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vitfil [10]
2 years ago
14

Find each product. 1) (5n - 5)(4n - 4)

Mathematics
1 answer:
Paraphin [41]2 years ago
6 0

Answer:

20n² - 40n + 20

Step-by-step explanation:

(5n - 5)(4n - 4)

= 5n(4n) + 5n(-4) - 5(4n) - 5(-4)

= 20n² - 20n - 20n + 20

= 20n² - 40n + 20

Another way to do this:

(5n - 5)(4n - 4)

= 5(n - 1) * 4(n - 1)

= 20(n - 1)(n - 1)

= 20(n - 1)²

= 20(n² - 2n + 1)

= 20n² - 40n + 20

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4(5x−3)+5x+5 = 118<br><br> solve for x
EleoNora [17]

Answer:

x=1+2/15

Step-by-step explanation:

4(5x-3)=5x+5=118

We move all terms to the left:

4(5x-3)-(5x+5)=0

We multiply parentheses

20x-(5x+5)-12=0

We get rid of parentheses

20x-5x-5-12=0

We add all the numbers together, and all the variables

15x-17=0

We move all terms containing x to the left, all other terms to the right

15x=17

x=17/15

x=1+2/15

   

   

8 0
1 year ago
A teacher uses 36 centimeters of tape to hang up 9 student projects. At that rate, how much tape would the teacher need to hang
Talja [164]

The teacher would need 40 centimeters of tape to hang 10 student projects.

Step-by-step explanation:

Given,

Tape used to hang projects = 36 centimeters

Number of projects hanged = 9

We will find unit rate;

9 projects = 36 centimeters

1 project = \frac{36}{9}\ centimeters

9

36

centimeters

1 project = 4 centimeters

Therefore,

Tape needed to hang 10 projects = 4*10 = 40 centimeters

The teacher would need 40 centimeters of tape to hang 10 student projects.

Keywords: unit rate, multiplication

5 0
1 year ago
A movie theater manager wants to determine whether popcorn sales have increased since the theater switched from using "butter-fl
labwork [276]

Answer:

The function that would correctly calculate the 90% range of likely sample means is given by:

B. 4,200±CONFIDENCE.T(0.10,140,12)

Step-by-step explanation:

In Microsoft Excel, the syntax

CONFIDENCE.T(alpha,standard-dev,size)  returns the confidence  interval for the population mean, using the students T-distribution.Alpha=1-90\%=10\%=0.10

The standard deviation is given as $140 and the sample size is 12.

In constructing the confidence  interval we use:

\bar X\pm CONFIDENCE.T(alpha,standard-dev,size)  

Let us substitute the values to get:

4,200\pm CONFIDENCE.T(0.10,140,12)

We use the T distribution because \sigma is unknown

8 0
1 year ago
The hypotenuse of a 45 -45° -90° triangle measures 18 cm. What is the length of one leg of the triangle?
sdas [7]
<h2>Steps</h2>

So the 45-45-90 triangle is considered to be a "special triangle" and has a rule with it. If the legs are x, then the hypotenuse is x√2. Since we know that the hypotenuse is 18, this means we can set up our equation as such:

x\sqrt{2} =18

From here we can solve for x. Firstly, divide both sides by √2.

x=\frac{18}{\sqrt{2}}

Next, we want to simplify this expression and to do that we first have to rationalize the denominator. With the right side, multiply the numerator and denominator by √2:

\frac{18}{\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{18\sqrt{2}}{2}\\\\\\x=\frac{18\sqrt{2}}{2}

Next, divide:

x=9\sqrt{2}

<h2>Answer</h2>

<u>In short, the length of one leg of the triangle is 9√2 cm.</u>

5 0
1 year ago
Read 2 more answers
The triangles shown below must be congruent.
leonid [27]
These triangles are congruent by AAS condition hence the statement is true
7 0
1 year ago
Read 2 more answers
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