[tex] \frac{1}{ \sqrt{7} -(- 2)} \\ rationalizing \: \: \: the \: \: \: denominator \: \: \: we \: \: \: have \\ = \frac{1}{ \sqrt{7} + 2 } \times \frac{ \sqrt{7} - 2}{ \sqrt{7} - 2} \\ = \frac{ \sqrt{7} - 2}{ {( \sqrt{7} )}^{2} - {(2)}^{2} } \\ = \frac{ \sqrt{7} - 2 }{7 - 4} \\ = \frac{ \sqrt{7} - 2}{3} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
Given that:
1/(√7 - 2)
The denominator is (√7-2).
We know
The rationalising factor of (√a-b) is (√a+b)
Therefore, the rationalising factor of √7-2 is √7+2.
On rationalising the denominator them
⇛[1/(√7-2)]×[(√7+2)/(√7+2)]
⇛[1(√7+2)]/[(√7-2)(√7+2)]
Since, (a-b)(a+b) = a²-b²
Where, a = √7 and b = √2.
⇛[1(√7+2)]/[(√7)²-(2)²]
⇛[1(√7+2)]/[(√7*7)-(2*2)]
⇛[1(√7+2)]/[7-4]
⇛[1(√7+2)]/3
⇛(√7+2)/3
Hence, the denominator is rationalised.
also read similar questions:
At the movie theatre, child admission is $5.50 and adult admission is $8.90. On Friday four times as many adults tickets as child tickets were sold, for a total sales of $986.40. How many child tickets were sold that day?
Answer:
You can use grouping, quantity and value to solve this question.
Child admission = $5.50
Adult admission = $8.90
Friday sales (Quantity):
Child = x
Adult = 4x
Total sales = 5x
Friday sales (Value):
Child = $5.50
Adult = 4 × $8.90
= $35.60
Total sales = $986.40
1 group = $5.50 + $35.60
= $41.10
Number of groups = $986.40 ÷ $41.10
= 24
The number of child tickets sold is 24.
An angle measures 152° more than the measure of its supplementary angle. What is the measure of each angle?
° and
°
Answer:
14° and 166°
Step-by-step explanation:
Ok, so a supplementary angle is 180°.
Let's say one angle is x and the other angle is x+152.
We know these angles add up to a supplementary angle (180°) so...
x+(x+152)=180
x+x+152=180
2x+152=180
2x=28
x=14
So now we know one angle is 14°, we also know the other angle is x+152, knowing that x=14 we can plug it in 14+152= 166° for the other angle.
Hope this helps :)
what is the slope of the line of (4,6) and (-16,-18)
Hi!
To solve this, we simply use the equation shown in the image below:
What this means is the change in y over the change in x.
We use the two points and plug them in the equation like so:
[tex]\frac{6 - - 18}{4--16} =\frac{6+18}{4+16} =\frac{24}{20} =\frac{6}{5}[/tex]
Therefore your answer is [tex]\frac{6}{5}[/tex].
Hope this helps! Have a fantastic day! :D
Let me know if you need any other help.
Write an inequality to represent the graph.
у
(0, 2)
-3
- 2 - 1
7
8
9
10
0
-1
5 6
(4,-1)
-2
-3
-4
-5
-6
Answer:
The answer is i think(4,1)
Step-by-step explanation:
please help me somebody will
Answer:
66/54
Step-by-step explanation:
12*100 please do it im in a hurry
Answer: 1200
Step-by-step explanation:
12*100 = 1200
Add the two 0’s in 100 to the end of 12 and get 1200
PLS HELP ASAP ILL GIVE 5 STARS
Hey there!
(5 * 6) * 4
= 30 * 4
= 120
So you’re basically looking for something that’s equivalent to 120
CHOICE A.
5 * (5 * 6)
= 5 * 30
= 150
So, Choice A is probably NOT the answer you’re looking for!
CHOICE B.
4 * (5 * 6)
= 4 * 30
= 120
Choice B. is probably the answer you’re probably looking for.
So, I recommend you to color it apricot. :)
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
A grocery store sells a bag of 6 oranges for $4.38. What is the unit cost?
Answer:
$0.73
Step-by-step explanation:
Unit cost means per cost. Hence, divide 4.38 by 6 to find the cost of 1 orange.
