MATHEMATICS COLLEGE

What is the best approximation for the perimeter of polygon ABCDE?

Answers

Answer 1

Answer:

Solution

- The coordinates of the points read from the graph given are:

A=(-2,3)

B=(0,6)

C=(5,4)

D=(3,-1)

E=(-1,-2)

- To find the perimeter, we can use the distance between two points formula to find the lengths of each side of the polygon after which we add them up.

- Thus, we have:

$\begin{gathered} D=√((y_2-y_1)^2+(x_2-x_1)^2)\text{ \lparen Distance between two points\rparen} \n \n AB=√((6-3)^2+(0--2)^2) \n AB=√(9+4)=√(13) \n \n BC=√((6-4)^2+(0-5)^2) \n BC=√(4+25)=√(29) \n \n CD=√((4--1)^2+(5-3)^2) \n CD=√(25+4)=√(29) \n \n DE=√((-2--1)^2+(-1-3)^2) \n DE=√(1+16)=√(17) \n \n AE=√((3--2)^2+(-2--1)^2) \n AE=√(25+1)=√(26) \end{gathered}$

- Thus, the Perimeter is

$\begin{gathered} P=AB+BC+CD+DE+AE \n P=√(13)+√(29)+√(29)+√(17)+√(26) \n P=23.598006...\approx24units \end{gathered}$

- Thus the best approximation is 24.3 units (OPTION B)

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42Solve the equation: 8 =a) z = 10b) z = 44c) z=3d) z=7

In the problem 14 = 2 = 7, which number is the divisor?

Answers

Answer:

14 and 7 or 14 and 2

Step-by-step explanation:

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Answer:

2, assuming you meant 14÷2=7

Step-by-step explanation:

You are making a 2 ingredient trail mix with almonds and raisins. There is a 5:7 ratio of almonds to raisins. How many ounces of almonds would be in a 3-pound bag of this trail mix? (There are 16 ounces in 1 pound.) *

Answers

Answer:

There would be 20 ounces of almonds in the bag

Step-by-step explanation:

System of Equations

To solve the problem, we'll set up these two variables:

x = ounces of almonds

y = ounces of raisins

The ratio of almonds to raisins in the trail mix is 5:7, thus:

$\displaystyle (x)/(y)=(5)/(7)$

Cross-multiplying:

7x=5y [1]

A 3-pound bag of this trail mix contains 3*16=48 ounces that include almonds and raisins, thus:

x + y = 48 [2]

Multiplying [2] by 5:

5x + 5y = 240

Substituting from [1]:

5x + 7x = 240

12x = 240

x = 240/12

x = 20

There would be 20 ounces of almonds in the bag

Math problems solve

Answers

what math problem do you need help with?

Dilution ProblemSamantha needs 115 liters of a solution that has a concentration of 14 g/ml for the manufacture of computer parts.
Samantha has an unlimited supply of a solution with a concentration of 21 g/ml.
Using the Formula C1×V1 = C2×V2 to answer the following questions
Round answers to the nearest 10th.

How many liters of 21 g/ml does Samantha need to equals the amount of soluble in the given solution?
(Concentration times Volume = grams of soluble, like salt)

Answers

Answer:

76.7 liters

Step-by-step explanation:

You have ...

C1×V1 = C2×V2

so ...

V2 = V1×(C1/C2) = (115 L)×(14/21) = 76 2/3 L

V2 ≈ 76.7 L

HELP!!! find the value of x

Answers

Answer:

don't know

.....................

Answer:

x = 12

Step-by-step explanation:

Consider three orthogonal triangles (see picture)

1. The smallest triangle

2. The medium triangle

3. The big triangle that holds both triangles.

All are orthogonal (or right triangles) so you can use Pythagoras Theorem:

"The area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides"

Use Pythagoras theorem on triangle 1.

$a^(2) = 3^(2) + 6^(2) = 45$

Now user Pythagoras on triangle 2.

$b^(2) = x^(2) + 6^(2) = x^(2) + 36$

Now use Pythagoras on triangle 3 (the big triangle).

$(3 + x )^(2) = a^(2) + b^(2)\nx^(2) + 6x + 9 = a^(2) + b^(2)$

Now replace the values for $a^(2)$ and $b^(2)$ from the two equations derived from triangle 1 and 2:

$x^(2) + 6x + 9 = 45 + x^(2) + 36$

The two $x^(2)$ get cancelled out, so:

$6x + 9 = 45 + 36\nx = 12$

TA DA!

Consider the optimization problem where A m × n , m ≥ n , and b m . a. Show that the objective function for this problem is a quadratic function, and write down the gradient and Hessian of this quadratic.

b. Write down the fixed-step-size gradient algorithm for solving this optimization problem.

c. Suppose that Find the largest range of values for α such that the algorithm in part b converges to the solution of the problem.

Answers

Answer:

Answer for the question :

Consider the optimization problem where A m × n , m ≥ n , and b m .

a. Show that the objective function for this problem is a quadratic function, and write down the gradient and Hessian of this quadratic.

b. Write down the fixed-step-size gradient algorithm for solving this optimization problem.

c. Suppose that Find the largest range of values for α such that the algorithm in part b converges to the solution of the problem.

is explained din the attachment.

Step-by-step explanation:

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Joe solved this linear system correctly. 6x + 3y =6y = -2x + 2These are the last two steps of his work.6x - 6x + 6 = 6 Which statement about this linear system must be true? A: x must equal 6B: y must equal 6 C: There is no solutionD: There are infinitely many solutions to this system