simplify [tex]\sqrt{80} + \sqrt{2\frac{2}{9}[/tex]

Answers

Answer 1

Answer:

[tex]\displaystyle \frac{14}{3}\sqrt{5}[/tex]

Step-by-step explanation:

Simplify:

[tex]\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}[/tex]

We must express the mixed fraction into an improper fraction:

[tex]2\frac{2}{9}=2+\frac{2}{9}=\frac{20}{9}[/tex]

[tex]\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle \sqrt{80} + \sqrt{\frac{20}{9}}[/tex]

Since 80 = 16*5 and 20=4*5

[tex]\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle \sqrt{16*5} + \sqrt{\frac{4*5}{9}}[/tex]

[tex]\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle 4\sqrt{5} + \frac{2}{3}\sqrt{5}[/tex]

Adding the fractions:

[tex]\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle (4 + \frac{2}{3})\sqrt{5}[/tex]

[tex]\mathbf{\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle \frac{14}{3}\sqrt{5}}[/tex]


Related Questions

Samuel orders four DVD's from an online music store. Each DVD costs $9.99. He has a 20% discount code and sales tax is 6.75%. What is the total cost of his order? Please helpppp

Answers

answer: $34.13

explanation:
4 • $9.99 = $39.96 before tax or discount

subtract discount:
$39.96 • 0.2 = $7.992
39.96-7.992 = 31.968

add tax:
31.968 • 1.0675
= $34.13

What is 27 times 30 to the power of 2?(“real” question)

Answers

Answer:

24300

Step-by-step explanation:

first find the square for 30 * 30

then multiply!

What is the 30th term of the linear sequence below?
−5,−7,−9,−11,−13
,

Answers

a1 = -5, d = -2
Use formula: an = a1 + (n-1)d
a30 = -5 + (30-1)(-2)
a30 = -5 + (-38)
a30 = -63
The 30th term should be -63

The drama club has $4000 to spend on their winter performance. They have already
spent $1500 on the set, and programs cost $1.75 each.
Thetinequality 1500 + 1.75x<=4000 can be used to determine the number
of programs, x, that can be ordered. Which statement about the number of
programs that can be ordered is true?

The drama club can purchase at least 1.428 programs

The drama club can purchase at most 1.428 programs

The drama club can purchase 1,429 programs

The drama club can purchase 4000 programs

Answers

Answer:

The drama club can purchase 1429 programs

Step-by-step explanation:

What is the slope of the line that passes through the points (4, -6) and (4, 6)?

Answers

Answer:

no slope

Step-by-step explanation:

m= y2-y1/x2-x1

m= 6-(-6)/4-4

m=12/0

m= no slope

2-1/3x=1/6x+1
x=?
Merry Christmas

Answers

Answer:

x=2

Step-by-step explanation:

Thanks sweetheart <3

Isosceles triangle MNis shown below with MN ~= PN. Ray NQ bisects angle MNP and intersects side MP at point Q. Name three pairs of congruent angles

Answers

Answer:

The answer is below

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are  obtuse, scalene, equilateral, isosceles etc.

An isosceles triangle is a triangle with two equal sides, the base angles of an isosceles triangle is equal.

Since ΔMNP is an isosceles triangle with MN = PN, then:

∠QMN = ∠QPN (base angles of an isosceles triangle are equal)

∠MNQ = ∠PNQ (NQ bisects ∠MNP producing two equal angles)

∠MQN = ∠PQN (right angles)

Find the slope of the lines that go through the following points.

Answers

Answer:

use the formula y2 - y1 / x2 - x1

Answer:

y2-y1 /x2-x1

Step-by-step explanation:

slope is the same as gradient

follow this principle (x,y)

Gradient (m) =y2-y1 /x2-x1

please help, im desperate ​

Answers

Answer:

i think 124...is the answer

HELP PLEASE 100 points IM BEING TIMED ILL EVEN GIVE A CROWN THING
Which rule describes the composition of transformations that maps ΔABC to ΔA"B"C"?

A.) 90 degree rotation about point 0 composition reflection across the x-axis
B.) Reflection across the x-axis composition 90 degree rotation about point 0
C.) 180 degree rotation about point 0 composition reflection across the x-axis
D.) Reflection across the x-axis composition 180 degree rotation about point 0

Answers

Answer: A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The guy above me was correct. I got a 99% on my test.

What is 5 + 5 + 5 + 5 + 5 (5 x 4) Easy question so you can get points! Explain and get brainliest!

A) 45
B) 120
C) 100
D) 25

Answers

B) 120 because you follow pemdas which arrives to the answer of 120

Answer:

A) 45

Step-by-step explanation:

BECAUSE 5 + 5 + 5 + 5 + 5 = 25

and 5 x 4 = 20

So, 25 + 20

= 45

A scale on a blueprint drawing of a house shows that 6 centimeters represents 3 meters.
What number of centimeters on the blueprint represents an actual distance of 27 meters?

