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2 years ago

The area of a rectangle is 56 square yards. Its length is 2 yards more than three times its width. Find its dimensions

Mathematics

1 answer:

Mandarinka [93]2 years ago

6 0

Its a quadratic. Since x cant be a negative number i used the x=4 answer to plug into the length and width

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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

What is the standard form of 1.46e-6

GalinKa [24]

Standard form would be 1.46e-6 because the variable has one degree and the number 6 does not have a degree.

3 0

3 years ago

Evaluate the following expression when b = -4 , -4.5b=

Elza [17]

Answer:

Step-by-step explanation:

The question is asking you to evaluate -4.5b, which is a simplified way of saying

-4.5 * b

Since we know that b = -4, we can insert that instead of b.

-4.5 * -4

The two negatives cancel each other out, so you're left with

4.5 * 4 = 18

6 0

3 years ago

Please answer ASAP this is due tomorrow

Kay [80]

Answer:

227.08in^2

You want to find the surface area for this problem. SA=2lw+2lh+2hw

Step-by-step explanation:

L=2.5

W=7.4

H=9.6

SA=2lw+2lh+2hw

SA=2(2.5x7.4)+2(2.5x9.6)+2(9.6x7.4)

SA=37+142.08+48

SA=227.08in^2

8 0

3 years ago

Mathematics <br><br> Solving inequality

lions [1.4K]

Answer:

x _> 9 I dont have the symbol on my phone so I just put the greater than sign there

Step-by-step explanation:

1. Subtract 3 from both sides

5x > 48 - 3

2. simplofy 48 - 3 to 45

5x > 45

3. Divide both sides by 5

x > 45/5

4. Then simplify 45/5 to 9 which gives us the answer

And again I dont have the sign thats why I used the greater than sign

3 0

2 years ago