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2 years ago

Rewrite in simplest rational exponent form √x • 4√x

Mathematics

1 answer:

nignag [31]2 years ago

3 0

Answer:

Step-by-step explanation:

$\sqrt{x} \cdot \sqrt{x} = \sqrt{x^2} = x^{ 2 \times \frac{1}{2}} = x$

$given :\\\\ \sqrt{x} \cdot 4\sqrt{x} = 4 \cdot\sqrt{x} \sqrt{x} = 4 \sqrt{x^2} = 4x$

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To measure the height of a tree, a surveyor walked a short distance from the tree and found the angle of elevation was 43.9°, th

padilas [110]

Answer:

The height of the tree is H = 77.06 m

Step-by-step explanation:

From Δ ABC

AB = height of the tree

$\tan 43.9 = \frac{AB}{BC}$

$\tan 43.9 = \frac{h}{x}$

h = 0.9623 x ------- (1)

From Δ ABD

$\tan 37.6 = \frac{h}{20+ x}$

h = 0.77 (x + 20) ----- (2)

Equating Equation 1 & 2 we get

0.9623 x = 0.77 (x + 20)

0.9623 x = 0.77 x + 15.4

x (0.1923) = 15.4

x = 80.08 m

Thus the height of the tree is given by

H = 0.9623 x

H = 0.9623 × 80.08

H = 77.06 m

Therefore the height of the tree is H = 77.06 m

4 0

3 years ago

Use the list method to write "the perfect square integers between 1 and 80 inclusive".

Len [333]

all of our square numbers from 1 to 80 are 1, 4, 9, 16, 25, 36, 49, 64.

5 0

2 years ago

Read 2 more answers

How do I find the measure of problem #13

lidiya [134]

Answer:

Set the two equations equal to each other if you want me to solve tell me.

So.... 15x+10=16x+3

-15 -15

10=1x+3

-3

7=x

5 0

2 years ago

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Find the 13th term of the arithmetic sequence -3x – 1,42 + 4,112 + 9, ...

Strike441 [17]

Answer:

The 13th term is 81x + 59.

Step-by-step explanation:

We are given the arithmetic sequence:

$\displaystle -3x -1, \, 4x +4, \, 11x + 9 \dots$

And we want to find the 13th term.

Recall that for an arithmetic sequence, each subsequent term only differ by a common difference d. In other words:

$\displaystyle \underbrace{-3x - 1}_{x_1} + d = \underbrace{4x + 4} _ {x_2}$

Find the common difference by subtracting the first term from the second:

$d = (4x+4) - (-3x - 1)$

Distribute:

$d = (4x + 4) + (3x + 1)$

Combine like terms. Hence:

$d = 7x + 5$

The common difference is (7x + 5).

To find the 13th term, we can write a direct formula. The direct formula for an arithmetic sequence has the form:

$\displaystyle x_n = a + d(n-1)$

Where a is the initial term and d is the common difference.

The initial term is (-3x - 1) and the common difference is (7x + 5). Hence:

$\displaystyle x_n = (-3x - 1) + (7x+5)(n-1)$

To find the 13th term, let n = 13. Hence:

$\displaystyle x_{13} = (-3x - 1) + (7x + 5)((13)-1)$

Simplify:

$\displaystyle \begin{aligned}x_{13} &= (-3x-1) + (7x+5)(12) \\ &= (-3x - 1) +(84x + 60) \\ &= 81x + 59 \end{aligned}$

The 13th term is 81x + 59.

3 0

3 years ago

A particular racing bicycle normally costs $3,000. If there is an 8.25% sales tax, what is the total price of the bicycle?

Alinara [238K]

Answer:$642

Step-by-step explanation:

Solution:

First, calculate the amount of sales tax by multiply the percent tax times the total cost:

0.07×600 =42

Next, add the amount of tax to the price of the computer:

600+42=642

3 0

2 years ago

Read 2 more answers