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2 years ago

5

Determine whether the two expressions are equivalent. If so, tell what property is applied. If not, explain why. 7 · (6 · t) and

(7 · 6) · t

1 answer:

Georgia [21]2 years ago

5 0

The two expressions are equivalent because the associative property of multiplication is applied, which means that no matter where you put the parenthesis, the two expressions will still be equal.

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-6•-2+3+3-4 evaluate the expression

12345 [234]

Answer:

$- 6 - 2 + 3 + 3 - 4 \\ = > - 6 - 2 + 6 - 4 \\ = > - 6 - 8 - 4 \\ = > - 14 - 4 \\ = - 18$

7 0

3 years ago

Use the method illustrated in the solutions to Exercise 9.2.39 to answer the following questions. (a) How many ways can the lett

Jobisdone [24]

Answer:

(a) 720 ways

(b) 120 ways

(c) 24 ways

Step-by-step explanation:

Given

$Word = DANCER$

$n =6$ --- number of letters

Solving (a): Number of arrangements.

We have:

$n =6$

So, the number of arrangements is calculated as:

$Total =n!$

This gives:

$Total =6!$

This gives:

$Total =6*5*4*3*2*1$

$Total =720$

Solving (b): DA as a unit

DA as a unit implies that, we have:

[DA] N C E R

So, we have:

$n = 5$

So, the number of arrangements is calculated as:

$Total =n!$

This gives:

$Total =5!$

This gives:

$Total =5*4*3*2*1$

$Total =120$

Solving (c): NCE as a unit

NCE as a unit implies that, we have:

D A [NCE] R

So, we have:

$n = 4$

So, the number of arrangements is calculated as:

$Total =n!$

This gives:

$Total =4!$

This gives:

$Total =4*3*2*1$

$Total =24$

8 0

2 years ago

A 14-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 9 fee

timama [110]

Answer:

10.7 feet

Step-by-step explanation:

The ladder, the ground and the wall form the shape of a right angled triangle as shown in the image below.

The hypotenuse of the triangle is 14 feet (length of ladder)

The base of the triangle is 9 feet long (the distance from the base of the ladder to the wall)

We need to find the height of the triangle. We can apply Pythagoras rule:

$hyp^2 = a^2 + b^2$

where hyp = hypotenuse

a = base of the triangle

b = height of the triangle

Therefore:

$14^2 = 9^2 + b^2\\\\196 = 81 + b^2\\\\b^2 = 196 - 81 = 115\\\\b = \sqrt{115} \\\\b = 10.7 feet$

The wall reaches 10.7 feet high.

3 0

3 years ago

Paige’s income statement for the month of December is shown. Paige monthly income statement for December. Total wages are 1,850

DedPeter [7]

Answer:

Paige’s net income for December is $950

Step-by-step explanation:

Here in this question, we are interested in calculating Paige’s net income for December

Mathematically;

Net income = Monthly wage - Total Expenses

From the question, monthly wage = $1,850 while the total expenses = $900

Thus, the net income will be ; $1,850 - $900 = $950

6 0

3 years ago

On the first day of travel, a driver was going at a speed of 40 mph. The next day, he increased the speed to 60 mph. If he drove

gogolik [260]

Velocity, distance and time:

This question is solved using the following formula:

$v = \frac{d}{t}$

In which v is the velocity, d is the distance, and t is the time.

On the first day of travel, a driver was going at a speed of 40 mph.

Time $t_1$ , distance of $d_1$ , v = 40. So

$v = \frac{d}{t}$

$40 = \frac{d_1}{t_1}$

The next day, he increased the speed to 60 mph. If he drove 2 more hours on the first day and traveled 20 more miles

On the second day, the velocity is $v = 60$ .

On the first day, he drove 2 more hours, which means that for the second day, the time is: $t_1 - 2$

On the first day, he traveled 20 more miles, which means that for the second day, the distance is: $d_1 - 20$

Thus

$v = \frac{d}{t}$

$60 = \frac{d_1 - 20}{t_1 - 2}$

System of equations:

Now, from the two equations, a system of equations can be built. So

$40 = \frac{d_1}{t_1}$

$60 = \frac{d_1 - 20}{t_1 - 2}$

Find the total distance traveled in the two days:

We solve the system of equation for $d_1$ , which gets the distance on the first day. The distance on the second day is $d_2 = d_1 - 20$ , and the total distance is:

$T = d_1 + d_2 = d_1 + d_1 - 20 = 2d_1 - 20$

From the first equation:

$d_1 = 40t_1$

$t_1 = \frac{d_1}{40}$

Replacing in the second equation:

$60 = \frac{d_1 - 20}{t_1 - 2}$

$d_1 - 20 = 60t_1 - 120$

$d_1 - 20 = 60\frac{d_1}{40} - 120$

$d_1 = \frac{3d_1}{2} - 100$

$d_1 - \frac{3d_1}{2} = -100$

$-\frac{d_1}{2} = -100$

$\frac{d_1}{2} = 100$

$d_1 = 200$

Thus, the total distance is:

$T = 2d_1 - 20 = 2(200) - 20 = 400 - 20 = 380$

The total distance traveled in two days was of 380 miles.

For the relation between velocity, distance and time, you can take a look here: brainly.com/question/14307500

3 0

2 years ago