A box with an open top has a square base and four sides of
equal height. The volume of the box is 490 ft³. If the surface
area is 329 ft², find the dimensions of the box.

We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:

Triangle 1:

Side adjacent to the right angle: 6 (let's call it 'a')

Side opposite to the right angle: x (let's call it 'b')

Triangle 2:

Side adjacent to the right angle: x (let's call it 'c')

Side opposite to the right angle: 10 (let's call it 'd')

Using the Pythagorean theorem, we can write the following equations for each triangle:

Triangle 1:\(a^2 + b^2 = 6^2\)

Triangle 2: \(c^2 + d^2 = 10^2\)

Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:

\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)

Substituting b = c, we get:

\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)

Now, let's add these two equations together:

\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)

Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12

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Answer:

x = 0

x = ±1

x = -2

x = -3

x = -4

Step-by-step explanation:

Use number line to find the values of x that fit the equation.

Answer:

The first graph

Step-by-step explanation:

-2x is the key here, when you add a subtraction sign to the x-axis it goes right.

+2x would be the graph on the bottom because it is translated to the left.

So the first graph on your picture is the answer.

Answer+Step-by-step explanation:

x² – 2x + 3 = (x - 1)² + 2

Then

The vertex of the parabola is the point (1 , 2)

then

The graph number 1 (on top) is the one which represents f

The value of x from the proportion relation is x = 1

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides

Given data ,

Let the proportion equation be represented as A

Now , the equation will be

Substituting the values in the equation , we get

x / 0.25 = 6 / 1.5

On simplifying the equation , we get

Multiply by 0.25 on both sides of the equation , we get

x = ( 6 x 0.25 ) / 1.5

On further simplification , we get

x = 6/6

x = 1

Therefore , the value of x = 1

Hence , the equation is x = 1

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Answer:

For number 9 and 11

9. is >

11. is <

Sorry I couldn't help with the rest! Goodluck!~

you are pig and all picture are you

Answer:

B: 1/5 = 4/x

Step-by-step explanation:

1cm = 5km

4cm = 20km

Answer:

A

Step-by-step explanation:

(A) would be correct.

A^x would yield (0.9^60)^x when plugged in. Since an exponent

on the parenthesis surrounding a number with an exponent already

just gets multiplied to the number's exponent, we'd end up with

      0.9^60*x , which is the same as the given example.

Answer:

3×10³ is the answer I have done this before

Answer:

0.417

*I rounded

Or fraction form, 5/12

Answer:

5/12

Step-by-step explanation:

or in decimal form its 0.416 with the 6 repeating

Answer:

See Below.

Step-by-step explanation:

1) Given:

\(3x+2y+7=5x+3y+10\)

2) Subtraction Property of Equality (subtract 2y from both sides):

\(3x+7=5x+y+10\)

3) Subtraction Property of Equality (subtract 5x from both sides):

\(-2x+7=y+10\)

4) Subtraction Property of Equality (subtract 10 from both sides):

\(-2x-3=y\)

5) Symmetric Property:

\(y=-2x-3\)

6) Slope-intercept form:

\(y=mx+b\text{, where $m$ is slope and $b$ is y-intercept.}\)

7) Substitution:

\(m=-2\)

37 degrees plus m mus equal 90 degrees; therefore, the equation that m must satisfy is

subtracting 37 from both sides of the equation gives us

The value of sin(7π/8) is 0.7071. This value can also be expressed as √2/2 or 1/√2.

When evaluating the function sin(7π/8), we will use the unit circle method and determine the value of sine at 7π/8 radians.The unit circle method is one way to figure out the value of the sine of an angle in radians. This method involves visualizing a circle of radius 1 unit that is centered at the origin of a Cartesian coordinate plane. In this unit circle, we can draw a ray originating from the center of the circle and passing through an angle θ on the terminal side.

The x-coordinate of the point of intersection of this ray and the unit circle is cos(θ), and the y-coordinate is sin(θ).First, we find the angle 7π/8 on the unit circle. As 7π/8 is an angle in the second quadrant, we will draw a circle of radius 1 unit centered at the origin of a coordinate plane and we will count the angles from the x-axis in a counterclockwise direction until we reach 7π/8 radians.

We will place a dot on the unit circle where the angle terminates.Then, we can drop a perpendicular line from the point of intersection of the ray with the unit circle to the x-axis to form a right triangle. This right triangle has hypotenuse 1 and adjacent side cos(7π/8).

