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Mariana [72]
2 years ago
12

The number of cities in a region over time is represented by the function C(x)=2.9(1.05)^x. The approximate number of people per

city is represented but the function P(x)=(1.05)^3x+5
Which Function best describes T(x), the approximate population in the region?

HELP!!! PLS

Mathematics
1 answer:
N76 [4]2 years ago
3 0

Answer:

B. T(x) = 2.9\cdot (1.05)^{4\cdot x + 5}

Step-by-step explanation:

The approximate population in the region is the product of the number of cities in a region and the approximate number of people per city, that is:

T(x) = C(x)\cdot P(x) (1)

If we know that C(x) = 2.9\cdot (1.05)^{x} and P(x) = (1.05)^{3\cdot x + 5}, then the formula for the approximate population in the region is:

T(x) = [2.9\cdot (1.05)^{x}]\cdot [(1.05)^{3\cdot x + 5}]

T(x) = 2.9\cdot (1.05)^{4\cdot x + 5}

Hence, correct answer is B.

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Estimate the perimeter of the figure to the nearest whole number.
Paha777 [63]

Answer:

The perimeter (to the nearest integer) is 9.

Step-by-step explanation:

The upper half of this figure is a triangle with height 3 and base 6.  If we divide this vertically we get two congruent triangles of height 3 and base 3.  Using the Pythagorean Theorem we find the length of the diagonal of one of these small triangles:  (diagonal)^2 = 3^2 + 3^2, or (diagonal)^2 = 2*3^2.

Therefore the diagonal length is (diagonal) = 3√2, and thus the total length of the uppermost two sides of this figure is 6√2.

The lower half of the figure has the shape of a trapezoid.  Its base is 4.  Both to the left and to the right of the vertical centerline of this trapezoid is a triangle of base 1 and height 3; we need to find the length of the diagonal of one such triangle.  Using the Pythagorean Theorem, we get

(diagonal)^2 = 1^2 + 3^2, or 1 + 9, or 10.  Thus, the length of each diagonal is √10, and so two diagonals comes to 2√10.

Then the perimeter consists of the sum 2√10 + 4 + 6√2.

which, when done on a calculator, comes to 9.48.  We must round this off to the nearest whole number, obtaining the final result 9.

4 0
3 years ago
Luke makes fruit cakes for a stall at a village fete. It costs Luke £1.80 for
zalisa [80]

Answer:

2.43

Step-by-step explanation:

1.80 x 0.35 + 1.80

5 0
3 years ago
Write each expression without the absolute value symbol |3x+12|
klasskru [66]

Answer:

Step-by-step explanation:

|3x+12|

one is as it is                                     one is the negative value of it

3x + 12                                                   - (3x + 12)

                                                               - 3x - 12

That is because both negative and positive values put in am absolute value become positive.

3 0
2 years ago
Match each graph with the correct slope of the line. drag and drop the answer
OLEGan [10]

Answer/Step-by-step explanation:

✔️Slope of the first graph:

Using two points on the line, (0, 1) and (3, 2),

slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 1}{3 - 0} = \frac{1}{3}

Slope = ⅓

✔️Slope of the second graph:

Using two points on the line, (0, 0) and (1, 1),

slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 0}{1 - 0} = \frac{1}{1} = 1

Slope = 1

✔️Slope of the third graph:

Using two points on the line, (0, 1) and (2, 2),

slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 1}{2 - 0} = \frac{1}{2}

Slope = ½

3 0
3 years ago
Read 2 more answers
The bases of a trapezoid are 16.8 yards and 6.9 yards. If the height is 2 yards, what is the area of the trapezoid?
Svet_ta [14]
Hello,
Here is the formula to find the area of the trapezoid:
A=1/2(b1+b2)×h
Where b1 represent big base
b2 represent small base
and h represent height
Now, we just need to replace the number to get the final answer:
A=1/2(16.8+6.9)×2
A=1/2(23.7)×2
A=23.7 square yards. As a result, the area of the trapezoid is 23.7 square yards. Hope it help!
8 0
3 years ago
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