simplify
[tex] \sqrt{15} ( - \sqrt{3n} + 4n)[/tex]
please show all work!​

Answers

Answer 1

Answer:

[tex] \displaystyle - 3 \sqrt{5n} + 4 \sqrt{15} n[/tex]

Step-by-step explanation:

we would like to simplify the following expression:

[tex] \displaystyle \sqrt{15} ( - \sqrt{3n} + 4n)[/tex]

recall distribution property thus:

[tex] \displaystyle - \sqrt{3n} \sqrt{15} + 4n \sqrt{15} [/tex]

remember that,

[tex] \displaystyle \sqrt{a} \sqrt{b} = \sqrt{ab} [/tex]

so assign variables:

[tex]a \implies 3n[/tex][tex]b \implies 15[/tex]

simplify Multiplication:

[tex] \displaystyle - \sqrt{45n} + 4 \sqrt{15} n[/tex]

rewrite 45 as 9×5:

[tex] \displaystyle - \sqrt{9 \times 5n} + 4 \sqrt{15} n[/tex]

utilize the formula:

[tex] \displaystyle - \sqrt{9 } \sqrt{5n} + 4 \sqrt{15} n[/tex]

simplify square:

[tex] \displaystyle \boxed{- 3 \sqrt{5n} + 4 \sqrt{15} n}[/tex]

and we're done!

Answer 2
Laws to be used:-

[tex]\boxed{\sf a(b+c)=ab+bc}[/tex]

[tex]\boxed{\sf \sqrt{p}\sqrt{q}=\sqrt{pq}}[/tex]

Solution

[tex]\\ \rm\longmapsto \sqrt{15}(-\sqrt{3n}+4n)[/tex]

[tex]\\ \rm\longmapsto -\sqrt{15}\sqrt{3n}+4\sqrt{15}n[/tex]

[tex]\\ \rm\longmapsto -\sqrt{3(15)n}+4\sqrt{15}n[/tex]

[tex]\\ \rm\longmapsto -\sqrt{3(3)(5)n}+4\sqrt{15}n[/tex]

[tex]\\ \rm\longmapsto -3\sqrt{5}n+4\sqrt{15n}[/tex]

Or we can break 15n

[tex]\\ \rm\longmapsto -3\sqrt{5}n+4\sqrt{3(5)n}[/tex]

[tex]\\ \rm\longmapsto -3\sqrt{5}n+4\sqrt{3}\sqrt{5n}[/tex]


Related Questions

angle A and angle B are supplementary angles.If m angle A=(7x+15 ^ and m angle B=(2x−3) then find the measure of ∠ A.

Answers

Angle A= 141 degrees

find the distance between each pair of points (-1,4) and (1,-1)​

Answers

Answer:

4.5

Step-by-step explanation:

find the difference,square them,add and find the square root

-1-1=-2

4-(-1)=4

2^2+4^2=4+16

=20

square root of 20=4.5(2dp)

2x+1<9
Compound inequality

Answers

Answer:

x < 4

Step-by-step explanation:

2x+1<9

Subtract 1 from each side

2x+1-1<9-1

2x< 8

Divide by 2

2x/2 <8/2

x < 4

The correct answer would be x<4

Evaluate the expression. Will choose brainliest

Answers

Answer:

-213

Step-by-step explanation:

3|3-5|^2-(-15)^2

3(4)-225

=12-225= -213

Answer:

-213

Step-by-step explanation:

=3|x+y|²-(xy)²

Subtitute value of x and y above:

=3(|3+-5|)²-(3×-5)²

=3(|-2|)²-(-15)²

=3(2)²-(225)

=3(4)-225

=12-225

=-213

Note: If you need to ask question,I'll gladly give you answee.Thanks

1-16 Please helppppp

Answers

Ok fort first second third four ten nine and eight

Find the value of x and QR if Q is between P and R.

PQ=2x
QR=x + 2
PR= 5x -10

Answers

Answer:

2x+x+2=5x-10

3x+2=5x-10

-3x -3x

2=2x-10

+10 +10

12=2x

2x/2=x 12/2=6

x=6

QR=x+2

6+2=8

QR=8

The value of x is 6 and the value of QR will be 8 units.

What is a line segment?

A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.

Given that the value of x and QR if Q is between P and R.

PQ=2x

QR=x + 2

PR= 5x -10

The value of x will be calculated as below:-

2x+x+2=5x-10

3x+2=5x-10

2=2x-10

12=2x

x = 12 / 2

x =6

The value of QR will be calculated as below:-

QR=x+2

6+2=8

Therefore, the value of x is 6 and the value of QR will be 8 units.

To know more about line segments follow

brainly.com/question/2437195

#SPJ2

3k = 126 ??????????????????????????