By the Pythagorean theorem, the opposite side is sqrt(1 - cos²(7π/8)).Hence, the value of sin(7π/8) is:sin(7π/8) = opposite/hypotenuse= sqrt(1 - cos²(7π/8))/1Now, we can use the trigonometric identity sin²(x) + cos²(x) = 1 to find the value of cos²(7π/8):cos²(7π/8) = 1 - sin²(7π/8)

We know that sin(π/8) = sin(π/8), so we can use the double-angle identity sin(2θ) = 2sin(θ)cos(θ) to find the value of sin(π/4) = sin(2(π/8)):sin(π/4) = 2sin(π/8)cos(π/8)Now, we can use the Pythagorean identity sin²(x) + cos²(x) = 1 to find the value of cos(π/8):cos(π/8) = sqrt(1 - sin²(π/8))

Finally, we can use the double-angle identity cos(2θ) = cos²(θ) - sin²(θ) to find the value of cos(π/4) = cos(2(π/8)):cos(π/4) = cos²(π/8) - sin²(π/8)= (1 - sin²(π/8)) - sin²(π/8)= 1 - 2sin²(π/8)Therefore, the value of sin(7π/8) is:sin(7π/8) = sqrt(1 - cos²(7π/8))/1= sqrt(1 - (1 - 2sin²(π/8)))/1= sqrt(2sin²(π/8))/1= sqrt(2)/2= 0.7071 (rounded to four decimal places)

Therefore, the value of sin(7π/8) is 0.7071. This value can also be expressed as √2/2 or 1/√2.

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Answer:

4.84cm squared

Step-by-step explanation:

square has 4 equal sides area = l x w l and w are 2.2*2.2

2.2*2

4.84cm squared

Hope this helps :D

Answer:4.84 cm^2

Step-by-step explanation:

Area = Length x Width

Area = 2.2 x 2.2

Area = 4.84 cm^2 (centimeters squared)

Answer:

16.75

Step-by-step explanation:

Y intercept is the Y value when x is equal to 0. In the point (0,1) x is 0 and y is 1, so the y-intercept is 1.Slope is-1/4.

When a line crosses the y-axis on a graph, that location is known as the y-intercept.It is always 0 for the associated x-coordinate.

By calculating rise over run, the slope can be determined.This is accomplished by splitting the discrepancies between the y- and x-coordinates. The values of the y-intercept and slope reveal details on the nature of the relationship between the two variables, x and y.

The slope is the change in Y over the change in x:

Slope = (0-1) / 4-0) = -1/4

Slope = -1/4

Y intercept is the Y value when x is equal to 0. In the point (0,1) x is 0 and y is 1, so the y-intercept is 1.

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The equation of the line with points (2,1) and (4,3) in slope intercept form is y = x -1

The slope intercept form with point(1,-1) and slope -3/5 is  y = -3x/5 - 2/5

When you know the slope of the line to be investigated and the provided point is also the y intercept, you may utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.

To get the intercepts, we may locate the vertex and either factor it or use the quadratic formula. A quadratic equation's intercept form is written as y = a (x p) (x q), where and are the intercepts, and and are the same value as in standard form.

Ax+By=C is the usual form for two-variable linear equations. A typical form linear equation is, for instance, 2x+3y=5. When an equation is provided in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.

In slope intercept form

y = mx + c

m is the slope and c is the y intercept

for (1,-1) and slope =-3/5

y = mx + c is  -1 = -3/5 * 1 + c ⇒ c = -2/5

The slope intercept form is  y = -3x/5 - 2/5

Similary we can find the value of others.

Now when we are having 2 points

for (2,1 ) and (4,3)

The slope is (y₂ - y₁)/(x₂-x₁) = (3-1)/(4-2) = 1

The equation will be

y = mx + c

1 = 1*2 + c

⇒ c = -1

The equation of the line in slope intercept form is y = x -1

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Answer:

b

Step-by-step explanation:

Answer:

\(\frac{3}{4}\)

Step-by-step explanation:

\(\frac{3}{5} = \frac{36}{x}\)

3x = 36 x 5

3x = 180

x = 60

Michael has 60 marbles.

Nick recieves 9 more marbles so he has 36 + 9 = 45 marbles

The new ratio will be:

\(\frac{45}{60}\)  = \(\frac{3}{4}\)

The solution to the inequality is all values of x less than 5. We can write the solution set using interval notation as (-∞, 5).

To solve the inequality -5x - 3 + 2x > -18, we need to isolate the variable x on one side of the inequality sign.

Starting with the given inequality:

-5x - 3 + 2x > -18

Simplifying the left-hand side by combining the like terms:

-3x - 3 > -18

Adding 3 to both sides:

-3x > -15

Dividing both sides by -3, and reversing the inequality sign since we are dividing by a negative number:

x < 5

Therefore, the solution to the inequality is all values of x less than 5. We can write the solution set using interval notation as (-∞, 5).

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Answer:

Kindly check explanation

Step-by-step explanation:

Given the model:

s = 10│x - 4│+ 50

s represents the sound level in decibels and x represents the number of measures of music played

To find x at s = 80

The equation becomes /

80 = 10│x - 4│+ 50

Subtract 50 from both sides of the equation

80 - 50 = 10 |x - 4| + 50 - 50

30 = 10 | x - 4 |

Divide both sides by 10

30/10 = 10|x - 4| / 10

3 = |x - 4|

|x - 4| is an absolute value expression

±3 = |x - 4|

x = 3 + 4 = 7

x = - 3 + 4 = 1

Finally, we can divide both sides of the equation by -120/r to get r = -120/(t - 120).

