A gift bag is shaped like a rectangular prism and has a volume of 1152 cubic inches.

The three methods to solve a 3 variable linear system of equations are substitution, elimination, and matrix inversion.

1. Substitution: This method involves isolating one of the variables in one of the equations, then substituting it into the other equations to solve for the other two variables.

2. Elimination: In this method, the coefficients of two of the variables in one of the equations are multiplied by constant values, so that when the two equations are added together, one of the variables is eliminated. The remaining variable can then be solved for, and the other two variables can be found using substitution.

3. Matrix Inversion: This method involves writing the system of equations in matrix form, then inverting the matrix using matrix algebra to solve for the three variables.

The three methods to solve a 3 variable linear system of equations are substitution, elimination, and matrix inversion. Substitution involves isolating one of the variables and substituting it into the other equations, elimination involves multiplying coefficients of two of the variables and adding the equations together to eliminate one of the variables, and matrix inversion involves writing the system of equations in matrix form and inverting the matrix to solve for the three variables.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

Answer:

second and fourth

Step-by-step explanation:

answered the question

Answer:

Save without the temptation of touching it. Earn attractive interest. Better Articulation. Showcase your Strengths.

The area of the larger figure that is similar to the smaller one is: 28.2 m².

Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:

Area of figure A / Area of figure B = a²/b².

Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:

Perimeter of smaller figure = 20 m

Area of smaller figure = 19.6 m²

Perimeter of larger figure = 34m

Area of larger figure = x

Therefore:

20/34 = a/b

Simplify:

10/17 = a/b.

Find the area (x) of the larger figure using the formula given above:

10²/12² = 19.6/x

100/144 = 19.6/x

100x = 2,822.4

x = 2,822.4/100

x ≈ 28.2 m²

Learn more about area of similar figures on:

https://brainly.com/question/17132861

#SPJ1

Answer:

easy

x=4 y=7 or

x=4 y=-1

Step-by-step explanation:

x=4 y=7 or

x=4 y=-1

Answer:

Mikaya and Olivia are correct to be suspicious

Step-by-step explanation:

Sum of the angles of a triangle is always 180

But, The sum of all angles of the triangle that Zuri solved = 93 + 63 + 36 = 192 ≠ 180

So, Zuri is wrong

The function f(x, y) = x^4 + y^4 - 4xy + 9 has a saddle point at (0, 0) and a local minimum at (1, 1).

To analyze the important aspects of the function f(x, y) = x^4 + y^4 - 4xy + 9, we need to determine its local maximum value(s), local minimum value(s), and saddle point(s).

Step 1: Calculate the first-order partial derivatives.

The partial derivative of f with respect to x, denoted as ∂f/∂x, can be found by differentiating each term with respect to x while treating y as a constant:

∂f/∂x = 4x^3 - 4y

The partial derivative of f with respect to y, denoted as ∂f/∂y, can be found by differentiating each term with respect to y while treating x as a constant:

∂f/∂y = 4y^3 - 4x

Step 2: Set the partial derivatives equal to zero and solve for x and y.

Setting ∂f/∂x = 0, we have:

4x^3 - 4y = 0

x^3 = y

Setting ∂f/∂y = 0, we have:

4y^3 - 4x = 0

y^3 = x

Step 3: Solve the system of equations to find critical points.

Substituting x^3 = y from the first equation into the second equation, we get:

y^3 = x = (x^3)^3 = x^9

x^9 - x = 0

Factoring out an x, we have:

x(x^8 - 1) = 0

From this, we find two critical points:

x = 0 and x^8 - 1 = 0

For x = 0, substituting back into the equation x^3 = y, we get:

y = 0

For x^8 - 1 = 0, we have:

x^8 = 1

x = 1 (since we're looking for real solutions)

Substituting x = 1 into the equation x^3 = y, we get:

y = 1

So, we have two critical points: (0, 0) and (1, 1).

Step 4: Calculate the second-order partial derivatives.

The second partial derivative of f with respect to x, denoted as ∂²f/∂x², is:

∂²f/∂x² = 12x^2

The second partial derivative of f with respect to y, denoted as ∂²f/∂y², is:

∂²f/∂y² = 12y^2

The mixed second partial derivative of f, denoted as ∂²f/(∂x∂y), is:

∂²f/(∂x∂y) = -4

Step 5: Evaluate the second-order partial derivatives at the critical points.

For the point (0, 0):

∂²f/∂x² = 0

∂²f/∂y² = 0

∂²f/(∂x∂y) = -4

For the point (1, 1):

∂²f/∂x² = 12

∂²f/∂y² = 12

∂²f/(∂x∂y) = -4

Step 6: Determine the nature of the critical points.

