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3 years ago

Factor completely. 5x2 - 45 5(x + 3)(x - 3) 5(x2 - 45) 5(x - 9)(x + 9) (5x + 9)(x - 5)

Mathematics

2 answers:

stellarik [79]3 years ago

4 0

$5x^2 - 45 = 5(x^2 - 9) = 5(x^2 - 3^2) = 5(x - 3) (x + 3)$

Answer: 5(x - 3) (x + 3)

Leona [35]3 years ago

4 0

Answer:

Option A is correct

$5(x+3)(x-3)$

Step-by-step explanation:

Using identity rule:

$(x^2-a^2) = (x-a)(x+a)$

To factor completely:

$5x^2-45$

Take 5 common out we have;

$5(x^2-9)$

Apply the identity rule

then;

$5(x+3)(x-3)$

Therefore, the complete factored of the given equation is: $5(x+3)(x-3)$

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A circle has a radius of 5 in. A central angle that measures 150° cuts off an arc.

marishachu [46]

Answer:

Part 1) The exact value of the arc length is \frac{25}{6}\pi \ in

Part 2) The approximate value of the arc length is 13.1\ in

Step-by-step explanation:

ind the circumference of the circle

The circumference of a circle is equal to

C=2\pi r

we have

r=5\ in

substitute

C=2\pi (5)

C=10\pi\ in

step 2

Find the exact value of the arc length by a central angle of 150 degrees

Remember that the circumference of a circle subtends a central angle of 360 degrees

by proportion

\frac{10\pi}{360} =\frac{x}{150}\\ \\x=10\pi *150/360\\ \\x=\frac{25}{6}\pi \ in

Find the approximate value of the arc length

To find the approximate value, assume

\pi =3.14

substitute

\frac{25}{6}(3.14)=13.1\ in

3 0

3 years ago

Suppose that $12,724 is invested at an interest rate of 6.1% per year, compounded continuously. Find the exponential function th

olchik [2.2K]

Answer:

Exponential Function: $A= P* e ^ {0.061t}$

Balance after

t=1 $ 13,524.32

t=2 $ 14,374.99

t=5 $ 17,261.69

t=10 $ 23,417.64

Step-by-step explanation:

Formula used to find amount in the account after time t, given the interest rate is compounded continuously

$A= Pe^r^t$

where: P= principal amount or amount invested

r= interest rate

t= time

A= amount after time t

in our question we are given:

P=$12,724

r= 6.1% or 0.061

$A= 12724 * e ^ (^0^.^0^6^1^)^t$

The above equation is exponential function that describes the amount in the account after time t in years

Now, for t = 1

$A= 12724 * e ^ {0.061 * 1}$

A= $ 13,524.32

t=2

$A= 12724 * e ^ {0.061 * 2}$

A= $ 14,374.99

t= 5

$A= 12724 * e ^ {0.061 * 5}$

A= $ 17,261.69

t=10

$A= 12724 * e ^ {0.061 * 10}$

A= $ 23,417.64

7 0

4 years ago

Mala has a collection of bangles. She has 20 gold bangles and 10 silver bangles. What is the percentage of bangles of each type?

Rainbow [258]

Answer:

Percentage of gold bangles is 66.6 and of silver bangles it is 33.3

Step-by-step explanation:

Given:

Number of gold bangles Mala has = $20$

Number of silver bangles she has = $10$

Total number of bangles = $20+10$ = $30$

We have to find the percentage of each type of bangles.

So,

Percentage of bangles = $\frac{No.\ of \ bangles\ each\ type}{Total\ no.\ of \ bangles} \times 100$

Percentage of gold bangles.

⇒ $\frac{20}{30} \times 100$

⇒ $\frac{20\times 100}{30}$

⇒ $\frac{2000}{30}$

⇒ $\frac{200}{3}$

⇒ $66.6\%$

Percentage of silver bangles.

⇒ $\frac{10}{30}\times 100$

⇒ $33.3\%$

Percentage of gold bangles, Mala has = 66.6 and of silver bangles it is = 33.3

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3 years ago

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dalvyx [7]

Answer:

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4 years ago

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Phantasy [73]

Answer:

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3 years ago