Therefore, the inverse of Janine's equation is r = -120/(t - 120).

In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. Take a look at the formula 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the word "equal."

Either identities or conditional equations are categories for equations. For each potential value, the variables provide an identity. Only certain combinations of the values for the variables allow a conditional equation to hold true. Two expressions are joined together in an equation by the equals sign ("=").

To find the inverse of Janine's equation, we need to solve for r in terms of t. Here is how we can do that:

First, we can rearrange the equation to get t - 120 = 1/r.

Then, we can divide both sides of the equation by 1/r to get t/r - 120/r = 1.

Finally, we can divide both sides of the equation by -120/r to get r = -120/(t - 120).

Therefore, the inverse of Janine's equation is r = -120/(t - 120).

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Answer: R=120t/120-t

Explanation: edmentum/plato :)

Answer:

Step-by-step explanation:

Use the Pythagoras Theorem to find x

Pythagoras theorem = \(a^2 + b^2 = c^2\)

In this case a is 10 c is 20 b is x

Remember that the longest side of a triangle is always named as c

\(10^2 + b^2 = 20^2\\100 + b^2 = 400\\b^2 = 400-100\\b^2 = \sqrt{300}\\ b = 17.32\\\)

Answer:

60

Step-by-step explanation:

I took the test, used the girl below's answer and failed :) that is the correct answer <3 gl

Answer:

x - 5y - 6

Step-by-step explanation:

- 6 + 4y - ( - x + 9y) ← distribute parenthesis by - 1

= - 6 + 4y + x - 9y ← collect like terms

= x - 5y - 6

To change to spherical coordinates, we can use the following formula:

x = ρ sin φ cos θ

y = ρ sin φ sin θ

z = ρ cos φ

We also note that the region of integration is a hemisphere with radius 3, and that the integrand contains x^2z+y^2z+z^3. Since we are integrating over a hemisphere, the bounds of ρ can be from 0 to 3, φ can be from 0 to π/2, and θ can be from 0 to 2π.

Next, we need to express the integrand in terms of ρ, φ, and θ. Substituting x, y, and z, we get:

x^2z + y^2z + z^3 = ρ^4 sin^2 φ cos^2 θ (ρ cos φ) + ρ^4 sin^2 φ sin^2 θ (ρ cos φ) + (ρ cos φ)^3

Simplifying, we get:

x^2z + y^2z + z^3 = ρ^5 cos^2 φ + ρ^3 cos^3 φ

Thus, the new integral is:

∫0^(2π) ∫0^(π/2) ∫0^3 (ρ^5 cos^2 φ + ρ^3 cos^3 φ) ρ^2 sin φ dρ dφ dθ

Integrating with respect to ρ, we get:

∫0^(2π) ∫0^(π/2) [ 1/6 ρ^6 cos^2 φ + 1/4 ρ^4 cos^3 φ ]_|ρ=0^3 sin φ dφ dθ

Simplifying and integrating with respect to φ, we get:

∫0^(2π) [ 9/5 sin^5 φ - 27/14 sin^7 φ ]_|φ=0^(π/2) dθ

Evaluating the limits, we get:

∫0^(2π) [ 9/5 - 27/14 ] dθ

Finally, evaluating the integral, we get:

∫0^(2π) [ 33/35 ] dθ = 66π/35

Therefore, the value of the integral after changing to spherical coordinates is 66π/35.

Answer:

Monday:

Cups of Sugar: 3

Tablespoon of Butter: 30

No. of Bananas: 75

Wednesday

Cups of Sugar: 1.12

Tablespoons of Butter: 11.2

No. of Bananas: 28

this is a question of set of equations and solution is as follows,

Williamston Daily newspaper started printing newspaper.

Three years ago they had 5900 subscribers.

every month there is an increase of 66 new subscribers.

n is the number of months the paper has been printed.

so, the linear model will be  

B= early subscriber + number of month × increments

B= 5900 + n × 66

B= 66 n + 5900

Example - subscribers after 3 months,

n = 3

= 66 x 3 +5900

= 198 + 5900

= 6000

set of equations

A system of equations is a set or collection of equations that you deal with all together at once. Linear equations are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.

Linear equations

Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.

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Using the quotient rule, it is found that the derivative of the function is given as follows:

\(f^{\prime}(x) = -\frac{1}{2\sqrt{s}(\sqrt{s}+2)^2}\)

Suppose a quotient function defined as follows:

\(f(x) = \frac{g(x)}{h(x)}\)

Then, the derivative is given by:

\(f^{\prime}(x) = \frac{g^{\prime}(x)h(x) - h^{\prime}(x)g(x)}{h(x)^2}\)

In this problem, we have that:

Then, since g'(x) = 0, the derivative is given by:

\(f^{\prime}(x) = -\frac{1}{2\sqrt{s}(\sqrt{s}+2)^2}\)

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