solve the following problem: natalia prints a photo of a covered bridge. the print measures 6 centimeters by 4 centimeters. she wants to resize the photo into the size of a postcard with a length of 15 centimeters. what will be the area of the postcard?(1 point) responses

The box dimensions with the least surface area are length and width x = 8 feet, and height h = 4 feet.

To find the dimensions of the box with a square base and no top that has a volume of 256 cubic feet and the least (minimum) surface area, we can follow these steps:
Define the variables
Let x be the length and width of the square base, and let h be the height of the box.
Write the volume equation
The volume of the box is given by the product of its length, width, and height: V = x * x * h = x^2 * h.
Since the volume is 256 cubic feet, we have x^2 * h = 256.
Write the surface area equation
The surface area of the box (without the top) is given by the sum of the areas of its sides: S = x^2 + 4 * x * h.
Solve for h from the volume equation
From the volume equation x^2 * h = 256, we can solve for h in terms of x: h = 256 / x^2.
Substitute h into the surface area equation
Substitute the expression for h into the surface area equation: S = x^2 + 4 * x * (256 / x^2).
Simplify the surface area equation
Simplify the surface area equation by canceling out terms: S = x^2 + 1024 / x.
Minimize the surface area
To minimize the surface area, take the derivative of S with respect to x and set it equal to zero:
dS/dx = 2 * x - 1024 / x^2 = 0.
Solve for x
To solve for x, multiply both sides by x^2 and rearrange the equation:
2 * x^3 = 1024.
Now, divide by 2 and take the cube root to find x:
x = (512)^(1/3) = 8 feet.
Find h
Using the value of x, find the height h:
h = 256 / x^2 = 256 / 64 = 4 feet.

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Answer:

The answer is 8.30

Step-by-step explanation:

Using cos 41 = x/11

x = cos 41 × 11

x = 8.30

Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

Answer:

D. 10^10

Step-by-step explanation:

Multiplying numbers with exponents rule : \(a^b*a^c=a^b^+^c\)

explanation of rule : we simply keep the bases the same and add the exponents.

10^3 • 10^7

keep the base as 10 and add the exponents

\(10^3 * 10^7 =10^3^+^7=10^1^0\)

Keep in mind that this only works when the bases are the same.

Answer:

\(\large\boxed{\boxed{\underline{\underline{\maltese{\pink{\pmb{\sf{\: ANSWER : \: \: \: \: 10^{10} }}}}}}}}\)

Step-by-step explanation:

The given expression, 10³ • 10⁷ has the same base but different exponential values. We know that,

So,

\(\large{\mathfrak{10^{3} * 10^{7} }}\)

= \(\large{\mathfrak{10^{3 + 7} }}\)

= \(\huge{\boxed{\mathfrak{10^{10} }}}\)  (3rd option)

_____

Hope it helps!

\(\mathfrak{Lucazz}\)

Answer:

you have to do the square root of the numbers given and minus so the answer you get that's the radical form(simplest)

Answer:

5

Step-by-step explanation:

The change in x from (0,5) to (3,9) is 3 - 0 which is 3. The change in y is 9 - 5 which is 4. Using the Pythagorean theorem (using the two points as the endpoints of the hypotenuse in a right triangle) we get:

\(3^2+4^2=c^2\) where c is the distance between the two points (the hypotenuse of the right triangle). The equation simplifies to:

\(9+16=c^2\)

Which simplifies to:

\(\sqrt{25} =c\)

Thus, c (the distance between (0,5) and (3,9) is 5.

Hope this helps :)

The Celsius temperature that has the same value as when converted to a Fahrenheit temperature is -40

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

F = 9/5C + 32

The Celsius temperature that has the same value as F implies that

C = F

Substitute the known values in the above equation, so, we have the following representation

C = 9/5C + 32

So, we have

C - 9/5C = 32

Evaluate the like terms

-4/5C = 32

So, we have

C = -32 * 5/4

Evaluate

C = -40

Hence, the value of C is -40

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The equation of line passes through the point (2, 3) will be;

⇒ y = 1/2x + 2

And, Graph of this equation of line is shown in figure.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (2, 3).

And, The perpendicular line is,

⇒ y - 4 = - 2 (x + 3)

⇒ y -  4 = - 2x - 6

⇒ y = - 2x - 2

Now,

Since, The equation of line passes through the point (2, 3).

So, We need to find the slope of the line.

Since, The product of slope of the perpendicular line is - 1.

Hence, Slope of the given perpendicular line is,

⇒ y = - 2x - 2

m = dy/dx = - 2

m = - 2

So, The slope of line is,

⇒ m₂ = - 1/m

         = 1/2

Thus, The equation of line with slope 1/2 is,

⇒ y - 3 = 1/2 (x - 2)

⇒ y - 3 = 1/2 (x - 2)

⇒ y - 3 = 1/2x - 1

⇒ y = 1/2x - 1 + 3

⇒ y = 1/2x + 2

Therefore, The equation of line passes through the point (2, 3) will be;

⇒ y = 1/2x + 2

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The statement " Arrhenius equation can rearrange to give a linear relationship by taking the natural logarithm." is true.

