How can I write repeated multiplication using powers?

Make and test a conjecture about the given quantity.

larisa [96]

Answer:

18. The conjecture is: The product of two negative even integers is an even integer.

Testing: Let integers be -4 and -6. [Two negative even integers]

Then (-4) × (-6) = 24 [Even integer]

19. The conjecture is: Sum of two negative odd integers is a negative even integer.

Testing: Let the two negative odd integers be -3 and -7.

Then -3 + (-7) = -10 is a negative even integer

20. The conjecture is: Sum of two even integers and two odd integers is an even integer.

Testing: Let integers be 4, 12, 13, 17 (Two even integers and two odd integers)

Then 4 + 12 + 13 + 17 = 46 (Even integer)

21. The statement is: p------->q [If you ran 1 mile, then you ran 5280 feet]

Decide whether statement is true: So if p is True then q is also True.

Hence p------->q is True. So the given statement is True.

Step-by-step explanation:

18. The product of two negative even integers.

Let the integers be -2m and -2n, m and n are positive integers

Product in (-2m) × (-2n) = 4mn = 2(2mn)

= 2p, p = 2mn

The conjecture is: The product of two negative even integers is an even integer.

Testing: Let integers be -4 and -6. [Two negative even integers]

Then (-4) × (-6) = 24 [Even integer]

19. The sum of two negative odd integers.

Let the integers be -(2m + 1) and -(2n + 1), m and n are positive integers

Then -(2m + 1) + [-(2n + 1)] = -2m - 1 - 2n - 1

= -2m - 2n - 2

= -2(+m + 2 + 1)

= -2p, p = m + n + 1

The conjecture is: Sum of two negative odd integers is a negative even integer.

Testing: Let the two negative odd integers be -3 and -7.

Then -3 + (-7) = -10 is a negative even integer

20. The sum of two even integers and two odd integers.

Let the integers be 2m, 2n, 2p + 1, 2q + 1 (m, n, p, q are positive integers)

Then, 2m + 2n + 2p + 1 + 2q + 1 = 2(m + n + p + q + 1)

= 2r, r = m + n + p + q + 1

The conjecture is: Sum of two even integers and two odd integers is an even integer.

Testing: Let integers be 4, 12, 13, 17 (Two even integers and two odd integers)

Then 4 + 12 + 13 + 17 = 46 (Even integer)

21. Let p: You ran 1 mile

Let q: You 5280 feet

The statement is: p------->q [If you ran 1 mile, then you ran 5280 feet]

Since 1 mile = 5280 feet

So if p is True then q is also True.

Hence p------->q is True. So the given statement is True.

6 0

3 years ago

Line A passes through the points (-5, 1) and (5, 11).

11111nata11111 [884]

Line A: $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{11 - 1}{5 - (-5)} = \frac{10}{5 + 5} = \frac{10}{10} = 1$
y - y₁ = m(x - x₁)
y - 1 = 1(x - (-5))
y - 1 = 1(x + 5)
y - 1 = 1(x) + 1(5)
y - 1 = x + 5
   + 1    + 1
   y = x + 6

Line B: $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{20 - (-1)}{-3 - 4} = \frac{20 + 1}{-7} = \frac{21}{-7} = -3$
   y - y₁ = m(x - x₁)
y - (-1) = -3(x - 4)
   y + 1 = -3(x) + 3(4)
   y + 1 = -3x + 12
   - 1 - 1
   y = -3x + 11

y = x + 6
y = -3x + 11

   x + 6 = -3x + 11
+ 3x     + 3x
   4x + 6 = 11
       - 6   - 6
   4x = 5
      4   4
       x = 1¹/₄
   y = x + 6
   y = 1¹/₄ + 6
   y = 7¹/₄
     (x, y) = (1¹/₄, 7¹/₄)

The answer is B.

4 0

4 years ago

A truck that can carry no more than 6900 lb is being used to transport refrigerators and upright pianos. Each refrigerator weigh

Sloan [31]

Well, first, you need to add up the amount of ten fridges and ten pianos. than you see if its heavier or lighter... > or <....... do you remember how to graph?

8 0

3 years ago

I need help this is confusing

den301095 [7]

B. Communitive property of addition

4 0

3 years ago

Read 2 more answers

The box-and-whisker plot shown represents the results of a final exam. Jimmy earned an 85 on the exam. Describe how his score co

ANEK [815]

Answer:

a) False

b) False

c) False

d) True

Step-by-step explanation:

Since it is not a multiple choice question, I have answered it as a true/false question.

First, let's identify where Jimmy's score (an 85) lies in the box-and-whisker plot. It is on the upper quartile, which is also a 75% or ¾ mark compared to the scores his classmates obtained.

To the right, are those that score better than Jimmy (the scores increase to the right). Thus, to find the fraction of students that scored higher than him, we take 1 whole minus ¾, which would give us ¼.

Fraction of students that scored lower than Jimmy= ¾

(Since when we count the position of Jimmy's score, we count it with respect to the lowest score in the class.)

8 0

3 years ago