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3 years ago

Factor each expression

1 answer:

8 0

1 -since everything includes 4a, we can factor that to get 4a(a-4b^3+2b^2c)
2 - since 5 and 3 add to 8 and multiply to 15, we can do (n+5)(n+3)
3 - since -5 and -4 add to -9 and multiply to 20, we can do (g-5)(g-4)
4 - since -10 and 3 add to -7 and multiply to 30, we can do (z-10)(z+3)
5 - we can factor out 4y to get 4y(y^2-9).

I got the numbers in 2, 3, and 4 with a guesstimating and checking approach

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Are f and g inverses of each other? Support your response algebraically

NeTakaya

Answer:

see explanation

Step-by-step explanation:

If f(x) and g(x) are the inverses of each other, then

f(g(x)) = g(f(x)) = x

f(g(x)) = f(x - $\frac{1}{2}$ ) = x - $\frac{1}{2}$ + $\frac{1}{2}$ = x

g(f(x)) = g(x + $\frac{1}{2}$ ) = x + $\frac{1}{2}$ - $\frac{1}{2}$ = x

Hence f(x) and g(x) are the inverse of each other

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3 years ago

A trapezoid with bases that measure 8 inches and 11 inches has a height of 3 inches. What is the area of the trapezoid?

gavmur [86]

Area= 1/2(height)×(base↓1+base↓2)
Area=1/2(3)×(8+11)
Area=1/2(3)×(19)
Area=1/2(57)
Area=57/2 OR 28.5
Thus, the area of the trapezium is 28.5inches^2

3 0

3 years ago

Which expression represents the phrase the sum of twice a number and 7

bixtya [17]

Answer:

2n+7

Step-by-step explanation:

3 0

3 years ago

A figure is composed of a semicircle and a right triangle. Determine the area of the shaded region. Use 3.14 for π and round to

Aliun [14]

Answer:

$A=9.5\ ft^2$

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of triangle plus the area of semicircle

$A=\frac{1}{2}bh+\frac{1}{2}\pi r^{2}$

we have

$b=4\ ft$

Find the height of the right triangle applying the Pythagorean Theorem

$5^2=h^2+4^2$

$h^2=9\\h=3\ ft$

The radius of the semicircle is half the height of triangle

$r=3/2=1.5\ ft$

substitute in the formula

$A=\frac{1}{2}(4)(3)+\frac{1}{2}(3.14)(1.5)^{2}$

$A=6+3.5=9.5\ ft^2$

5 0

3 years ago

Read 2 more answers

A florist can make a grand arrangement in 18 minutes or a simple arrangement in 10 minutes. The florist makes at least twice as

Colt1911 [192]

Answer:

See explanation

Step-by-step explanation:

Let x be the number of simple arrangements and y be the number of grand arrangements.

1. The florist makes at least twice as many of the simple arrangements as the grand arrangements, so

$x\ge 2y$

2. A florist can make a grand arrangement in 18 minutes $=\dfrac{3}{10}$ hour, then he can make y arrangements in $\dfrac{3}{10}y$ hours.

A florist can make a simple arrangement in 10 minutes $=\dfrac{1}{6}$ hour, so he can make x arrangements in $\dfrac{1}{6}x$ hours.

The florist can work only 40 hours per week, then

$\dfrac{3}{10}y+\dfrac{1}{6}x\le 40$

3. The profit on the simple arrangement is $10, then the profit on x simple arrangements is $10x.

The profit on the grand arrangement is $25, then the profit on y grand arrangements is $25y.

Total profit: $(10x+25y)

Plot first two inequalities and find the point where the profit is maximum. This point is point of intersection of lines $x=2y$ and $\dfrac{3}{10}y+\dfrac{1}{6}x=40$

But this point has not integer coordinates. The nearest point with two integer coordinates is (126,63), then the maximum profit is

$\$(10\cdot 126+25\cdot 63)=\$2,835$

8 0

3 years ago