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4 years ago

8

Which of these is another way to write the function

itle="g(x)=3^{x}" alt="g(x)=3^{x}" align="absmiddle" class="latex-formula">?
A. g(x)=9(3^x−2)
B. g(x)=9(3^x+2)
C. g(x)=3(9^x+2)
D. g(x)=3(9^x−2)

1 answer:

mylen [45]4 years ago

5 0

Answer:

A. g(x)=9(3^(x−2))

Step-by-step explanation:

g(x) = 3^x = 3^(x-2+2) = (3^2)(3^(x-2))

g(x) = 9(3^(x-2)) . . . . . matches choice A

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What is the solution for -10 < x - 9?

enyata [817]

<span>-10 < x - 9

</span><span>-10+9 < x - 9+9

-1<x, or
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3 years ago

Can you’ll help me pls , I really need help.

Olegator [25]

Answer:

-t + 4.5>7

Step-by-step explanation:

-18 = t

-t = 18

18+4.5 = 22.5

22.5>7

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3 years ago

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Julisha poured 0.9 liter of water into an

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3 years ago

Officials begin to release water from a full man-made lake at a rate that would empty the lake in 10 weeks, but a river that can

Romashka [77]

Answer:

It takes 20 weeks to empty the lake

Step-by-step explanation:

Some rate, let's call it $R_{empty}$ empties the lake in 10 weeks and a river (with rate $R_{river}$ can fill the lake in 20 weeks. The idea behind the solution of this type of problem is always set the rate to the same units. Let's see this:

$R_{empty}=\frac{1\ lake}{10\ weeks}$ which implies that this rate empties 0.1 of the lake per week, thus, $R_{empty}=0.1/week$ .

Using the same idea, we can obtain that the filling rate of the river is:

$R_{river}=\frac{1\ lake}{20\ weeks} = 0.05 /week$

Since both rates are acting at the same time, the total rate of flowing water (either in or out the lake) would be given by:

$R_{total}=R_{empty}+R_{river}\\R_{total}= -0.1 + 0.05=-0.05/week$ , which means that the lake is being empty at a rate of -0.05 week and using the rule of three:

$\frac{0.05}{1} = \frac{1}{total\ of\ weeks} \\total\ of\ weeks = \frac{1}{0.05}=\frac{1}{\frac{1}{20} }\\ total\ of\ weeks = 20$

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5 0

3 years ago

Line segment ON is perpendicular to line segment ML, and PN = 10.

Ne4ueva [31]

we know that

Triangle MOL is an isosceles triangle

because

$MO=OL=radius\ of\ circle=25\ units$

$ON=25\ units$

$ON=OP+PN\\ 25=OP+10\\ OP=25-10\\ OP=15\ units$

Find the base MP

Applying the Pythagorean Theorem in the right triangle MPO

$MO^{2} =MP^{2}+PO^{2}\\ MP^{2}=MO^{2}-PO^{2}\\ MP^{2}=25^{2}-15^{2}\\ MP^{2}=400\\ MP=20\ units$

$ML=2*MP\\ ML=2*20\\ ML=40\ units$

Find the area of triangle MOL

$A=\frac{1}{2}ML*PO\\ \\ A=\frac{1}{2}*40*15\\ \\ A=300\ unit^{2}$

therefore

the answer is

the area of triangle MOL is

$300$ square units

3 0

3 years ago

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