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3 years ago

Proportions in Triangles (2)

Mathematics

1 answer:

forsale [732]3 years ago

6 0

Answer:

x = 6

Step-by-step explanation:

An angle bisector divides the segments on either side of it so they are proportional. That is ...

x/12 = 5/10

x = 12(5/10) = 6 . . . . . multiply by 12

You might be interested in

4.5/y = 12.5/4 PLEASE HELP!!! SOS

garik1379 [7]

Answer:

y = 1.44

Step-by-step explanation:

What are you aiming to do here? Please share all instructions with each problem.

If you want to solve 4.5/y = 12.5/4 for y: Multiply both sides by 4y:

18 = 12.5y. Then y = 1.44

7 0

3 years ago

Minimizing Packaging Costs If an open box has a square base and a volume of 107 in.3 and is constructed from a tin sheet, find t

uysha [10]

Answer:

The dimensions of the box that minimizes the amount of material of construction is

Square base = (5.98 × 5.98) in²

Height of the box = 2.99 in.

Step-by-step explanation:

Let the length, breadth and height of the box be x, z and y respectively.

Volume of the box = xyz = 107 in³

The box has a square base and an open top.

x = z

V = x²y = 107 in³

The task is to minimize the amount of material used in its construction, that is, minimize the surface area of the box.

Surface area of the box (open at the top) = xz + 2xy + 2yz

But x = z

S = x² + 2xy + 2xy = x² + 4xy

We're to minimize this function subject to the constraint that

x²y = 107

The constraint can be rewritten as

x²y - 107 = constraint

Using Lagrange multiplier, we then write the equation in Lagrange form

Lagrange function = Function - λ(constraint)

where λ = Lagrange factor, which can be a function of x and y

L(x,y,z) = x² + 4xy - λ(x²y - 107)

We then take the partial derivatives of the Lagrange function with respect to x, y and λ. Because these are turning points, at the turning points each of the partial derivatives is equal to 0.

(∂L/∂x) = 2x + 4y - 2λxy = 0

λ = (2x + 4y)/2xy = (1/y) + (2/x)

(∂L/∂y) = 4x - λx² = 0

λ = (4x)/x² = (4/x)

(∂L/∂λ) = x²y - 107 = 0

We can then equate the values of λ from the first 2 partial derivatives and solve for the values of x and y

(1/y) + (2/x) = (4/x)

(1/y) = (2/x)

x = 2y

Hence, at the point where the box has minimal area,

x = 2y

Putting these into the constraint equation or the solution of the third partial derivative,

x²y - 107 = 0

(2y)²y = 107

4y³ = 107

y³ = (107/4) = 26.75

y = ∛(26.75) = 2.99 in.

x = 2y = 2 × 2.99 = 5.98 in.

Hence, the dimensions of the box that minimizes the amount of material of construction is

Square base = (5.98 × 5.98) in²

Height of the box = 2.99 in.

Hope this Helps!!!

5 0

3 years ago

Suppose the matrix representing a system of difference equations contains a column of zeros. What does this imply about the syst

zhuklara [117]

Answer:

It is a singular matrix system.

Step-by-step explanation:

A column of all zeros in a matrices says that the variable associated with that column has no effect on the output.

For example If the first column of a matrix consists of zeros, this means that the coefficient of the first variable is zero in every equation in the system . This means that if there is any solution at all, then there must be an infinite number of them, since you can set that first variable to any value at all and still satisfy all of the equations.

5 0

4 years ago

Riley spent $1350 on housing which was 60% of her budget what is her whole budget in $

Irina18 [472]

Answer:

$2250

60% of x = 1350

x= 2250

6 0

3 years ago

Use the box plot to answer the questions. What is the range of Charles’s scores? What is the median of Charles’s scores? What is

vekshin1

Box-plot describes 5 important data of the observations. We get following values for range, median and IQR as:

The range of Charles' scores is 20
The median of Charles' scores is 90
The IQR of Charles' scores is 8

<h3>How does a boxplot shows the data points?</h3>

A box plot has 5 data description.

The leftmost whisker shows the minimum value in the data.
The rightmost whisker shows the maximum value in the data.
The leftmost line in the box shows the first quartile.
The middle line shows the median, also called second quartile.
The last line of the box shows the third quartile.

<h3>How to find the interquartile range?</h3>

IQR(inter quartile range) is the dfference between third and first quartile. (Its the horizontal length of the box)

<h3>What is the range of a data set?</h3>

Range = Maximum value of the data set - Minimum value of the dataset

The missing box plot is attached below for the given problem.

From the given data, we see that, the left and right whiskers are on 80 and 100 respectively.

The left and right limit of the box are on 85 and 93 respectively.

The middle line lies on 90.

Thus, we get:

Minimum score = left whisker = 80
Maximum score = right whisker = 100
First quartile = left limit of box = 85
Third quartile = right limit of box = 93
Second quartile = median = middle line's position in the box = 90

Thus, we get:

Range of Charles' score = Max - min value = 100 = 80 = 20
Median of Charles' score = 90
IQR = third quartile - first quartile = 93 - 85 = 8

Learn more about box plot here:

brainly.com/question/1523909

8 0

2 years ago