Mathematics: Write an exponential function in the form y=ab^x that goes through points (0,6) and (5, 6144)

4 cm by 5 cm (4 x 5)Step-by-step explanation:The area of a rectangle with length and width is given by . Since the length of the rectangle is 7 less than 3 times its width, we can write the length as . Therefore, substitute into :Distribute:Subtract 20 from both sides:Factor:Since is extraneous (our dimensions cannot be negative), our answer is . Thus, the length must be and the dimension of the rectangle are 4 cm by 5 cm (4 x 5)....

Write an exponential function in the form y=ab^x

Ответ:

arthurcasella

18.07.2021

Mathematics

4 cm by 5 cm (4 x 5)

Step-by-step explanation:

The area of a rectangle with length and width is given by A=lw . Since the length of the rectangle is 7 less than 3 times its width, we can write the length as 3w-7 . Therefore, substitute l=3w-7 into A=lw :

$A=lw,\\20=(3w-7)w$

Distribute:

20=3w^2-7w

Subtract 20 from both sides:

3w^2-7w-20=0

Factor:

$(w-4)(3w+5)=0,\\\begin{cases}w-4=0, w=\boxed{4},\\3w+5=0, 3w=-5, w=\boxed{-\frac{5}{3}}\end{cases}$

Since $w=-\frac{5}{3}$ is extraneous (our dimensions cannot be negative), our answer is w=4 . Thus, the length must be $20=4l, l=\frac{20}{4}=\boxed{5}$ and the dimension of the rectangle are 4 cm by 5 cm (4 x 5).

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Write an exponential function in the form y=ab^x that goes through points (0,6) and (5, 6144)

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