Greatest comment factor of 14^3 and 13^4

Answers

Answer 1

Answer:

Answer:

14^3 = 2,744. Common factors are 1,2,4,7,8,14,28,49,56...

13^4 = 2,197. Common factors are 1, 13, 169, and 2197.

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Find the acute angle between the diagonal of rectangle whose sides are 5cm and 7cm

Answers

Answer:

The arc tangent of angle a = (5/7)

angle a = 35.538 Degrees

Of course, we might be solving for angle b so,

angle b = 90 -35.538 Degrees = 54.462 Degrees

Step-by-step explanation:

Describe the steps that transform the graph of the function y=x^2 to y=2(x+3)^2. Which attributes are not affected by the transformation?

Answers

Step-by-step explanation:

y=2(x+3)² y=x²

x²=2(x²+9+6x)

x²=2x²+18+12x

0=x²+18+12x

x²+18+12x=0

Answer:

Step-by-step explanation:

shift 3 units left then stretch vertically 2 times

Determine the maximized area of a rectangle that has a perimeter equal to 56m by creating and solving a quadratic equation. What is the length and width?

Answers

Answer:

Area of rectangle = $196\,m^2$

Length of rectangle = 14 m

Width of rectangle = 14 m

Step-by-step explanation:

Given:

Perimeter of rectangle is 56 m

To find: the maximized area of a rectangle and the length and width

Solution:

A function $y=f(x)$ has a point of maxima at $x=x_0$ if $f''(x_0)<0$

Let x, y denotes length and width of the rectangle.

Perimeter of rectangle = 2( length + width )

$=2(x+y)$

Also, perimeter of rectangle is equal to 56 m.

So,

$56=2(x+y)\nx+y=28\ny=28-x$

Let A denotes area of rectangle.

A = length × width

$A=xy\n=x(28-x)\n=28x-x^2$

Differentiate with respect to x

$(dA)/(dx)=28-2x$

Put $(dA)/(dx)=0$

$28-2x=0\n2x=28\nx=14$

Also,

$(d^2A)/(dx^2)=-2<0$

At x = 14, $(d^2A)/(dx^2)=-2<0$

So, x = 14 is a point of maxima

So,

$y=28-x=28-14=14$

Area of rectangle:

$A=xy=14(14)=196\,m^2$

Length of rectangle = 14 m

Width of rectangle = 14 m

Which of the following are steps to use when formulating an equation? Check all that apply. A. Make a table

B. Read the problem

C. Write each fact as a variable expression

D. Write each fact as a sentence

Answers

Answer:A , C , D

Step-by-step explanation:I just did it and those were the answers

Answer:

A and B

Step-by-step explanation:

Find the constant of proportionality (unit rate) for each set of valuesprofit per shirt sold
shirts: 5 10 15
profit: $7.50 $15.00 22.50

Answers

Answer:

$1.50

Step-by-step explanation:

To find the unit rate, we can divide the number of shirts to the profit that was made to find the unit cost per shirt.

7.50 / 5 = $1.50

15 / 10 = $1.50

22.50 / 15 = $1.50

Best of Luck!

Answer: 1.5

Step-by-step explanation:

7.50/5 = 1.5

15/10 = 1.5

22.50/15 = 1.5

3x-165=7x=105
What is x?

Answers

Answer:

tutoring is available right now

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