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\boxed{\mathsf{3k = 126}}[/tex]

[tex]\huge\boxed{\textsf{\bf DIVIDE 3 to BOTH SIDES}}[/tex]

[tex]\huge\boxed{\mathsf{\dfrac{3k}{3}= \dfrac{126}{3}}}}[/tex]

[tex]\huge\boxed{\mathsf{\bf CANCEL\ out: \dfrac{3}{3}\ because\ it\ gives \ you\ 1}}}[/tex][tex]\huge\boxed{\bf KEEP: \dfrac{}{}\ because\ it\ answers\ for\ the\ }\\\huge\boxed{\bf k-value}[/tex]

[tex]\huge\boxed{\mathsf{k = \dfrac{126}{3}}}\\\huge\boxed{\mathsf{\dfrac{126}{3} = k}}[/tex]

[tex]\huge\boxed{\textsf{\bf SIMPLIFY ABOVE}}[/tex]

[tex]\huge\boxed{\mathsf{Therefore, your \ answer \ is: k = 42}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Collect 5 large numbers and 5 small numbers related in life and express them as exponents.

Answers

Answer:

the large numbers are

125,100,234,450,650,550

I hope u will be able to make it in an exponents form if u can not feel free to ask me

the small numbers are

10,20,30,40,50

Have a happy day ahead

Natasha's rectangle measures 4 1/2 units by 2 1/4 units. What is its area?

Answers

Answer:

Answer: 49/6units^{2}49/6units

2

Step-by-step explanation:

You can convert from mixed number to fractions as following:

2 1/3=((2*3)+1)/3=7/3 units

3 1/2=((3*2)+1)/2=7/2 units

Then you can calculate the area of the rectangle as you can see below:

\begin{gathered}Area=lenght*width\\Area=7/2units*7/3units\\Area=49/6units^{2}\end{gathered}

Area=lenght∗width

Area=7/2units∗7/3units

Area=49/6units

2

Answer:

[tex]10\frac{1}{8}[/tex]

Step-by-step explanation:

→ Multiply the fractions together

[tex]4\frac{1}{2} *2\frac{1}{4}[/tex]

→ Convert to improper fractions

[tex]\frac{9}{2} *\frac{9}{4}[/tex]

→ Multiply across

[tex]\frac{81}{8}[/tex]

→ Convert back to mixed number

[tex]10\frac{1}{8}[/tex]

Evaluate. Express your answer in scientific notation.
5.09 x 104 – 4.95 x 104

Answers

Answer:

-163.64..................

(1.2E-3) x (4.6E-1) =

Answers

Answer:

0.0012*​x*​0.46

Step-by-step explanation:

kiara starts with k marbles iin her collection. she loses 16

Answers

Answer:

Answer: k - 16

Step-by-step explanation:

If she looses, it becomes less or smaller. Subtraction produces that result. K is a fairly large number. 16 is much smaller. So she has K - 16 left.

K - 16

Construct 45° by using set square​

Answers

Place 45

set-square and make an angle of 45

by drawing the rays BD and BC

m∠ABC = (9x + 4)° and m∠DEF = (13x − 22)°. If ∠ABC and ∠DEF are supplementary, what is the measure of each angle?

Answers

Answer:

∠ABC measures 85° and ∠DEF measures 95°.

Step-by-step explanation:

We are given that ∠ABC and ∠DEF are supplementary. Then by definition:

[tex]\displaystyle m\angle ABC + m\angle DE F = 180^\circ[/tex]

Substitute:

[tex]\displaystyle \left(9x+4\right) + \left(13x-22\right) = 180[/tex]

Solve for x. Combine like terms:

[tex]22x -18 = 180[/tex]

Add:

[tex]\displaystyle 22x = 198[/tex]

And divide. Hence:

[tex]\displaystyle x = 9[/tex]

To find the measure of ∠ABC, substitute and evaluate:

[tex]\displaystyle \begin{aligned}m\angle ABC &= 9x + 4 \\ &= 9(9) + 4 \\ &= 81 + 4 \\ &= 85^\circ \end{aligned}[/tex]

And:

[tex]\displaystyle \begin{aligned}m\ngle DE F &= 13x - 22 \\ &= 13(9) - 22 \\ &= 117-22 \\&= 95^\circ \end{aligned}[/tex]

In conclusion, ∠ABC measures 85° and ∠DEF measures 95°.

by Find the value of 5% of 300​

Answers

Answer:

15

Step-by-step explanation:

5/100*300

100 can be cut for 100 and 300

so 5/1*3

ans 15

Answer:

Percentage Calculator: What is 5 percent of 300? = 15.

Hope it helps you.

What type of number is the square root of 5?​

Answers

Answer:

That is called an 'irrational algebraic number'

Hope this helps!! :)

x2 + 2xy + y2 - m2
Factorise

Answers

Answer:

x^2 + 2xy + y^2 - m^2

= (x+y)^2-m^2

26. September 9, 1981 (9/9/81) was a square-root year date because both the
month and the day are square roots of the last two digits of the year.
How many square-root dates will there be during the 21st century?

Answers

Answer:

Step-by-step explanation:

A century has 100 years in it. months only has a max of 31 dates. The following years are perfect squares, 01,04,09,16,25,36,49 64,81,100

It will be 10 square root dates.

If the function is f(x)=−3x+7, what is f(1/3)=

Answers

Answer:

6 is the answer. Hope this helps you! Stay blessed .

What is the relationship between the number of sides in a regular polygon and
number of lines of symmetry?

Answers

Answer:

Divide 360 by the difference of the angle and 180 degrees. For example, 360 divided by 15 equals 24, which is the number of sides of the polygon. Divide 360 by the amount of the exterior angle to also find the number of sides of the polygon.

Is 8.24 a rational number?

Answers

Answer:

8.24 is not a rational number

Step-by-step explanation:

The simple way to remember or find if the number is rational or not is that

* Rational numbers are always in the form of p/q and q should not be equal to zero

here u can even see 8.24 can be written as 8.24/0 so it is clearly showing that it is not a rational number

What is the volume of the rectangular prism?
3 in.
4 in.
54 in.
O A
A 12 in.
O
00
24 in 3
o
C
60 in
D. 73, in
in 3
.

Answers

Answer:

71.75 in^3

Step-by-step explanation:

If the values are

3 1/2in 5 1/4in 4in

then multiply all three of them

71.75 in^3

Hope I helped!

Given m||n, find the value of x.
+
mm
(6x-20)
(6x-4)
PLS HELP ASAP

Answers

Answer:

17°

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

Answer:

x=17

Step-by-step explanation:

The angles add to 180

6x-20 + 6x-4 = 180

Combine like terms

12x -24 =180

Add 24 to each side

12x = 180+24

12x = 204

12x/12 = 204/12

x =17

23. The table shows the number of hours a group of friends
worked doing various jobs and the amount each earned.
Select the correct hourly rate to complete the table. Then
place a checkmark in the row for the person who had the
greatest hourly rate.
Hours
Amount Earnings Greatest
Worked Earned (s) per hour ($) Hourly Rate?
36.25
Caleb
5
Jeremy
7.5
65.25
Maria
4.25
34.00
Rosa
8
54.00

Answers

calebs hourly rate- $7.25
jeremys hourly rate- $8.70
maria’s hourly rate- $8.00
rosas hourly rate- $6.76

I NEED HELP RN PLEASEE need part 1 and 2 plz asap

Answers

Answer:

A. 2+6+10+14+18+22+26+30+34+38

B. 6+18+54+162+486+1458+4374+13122+39366+118098

Step-by-step explanation:

I. In A. you can see 2 is plus by 4 = 6

                                6 is plus by 4 = 10

                                ... is plus by 4 ...

So the term was plus by 4

II. In B. you can see 6 is multiply by 3 = 18

                                18 is multiply by 3 = 54

                                 ... is multiply by 3 ...

So the term was multiply by 3

Leave comment if you're curious.

Drag the numbers below to put them in order from least to greatest:
2.2
2.291 2.27% 2.14 2.26 2.221
Wats the answer?

Answers

2.27% is the least number because since it is a percentage when converted it is 0.0227.
So the answer is :
2.27%, 2.14, 2.2, 2.221, 2.26, 2.291

Show work please

[tex] \sqrt{ \frac{45}{5} } [/tex]

Answers

Answer: 3

Step-by-step explanation:

[tex]\sqrt{ \dfrac{45}{5}} =\sqrt{9}=\bold3[/tex]

Answer:

3

Step-by-step explanation:

We don't really need to simplify this, but if you do:

45/5 is the same as 45 ÷ 5 so

45/5 = 9

Now we have to find the square root of 45/5(or 9). The square root of a number(x for example) is the number(y) that multiplied by itself once will equal x or y · y = x.

For this you can use a calculator:

[tex]\sqrt{\frac{45}{5} }[/tex] = 3

or

[tex]\sqrt{9}[/tex] = 3

Hey yall I need help right now I don't feel well. I'm giving 30 points for this.
How do you simplify _/(square root) of 150 x(to the tenth power)y(to the 13th power)
Thanks. Sorry I couldn't write it out my dual enrolling class doesn't lemme copy.

Answers

You can delete mine if you want but try to get soon ASAP!

Real quick

what is the radius of 16 cm simplest form

Answers

Answer:

8cm

Explanation:

If the 16 cm is the diameter then the radius is 8 cm

2. Discounts - You go to the store the next day and the $28.62 shirt is on sale for 15%
off, how much is the shirt before tax?

Answers

Answer:

a = 15 /100  * 28.62 = 4293 /1000

= 4.293

Hope this helps! :)

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