Using the second partial derivative test:

For the point (0, 0):

D = (∂²f/∂x²)(∂²

f/∂y²) - (∂²f/(∂x∂y))^2 = (0)(0) - (-4)^2 = -16

Since D < 0, it is a saddle point.

For the point (1, 1):

D = (∂²f/∂x²)(∂²f/∂y²) - (∂²f/(∂x∂y))^2 = (12)(12) - (-4)^2 = 144 - 16 = 128

Since D > 0 and ∂²f/∂x² > 0, it is a local minimum.

In summary, the important aspects of the function f(x, y) = x^4 + y^4 - 4xy + 9 are:

- There is a saddle point at (0, 0).

- There is a local minimum at (1, 1).

To learn more about saddle point click here: brainly.com/question/32518639

#SPJ11

Answer:

y = 10

Step-by-step explanation:

Since we are given that x=5, we can substitute x for 5 in the given equation:

5 + 2y - 25 = 0

Then, we can solve for y:

2y = 25 - 5

2y = 20

y = 10

Answer:10

Step-by-step explanation: 5+2x10-25=0

5+20 equal 25

Answer:

i think its y=-1

Step-by-step explanation:

hope u get it right

The parameterization of the ellipse in a counterclockwise manner is x = 3cos(t) y = 2sin(t) where t varies from 0 to 2π.

One common way to parameterize an ellipse is to use trigonometric functions such as sine and cosine. We can write the equation of the ellipse as:

4x² + 9y² = 36

We can then use the following parameterization:

x = 3cos(t) y = 2sin(t)

where t is the parameter that varies between 0 and 2π, traversing the ellipse once in a counterclockwise manner.

To see why this parameterization works, let's substitute x and y into the equation of the ellipse:

4(3cos(t))² + 9(2sin(t))² = 36

Simplifying this equation gives:

36cos²(t) + 36sin²(t) = 36

Which is true for any value of t. This shows that our parameterization does indeed describe the ellipse 4x² + 9y² = 36.

Furthermore, we can see that when t=0, we get x=3 and y=0, which is the starting point (3,0). As t varies from 0 to 2π, x and y will trace out the ellipse exactly once in a counterclockwise manner.

Therefore, the parameterization of the ellipse 4x² + 9y² = 36 that begins at the point (3,0) and traverses once in a counterclockwise manner is:

x = 3cos(t) y = 2sin(t)

where t varies from 0 to 2π.

To know more about parameterization here

https://brainly.com/question/14762616

#SPJ4

By simple algebra, The number of counters in each box is 2.

Algebra is the study of mathematical symbols and the methods for incorporating them into formulas.

Since algebra is the first math subject most students take where they must deal with variables, complex concepts, and problem-solving abilities, many find it scary.

Given,

counter in Box A = 6y+2

counter in Box b=4y+6

Since there are the same amount of counters in both boxes.

hence

6y+2=4y+6

6y-4y=6-2

2y=4

y=2

To know more about algebra visit:-

brainly.com/question/24875240

#SPJ1

To achieve better accuracy when adding the numbers from 0.01 to 1.00, it is recommended to add the numbers in ascending order (from smallest to largest) to minimize the accumulation of rounding errors and maintain higher precision during intermediate calculations. Thus, starting with 0.01 and ending with 1.00 would provide better accuracy.

To achieve better accuracy when adding the numbers from 0.01 to 1.00, it is generally recommended to use an order that minimizes the accumulation of rounding errors. In this case, it is advisable to start with the smaller numbers and progress towards the larger ones.

By adding the numbers in ascending order (from 0.01 to 1.00), the rounding errors at each step will have a smaller impact on the overall result. This is because adding smaller numbers together first helps maintain a higher level of precision during intermediate calculations.

Therefore, to achieve better accuracy, you should add the numbers in ascending order, starting with 0.01 and ending with 1.00.

To know more about rounding errors refer here:

https://brainly.com/question/2992673#

#SPJ11

Answer:

Step-by-step explanation:

d^2=h^2+w^2

a)

w^2=42^2-h^2, h=21

w^2=1764-441

w^2=1323

w=36.373

b)

36.373+2(2) by 21+2(2)

w=40.373, h=25

Answer:

34

Step-by-step explanation:

you first write the equation:

(8-3) / (8+x-7) = 1/7, where x is the number of non blue socks

so, 5/(1+x) = 1/7

1+x = 35, so x=34

In this scenario, we can use the concept of relative velocity to determine the speed of the car.

The police officer's speed is given as 120 mph, and the rate at which the distance between the helicopter and the car is decreasing is given as 190 mph. We can consider the horizontal motion for simplicity.

Let's denote the speed of the car as Vc. Since the radar detects that the distance between the car and the helicopter is decreasing, the relative velocity between them is the difference between their velocities.