The Arrhenius equation is an important tool in chemical kinetics that describes the temperature dependence of reaction rates. It relates the rate constant of a chemical reaction to the activation energy and temperature at which the reaction occurs. The equation is given by:

\($k = A\mathrm{e}^{-\frac{E_a}{RT}}$\)

where \($k$\) is the rate constant,\($A$\)is the pre-exponential factor, \($E_a$\) is the activation energy, \($R$\)is the gas constant, and \($T$\) is the temperature in Kelvin.

Although this equation is useful, it is not always easy to interpret experimentally. The natural logarithm of both sides of the equation can be taken, resulting in the following equation:

\($\ln k = \ln A - \frac{E_a}{RT}$\)

This equation can be rearranged into the form of a linear equation,

\($y = mx + b$\),

by defining:

\($y = \ln k$\)

\($m = -\frac{E_a}{R}$\)

\($x = \frac{1}{T}$\)

\($b = \ln A$\)

Therefore, we have:

\($y = mx + b$\)

which can be plotted as a straight line. By analyzing the slope and intercept of this line, we can determine the values of the activation energy and pre-exponential factor, which are important parameters in understanding the kinetics of a chemical reaction.

In summary, the Arrhenius equation can be rearranged to give a linear relationship by taking the natural logarithm of both sides of the equation. This linear form is often useful for analyzing experimental data and determining the activation energy and pre-exponential factor of a reaction, which are important parameters in understanding the kinetics of chemical reactions.

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Answer:

2(9.2+x)=12.5

Step-by-step explanation:

Henry is adding 9.2 to your number, x, and after he adds it, he doubles it. This will then allow him to get the answer 12.5

Converse of the statements will be as If two lines are parallel, then they have equal slopes. Conditional statement will be; If two lines have same slopes, then the lines are parallel.

Lines in a plane that are regularly spaced apart are known as parallel lines. Parallel lines don't overlap each other. Perpendicular lines are those that cross at a straight angle of 90 degrees.

Only the slopes of two lines are same then it can be said to be parallel. If two lines have different y-intercepts and equal slopes, they are said to be parallel.

Converse of the statements will be as If two lines are parallel, then they have equal slopes.

Conditional statement will be; If two lines have same slopes, then the lines are parallel.

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All you have to do is, make the operations.

Step 1

break the parenthesis and add the terms

so, the answer is -22

Step-by-step explanation:

Its the bottom question sir

Triangle ABC and ADC are similar if BE is parallel to CD.

What does a triangle similarity mean?

Two triangles are comparable if the measurements of their corresponding sides are proportionate. The same is true if the lengths of two sides in one triangle are proportional to the lengths of the corresponding sides in another triangle and the included angles are congruent.

What is the triangle Theorem's similarity?

According to the fundamental theorem of similarity, a line segment can divide two triangle sides into proportionate segments if and only if it is parallel to the third side of the triangle.

We are given that BE is parallel to CD.

As per the theorem of similarity, the two triangles are similar when the a line segment of the triangle is parallel to that of another triangle.

So, from this we get that the Triangle ABC and ADC are similar.

Hence, Triangle ABC and ADC are similar.

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There are 4,826,640 possible ways to award first, second, and third prizes in a contest with 170 contestants.

To calculate this, use the formula nP3, where n is the number of contestants (170) and P3 represents the permutation of 3 elements. This can be simplified to P(170, 3) = 170! / (170 - 3)! = 170 x 169 x 168 = 4,826,640.

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Answer:

amount invested in the account that earns 10% interest  = Rs 3500

amount invested in the account that earns 8% interest  =Rs 5500

Step-by-step explanation:

Two equations can be derived from the question

x + y = 9000 equation 1

0.08x + 0.1y = 790 equation 2

x = amount invested in the account that earns 8% interest

y =  amount invested in the account that earns 10% interest

multiply equation 1 by 0.08

0.08x + 0.08y = 720 equation 3

subtract equation 3 from 2

0.02y = 70

divide both sides of the equation by 0.02

y = 70 / 0.02

y = 3500

Substitute for y in equation 1

x + 3500 = 9000

x = 9000 - 3500 = 5500

Answer:

-7

Step-by-step explanation:

3=-3x-18

3x=-18-3

3x=-21

x=-7

Answer:

Two, times a number minus three, plus seven.

Hope this is what you were looking for.

Answer:

(x,y)--(-X, "): A' is at (5, -1)

Step-by-step explanat

Answer:

(x,y)→(−x,−y); A' is at (5, −1)

Step-by-step explanation:

The speed of the plane relative to the ground if no action is taken by the pilot is 79.5 km/h westward.

