Rationalize the denominator!
Question in the picture

Rationalize The Denominator! Question In The Picture

Answers

Answer 1

Answer:

A

Step-by-step explanation:

[tex]\frac{10}{9+\sqrt{7} }[/tex]

To rationalise the denominator multiply the numerator and denominator by the conjugate of the denominator.

the conjugate of 9 + [tex]\sqrt{7}[/tex] is 9 - [tex]\sqrt{7}[/tex]

= [tex]\frac{10(9-\sqrt{7}) }{(9+\sqrt{7})(9-\sqrt{7}) }[/tex] ← expand denominator using FOIL

= [tex]\frac{90-10\sqrt{7} }{81-7}[/tex]

= [tex]\frac{90-10\sqrt{7} }{74}[/tex] ( divide terms on numerator/ denominator by 2 )

= [tex]\frac{45-5\sqrt{7} }{37}[/tex] → A

Answer 2

Answer:

A[tex]\frac{45-5\sqrt7}{37}[/tex]

Step-by-step explanation:

Easy. First let's multiply numerator and denominator by [tex]9-\sqrt7[/tex] since we will create a difference of squares to get rid of the root, then start doing the calculations

[tex]\frac{10(9-\sqrt7)}{(9+sqrt7)(9-\sqrt7)}=\frac{10(9-\sqrt7)}{81-7} = \frac{10(9-\sqrt7)}{74} =\\\frac{5(9-\sqrt7)}{37}=\frac{45-5\sqrt7}{37}[/tex]


Related Questions

HELP MY GRADE 9 PLS AND THANK YOU

Answers

Answer:

64x²y²

Step-by-step explanation:

Use the great smart calculator

hope it helpz uuuuuuu

Hey would really appreciate the help!

Answers

Answer:

a. (2c+1b)-1w

b. monomial

Step-by-step explanation:


what’s the answer and how did you get it? please help

Answers

Answer:

1/m^5

Step-by-step explanation:

express with a positive exponent using x^-n = 1/x^n

Answer:

[tex]c)\: \cfrac{1}{m^5}[/tex]

Step-by-step explanation:

[tex]m^{-5}[/tex]

Apply the exponent rule:

[tex]m^{-5}[/tex]

[tex]\cfrac{1}{m^5}[/tex]

Hope it helps! :)

8x3+26x2+19x+3 is divided by 4x+3

Answers

Answer:

Remainder=35.25

Quotient = 2x²+8x+10.7

HELPPPP THIS IS SO HARD

Answers

Answer:

  T'''(2, 6)

Step-by-step explanation:

The transformations used in this problem are ...

  (x, y) ⇒ (-x, -y) . . . . . rotation 180° about the origin

  (x, y) ⇒ (x +h, y +k) . . . . translation h right and k up

  (x, y) ⇒ (y, x) . . . . . . reflection over the line y=x

__

Applying these transformations to point T(-5, -4), we have ...

1.  T(-5, -4) ⇒ T'(5, 4)

2. (h, k) = (1, -2), so we get ...

  T'(5, 4) ⇒ T"(5 +1, 4 -2) = T"(6, 2)

3. T"(6, 2) ⇒ T'''(2, 6) . . . . straightforward application of the separate transformations

Choose the correct product of (7x − 6)2. 49x2 84x 36 49x2 − 36 49x2 36 49x2 − 84x 36.

Answers

Answer:

the answer for this question is 49x²-84x+36

hope it helps

Answer:49x²-84x+36

Step-by-step explanation:

the Nth term of a geometric sequence is given by this equation, solve it and show ALL of your steps. 4 through 7

Answers

Answer:

I dont know the answers but here is an example( look at screenshots)

Step-by-step explanation:

The points F(4,
-2), G(9,
-6), H (8, -1), and I (5, 2) form a quadrilateral. Find
the desired slopes and lengths, then fill in the words that BEST identifies the type of
quadrilateral.

(PICTURE BELOW)

Answers

slope of GH

and

lenght of FG

Tamika swims 2 7/10 kilometers a day,

4 days a week. How far does she swim

each week? Find 4 x2 7/10

Answers

she swims 10.8, according to calculator

A square has a perimeter of 39.6 millimeters. What is the length of each side?​

Answers

Answer:

9.9 millimeters

Step-by-step explanation:

To find the perimeter of a square,

Equation: 4 • length = P

So in this case, we're just working backwards. To find the length, divide.

