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2 years ago

Josh is trying to factor the expression -20a - 8 + 12b. He writes -4(5a + 2 + 3b)

Mathematics

1 answer:

KiRa [710]2 years ago

5 0

Answer:

A - He forgot to change the variable b to a negative

B - -4 (5a + 2 -3b)

C - -2 (10a + 4 - 6b)

Step-by-step explanation:

A; The reason that the variable b must be negative is because Josh is dividing by a negative factor, negative four. Therefore, if the number is positive, it must be turned negative, and if the number is negative, it must be turned positive.

B - To factor the expression correctly, take the expression Josh had originally created [-4 (5a + 2 + 3b)] and change the incorrect symbol, plus (+) for 3b to minus (-) to indicate a negative number.

C - This factored expression is equivalent as it shares a factor, -2, and a simplified set of variables within the parenthesis. Therefore, to get said variables, divide each number by the factor presented.

-20/-2 = 10

-8/-2 = 4

12/-2 = -6

Hope this helps!

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Find the coordinates of the midpoint of LB if L(8,5) and B(-6,2)<br><br> 10 points!!!

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Answer:

A, (1, 3+1/2)

Step-by-step explanation:

Midpoint formula for reference: m= {(x1 + x2)/2, (y1 + y2)/2}

Plugging in the points we get: m= {(8 - 6)/2, (5 + 2)/2}

Now we simplify using PEMDAS. First step is parentheses.

m= {2/2, 7/2}

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m= {1, 3+1/2}

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1 year ago

Chelsea is graphing the function f(x) = 20(One-fourth)x. She begins by plotting the initial value. Which graph represents her fi

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2 years ago

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The box plot compares Marta’s and Ani’s diving scores in the first several meets of the season.

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Answer:

i hope this helps

Step-by-step explanation:

The answer would be A, or "A box-and-whisker plot. The number line goes from 0 to 12, and the box ranges from 4 to 10. A line divides the box at 7.

Step-by-step explanation:

If you plot the data (2, 4, 6, 8, and 12) it looks something like the poor box-and-whisker plot below

⊕← | Ф | →⊕

|---|---|---|---|---|---|---|---|---|---|---|---|

0 1 2 3 4 5 6 7 8 9 10 11 12

Description A describes that exact box-and-whisker plot.

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A store sells 8 colors of balloons with at least 28 of each color. How many different combinations of 28 balloons can be chosen?

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Answer:

(a) $Selection = 6724520$

(b) $At\ most\ 12 = 6553976$

(c) $At\ most\ 8 = 6066720$

(d) $At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 5896638$

Step-by-step explanation:

Given

$Colors = 8$

$Balloons = 28$ --- at least

Solving (a): 28 combinations

From the question, we understand that; a combination of 28 is to be selected. Because the order is not important, we make use of combination.

Also, because repetition is allowed; different balloons of the same kind can be selected over and over again.

So:

$n => 28 + 8-1$ $= 35$

$r = 28$

$Selection = ^{35}^C_{28$

$Selection = \frac{35!}{(35 - 28)!28!}$

$Selection = \frac{35!}{7!28!}$

$Selection = \frac{35*34*33*32*31*30*29*28!}{7!28!}$

$Selection = \frac{35*34*33*32*31*30*29}{7!}$

$Selection = \frac{35*34*33*32*31*30*29}{7*6*5*4*3*2*1}$

$Selection = \frac{33891580800}{5040}$

$Selection = 6724520$

Solving (b): At most 12 red balloons

First, we calculate the ways of selecting at least 13 balloons

Out of the 28 balloons, there are 15 balloons remaining (i.e. 28 - 13)

So:

$n => 15 + 8 -1 = 22$

$r = 15$

Selection of at least 13 =

$At\ least\ 13 = ^{22}C_{15}$

$At\ least\ 13 = \frac{22!}{(22-15)!15!}$

$At\ least\ 13 = \frac{22!}{7!15!}$

$At\ least\ 13 = 170544$

Ways of selecting at most 12 =

$At\ most\ 12 = Total - At\ least\ 13$ --- Complement rule

$At\ most\ 12 = 6724520- 170544$

$At\ most\ 12 = 6553976$

Solving (c): At most 8 blue balloons

First, we calculate the ways of selecting at least 9 balloons

Out of the 28 balloons, there are 19 balloons remaining (i.e. 28 - 9)

So:

$n => 19+ 8 -1 = 26$

$r = 19$

Selection of at least 9 =

$At\ least\ 9 = ^{26}C_{19}$

$At\ least\ 9 = \frac{26!}{(26-19)!19!}$

$At\ least\ 9 = \frac{26!}{7!19!}$

$At\ least\ 9 = 657800$

Ways of selecting at most 8 =

$At\ most\ 8 = Total - At\ least\ 9$ --- Complement rule

$At\ most\ 8 = 6724520- 657800$

$At\ most\ 8 = 6066720$

Solving (d): 12 red and 8 blue balloons

First, we calculate the ways for selecting 13 red balloons and 9 blue balloons

Out of the 28 balloons, there are 6 balloons remaining (i.e. 28 - 13 - 9)

So:

$n =6+6-1 = 11$

$r = 6$

Selection =

$^{11}C_6 = \frac{11!}{(11-6)!6!}$

$^{11}C_6 = \frac{11!}{5!6!}$

$^{11}C_6 = 462$

Using inclusion/exclusion rule of two sets:

$Selection = At\ most\ 12 + At\ most\ 8 - (12\ red\ and\ 8\ blue)$

$Only\ 12\ red\ and\ only\ 8\ blue\ = 170544+ 657800- 462$

$Only\ 12\ red\ and\ only\ 8\ blue\ = 827882$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = Total - Only\ 12\ red\ and\ only\ 8\ blue$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 6724520 - 827882$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 5896638$

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2 years ago

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