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Alekssandra [29.7K]
3 years ago
7

Please Help me! Algebra 1

Mathematics
1 answer:
dem82 [27]3 years ago
7 0

Option a: The number of bacteria at time x is 0.

Option b: An exponential function that represents the population is y=200(1.5)^x

Option c: The population after 10 minutes is 11534(app)

Explanation:

It is given that the coordinates of the graph are (0,200), (1,300) and (2, 450)

Option a: To determine the number of bacteria x when y = 200

From the graph, we can see that the line meets y = 200 when x = 0

Thus, the coordinates are (0,200)

Hence, the number of bacteria at time x is 0 when y = 200.

Option b: Now, we shall determine the exponential function of the population.

The general formula for exponential function is y=a \cdot b^{x}

Where a is the starting point and a=200

b is the common difference.

To determine the common difference, let us divide,

\frac{300}{200} =1.5

Also, \frac{450}{300} =1.5

Hence, the common difference is b=1.5

Thus, substituting the values a=200 and b=1.5 in the formula y=a \cdot b^{x},

we have, y=200(1.5)^x

Hence, An exponential function that represents the population is y=200(1.5)^x

Option c: To determine the population after 10 minutes, let us substitute x=10 in y=200(1.5)^x, since the x represents the population of the bacteria in minutes.

Thus, we have,

\begin{aligned}y &=200(1.5)^{x} \\&=200(1.5)^{10} \\&=200(57.67) \\&=11534\end{aligned}

Hence, the population after 10 minutes is 11534(app)

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What is the maximum area for a rectangle whose perimeter is 48 meters?
MakcuM [25]

Answer:

12m²

Step-by-step explanation:

For a rectangle, with length L and width W,

the perimeter is given as

Perimeter,

P = (2 x Length)  + (2 x Width)

P = 2L + 2W

It is given that the perimeter is 48, hence

48 = 2L + 2W   (divide both sides by 2)

24 = L + W

or

L = 24 - W -----> eq 1

Also realize that the Area of a Rectangle is given by

A = L x W  -----> eq 2

Substituting eq 1 into eq 2,

A = (24 - W) x W

A = -W² + 24W

Recall that for a quadratic equation y = ax² + bx + c, the maxima or minima is given by y(max) =  -b/2a

In this case, b = 24 and a = -1

-b/2a = -24/[ 2(-1) ] = 12

Hence for A to be maximum A(max) = 12m² (Answer)

5 0
3 years ago
Hellpppp<br><br> what's the missing number? 7/16 = ?/64<br><br> a) 4<br> b) 21<br> c) 28<br> d) 55
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Answer: 28

EXPLANATION:
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3 0
3 years ago
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s344n2d4d5 [400]

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PIT_PIT [208]
The LCM of 6 and 15 is 30:)
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Please do them step by step;
ELEN [110]
For the first one c-9=(2)(4)+6
You are gonna multiply 2 and 4 first, 2*4=8. Now you have c-9=8+6. 8+6=14. So now the equation is c-9=14. Now we are going to add 9 to both sides. So c=23
For the second equation 10+y=90. We are going to subtract 10 from both sides. So, y=80.
Third, add 4 to both sides. a=10.
Fourth, subtract 8 from both sides. d=-9
Fifth, 5+2(3+4)=-x.
First we are going to add 3 and 4. 3+4=7. 5+2(7)=-x. Next we are going to multiply 2 and 7. 2*7=14. 5+14=-x. 5+14=19. So our equation is 19=-x. Next we are going to multiply both sides by -1. Making our final equation x=-19.
c=23
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