All categories

2 years ago

What is the simplified form of 3 StartRoot 135 EndRoot?

Mathematics

2 answers:

jek_recluse [69]2 years ago

5 0

Answer:

$9 \sqrt{135}$

Step-by-step explanation:

Express 135 as a product of 15 and 9:

$135=15*9$

So:

$3\sqrt{15*9}$

Now, use the following property:

$\sqrt[n]{a*b} =\sqrt[n]{a}\hspace{3} \sqrt[n]{b}$

Therefore:

$3\sqrt{15} \sqrt{9}$

Since the square root of 9 is 3, the simplified form of $3\sqrt{135}$ :

$3\sqrt{15} \sqrt{9}=3*3\sqrt{15} =9\sqrt{15}$

svetoff [14.1K]2 years ago

3 0

$\bf 3\sqrt{135}~~ \begin{cases} 135=&3\cdot 3\cdot 15\\ &3^2\cdot 15 \end{cases}\implies 3\sqrt{3^2\cdot 15}\implies 9\sqrt{15}$

You might be interested in

which statement could be used to explain why f(x) = 2x – 3 has an inverse relation that is a function? a. the graph of f(x) pass

alex41 [277]

F(x) is a one-to-one function.

4 0

2 years ago

Read 2 more answers

This line plot shows something about trails in a state park. What is true about the data in this line plot?

Zepler [3.9K]

Answer:

The total length of the Dogwood Trail is 24 kilometers

The difference between the lengths of the trails is 6 kilometers

Step-by-step explanation:

The complete and correct question is

The diagram shows two different nature trails in a state park. The solid line shows the Dogwood Trail. The dashed line shows the Elm Trail.

Which of the following statements are true about the lengths of the trails? Check all that apply.

1.The total length of the Dogwood Trail is 16 kilometers.

2.The total length of the Dogwood Trail is 24 kilometers.

3.The Elm Trail is longer than the Dogwood Trail.

4.The difference between the lengths of the trails is 2 kilometers.

5.The difference between the lengths of the trails is 6 kilometers.

The picture in the attached figure

step 1

Find the value of a

Applying the Pythagorean Theorem in the right triangle ABC

$13^2=a^2+5^2\\a^2=169-25\\a^2=144\\a=12\ km$

step 2

Find the value of b

Applying the Pythagorean Theorem in the right triangle CDE

$5^2=b^2+3^2\\b^2=25-9\\b^2=16\\b=4\ km$

step 3

Find the total length of the Dogwood Trail (solid blue line)

The total length is equal to

$AD=AB+BC+CE+ED$ ---> by segment addition postulate

substitute the given values

$AD=a+5+b+3=(a+b+8)\ km$

substitute the value of a and b

$AD=(12+4+8)=24\ km$

step 4

Find the total length of the Elm Trail (dashed red line)

The total length is equal to

$AD=AC+CD$ ---> by segment addition postulate

substitute the given values

$AD=13+5=18\ km$

Verify the following statements

Part 1) The total length of the Dogwood Trail is 16 kilometers

The statement is false

Because

The total length of the Dogwood Trail is 24 kilometers (see the explanation)

Part 2) The total length of the Dogwood Trail is 24 kilometers

The statement is true (see the explanation)

Part 3) The Elm Trail is longer than the Dogwood Trail

The statement is false

Because

The Elm Trail is smaller than the Dogwood Trail

$18\ km < 24\ km$

Part 4) The difference between the lengths of the trails is 2 kilometers

The statement is false

Because

The difference is equal to

$24-18=6\ km$

Part 5) The difference between the lengths of the trails is 6 kilometers

The statement is true

Because

The difference is equal to

$24-18=6\ km$

4 0

2 years ago

Read 2 more answers

As a promotion, the first 50 customers who entered a certain store at a mall were asked to choose from one of two discounts. The

qaws [65]

Answer:

A) Yes, because P (F∩S) = 0

Step-by-step explanation:

Hello!

50 customers of a store were asked to choose between two discounts:

Discount 1: 20% off all purchases for the day.

Discount 2: 10% off all purchases for the week.

28 choose discount 1

22 choose discount 2

F: the selected person choose discount 1.

S: the selected person choose discount 2.

Two events are mutually exclusive when the occurrence of one of them prevents the other from occurring in one repetition of the trial and the intersection between these two events is void with zero probability of happening.

In this case, since the customers were asked to choose one out of the two events, if the customer chooses the first one, then he couldn't have chosen the second one and vice-versa. Then the intersection between these two events has zero probability, symbolically:

P(F∩S)=0

I hope it helps!

8 0

2 years ago

Haley substituted the values of a, b, and c into the quadratic formula below. x = StartFraction negative (negative 10) plus or m

Leokris [45]

Where does that StartFraction ... mess come from? -- I've seen it in other questions.

$x = \dfrac{- -10 \pm \sqrt{(-10)^2 - 4(7)(-2)}}{2(7)}$

Comparing that to the general quadratic formula

$x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$

we see b=-10 (agreeing in both places) a=7 (two places), c=-2

Answer: 7x² - 10x - 2 = 0

5 0

2 years ago

Read 2 more answers

Hospital sends an invoice to a patient. The patient schedules a payment plan in which she makes an initial payment of $1,451 the

Korvikt [17]

First month she payed 1451 dollars

Second month she payed 1/3 of that, which is:
1451/3 = 483.66

Third month she payed 1/3 of 483.66 because as text says, every next month she pays 1/3 of previous month payed amount.

483.66/3 = 161.22

Forth month she payed

161.22/3 = 53.74

In total she payed:

$2149.62 - B.

hope this helps :)

3 0

2 years ago

Read 2 more answers