Relative velocity = Speed of the car - Speed of the helicopter

190 mph = Vc - 120 mph

To find the speed of the car, we rearrange the equation:

Vc = 190 mph + 120 mph

Vc = 310 mph

Therefore, the speed of the car, as detected by the radar, is 310 mph.

Hold on, our servers are swamped. Wait for your answer to fully load

Step-by-step explanation:

100 ml of the first solution and 200 ml of the second are required.

Answer:

3

Step-by-step explanation:

Answer:

-9/4  Negative As a Fraction

How I got the answer:

2 (x+3) = (1/8) (x+2)

x+ 3 = -3 (x+ 2)

x = -9/4

I helped you so mark me BRAINLIEST

50 books can be purchased with $ 350.

We have the data:

Books Cost (dollars)    Amount left (dollars)

            1                                    343

            2                                   336

            3                             336 - 7 = 329

            4                             329 - 7 = 322

            7                             322 - 21 = 301

           14                             301 - 49 = 252

Cost of 1 book = $ 7

Cost of b books = 7 × b = 7 b    

Amount of budget after b books = 350 - 7 b

We can buy = 350 / 7 = 50 books before spending the entire amount.

Therefore, we get that 50 books can be purchased with $ 350.

Learn more about cost here:

https://brainly.com/question/2021001

#SPJ9

Examples of Linear function are 6x + y = -1; and y = x + 5;

A linear function is the function that consists of one independent variable and one dependent variable without any exponents or powers.

The order of a linear function is always 1.

An example of such an equation can be:

6x + y = -1

Another definition of a linear function is the function that represents a straight line on the graph.

Except y=0; x=0; As y=0 represents the y-axis on the graph while x=0 represents the x-axis on the graph. Any other straight line other that these are known as Linear function.

Example of such a linear function can be:

y = x + 5

Learn more about Linear Functions at:

brainly.com/question/20286983

#SPJ4

cos(30)=x/8

Rewrite the equation as

x/8=cos(30)

Multiply both sides of the equation by

8

.

8

⋅

x/8=8⋅cos(30)

Simplify both sides of the equation.

Tap for more steps...

x=4√3

The result can be shown in multiple forms.

Exact Form:

x=4√3

Decimal Form:

x=6.9282032

Answer:

see explanation

Step-by-step explanation:

Using the identity

tan x = \(\frac{sinx}{cosx}\)

Consider the left side

\(\frac{1-tan^2x}{1+tan^2x}\)

= \(\frac{1-\frac{sin^2x}{cos^2x} }{1+\frac{sin^2x}{cos^2x} }\) ( multiply numerator and denominator by cos²x to clear fractions

= \(\frac{cos^2x-sin^2x}{cos^2x+sin^2x}\) ← ( cos²x + sin²x = 1 ]

= cos²x - sin²x

= right side , thus proven

Step-by-step explanation:

supplementary angles : angles that add up to 180 degrees

complementary angles: angles that add up to 90 degrees

adjacent angles: angles next to each other

vertical angles: angles directly across from each other

alternate interior angles: angles inside of 2 lines In opposite side of transversal.

alternate exterior angles: angles outside of 2 lines in opposite side of transversal

corresponding angles: angles on same side of transversal and same relative position to lines crossed by transversal.

please mark me brainliest, thanks

To evaluate the integral ∫x⁴(x⁵−1)⁴⁹dx by making the substitution u=x⁵−1, we can rewrite the integral in terms of u and then solve it using the power rule of integration.

Let's start by making the substitution u=x⁵−1. To find the differential du in terms of dx, we can differentiate both sides of the equation with respect to x:

du/dx = d/dx (x⁵−1)

du/dx = 5x⁴

Solving for dx, we get dx = du / (5x⁴).

Now, we can rewrite the integral in terms of u:

∫x⁴(x⁵−1)⁴⁹dx = ∫(u⁴⁹)(1/5x⁴) du.

Using the property of exponents, we can simplify this to:

(1/5) ∫u⁴⁹ du.

Integrating u⁴⁹ with respect to u, we get (1/5) * (1/50) u⁵⁰ + C, where C is the constant of integration.

Substituting back u=x⁵−1, we have:

(1/5) * (1/50) (x⁵−1)⁵⁰ + C.

Therefore, the evaluated integral is (1/2500) (x⁵−1)⁵⁰+ C.

To learn more about integral visit:

brainly.com/question/32151209

#SPJ11

The dollar gains depreciated relative to the pound when the price of pounds in dollars increases, for instance, from $1 = 1 pound to $2 = 1 pound.

Devaluation of a currency can take place in both absolute and relative terms. When the value of one currency declines in relation to the values of other currencies, this is referred to as a relative devaluation. For instance, the British pound sterling may be worth more today than it did yesterday in terms of US dollars.

