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statuscvo [17]
3 years ago
15

Solve the linear equation

frac%7B3%7D%7B4%7D%29%5E%7Bx-7%7D" id="TexFormula1" title="(\frac{16}{9})^{-2x+5} = (\frac{3}{4})^{x-7}" alt="(\frac{16}{9})^{-2x+5} = (\frac{3}{4})^{x-7}" align="absmiddle" class="latex-formula">

Mathematics
2 answers:
Oxana [17]3 years ago
8 0

Graph both equations and find the X value when the lines cross.

See attached picture of the graph

X = 1

Or you could take logarithms of both sides where log(a^b) = b loga to also find the value of x.

Katen [24]3 years ago
7 0

Answer:

x = 1

Step-by-step explanation:

Given in the question,

(16/9)^{-2x+5} = (3/4)^{(x-7)}

Take logarithm on both sides

ln(16/9)^{-2x+5} = ln(3/4)^{(x-7)}

Apply power rule of logarithm

(-2x+5)ln(16/9) = (x-7)ln(3/4)

cross multiply

(-2x+5)/(x-7) = \frac{ln(3/4)}{ln(16/9)}

-1/2 = (-2x+5)/(x-7)

-(x-7) = 2(-2x+5)

-x + 7 = -4x + 10

rearrange the terms, x terms to left and constant to right

-x + 4x = 10 - 7

3x = 3

x = 1

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okay so a circle has half a line of 11 in. , what's the circumference and area?? i'm not good at math and so confused
omeli [17]

Answer:

C = 69.12 in.

A = 380.13 in.²

Step-by-step explanation:

Circumference of a circle is the length around the circle.

Circumference, C = 2πr

where,

Radius (r) = 11 in. (Given)

To find the circumference, substitute r = 11 into the circumference formula

C = 2*π*11

Input this into your calculator, you would get:

C = 69.1150384

C = 69.12 in. (Approximated to nearest hundredth)

Area = πr²

Plug in the value of r

A = π*11²

A = 380.132711

A = 380.13 in.² (to nearest hundredth)

5 0
3 years ago
Two triangular roofs are similar. The ratio of the corresponding sides of these roofs is 2:3. If the altitude of the smaller roo
schepotkina [342]

Answer:  6.75 feet

Step-by-step explanation:

Since, the ratio of the side of the similar triangle = 2 : 3

Thus, by the property of similar triangle,

The ratio of the altitudes of the triangle = 2 : 3

Let the altitude of smaller triangle = 2 x

And, the altitude of larger triangle = 3 x

Where x is any number.

According to the question,

2 x = 4.5

x = 2.25

Therefore, the altitude of larger triangle = 3 × 2.25 = 6.75 feet

5 0
3 years ago
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Answer:

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Step-by-step explanation:

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4 0
3 years ago
Once You write down your physical activity goal what is the second step
MAVERICK [17]
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6 0
3 years ago
Ellen is playing a video game in which she captures butterflies. There are 3 butterflies onscreen, but the number of butterflies
Over [174]

Answer:

A) The expression is given by 3*2^n.

B) The remaining butterflies after Ellen captures 7 butterflies is 41.

Step-by-step explanation:

A) As the number of butterflies keeps doubling every minute so the repeating number is 2 thus we use the term 2^n where n given the number of minutes passed.

Initially there were 3 butterflies on the screen so we multiply the term 2^n with the initial number of butterflies 3. So the expression becomes:

             Number \of\ Butterflies\ after\ n\ minutes = 3*2^n

B) After 4 minutes Ellen captures 7 butterflies from the total, So we subtract the term 7 from the number of butterflies we calculated through the expression.

           Number \of\ Butterflies\ after\ n\ minutes = 3*2^n

So, after 4 minutes

           Number \of\ Butterflies\ after\ 4\ minutes = 3*(2)^4

           Number \of\ Butterflies\ after\ 4\ minutes = 3*(16)

           Number \of\ Butterflies\ after\ 4\ minutes = 48

As Ellen has captured 7 butterflies, So:

            Number \of\ Butterflies\ remaining = 48-7

            Number \of\ Butterflies\ remaining = 41

5 0
4 years ago
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