4.38 ÷ 6
[tex]=\frac{4.38}{6}[/tex]
= 0.73
Therefore, the unit cost is 0.73 dollars.
help. i need itttttt
Answer:
In a parallelogram, opposite sides are the same length. If PR = ST, then the same would happen for the other sides.
Step-by-step explanation:
Help math if f(x) =
PLEASEEEEE MY LIFE DEPENDS ON THIS
I will send good fortune your way if you answer correctly (and points)
WILL MARK BRAINLIEST PLEASE HELP THIS IS DUE NOW AND NO LINKS!!!
First National Bank is offering 4.25% interest on an account. Susan makes an
initial deposit of $20,000. Calculate the interest camed over 20 years if the
bank...
a) Calculates the interest using simple interest (I -- Prt).
b) Calculates the interest using compound interest compounded annually.
c) Calculates the interest using compound interest compounded quarterly.
d) Calculates the interest using compound interest compounded monthly.
The simple interest earned is $17,000.
The interest earned with annual compounding is $25,978.13.
The interest earned with quarterly compounding is $26,583.59.
The interest earned with monthly compounding is $26,722.72.
The formula that can be used to determine simple interest is: principal x time x interest rate
$20,000 x 20 x 0.0425 = $17,000
The formula that can be used to determine the interest earned with compounding is: Future value - amount invested.
The formula that can be used to determine future value is:
FV = P (1 + r/m)^nm
FV = Future value
P = Present value
R = interest rate
m = number of compounding
N = number of years
Annual compounding = $20,000 x (1.0425)^20 = $45,978.13
Interest earned = $45,978.13 - $20,000 = $25,978.13
Quarterly compounding = $20,000 x (1 + 0.0425/4)^80 = $46,583.59
Interest earned = $46,583.59 - $20,000 = $26,583.59
Monthly compounding = $20,000 x (1 + 0.0425 /12) ^240 = $46,722.72
Interest earned = $46,722.72 - $20,000 = $26,722.72
To learn more about future value, please check: https://brainly.com/question/18760477
Compound interest compounded quarterly is given every ______ months. *
1 point
1
3
6
Compound interest compounded semiannually is given every ___ months. *
1 point
1
3
6
The algebraic equation for interest is______. *
1 point
y=mx+b
e=mc2
i=prt
Principal $2000, rate 3.1%, 2 months, compounded monthly. Calculate the balance at the end of 2 months. *
1 point
$2010.35
$2025.62
$2003.10
What is your favorite Christmas cookie? *
1 point
chocolate chip
sugar cookie
peanut butter
other
Calculate the simple interest earned: principal $1000, rate 4%, 7 days *
1 point
$10.00
$0.77
$23.33
How is compound interest similar to a snowball rolling down a snow covered hill? *
1 point
The interest rate used to calculate earned interest is represented as a percent. True or False *
1 point
True
False
First name *
Given the same principal, rate and time which investment calculation would earn less? *
1 point
simple interest
compound interest
Last name *
Which word refers to the money deposited into an interesting bearing account ? *
1 point
cash
principal
bling
Answer:
3 months, 6 months, interest is 1 point or 0.01 for every percent, 2010.35, peanut butter but why is this a question, 0.77, It is similar to a snowball because as time goes on the account grows at the same percent but it is more money so it is a larger amount. This is very common in dividend investing. next question, yes it is a percent, simple because compound is always more or the same, I would say principal but I am not sure
Step-by-step explanation:
Complete the point-slope equation of the line through -8,1 and -6,5
Answer:
y+1=3(x+8)
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(5-(-1))/(-6-(-8))
m=(5+1)/(-6+8)
m=6/2
m=3
y-y1=m(x-x1)
y-(-1)=3(x-(-8))
y+1=3(x+8)
PLEASE HELP! WILL MARK BARINLIEST IF ANSWER CORRECTLY (Screenshot)
Answer:
14
Step-by-step explanation:
3+3+4+4 = 14
solve each system of linear equations 3x+y=9, 7x+y=32
Answer:
x=23/4, y=-33/4
Step-by-step explanation:
3x+y=9
7x+y=32
3x+y=9
y=9-3x
7x+y=32
7x+(9-3x)=32
7x+9-3x=32
4x+9=32
4x=23
x=23/4
3x+y=9
3(23/4)+y=9
69/4+y=9
y=-33/4
The solution set to the given system of linear equations is -
{x} = 5.75 and {y} = - 8.25.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a system of linear equations as -
3x + y = 9
7x + y = 32
We can write -
3x + y = 9
y = 9 - 3x
Now, we can write the equation as -
7x + y = 32
7x + 9 - 3x = 32
4x + 9 = 32
4x = 23
x = 5.75 .... (1)
The, we can write {x} as -
y = 9 - 3 x 5.75
y = 9 - 17.25
y = - 8.25 ... (2)
Therefore, the solution set to the given system of linear equations is -
{x} = 5.75 and {y} = - 8.25.