39.6/4 = 9.9

Answer:

9.9 mm

Step-by-step explanation:

let [tex]x[/tex] = length of one edge of the square

perimeter of a square = 4[tex]x[/tex]

⇒ 39.6 = 4[tex]x[/tex]

⇒ [tex]x[/tex] = 39.6 ÷ 4 = 9.9 mm

Rita had only $5.00 in her piggy bank, and she decided to start saving more. She saves $5.00 every 6 days. After how many days will she have $30.00 in the piggy bank

Answers

Answer:

30 days

Step-by-step explanation:

she starts with $5, so she needs $25 more to have $30.

if she saves $5 ever six days, she needs to do this five times to reach $30.

6*5=30

good luck :)

24 days
dollars 5x6payments=30$ overall payments6-2 payments she already made =4 4needed payments•6days between payments=24

Which expression is equivalent to the following complex fraction?

Answers

Answer:

The answer is 2y -1 over 3y+1 ( last multiple choice)

Step-by-step explanation:

- move the y's beside the 3 and 2 to get rid of the 1/y fraction

y=28(0.25)^x WHAT IS THE FREAKING PERCENT? Thank you! <3?

Answers

Answer:

75%

Step-by-step explanation:

You go to a restaurant and have $45 to spend. You get a drink for $3.00 and an appetizer for
$11. How much can you spend on the rest of your meal and still be able to a 20% tip and 7%
tax? Show the equation you set up and the steps how you find the amount you can spend.

Answers

Answer:

if the tip is 20% and 7%, it means that the meal MUST cost less than 32.85.

the reason behind this is that if we have $45 to spend it means that each 1% is 0.45 and 0.45x27=12.15 meaning that if we subtract this from $45 we get 32.85.

Now we have already spent $14 on our drink and appetizer so 32.85-14=18.85 we can only spend 18.85 on our meal


9. Which set of ratios below is NOT equivalent
to 3:4?
the
bu
A. 6 to 9,
q
12
B.) 9 to 12, 20
15

Answers

Answer:

A

Step-by-step explanation: {reduction}

{[tex]\frac{2X3}{3X3}=\frac{2}{3}[/tex]} {[tex]\frac{3X3}{3X4}=\frac{3}{4}[/tex]}

A. 6 to 9 7'5 [tex]\frac{6}{9}=\frac{2}{3} , \frac{9}{12}=\frac{3}{4}[/tex]

{[tex]\frac{3X3}{3X4}=\frac{3}{4}[/tex]}

B. 9 to 12 7'5 [tex]\frac{9}{12}=\frac{3}{4} , \frac{15}{20}=\frac{3X5}{4X5}=\frac{3}{4}[/tex]

C. [tex]\frac{15}{20}=\frac{3}{4} ,[/tex] 24 = 32 = 3 × 8: 4 ×8 = 3 = 4

D. [tex]\frac{30}{40}=\frac{3X10}{4X10}=\frac{3}{4} , 18:24=3X6=4X6=3:4[/tex]

choose A

Two fair 6 sided number cubes are rolled. What is the probability of rolling a sum of 11?

Question 3 options:

1/6

1/36

1/18

11/36

Answers

Draw a sample space diagram showing the sum of rolling two dice. It should be 6 rows by 6 columns therefore there are 36 different outcomes possible.
There are two ways to make a sum of 11: 5,6 or 6,5. This means that the probability is 2/36 which equals 1/18.

8 and 9 plus explanation pls

Answers

Answer:

42

Step-by-step explanation:

What is the volume of this sphere? Use 3. 14 for pi and round to the nearest hundredth when necessary. 50. 24 m³ 267. 95 m³ 1607. 68 m³ 2143. 57 m³.

Answers

Volume of a figure is the measurement of space occupied by the figure. The volume of the specified sphere is given by Option B: 267. 95 m³

What is the volume of sphere?