Given information: The speed of the plane with respect to still air is 160 km/h.

West wind starts to blow at a constant speed of 80.5 km/h.

Let us consider Vp be the speed of the plane relative to the groundVw be the speed of the wind

So, the speed of the plane with respect to the ground is given by

                         Vp = Vp + VwVp = 160 + (-80.5)

Thus, the speed of the plane relative to the ground if no action is taken by the pilot is 79.5 km/h westward.

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Check the picture below.

since the triangle is equilateral, is also equiangular.

\(a\sqrt{3}=\sqrt{6}\implies a=\cfrac{\sqrt{6}}{\sqrt{3}}\implies a=\cfrac{\sqrt{2\cdot 3}}{\sqrt{3}}\implies a=\cfrac{\sqrt{2}\sqrt{3}}{\sqrt{3}}\implies a=\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ 2a=x\implies {\Large \begin{array}{llll} 2\sqrt{3}=x \end{array}}\)

There are n different values that the remainder r can take on when \(n^2\) is divided by n 4.

We can use the Remainder Theorem to solve this problem. The Remainder Theorem states that when a polynomial f(x) is divided by (x-a), the remainder is f(a).

Using this theorem, we can see that \(n^2\) divided by n 4 leaves a remainder of \(n^2 - kn 4\), where k is some integer. We want to find how many different values r can take on, which is the same as finding how many different values \($n^2 - kn 4$\) can take on.

Let's rewrite \(n^2 - kn 4 as n(n - k 4)\). This expression tells us that n and n - k 4 have the same remainder when divided by n 4. Therefore, n - k 4 can only take on n different values, namely \(0, n, 2n, \ldots, (n-1)n.\)

For each of these n values, we can find a corresponding value of k that satisfies\($n^2 - kn 4 \equiv r \pmod{n 4}$\), namely \(k = (n^2 - r)/(n 4).\) Therefore, there are exactly n different values that r can take on.

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Sarah will require 5 and five-eights pounds of clay to make 18 small vases as calculated using proportion.

She use 2.5 pounds for 8 vase.

Let us consider she uses x pounds for 18 vase.

Ratio of clay to vase is given by 2.5 : 8

Second ratio of clay to vase = x : 18

Now we know that by the properties of proportion ,

2.5 : 8 :: x : 18

This can be written algebraically as :

2.5 / 8 = x / 18

solving for x we get :

x = 45 / 8 = 5 5/8

Therefore 5 and five eighths pounds of clay is required to make 18 vase.

Ratio and fractions serve as the key pillars on which proportion is explained. Two ratios are equal when they are written as a fraction, such as a/b, ratio a:b, and then a proportion.

In this case, A and b can be any two integers. Understanding ratios and proportions is necessary in order to fully comprehend the many concepts found in science and mathematics.

By establishing a connection between two or more extra quantities, it aids in comparison.

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Answer: (A)

Step-by-step explanation:

The row of the table that reveals the x-intercept of the function f is given as follows:

Second row.

A function has two intercepts, which are listed as follows:

The definition of each type of intercept is given as follows:

From the second row of the table, we have that when x = -4, f(x) = 0, hence the x-intercept of the function is of x = -4.

The y-intercept is of y = -16, as from the fourth row, when x = 0, y assumes a value of 16.

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Answer:

false

Step-by-step explanation:

Answer:

A rational number can be written as a fraction. Try finding the square root of 50 and see if you can rewrite it in fraction form.

Step-by-step explanation:

A mathematical expression is neither true nor false; it is evaluated rather than being assigned a truth value.

A mathematical expression, by itself, is not considered true or false because it does not make a specific claim or statement. An expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division. It represents a computation or evaluation, but it does not assert any truth value.

For example, the expression "2 + 3" is simply a calculation that evaluates to the value 5. It does not make a claim or statement that can be determined as true or false. Similarly, expressions like "\(x^2 + 4\)" or "sin(θ) + cos(θ)" represent mathematical computations but do not have a truth value.

To determine the truth value of a mathematical statement, you need an equation or inequality that makes a specific claim or relationship between mathematical expressions. For instance, the equation "2 + 3 = 5" is a mathematical statement that can be determined as true, while the inequality "x > 5" depends on the value of x and can be evaluated as true or false.

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We need to analyze the units of each of the magnitudes and solve the operations between them:

A possible unit for potential energy is kg*m^2/s^2.

Also we can use distributive property to replace some of the units by derived units, for example, Newtons:

Answer:

Step-by-step explanation:

The answer is 120.3676. i assume you are converting between grams MgSO4 and mole. You can view more details on each measurement unit: molecular weight of MgSO4

Answer:

0.85

Step-by-step explanation:

Answer:0.83

Step-by-step explanation: