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3 years ago

Valerie used the distributive property to write an equivalent expression.

Mathematics

2 answers:

murzikaleks [220]3 years ago

5 0

Answer:

She did no divide each addend correctly

Step-by-step explanation:

Given

12 + 32 ← factor out 4 from each addend

= 4(3 + 8)

As 4 × 3 = 12 and 4× 8 = 32

Valerie had 12 + 32 = 4(1 + 10) ← incorrect statement

Sergio [31]3 years ago

5 0

Answer:

Step-by-step explanation:

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15n + 24 - 4(n - 3) + 6 - 2n = 105

elena55 [62]

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3 years ago

Read 2 more answers

How can you determine if you need to use a combination or permutation to count the number of outcomes? Which will usually have m

Nadya [2.5K]

Answer with Step-by-step explanation:

Permutation : It is an arrangement of r elements out of n elements.

Combination : it is a selection of r element out of n elements .

Suppose we have a set

S={1,2,3}

If two elements are taken at a time then

Using permutation formula

Total number of outcomes= $3P_2$

Total number of outcomes= $\frac{3!}{(3-2)!}$

Total number of outcomes=3!= $3\times 2\times1=6$

Using combination formula

$\binom{n}{r}=\frac{n!}{r!(n-r)!}$

Total number of outcomes= $\binom{3}{2}=\frac{3!}{2!1!}$

Total number of outcomes= $\frac{3\times2!}{2!}$

Hence, total number of outcomes=3

Total number of outcomes determined by permutation have more outcomes.

Because permutation is an arrangement of elements therefore, it consider order of arrangement of element but combination is a selection of elements it does no consider order of elements

Arrangements of two elements out of 3 elements

{1,2},{2,3},{2,1},{3,2},{1,3},{3,1}

By using combination if two elements taken at a time then combination

{1,2},{2,3},{1,3}

4 0

3 years ago

Two friends Vicky and Micky start a business together. They decided to share their capitals depending up on the variable expendi

elixir [45]

Answer:

a- x = 5/3, or x = -7/2

b- 675

c - 5·x + 2

Step-by-step explanation:

The polynomial representing the capital of the two partners = 6·x² + 11·x - 35

a. The total share is the capital of the two partners together = 6·x² + 11·x - 35

∴ When their total share is equal to 0, we have;

6·x² + 11·x - 35 = 0

Factorizing the above equation with a graphing calculator gives;

(3·x - 5)·(2·x + 7)

Therefore;

x = 5/3, or x = -7/2

b- The total expenditure, when x = 10 is given by substituting the value of <em>x </em>in the polynomial 6·x² + 11·x - 35, as follows;

When x = 10

6·x² + 11·x - 35 = 6 × 10² + 11 × 10 - 35 = 675

The total expenditure of Vicky and Micky when x = 10 is 675

c - The sum of their expenditure is (3·x - 5) + (2·x + 7) = 5·x + 2

7 0

3 years ago

Ricardo spends 2 2/3 hours practicing soccer on

ladessa [460]

Answer:

10 7/12 hours

Step-by-step explanation:

so we have to multiply 2 2/3 twice since he does that many hours for 2 days. We then have to multiply 1 3/4 three times since he does that many hours for 3 days. Lets first convert 2 2/3 into a mixed fraction. 2 2/3 = 3 times 2 =6 +2=8 over 3. 1 3/4=4 times 1=4+3=7 over 4. 8/3 times 2 equals 16/3 which eqials

5 1/3 hours. 7/4 times 3 equals to 21/4 which equals to 5 1/4. Lets now add

5 1/3 and 5 1/4. 5+5=10 but the fractions are not the same. Therefore, we need to make it to a common denominator. 4 times 3 equals to 12 so 4/12 plus 3/12 equals 7/12. Final answer equals to 10 7/12.

3 0

3 years ago

Points (3,1) and (1,4) lie on line k. What is the slope of the line that is perpendicular to k?

denis-greek [22]

First we need to find the slope of line k. Using the slope formula, we fill in accordingly: $m= \frac{4-1}{1-3}$ . The slope is -3/2. The slope of a line that is perpendicular to line k will have the opposite sign (so, positive) and will be the reciprocal of the line k's slope (so, 2/3). You could also say, more "mathematically legal", that the product of the slopes of perpendicular lines is -1, but it's easier to just say that they are opposite reciprocals. The slope you're looking for is 2/3. Choice 3 above.

6 0

3 years ago