If the given sphere is of radius r units, then its volume is given as:

[tex]V= \dfrac{4}{3} \pi r^3 \: \rm unit^3[/tex]

For the given sphere, its diameter is 8 units, thus, its radius is half of its diameter and thus, of 4 units.

Thus, volume of specified sphere is obtained as:

[tex]V= \dfrac{4}{3} \pi r^3 \: \rm unit^3\\\\V = \dfrac{4}{3} \pi (4)^3 =\dfrac{256}{3} \times 3.14 \approx 267.95 \: m^3[/tex]

Thus,

Volume of a figure is the measurement of space occupied by the figure. The volume of the specified sphere is given by Option B: 267. 95 m³

Learn more about volume of sphere here:

https://brainly.com/question/381274

How do I do this? Please help!

Answers

I already answered this question, if you look back in your questions you should find this answered along with another one. I'll do it again just in case you don't find it.

Answer:

{y,x} = {-4,-2}

Expanation:

Solve by Substitution :

// Solve equation [1] for the variable  y

 [1]    y = 2x

// Plug this in for variable  y  in equation [2]

  [2]    -2•(2x) - 8x = 24

  [2]     - 12x = 24

// Solve equation [2] for the variable  x

  [2]    12x = - 24

  [2]    x = - 2

// By now we know this much :

   y = 2x

   x = -2

// Use the  x  value to solve for  y

   y = 2(-2) = -4

Math asap!! Will give brainliest

Answers

Step-by-step explanation:

line QS = RS

line KJ = half of line KC

A small school employs 5 teachers who make between $40,000,and 70,000 per year.
The newest teacher, Valerie, decides to teach part-time which decreases her salary from 40,000 to 20,000 per year. The rest of the salaries stay the same.
How will decreasing Valerie's salary affect the mean and median?
HELP PLEASE

Answers

Answer:

Its B

Step-by-step explanation:

No of teachers in the school = 5

Salaries they make =40000 to 70000

When one of the five teachers reduce salary to 20000/- per year, median may or may not shift one number to the left

Mean will definitely decrease by difference/5 = 4000 dollars

Thus mean will defintely change by reduction of 4000 dollars.

Median has a chance to remain the same or may shift left side one item.

.i need help w this pls!!​

Answers

The answer is x-y
——. Tried to make it look like a
y Fraction
If you can’t read it like that then x-y / y

For simplifying this fraction, let first consider it as

[tex]{:\implies \quad \sf \dfrac{x}{y}-1}[/tex]

If we take LCM, and simplify it further, we will be having ;

[tex]{:\implies \quad \sf \dfrac{x\cdot 1-1\cdot y}{y}}[/tex]

[tex]{:\implies \quad \boxed{\bf{\dfrac{x-y}{y}}}}[/tex]

This is the required answer

helpp pleacee??!!!!!

Answers

Answer:

9

Step-by-step explanation:

I need to write 20 characters

In​ basketball, some baskets are worth two points. Others are worth three points. In one​ game, the ratio of​ three-point baskets to​ three-point tries for one team was 3 : 4. If the team scored 27 points from​ three-point baskets, how many​ three-point tries did the team​ have?

Answers

Answer:

Writing the information in the form of ratio

Three point basket = Three point tries

3 : 4

27 : x

Think about multiplication , how many 3s do you need to make 27 ?

Its 27 ÷ 3= 9

Because you need 9 lots of 3, Then to make it proportional , you'd need 9 lots of 4

9×4 = 36

Three points tries is 36

If f(x)= x^2-25 and g(x)=x-5, what is the domain of (f/g)(x)?

Answers

Answer:

B) all real values of x except x=5

Step-by-step explanation:

If [tex]f(x)=x^2-25[/tex] and [tex]g(x)=x-5[/tex], then [tex]\bigr(\frac{f}{g}\bigr)(x)=\frac{f(x)}{g(x)}=\frac{x^2-25}{x-5}=\frac{(x-5)(x+5)}{(x-5)}[/tex].

Given that [tex]x-5[/tex] exists in both the numerator and denominator, this creates a hole on the graph of the function where [tex]x=5[/tex] since [tex]5-5=0[/tex]all real values of x except x=5 is correct.

Review the attached graph for more information

A random sample of 24 corporate-owned stores finds an average number of customers of 313 with a standard deviation of 34.9. What is the upper bound of a 95% confidence interval for the average number of customers in corporate-owned stores

Answers

Answer:

95% is 1700 customers

Step-by-step explanation:

JK i actually dont know but thnks for the points BTW

what is 4.09 less than 5.6 ??

Answers

Answer: -1.51, or it could be 4.09 < 5.6 (Im sorry if I get it wrong I just wanted to help)

Step-by-step explanation:

The value of the subtraction is 1.51.

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given numbers are 4.09 and 5.6. The value of 4.09 less than 5.6 will be calculated as:-

Subtraction = 5.6 - 4.09

Subtraction = 1.51

Therefore, the value of the subtraction is 1.51.

To know more about an expression follow

https://brainly.com/question/25421984

#SPJ2

In the figure above, the measure of <BDE is 20 and CD is perpendicular to DE. What is the measure of <ADC ?​

Answers

Answer:

∠ ADC = 110°

Step-by-step explanation:

∠ CDE = 90° ( angle between perpendicular lines ) , then

∠ CDB + ∠ BDE = 90°

∠ CDB + 20° = 90° ( subtract 20° from both sides )

∠ CDB = 70°

∠ ADC and ∠ CDB are adjacent angles on a straight line and sum to 180° , so

∠ ADC + ∠ CDB = 180° , that is

∠ ADC + 70° = 180° ( subtract 70° from both sides )

∠ ADC = 110°

Solve the equation below pls show your work no links pls.
[tex](9^{2} )^{-1/3}[/tex]

Answers

Given :-

[tex](9^{2} )^{-1/3}[/tex]

To Find :-

To solve the expression .

Solution :-

Given expression to us is ,

[tex](9^{2} )^{-1/3}[/tex]

We know that ,

[tex] 9 = 3^2[/tex]

So our expression becomes ,

[tex]\{ (3^2)^2\}^{\frac{-1}{3}}[/tex]

And , [tex] (a^m)^n =a^{mn}[/tex] . Using this ,

[tex] (3^4)^{\frac{-1}{3}}[/tex]

Again using the same law ,

[tex] 3^{\frac{-4}{3}}[/tex]

We know that , [tex] a^{-m}=\frac{1}{a^m}[/tex] . Therefore ,

[tex] (3^{-4})^{\frac{1}{3}}[/tex]

[tex]\\\bigg( \dfrac{1}{3^4}\bigg)^{1/3}[/tex]

[tex]\\ \dfrac{1}{\sqrt[3]{3^4}}[/tex]

Simplify ,

[tex] \dfrac{1}{3\sqrt[3]{3}}[/tex]

This is the simplified expression.

I hope this helps.

Nick was surveying his field and saw some cows and ducks. Nick counted a total of 80 heads and
248 legs. Assuming there are no mutations in the animals, determine exactly how many ducks and cows he saw. Let
X represent the number of ducks and y represent the cows.
Total Equation:
Legs Equation:
How many ducks?
How many cows?

Answers

Answers:

Total equation:  x+y = 80Legs equation:  2x+4y = 248How many ducks? 36How many cows? 44

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

Further explanation:

x = number of ducksy = number of cows

x+y = 80 is the total equation (ie the head count equation) since we assume each animal has 1 head, and there are 80 heads total.

That equation can be solved to y = 80-x after subtracting x from both sides.

The legs equation is 2x+4y = 248 because...

2x = number of legs from all the ducks only4y = number of legs from all the cows only2x+4y = total number of legs from both types of animals combined

We're told there are 248 legs overall, so that's how we ended up with 2x+4y = 248

------------

Let's plug y = 80-x into the second equation and solve for x.

2x+4y = 248

2x+4( y ) = 248

2x+4( 80-x ) = 248

2x+320-4x = 248

-2x+320 = 248

-2x = 248-320

-2x = -72

x = -72/(-2)

x = 36

There are 36 ducks

Now use this x value to find y

y = 80-x

y = 80-36

y = 44

There are 44 cows.

------------

Check:

36 ducks + 44 cows = 80 animals total

36*2 + 44*4 = 72 + 176 = 248 legs total

The answers are confirmed.

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