Answers

Answer:

Step-by-step explanation:

Which function has the same range f(x) =-5/7 (3/5)^x? Hurry !!!

Answers

answer is

B). g(x) = -5/7 (3/7)^-x

Answer: b

g(x) = -5/7 (3/7)^-x

Step-by-step explanation: have a great day :)

What is the slope of 2,10 and 4,20 please answer rn

Answers

Answer:

2/10?

Step-by-step explanation:

pls help me answer this​

Answers

Answer:

The answer for the question is "C. 180"

Find tan θ if sec θ = square root of thirty seven divided by six and sin θ < 0.

Answers

Answer:

1/6

Step-by-step explanation:

sec = 1/cos = [tex]\sqrt{37}[/tex]/6 and cos is adj/hyp so the other side of the triangle is 1 and tan = sin/cos so 1/6

Please help! Solve for g

Answers

Answer:

g= - 32

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

Step 2: Flip the equation.

Step 3: Add 5 to both sides.

Step 4: Multiply both sides by 4/(-1).

g=−32

Answer:

g = -32

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

3 = g/-4 - 5

Step 2: Solve for g

Add 5 to both sides:                    8 = g/-4Multiply -4 on both sides:            -32 = gRewrite:                                        g = -32

Step 3: Check

Plug in g into the original equation to verify it's a solution.

Substitute in g:                    3 = -32/-4 - 5Divide:                                  3 = 8 - 5Subtract:                              3 = 3

Here we see that 3 does indeed equal 3.

∴ g = -32 is the solution to the equation.

Solve the equation sin^2x=3Cos^2X.

I would love to graduate...so thanks in advance!

Answers

Answer:

240°

Step-by-step explanation:

[tex]sin^2x=3cos^2x \\ \\ sin^2x=3(1 - sin^2x )\\ \\ sin^2x=3 - 3sin^2x \\ \\ sin^2x + 3sin^2x=3 \\ \\ 4sin^2x=3 \\ \\ sin^2x= \frac{3}{4} \\ \\ sinx= \sqrt{ \frac{3}{4} } \\ \\ sinx= \frac{ \sqrt{3} }{2} \\ \\ sinx= sin \: 60 \degree \\ \\ in \: the \: second \: quadrant \\ sinx= sin \: (180 \degree - 60 \degree ) = sin \: 120 \degree \\ \\ in \: the \: third \: quadrant \\ sin x= sin \: (180 \degree + 60) \degree = sin \: 240 \degree[/tex]

what is the slope of the graph of y=12x-19

Answers

Answer:

The slope is 12

Step-by-step explanation:

Remember the slope formula y=mx+b

m= the slope

b= y-intercept

What is 135 less than the product of 57 and 219?

Answers

Answer: something in the negatives

Step-by-step explanation:

if L is parallel to M, find the value of each variable(s)

Answers

Answer:

see below

Step-by-step explanation:

5.  9x + 2 = 119°                    alternate interior angles are congruent

          9x = 117

           x = 13°

6.  12x - 8 + 104° = 180°       same side interior angles are supplementary

            12x + 96 = 180

                     12x = 84

                        x = 7°

7.  5x + 7 = 8x - 71                alternate exterior angles are congruent

         -3x = -78

            x = 26°

8.  4x - 7 = 7x - 61                corresponding angles are congruent

        -3x = -54

          x = 18°

9.  9x + 25 = 13x - 19          corresponding angles are congruent

            -4x = -44

               x = 11°

    13x - 19 + 17y + 5 = 180°        straight line adds up to 180°

    13(11) - 19 + 17y + 5 = 180

       143 - 19 + 17y + 5 = 180

                    17y + 129 = 180

                              17y = 51

                                  y = 3°

10.  6x - 7 + 3x - 29 = 180°     same side interior angles are supplementary

                   9x - 36 = 180

                           9x = 216

                             x = 24°

     6x - 7 = 8y + 17                   vertical angles are congruent

      6(24) - 7 = 8y + 17

         144 - 7 = 8y + 17

               137 = 8y + 17

               120 = 8y

                  y = 15°

11.  49 + 3x = 7x - 23                corresponding angles are congruent

            -4x = -72

               x = 18°

 

      3x = 11y - 1                         corresponding angles are congruent

      3(18) = 11y - 1      

          54 = 11y - 1

          55 = 11y

            y = 5°

12.  5x - 38 = 3x - 4                alternate interior angles are congruent

             2x = 34

               x = 17°

 

      7y - 20 + 5x - 38 + 90 = 180°        sum of triangle interior angle equals 180

      7y - 20 + 5(17) - 38 + 90 = 180°      

      7y - 20 + 85 - 38 + 90 = 180°    

                              7y + 117 = 180

                                      7y = 63

                                       y = 9°

what is the answer to this?​

Answers

Answer:

[tex] < 1 = 48[/tex]

Step-by-step explanation:

[tex] < 1 + 132 = 180[/tex]

[tex] < 1 = 180 - 132[/tex]

[tex] < 1 = 48[/tex]

because it's a straight angle(180)

Un agricultor tiene una finca de una hectárea la mitad le dedica a cultivar tomates los 2/5 lo dedica a lechugas y el resto cebollas. A qué fracción dedicará cebollas. B qué superficie dedica a cada cultivo.