A currency's value declines when compared to other currencies, which is known as currency depreciation. Political unrest, interest rate differences, weak economic fundamentals, and investor risk aversion are a few examples of the causes of currency devaluation.

To know more about  Depreciated relative visit:

https://brainly.com/question/13522166

#SPJ4

The value of the algebraic expression 11.5x + 10.9y  at x = 6 and y = 7 is 145.3

What is an algebraic expression?

Algebraic expression consists of variables and numbers connected with addition, subtraction, multiplication and division

The given algebraic expression is 11.5x + 10.9y

We have to find the value of the algebraic expression at x = 6 and y = 7

Putting x = 6 and y = 7 in the algebraic expression,

\(11.5 \times 6 + 10.9 \times 7\)

69 + 76.3

145.3

To learn more about algebraic expression, refer to the link-

https://brainly.com/question/2164351

#SPJ1

A) we would send Order A to Factory 3.

B) we would send both Order B and Order C to Factory 3.

B 7,000 Factory 3

C 30,000 Factory 3

Total number of units produced for the company today: 37,000

Average cost per unit for all production today: $9.00

To make decisions about which factory to send the orders to on Monday and Tuesday, we need to compare the costs per unit for each factory and consider the total number of units to be produced. Let's go through each day's scenario and make the production decisions.

a) Monday: Order A for 15,000 units

To decide which factory to send the order to, we compare the costs per unit for each factory. We select the factory with the lowest cost per unit to minimize the average cost per unit for the company.

Let's assume the costs per unit for each factory are as follows:

Factory 1: $10 per unit

Factory 2: $12 per unit

Factory 3: $9 per unit

To calculate the total cost for each factory, we multiply the cost per unit by the number of units:

Factory 1: $10 * 15,000 = $150,000

Factory 2: $12 * 15,000 = $180,000

Factory 3: $9 * 15,000 = $135,000

Based on the calculations, Factory 3 has the lowest total cost for producing 15,000 units, with a total cost of $135,000. Therefore, we would send Order A to Factory 3.

b) Tuesday: Order B for 7,000 units and Order C for 30,000 units

We have two options: sending each order to a separate factory or sending both orders to the same factory. We need to compare the average cost per unit for each option and select the one that results in the lowest average cost per unit.

Let's assume the costs per unit for each factory remain the same as in the previous example. We will calculate the average cost per unit for each option:

Option 1: Sending orders to separate factories

For Order B (7,000 units):

Average cost per unit = ($10 * 7,000) / 7,000 = $10

For Order C (30,000 units):

Average cost per unit = ($9 * 30,000) / 30,000 = $9

Total number of units produced for the company today = 7,000 + 30,000 = 37,000

Average cost per unit for all production today = ($10 * 7,000 + $9 * 30,000) / 37,000 = $9.43 (rounded to two decimal places)

Option 2: Sending both orders to the same factory (Factory 3)

For Orders B and C (37,000 units):

Average cost per unit = ($9 * 37,000) / 37,000 = $9

Comparing the two options, we see that both options have the same average cost per unit of $9. However, sending both orders to Factory 3 simplifies the production process by consolidating the orders in one factory. Therefore, we would send both Order B and Order C to Factory 3.

Production Report for Tuesday:

Order # of Units Factory

B   7,000      Factory 3

C  30,000    Factory 3

Total number of units produced for the company today: 37,000

Average cost per unit for all production today: $9.00

for more such question on production visit

https://brainly.com/question/31135471

#SPJ8

Around 68% of values are within 1 standard deviation from the mean with the probability that an exponentially distributed random variable takes on a value within one standard deviation of its mean.

As the empirical rule says, or also know as the 68-95-99.7 rule, tells where most of the values lie in a normal distribution, with this we know that:

Around 68% of values are within 1 standard deviation from the mean.

And around 95% of values are within 2 standard deviations from the mean.

And around 99.7% of values are within 3 standard deviations from the mean.

The empirical rule is a quick way to get an overview of the data and check for any outliers or extreme values that don’t follow the pattern.

If data from small examples do not follow the pattern closely, then other distributions like the t-distribution must be more appropriate. Once the identification of the distribution of the variable is done, then appropriate statistical tests can be applied.

To learn more about empirical rule, click here:

brainly.com/question/30700783

#SPJ4

Answer:let the cost be y

and the number of months be x

given that the cost is modeled as

y= 15x+25

we can solve for the charges after a series of months

say we want to calculate the charges for 5 month, we then have to put x=5 in the expression

y=15x+25.

y= 15(5)+25

y= 75+25

y=100

the charges for 5 months is $100

you can estimate for any number of months just put the number of months for x  

Step-by-step explanation: