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MAVERICK [17]
2 years ago
7

Nia found a fraction that is equivalent to 3_/8. Is Nia’s fraction work, shown below, correct? Explain. 3 × 4/8 × 3= 12/24

Mathematics
1 answer:
MAVERICK [17]2 years ago
3 0

Answer:

No because 3/8 is not equivalent to 12/24

Step-by-step explanation:

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Determine whether each expression is equivalent to 49^2t – 0.5.
vampirchik [111]

Answer:

None of the expression are equivalent to 49^{(2t - 0.5)}

Step-by-step explanation:

Given

49^{(2t - 0.5)}

Required

Find its equivalents

We start by expanding the given expression

49^{(2t - 0.5)}

Expand 49

(7^2)^{(2t - 0.5)}

7^2^{(2t - 0.5)}

Using laws of indices: (a^m)^n = a^{mn}

7^{(2*2t - 2*0.5)}

7^{(4t - 1)}

This implies that; each of the following options A,B and C must be equivalent to 49^{(2t - 0.5)} or alternatively, 7^{(4t - 1)}

A. \frac{7^{2t}}{49^{0.5}}

Using law of indices which states;

a^{mn} = (a^m)^n

Applying this law to the numerator; we have

\frac{(7^{2})^{t}}{49^{0.5}}

Expand expression in bracket

\frac{(7 * 7)^{t}}{49^{0.5}}

\frac{49^{t}}{49^{0.5}}

Also; Using law of indices which states;

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

\frac{49^{t}}{49^{0.5}} becomes

49^{t-0.5}}

This is not equivalent to 49^{(2t - 0.5)}

B. \frac{49^{2t}}{7^{0.5}}

Expand numerator

\frac{(7*7)^{2t}}{7^{0.5}}

\frac{(7^2)^{2t}}{7^{0.5}}

Using law of indices which states;

(a^m)^n = a^{mn}

Applying this law to the numerator; we have

\frac{7^{2*2t}}{7^{0.5}}

\frac{7^{4t}}{7^{0.5}}

Also; Using law of indices which states;

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

\frac{7^{4t}}{7^{0.5}} = 7^{4t - 0.5}

This is also not equivalent to 49^{(2t - 0.5)}

C. 7^{2t}\ *\ 49^{0.5}

7^{2t}\ *\ (7^2)^{0.5}

7^{2t}\ *\ 7^{2*0.5}

7^{2t}\ *\ 7^{1}

Using law of indices which states;

a^m*a^n = a^{m+n}

7^{2t+ 1}

This is also not equivalent to 49^{(2t - 0.5)}

6 0
3 years ago
Find the distance between the following two points: (-1, -2) and (-1, 3)
scZoUnD [109]
5 because -2+5=3 explanation
6 0
2 years ago
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sketch a graph of the following - At midnight the water at a particular beach is at high tide. At the same time a gauge at the e
never [62]
            In the attachment is a graph of the cosine function that represents changing of the tide.
            y max = 10 ft  at midnight
            y min = 5 ft at 6 AM
Download docx
5 0
3 years ago
Help!!! Which one no need to explain!
azamat

Answer: A add the equations and C: Subtract the bottom equation from the top equation.

Step-by-step explanation: By adding the equations, you are left with

12x=8 which successfully eliminates the y values and subracting the bottom equation from the top equation.

Hope this helps!  :)

5 0
3 years ago
The data table represents the distance between a well-known lighthouse and a cruise ship over time. The cruise ship is travellin
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Find the velocity first, the "slope".

m=(y2-y1)/(x2-x1)

m=(95.5-53)/(4-2)

m=21.25  ?  Your equations are wrong, I'll double check with another set of points...

m=(350.5-308)/(16-14)

m=21.25  LOL, yep none of your lines has the correct slope.

Anyway...

y=21.25x+b, using any point we can solve for the y-intercept, or "b", (2, 53)

53=21.25(2)+b

53=42.5+b

10.5=b so the distance to the lighthouse as a function of time is:

y=21.25x+10.5

So essentially, you should fire your teacher or burn that book you are using :)

6 0
3 years ago
Read 2 more answers
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