Answers

The given area of the farm, A_0=1 hectare.

The fraction of the farm for cultivating tomatoes = 1/2

The fraction of the farm for cultivating lettuce = 2/5

The remaining fraction of farm for onion = 1-(1/2+2/5)=1/10

Therefore, the fraction of farm dedicated to onion is 1/10.

Now, the area dedicated to tomatoes = 1/2 of the area of land.

=1/2 x 1 = 1/2 hectare.

The area dedicated to lettuce = 2/5 of the area of land.

=2/5 x 1 = 2/5 hectare.

The area dedicated to onion = 1/10 of the area of land.

=1/10 x 1 = 1/10 hectare.

plz help me with this homework i have

Answers

the answer is D i’m pretty sure
i’m also pretty sure that it’s d, i’m not the best at it though but that’s the one i got

A zoo has the ratio to zebras (1 giraffe for every 4 zebras) What percent of this grouping of animals are giraffes? What percent of this grouping are zebras?

Answers

Answer:

20% of the animals are giraffes

80% of the animals are zebras

=====================================

Explanation:

Let's say there are 5 animals. This would mean there's 1 giraffe and 4 zebras, since we have four zebras per giraffe.

The percentage of giraffes is 1/5 = 0.20 = 20%

and the percentage of zebras is 4/5 = 0.80 = 80%

The requried percentage of giraffes is 20% and the percentage of Zebras is 80%.

What is the Ratio?

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

What are percentages?

the percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,

A zoo has the ratio to zebras (1 giraffe for every 4 zebras)
The total proportion of the zebras and giraffes = 5,
Percentage of giraffe = 1 / 5 × 100% = 20%
Percentage of zebras = 4 / 5 × 100% = 80%

Thus, the requried percentage of giraffes is 20% and the percentage of Zebras is 80%.

Learn more about percentages here:

brainly.com/question/13450942

#SPJ5

Plz help This is a very important thing I have to do and it depends 50% of my grade so please help...!

Answers

Answer:

A.B

Step-by-step explanation:

5 - sqrt1.35 =  ~3.8

A) 3 / sqrt2 = ~2.1

B) 5 / sqrt3 = ~2.9

C) 3 + 2sqrt2 = ~5.8

D) 4 + 8/sqrt50 = ~5.1

A simple off bacteria is debating according to the half life model. If the simple begins with 800 bacteria, and after 18 minutes there is 240 bacteria, after how many minutes will there be 40 remaining

Answers

Answer:

After 43 minutes, the bacteria will be 40 remainings.

Step-by-step explanation:

Given that:

Initial population of bacteria [tex]A_o[/tex] = 800

After time (t) = 18 mins

A = 240

Using the model:

[tex]A = A_o e^{k*t}[/tex]

[tex]240=800 e^{k*18}[/tex]

[tex]\dfrac{240}{800}= e^{18k}[/tex]

[tex]0.3= e^{18k}[/tex]

By applying natural log on both sides, we get:

In(0,3) = 18k (In e)

- 1.20397 = 18 k * (1)

18 k = -1.20397

k =  -1.20397/ 18

k = - 0.06688

k ≅ -0.07

After time (t), the bacteria population (A) = 40

Now;

[tex]40 = 800 e^{k*t}[/tex]

[tex]\dfrac{40 }{800}= e^{-0.07*t}[/tex]

[tex]0.05= e^{-0.07*t}[/tex]

In (0.05) = -0.07t * In (e)

- 2.9957 = - 0.07t

t = - 2.9957/ -0.07

t = 42.795

t ≅ 43 minutes

Thus, after 43 minutes, the bacteria will be 40 remainings.

What is that "break even" cost? *

Answers

Answer:

$61

Step-by-step explanation:

When each company sells 6 shirts, they have $48 (CS) and $45 (TT). When you add their shipping prices, they both have $61.

Jordan is knitting a sweater. He keeps track of how many balls of green and yellow yarn he uses in the table below.
If he uses 15 balls of yellow yarn, how many balls of green yarn will he need?

Answers

Answer:

the answer is B i think ..............

10
Because if you divide the x column by the y column you get 0.666666666667 (a lot of 0s basically) and 10/15 gets you the same answer

How many five card hands can
be dealt from a standard deck of
52 cards?

Answers

Answer:

2

Step-by-step explanation:

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