To solve more questions on algebraic expressions, visit the link below -
brainly.com/question/1041084
#SPJ1
Convert 27 inches to feet in dimensional analysis .
Answer:
2.25 feet.
Step-by-step explanation:
Formula: divide the value in inches by 12 because 1 foot equals 12 inches.
So, 27 inches = 27 /12 = 2.25 feet.
Expand ; 3(1-x/2)^2
Answer:
[tex]3 {( \frac{1 - x}{2}) }^{2} = 3 \times {(1 - x)}^{2} \div {2}^{2} \\ =3 \times (1 - 2 \times 1 \times x + {x}^{2}) \div 4 \\ = 3 \times (1 - 2x + {x}^{2} ) \div 4 \\ = \frac{3}{4} (1 - 2x + {x}^{2})[/tex]
[tex] \bold \pink{ \underline{hope \: it \: helps}}[/tex]
The local movie theater, Scene It Cinema, had a special showing of the latest dinosaur movie. There were 6 youth tickets sold for every 5 adult tickets sold.
If there were 70 adult tickets sold, how many movie tickets were sold altogether?
Answer:
Let the youth and adult tickets be y and x respectively.
6y + 5x ---> (1)
From statement (1):
(1) × 14
84y + 70x
For every 70 adult tickets sold, 84 youth tickets were sold.
Total number of tickets sold= 70 + 84
= 154
twin oaks soccer field is a rectangle. The longer side of the field is 108 yards long. The shorter side is 56 yards long. What is the perimeter of the field?
Answer:
P = 328 yards
Step-by-step explanation:
formula is P= 2l + 2w
[tex]p = 2(108) + 2(56) \\ = 216 + 112 \\ = 328 \: yards[/tex]
Which graph represents the function?
Answer:
I believe it's the middle graph. since their is a closed dot on the first line and the other 2 inequality symbols indicate that their are 2 open dots, I think the middle is correct
What is the smallest number that is a multiple of both 4 and 6
Answer:
2
Step-by-step explanation:
4 2x2 is 4
2x3 is 6
sorry for the long type it says 20 character above
Mark’s birthday is 32 weeks away. How many days until his birthday?
I can write an equation
Answer: y = -x + 2
Step-by-step explanation:
If you are familliar with the point-slope form this is very helpful
Point-slope:
[tex]y-y_1=m(x-x_1)[/tex]
Plug in our values of [tex]m = -1, y_1=-1,x_1=3[/tex] to get:
[tex]y-(-1) = -1(x-3)[/tex]
Simplify
[tex]y+1=-x+3[/tex]
[tex]y=-x+2[/tex]
Is the sum of 3/5 and v13 a rational or Irrational number
Answer:
The sum of 3/5 and Square root of 13 is irrational. Since square root of 13 is irrational. And when you add it gives u irrational.
Guys please i need help on this, i will give brainliest to the right answers
Answer:
C) Discrete made up of individual points
The Gordon family plans to buy a TV. One TV has a purchase price of $330 and an estimated yearly operating cost of $14. The other has a purchase price of $369 and an estimated yearly operating cost of $9. Which TV should the Gordons buy if they plan to keep it for 8 years
The graph of an equation with a negative discriminant always has which characteristic?
Answer:
answer below
Step-by-step explanation:
equation with a negative discriminant: negative number under the square root
1. will produce imaginary number "i"
2. the function will get two complex solutions
what is 345.543 multyply by 46.34 devide by 666.89 ???? help faster 3 minutes remaining
Answer:
24.010
Step-by-step explanation:
hope it helps
Help me with these worksheets pls
Anything would help BUT PLS ANSWER IT CORRECTLY, If you don't know, just IGNORE THIS AND DON'T JUST COME FOR THE POINTS.
Answer:
1. yes
2.no
3.yes
4.no
5.yes
