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3 years ago

Match the corresponding function formula with each function when h(x) = 3x + 2 and g(x) = 2 x .

2 answers:

7 0

The correct functions are
h(x) = 3x + 2
g(x) = 2^x

I proceed to calculate the different values of K (x)
case 1) k(x) = g(x) ∘ h(x)
g(x) ∘ h(x)=g(h(x))
k(x) = [2]^[3x + 2]-----------> is the option 4. k(x) = 2^(3x + 2 )

case 2) k(x) = g(x) + h(x)
k(x) = [2^x]+[3x + 2]=2^x+3x+2--------> is the option 1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)
k(x) = [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)
is the option 3.) k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)
k(x) = [2^x]-[3x + 2]=2^x-3x-2--------> is the option 2.) k(x) = 2^x - 3x - 2

case 5) k(x) = g(x) × h(x)
k(x) = [2^x]*[3x + 2]-----------> is the option 5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)
h(x) ∘ g(x)=h(g(x))
k(x)=3*[2^x]+2---------------> is the option 6. k(x) = 3(2^x) + 2

Aleksandr-060686 [28]3 years ago

6 0

To simplify the other user's answer (which is correct):

1 = B

2 = D

3 = C

4 = A

5 = E

6 = F

Alternatively, your right boxes should look like:

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PLSS ANSWER MY QUESTION

Taya2010 [7]

Answer:

1) Area of frame: $140cm^2$ ; Area of picture: $40cm^2$ ; Total Area: $180cm^2$ .

2) Area 1 = $48cm^2$ ; Area 2 = $12cm^2$ ; total area = $60cm^2$ [first answer line : $60cm^2$ ]

Step-by-step explanation:

1. So to answer this question, you have to find the inner photo area first (which you will then subtract from the overall rectangle area to get the photo frame area).

To find area, you multiply length x width. For this question, there are not enough measurements given to initially multiply length and width. So, assuming that the photo is centered on the frame and the frame width is consistent along all sides, you find the difference between the overall length (12) and the picture length (5).

12 - 5 = 7

The leftover area (outside of the picture) is 7 cm (half of seven on both sides), so one side can be assumed to be : 3.5 cm

this means that 15 cm - 3.5 cm of both sides lengths (difference between the two lengths given) is the height of the photo, 15 - 3.5(2) = 8

So, the dimensions/measurements of the photo are 5 cm by 8 cm.

This means that the inner photo area is 40 (5 x 8) cm

The area of the frame will be the area of the total rectangle [12 x 15] - the inner photo area [40]. [ (12)(15) - 40 ]

[180 - 40] = 140 cm

(area is measured in squared units, so the area of the frame should be written as $140cm^{2}$ ; and the area of the photo should be written as $40cm^{2}$ )

The total area is the entire area of the rectangle: (12)(15) = 180. (This should be written as $180cm^2$ )

--------------------------------------

2) Finding the area of a shape that isn't a simple rectangle is easier if you separate the shape into smaller rectangles. I will separate the two rectangles into 4 x 12 and 2 x 6 [6 cm would be the remaining side length if you remove the length of 4].

{you can separate the shape in multiple ways, so my answer is only one answer to this problem out of other splits.}

as mentioned, the area is length x width.

4 x 12 = 48.

2 x 6 = 12. Once again, you should write area in squared units.

(the area 1 should be written as $48cm^{2}$ ; the area 2 should be written as $12cm^2$ )

you can combine the separated areas (add them) to find the total area. 48 + 12 = 60.

(the total area should be written in squared units also, so the total area should be written as: $60cm^2$ )

The area of the figure is $60cm^2$

8 0

2 years ago

Last one anyone that can help me out?

Usimov [2.4K]

Answer:

Part a. t = 7.29 years.

Part b. t = 27.73 years.

Part c. p = $3894.00

Step-by-step explanation:

The formula for continuous compounding is: A = p*e^(rt); where A is the amount after compounding, p is the principle, e is the mathematical constant (2.718281), r is the rate of interest, and t is the time in years.

Part a. It is given that p = $2000, r = 2.5%, and A = $2400. In this part, t is unknown. Therefore: 2400 = 2000*e^(2.5t). This implies 1.2 = e^(0.025t). Taking natural logarithm on both sides yields ln(1.2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(1.2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(1.2)/0.025. This means that t = 7.29 years (rounded to the nearest 2 decimal places)!!!

Part b. It is given that p = $2000, r = 2.5%, and A = $4000. In this part, t is unknown. Therefore: 4000 = 2000*e^(2.5t). This implies 2 = e^(0.025t). Taking natural logarithm on both sides yields ln(2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(2)/0.025. This means that t = 27.73 years (rounded to the nearest 2 decimal places)!!!

Part c. It is given that A = $5000, r = 2.5%, and t = 10 years. In this part, p is unknown. Therefore 5000 = p*e^(0.025*10). This implies 5000 = p*e^(0.25). Making p the subject gives p = 5000/e^0.25. This means that p = $3894.00(rounded to the nearest 2 decimal places)!!!

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3 years ago

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Roman55 [17]

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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