x²(0, 0) = 2

∂²ƒ/∂y²(0, 0) = -1

∂²ƒ/∂x∂y(0, 0) = 0

Now, let's compute the discriminant D:

D = ∂²ƒ/∂x²(0, 0) × ∂²ƒ/∂y²(0, 0) - (∂²ƒ/∂x∂y(0, 0))²

= 2 × (-1) - 0²

= -2

Since D < 0 and ∂²ƒ/∂x²(0, 0) > 0, the discriminant test tells us that (0, 0) is a local maximum.

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The coordinates of the vertex for the parabola defined by the given quadratic function is `(-2, -8)`.

The vertex for the parabola defined by the given quadratic function can be found using the formula `(-b/2a, f(-b/2a))`.

From the question above, the function: `f(x) = 4x² + 16x + 8`

To find the vertex, we need to express it in the standard form `f(x) = a(x - h)² + k`

where (h, k) is the vertex and a is the coefficient of the squared term.

To do this, we can complete the square:

`f(x) = 4(x² + 4x) + 8` `f(x) = 4(x² + 4x + 4 - 4) + 8`

`f(x) = 4((x + 2)² - 4) + 8` `

f(x) = 4(x + 2)² - 8`

Now we have the equation in the standard form, where a = 4, h = -2 and k = -8.

Thus, the vertex is: `(-2, -8)`

Therefore, the coordinates of the vertex for the parabola defined by the given quadratic function is `(-2, -8)`.

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