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2 years ago

Choose the expanded form of this expression. 4(14a + b – 6) A. a + b – 24 B. 4a – 6b C. 4a + b – 6 D. a + 4b – 24

Mathematics

2 answers:

inn [45]2 years ago

8 0

Answer:

D. a + 4b – 24

Step-by-step explanation:

4(1/4a + b – 6)

distribute

4*1/4a + 4* b -4*6

a +4b-24

natta225 [31]2 years ago

8 0

Answer:

$a+4b-24$

Step-by-step explanation:

1) The Distributive Property of Multiplication says that any factor (e.g. number), multiplying a sum/subtraction within parenthesis. This factor can be distributed, and then multiplies each addend. As it follows:

$4(\frac{1}{4}a+b-6)=\\4(\frac{1}{4}a)+4b+4(-6)=\\a+4b-24$

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I tell you these facts about a mystery number, $c$: $\bullet$ $1.5 < c < 2$ $\bullet$ $c$ can be written as a fraction wit

makkiz [27]

Answer:

Possible answer: $\displaystyle c = \frac{16}{10} = \frac{8}{5} = 1.6$ .

Step-by-step explanation:

Rewrite the bounds of $c$ as fractions:

The simplest fraction for $1.5$ is $\displaystyle \frac{3}{2}$ . Write the upper bound $2$ as a fraction with the same denominator:

$\displaystyle 2 = 2 \times 1 = 2 \times \frac{2}{2} = \frac{4}{2}$ .

Hence the range for $c$ would be:

$\displaystyle \frac{3}{2} < c < \frac{4}{2}$ .

If the denominator of $c$ is also $2$ , then the range for its numerator (call it $p$ ) would be $3 < p < 4$ . Apparently, no whole number could fit into this interval. The reason is that the interval is open, and the difference between the bounds is less than $2$ .

To solve this problem, consider scaling up the denominator. To make sure that the numerator of the bounds are still whole numbers, multiply both the numerator and the denominator by a whole number (for example, 2.)

$\displaystyle \frac{3}{2} = \frac{2 \times 3}{2 \times 2} = \frac{6}{4}$ .

$\displaystyle \frac{4}{2} = \frac{2\times 4}{2 \times 2} = \frac{8}{4}$ .

At this point, the difference between the numerators is now $2$ . That allows a number ( $7$ in this case) to fit between the bounds. However, $\displaystyle \frac{1}{c} = \frac{4}{7}$ can't be written as finite decimals.

Try multiplying the numerator and the denominator by a different number.

$\displaystyle \frac{3}{2} = \frac{3 \times 3}{3 \times 2} = \frac{9}{6}$ .

$\displaystyle \frac{4}{2} = \frac{3\times 4}{3 \times 2} = \frac{12}{6}$ .

$\displaystyle \frac{3}{2} = \frac{4 \times 3}{4 \times 2} = \frac{12}{8}$ .

$\displaystyle \frac{4}{2} = \frac{4\times 4}{4 \times 2} = \frac{16}{8}$ .

$\displaystyle \frac{3}{2} = \frac{5 \times 3}{5 \times 2} = \frac{15}{10}$ .

$\displaystyle \frac{4}{2} = \frac{5\times 4}{5 \times 2} = \frac{20}{10}$ .

It is important to note that some expressions for $c$ can be simplified. For example, $\displaystyle \frac{16}{10} = \frac{2 \times 8}{2 \times 5} = \frac{8}{5}$ because of the common factor $2$ .

Apparently $\displaystyle c = \frac{16}{10} = \frac{8}{5}$ works. $c = 1.6$ while $\displaystyle \frac{1}{c} = \frac{5}{8} = 0.625$ .

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How many pairs of whole numbers have a sum of 110

kap26 [50]

There are different definitions of "whole numbers".

Some define it as an integer (i.e. positive or negative) [some dictionaries]

Some define it as a non-negative integer. [most math definitions]

We will take the math definition, i.e. 0<= whole number < ∞

To find pairs (i.e. two) whole numbers with a sum of 110, we start with

0+110=110

1+109=110

2+108=110

...

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55+55=110

Since the next one, 56+54=110 is the same pair (54,56) as 54+56=110, we stop at 55+55=110 for a total of 56 pairs.

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tia_tia [17]

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<u>The Side-Splitter Theorem</u>: States that If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those two sides proportionally

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<u>the answer is</u>

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Answer:

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