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2 years ago

Simplify the radical expression sqrt 21y * 5sqrt 49y

Mathematics

1 answer:

olchik [2.2K]2 years ago

3 0

<span> sqrt 21y * 5sqrt 49y
= sqrt(21y) * 5*7*sqrt(y)
= sqrt(y) [ sqrt(21) * 35 ] (answer)</span>

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The hypotenuse of a right triangle is 1 centimeter longer than one side and 4 centimeters longer than three times the other side

snow_tiger [21]

Answer:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

Step-by-step explanation:

Represent:

The opposite with a
The adjacent with b
The hypotenuse with c

Given that:

$c = 1 + a$

$c = 4 + 3b$

Required

Solve for a, b and c

$c = c$

So, we have:

$1 + a = 4 + 3b$

Subtract 1 from both sides

$a = 4 -1 + 3b$

$a = 3 + 3b$

Apply Pythagoras Theorem

$c^2 = a^2 + b^2$

Substitute 3 + 3b for a and 4 + 3b for c

$(4 + 3b)^2 = (3 + 3b)^2 + b^2$

Open brackets

$16 + 12b+12b+9b^2 = 9 + 9b+9b+9b^2 +b^2$

$16 + 24b+9b^2 = 9 + 18b+10b^2$

Collect Like Terms

$10b^2 - 9b^2 + 18b - 24b + 9 - 16 = 0$

$b^2 - 6b -7 = 0$

Expand

$b^2 +b-7b-7=0$

Factorize:

$b(b+1)-7(b+1) =0$

$(b-7)(b+1) = 0$

Split:

$b - 7 = 0\ or\ b+1=0$

$b = 7\ or\ b=-1$

But the adjacent of a triangle can't have a negative measurement.

So:

$b = 7$

Recall that:

$c = 4 + 3b$

$a = 3 + 3b$

Substitute 7 for b in the above expressions

$c = 4 + 3 * 7$

$c = 4 + 21$

$c = 25$

$a = 3 + 3 * 7$

$a = 3 + 21$

$a = 24$

Hence, the dimensions of the triangle are:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

5 0

2 years ago

Four interior angles of a pentagon measure 156 degrees 72 degrees 98 degrees and 87 degrees. What is the measure of the final in

zepelin [54]

Answer:

127°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180°(n - 2) ← n is the number of sides

here n = 5 ( Pentagon), hence

sum = 180° × 3 = 540°

To find the fifth angle subtract the sum of the 4 given angles from 540

angle = 540° - (156 + 72 + 98 + 87) = 540° - 413° = 127°

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3 years ago

Explain what is 90% of 180

Yakvenalex [24]

Answer:

The answer is 162.

Step-by-step explanation:

To find the percentage of a number:

Turn the percentage into a decimal. 90% to .90

Multiply the decimal by the number you want to find the percentage of. .90 x 180

The answer is the product.

4 0

2 years ago

Which statement illustrates the associative property of addition?

Alex73 [517]

I think it’s B because

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2 years ago

Simplify the expression 0.032 ÷ (8 × 10^-2)

Allisa [31]

$\frac{0.032}{8\times10^{-2}} = \frac{0.032}{0.08} = 0.4$

Your answer is 0.4

3 0

2 years ago