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IrinaK [193]
3 years ago
11

Is 3^100/3^99 greater than,less than, or equal to 3??

Mathematics
1 answer:
oksian1 [2.3K]3 years ago
6 0

Answer:

\frac{3^{100}}{3^{99}} = 3

Step-by-step explanation:

\frac{a^{m}}{a^{n}}=a^{m-n}, m>n\\\\

Therefore,

\frac{3^{100}}{3^{99}}=3^{100-99}=3^{1}=3\\\\\frac{3^{100}}{3^{99}} = 3

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Sarah read her book for 2 1/8 hours on Monday, 1 1/2 hours on Wednesday, and 1 3/4 hours on Friday. How many hours did she read
Bezzdna [24]

Answer:

Step-by-step explanation:

Add the fractions by finding the greatest common factor of them all. if not any break up into 2 then add the other fraction to i

3 0
3 years ago
What is the area of a triangle with vertices (3,0) (9,0) (7,6)
Nezavi [6.7K]

Answer:

The area of the triangle is of 21 units of area.

Step-by-step explanation:

The area of a triangle with three vertices (x_1,y_1),(x_2,y_2),(x_3,y_3) is given by the determinant of the following matrix:

A = \pm 0.5 \left|\begin{array}{ccc}x_1&y_1&1\\x_2&y_2&1\\1_3&y_3&1\end{array}\right|

In this question:

Vertices (3,0) (9,0) (7,6). So

A = \pm 0.5 \left|\begin{array}{ccc}3&0&1\\9&0&1\\7&7&1\end{array}\right|

A = \pm 0.5(3*0*1+0*1*7+1*9*7-0*7*1-0*9*1-3*1*7)

A = \pm 0.5*(63-21)

A = \pm 0.5*42 = 21

The area of the triangle is of 21 units of area.

5 0
2 years ago
What is the simplified value of the exponential expression 64 1/4
katrin [286]
\bf a^{\frac{ n}{ m}} \implies  \sqrt[ m]{a^ n} 
\qquad \qquad
\sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\
-------------------------------\\\\
64^{\frac{1}{4}}\qquad \boxed{64=2^6}\qquad (2^6)^{\frac{1}{4}}\implies 2^{6\cdot \frac{1}{4}}\implies 2^{\frac{6}{4}}\implies 2^{\frac{3}{2}}
\\\\\\
\sqrt[2]{2^3}\implies \sqrt{2^{2+1}}\implies \sqrt{2^2\cdot 2^1}\implies 2\sqrt{2}
3 0
3 years ago
Nas funções f(x) = -3x+9; f(x) = 2x-4 e f(x) = 5x-5, caso construamos seus respectivos gráficos, informe respectivamente os pare
Likurg_2 [28]

1st option

{(3,0) e (0,9)}; {(2,0) e (0,-4)}; {(1,0) e (0,-5)}

see screenshot

sorry btw, no hablo espanol

8 0
2 years ago
Which equation represents a proportional relationship? A. y = x + 1 3 y=x+13 B. y = 1 − 1 3 x y=1-13x C. y = 3 x + 1 3 y=3x+13 D
34kurt

Answer:

Option D. y=\frac{1}{3}x

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=k or y=kx

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

<u><em>Verify each case</em></u>

case A) we have

y=x+\frac{1}{3}

Remember that

the line must pass through the origin

so

For x=0, y=0

In this case

For x=0

y=0+\frac{1}{3}=\frac{1}{3}

so

The line not passes through the origin

therefore

The equation A not represent a proportional relationship

case B) we have

y=1-\frac{1}{3}x

Remember that

the line must pass through the origin

so

For x=0, y=0

In this case

For x=0

y=1-\frac{1}{3}(0)=1

so

The line not passes through the origin

therefore

The equation B not represent a proportional relationship

case C) we have

y=3x+\frac{1}{3}

Remember that

the line must pass through the origin

so

For x=0, y=0

In this case

For x=0

y=3(0)+\frac{1}{3}=\frac{1}{3}

so

The line not passes through the origin

therefore

The equation C not represent a proportional relationship

case D) we have

y=\frac{1}{3}x

Remember that

the line must pass through the origin

so

For x=0, y=0

In this case

For x=0

y=\frac{1}{3}(0)=0

so

The line passes through the origin

therefore

The equation D represent a proportional relationship

3 0
3 years ago
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