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gtnhenbr [62]
2 years ago
6

A large open meadow near your city is shrinking in size because developers have started building new homes there.

Mathematics
1 answer:
valentinak56 [21]2 years ago
8 0

Answer:

    t=-10\log 0.32

Explanation:

<u>Equation:</u>

         A=1,562.5\times 10^{(-0.1t)}

This is a decaying exponential function, because the exponent is negative.

Then, the larger the value of t (number of months), the smaller A (the number of hectares).

The factor 1,562.5 is the initial number of hecares, when t = 0.

You must find the value of t when A equals 500, thus solve the equation:

     500=1,562.5\times 10^{(-0.1t)

Divide both sides by 1,562.5

     \dfrac{500}{1,562.5}=10^{(-0.1t)}

    0.32=10^{(-0.1t)}

Take base-10 logarithms on both sides:

    \log 0.32=-0.1t

    t=-\dfrac{\log 0.32}{0.1}\\\\\\t=-10\log 0.32

Note that the logarithm of a number decimal number is negative number, thus t will be positive. When you compute that, it is about 4.9 months.

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Which graph matches the equation y+3=2(x+3)?
Vlad1618 [11]

Answer:

The graph that includes points (-3,-3) and (0,3)

Step-by-step explanation:

In the pictures attached, the options are shown.

The equation:

y+3=2(x+3)

has the point-slope form, which is:

y-y₁=m(x-x₁)

where (x₁, y₁) is a point on the line and <em>m</em> is its slope. This means that (-3,-3) is on the line. To know the y-intercept of the line, we have to replace x = 0 into the equation, as follows:

y+3=2(0+3)

y+3 = 6

y = 6 - 3

y = 3

Then, point (0, 3) is on the line.

8 0
2 years ago
Cube-shaped blocks are packed into a cube-shaped storage container. ​ The edge length of the storage container is 212 feet. The
igor_vitrenko [27]

Answer:

The volume of cube-shaped block is 0.125 cubic feet.

Step-by-step explanation:

We are given the following in the question:

Edge length of storage container =

2\dfrac{1}{2}\text{ feet}

Edge length of block =

\dfrac{1}{5}\times \text{Edge length of container}

Putting value we get,

Edge length of block =

\dfrac{1}{5}\times 2\dfrac{1}{2}\\\\=\dfrac{1}{5}\times \dfrac{5}{2}\\\\=\dfrac{1}{2}\text{ feet}

Volume of cube-shaped block = Volume of cube

V = \text{(Edge)}^3\\\\V =(\dfrac{1}{2})^3\\\\V = \dfrac{1}{8}\text{ cubic feet}\\\\V = 0.125\text{ cubic feet}

Thus, the volume of cube-shaped block is 0.125 cubic feet.

7 0
2 years ago
While shopping for clothes Tracy spent $38 less than three times what Daniel spent right and solve an equation to find how much
Gnom [1K]

Answer:

y=3x-38

Step-by-step explanation:

We know that Tracy spent $38 in less than 3 times than what Daniel spent. Given this information we can put our eqaution together.

Y=3x-38

Hope this helps! :)

6 0
2 years ago
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is
anzhelika [568]
You need to solve for one variable in equation 1 and substitute it in equation 2 to solve.

Equation 1: x+y=24
x= number of 3 pt questions
y= number of 5 pt questions
24= Total number of questions

Equation 2: 3x+5y=100
100= Total point value possible on test
3x= point value of 3 pt questions
5y= point value of 5 pt questions

x+y=24
Subtract y from both sides
x=24-y

Substitute in equation 2:
3x+5y=100
3(24-y) +5y=100
72-3y+5y=100
72+2y=100
Subtract 72 from both sides
2y=28
Divide both sides by 2
y=14

Substitute y=14 back in to solve for x:
3x+5y=100
3x+5(14)=100
3x+70=100
Subtract 70 from both sides
3x=30
Divide both sides by 3
x=10

So there are 10 three point questions
There are 14 five point questions.

Hope this helped! :)
6 0
2 years ago
Read 2 more answers
Jana earns $25 per week for mowing the lawn and deposits the money into her savings account. The amount of money in Jana’s accou
Verizon [17]

Answer:

  The amount of money in the account in addition to that earned from mowing lawns.

Step-by-step explanation:

125 is the amount in the account when 0 weeks are spent mowing lawns. Presumably, it is the initial value of the account before the first lawn money is added.

5 0
2 years ago
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