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3 years ago

5

Bakery makes cupcakes and three different flavors chocolate, vanilla, and strawberry, with two choices of topics, butterscotch o

r pumpkin in two different sizes small or large how many different outcomes are there?

1 answer:

muminat3 years ago

7 0

Answer:

24 or 12

Step-by-step explanation:

Multiplication

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A line has a slope of -5 and has a point of (-2,2) and (-1, -3). Write the equation for the line in slope intercept form.

liq [111]

9514 1404 393

Answer:

y = -5x -8

Step-by-step explanation:

The y-intercept can be found from ...

b = y -mx

Using the first point, we have ...

b = 2 -(-5)(-2) = -8

Then the slope-intercept equation is ...

y = mx + b . . . . . . . . for slope m and y-intercept b

y = -5x -8

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The following are common multiples for

butalik [34]

Answer:

D 9 an d12

Step-by-step explanation:

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Average rate of change

Nana76 [90]

The average rate of change has a relationship with slopes. In this way, we can write the slope of a line as follows:

$Slope=\frac{Change \ y}{Change \ x}$

To find the Average Rate of Change (ARC), we need to compute the following:

$ARC=\frac{s_{2}-s_{1}}{y_{2}-y_{1}}=slope \\ \\ where: \\ \\ s_{2}: Number \ of \ students \ in \ 2011 \\ s_{1}: Number \ of \ students \ in \ 2001 \\ \\ y_{2}: Year \ 2011 \\ y_{1}: Year \ 2001$

So:

$ARC=\frac{305-775}{2011-2001}=-47$

As you can see we have a negative sign. This means that the enrollment at the college has been decreasing at a rate of 47 students per year.

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3 years ago

Which of the following is an arithmetic sequence

Ludmilka [50]

Answer:

A sequence that has a contant addition/subtraction to get to the next term

for example:

-3, 0, 3, 6, ...

to get to the next term, we'll need to add 3 each time

Step-by-step explanation:

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3 years ago

Write the polynomial as a square of a binomial or as an expression opposite to a square of a binomial:

spayn [35]

Answer:

A) $0.25x^2-0.6xy+0.36y^2=\left(0.5x-0.6y\right)^2$

B) $-a^2+0.6a-0.09=-\left(10a-3\right)^2$

C) $\frac{9a^4}{16}+a^3+\frac{4a^2}{9}=a^2(\left(9a+8\right)^2)$

D) $-16m^2-24mn -9n^2=-\left(4m+3n\right)^2$

Step-by-step explanation:

The square of a binomial is the sum of: the square of the first terms, twice the product of the two terms, and the square of the last term.

$(a+b)^2 = a^2 + 2ab + b^2\\\\(a-b)^2 = a^2 - 2ab + b^2$

To find the square of the binomial of the following polynomials you must:

A) $0.25x^2-0.6xy+0.36y^2$

Apply radical rule: $a=\left(\sqrt{a}\right)^2$

$0.25=\left(\sqrt{0.25}\right)^2\\0.36=\left(\sqrt{0.36}\right)^2$

$\left(\sqrt{0.25}\right)^2x^2-0.6xy+\left(\sqrt{0.36}\right)^2y^2$

Apply exponent rule: $a^mb^m=\left(ab\right)^m$

$\left(\sqrt{0.25}\right)^2x^2=\left(\sqrt{0.25}x\right)^2\\\left(\sqrt{0.36}\right)^2y^2=\left(\sqrt{0.36}y\right)^2$

$\left(\sqrt{0.25}x\right)^2-0.6xy+\left(\sqrt{0.36}y\right)^2$

Rewrite $0.6xy$ as $2\cdot \:0.5x\cdot \:0.6y$

$\left(\sqrt{0.25}x\right)^2-2\cdot \:0.5x\cdot \:0.6y+\left(\sqrt{0.36}y\right)^2$

Apply perfect square formula: $\left(a-b\right)^2=a^2-2ab+b^2$

$a=0.5x,\:b=0.6y$

$\left(\sqrt{0.25}x\right)^2-2\cdot \:0.5x\cdot \:0.6y+\left(\sqrt{0.36}y\right)^2=\left(0.5x-0.6y\right)^2$

B) $-a^2+0.6a-0.09$

Multiply both sides by 100

$-a^2\cdot \:100+0.6a\cdot \:100-0.09\cdot \:100\\-100a^2+60a-9$

Factor out common term -1

$-\left(100a^2-60a+9\right)$

Break the expression into groups and factor out common terms

$-(\left(100a^2-30a\right)+\left(-30a+9\right))\\-(10a\left(10a-3\right)-3\left(10a-3\right))\\-(\left(10a-3\right)\left(10a-3\right))\\-\left(10a-3\right)^2$

C) $\frac{9a^4}{16}+a^3+\frac{4a^2}{9}$

Apply exponent rule: $a^{b+c}=a^ba^c$

$a^3=aa^2\\a^4=a^2a^2$

$\frac{9a^2a^2}{16}+aa^2+\frac{4a^2}{9}$

Factor out common term $a^2$

$a^2\left(\frac{9a^2}{16}+a+\frac{4}{9}\right)$

Factor $\frac{9a^2}{16}+a+\frac{4}{9}\right$

Find the Least Common Multiplier (LCM) of 16, 9 which is 144.

Multiply by LCM

$\frac{9a^2}{16}\cdot \:144+a\cdot \:144+\frac{4}{9}\cdot \:144\\81a^2+144a+64$

$81a^2+144a+64=\left(9a\right)^2+2\cdot \:9a\cdot \:8+8^2$

Apply perfect square formula: $\left(a+b\right)^2=a^2+2ab+b^2$

$a=9a,\:b=8$

$81a^2+144a+64=\left(9a+8\right)^2$

$\frac{9a^4}{16}+a^3+\frac{4a^2}{9}=a^2(\left(9a+8\right)^2)$

D) $-16m^2-24mn -9n^2$

Factor out common term -1

$-\left(16m^2+24mn+9n^2\right)$

Break the expression into groups and factor out common terms

$\left(16m^2+12mn\right)+\left(12mn+9n^2\right)\\4m\left(4m+3n\right)+3n\left(4m+3n\right)\\\left(4m+3n\right)\left(4m+3n\right)\\-\left(4m+3n\right)\left(4m+3n\right)\\-\left(4m+3n\right)^2$

$-16m^2-24mn -9n^2=-\left(4m+3n\right)^2$

3 0

3 years ago