The denominator now becomes a rational number, and we have rationalized the denominator.
To rationalize a denominator means to eliminate any radicals or square roots from the denominator of a fraction. The process of rationalizing the denominator can involve different techniques, depending on the structure of the denominator.
In general, there are three common methods for rationalizing the denominator:
Multiplying both the numerator and the denominator of the fraction by the conjugate of the denominator.
Using the square root property to simplify the denominator.
Simplifying the fraction by factoring the denominator and canceling common factors.
Let's consider an example:
Suppose we have the fraction 5/√2.
To rationalize the denominator, we need to eliminate the radical from the denominator. One way to do this is to multiply both the numerator and the denominator by the conjugate of the denominator, which is √2.
To see why this works, recall that the product of the sum and difference of two terms is equal to the difference of their squares:
[tex](a + b)(a - b) = a^2 - b^2[/tex]
In our case, if we multiply 5/√2 by (√2)/(√2), we get:
5/√2 × (√2)/(√2) = (5√2)/2
The denominator now becomes a rational number, and we have rationalized the denominator.
It's worth noting that in some cases, we may need to simplify the denominator further by using the square root property or factoring the denominator. But in this case, multiplying by the conjugate is sufficient to rationalize the denominator.
for such more question on rational number
https://brainly.com/question/19079438
#SPJ11
!!!!!!PLEASE HELP WILL GIVE BRAINLIEST!!!!!!!
which of the following is a irratinol number
A. 1 squared
B. 41 squared
C.- 9 squared
D.-64 squared
Helpppp?? I need help on this cause I just don’t wanna solve it
Answer:
3 and 3/5
Step-by-step explanation:
Martha spent $12.35 at the local farmer's market. She bought 3 bundles of collards and paid $4.30 for some fruit. How much did each bundle of collards cost?
Answer:
12.35-4.30=8.05
8.05÷3= 2.68333333333333....
≈2.68
A rental car company offers a rental package for a mid-size car. The cost is comprised of a fixed \$ 40$40 administrative fee for the cleaning and maintenance of the car plus a rental cost of \$ 45$45 per day. Using xx for the number of days and yy for the total cost in dollars, construct a linear function to model the relationship between the number of days and the total cost of renting a mid-size car.
Answer:
y = 40 + 45x
Step-by-step explanation:
Fixed administrative fee for the cleaning and maintenance of the car = $40
rental cost = $45 per day
x = number of days
y = total cost in dollars
y = 40 + 45x
This shows the relationship between the number of days and the total cost of renting a mid-size car.
PLZ HELP!!! WILL GIVE HIGHEST POINTS IF THE ANSWER IS CORRECT!!!
Answer: -5 Hope this helps :)
Step-by-step explanation:
Brainlist Plz?
what is the HCF prime factorization of 30 and 36
Answer:
We found the factors and prime factorization of 30 and 36. The biggest common factor number is the GCF number. So the greatest common factor 30 and 36 is 6.
Step-by-step explanation:
help me please!!!!!!!!!!!!!!!!
mr. russell questions:
1: false.
2: false.
3: true
4: false.
5: true.
the last question: D.
The speed limit on a road is 45 mph what is the rate in miles per minute
The rate in miles per minute is 320
Julie has $80,000 to invest. She invests part at 5%, one fourth this amount at 6%, and the balance 7%. Her total annual income from interest is $4,700. Find the amount invested at each rate.
Answer:
Julie invested $ 25,000 at 7%, $ 20,000 at 6%, and $ 35,000 at 5%.
Step-by-step explanation:
Given that Julie has $ 80,000 to invest, and she invests part at 5%, one fourth this amount at 6%, and the balance 7%, knowing that her total annual income from interest is $ 4,700, to find the amount invested at each rate se you must perform the following calculation:
80,000 / 4 = 20,000
20,000 x 0.06 = 1,200
4,700 - 1,200 = 3,500
60,000 x 0.07 + 0 x 0.05 = 4,200
50,000 x 0.07 + 10,000 x 0.05 = 4,000
40,000 x 0.07 + 20,000 x 0.05 = 3,800
30,000 x 0.07 + 20,000 x 0.05 = 3,600
25,000 x 0.07 + 35,000 x 0.05 = 3,500
Thus, Julie invested $ 25,000 at 7%, $ 20,000 at 6%, and $ 35,000 at 5%.
Can someone help me with this answer thank you
Answer: bro cmon this is simple m8 but i will still help :D
Step-by-step explanation:35x3=105 and 28x5=140 the outfit couldve been 245 dollars in total!
Please I need this now
Whoever can answer this I will make a brainliest
Answer:
djchdjcycuchrivivurtiytvivytivi8fr cgdyhcd8w
Work out
51.43% of 377.59cm
Give your answer founded to 2 DP
Answer:
194.194537 centimeters
Step-by-step explanation:
Answer:
194.19cm
Step-by-step explanation:
yeah yeah yeah yeah
Someone help please!
X+3y=-7 5x+6y=-8
Step-by-step explanation:
I have used substitution method here to find the value of x and y.
Let
cos
(
2
∘
)
≈
0.9994
What is the the value of
x
, in degrees, for
sin
(
x
)
≈
0.9994
?
Answer:
can write it again soon as you can do it again
In circle O, AC and BE are diameters. The measure of arc DC is 50°. What is the measure of EBC?
Answer:
The angle measure would be 40°
Step-by-step explanation:
Right angles have a measure of 90. Since DC is 50, 90-50 is 40.
The angle measure of ∠EBC would be 40°.
What is arc?The arc is a portion of the circumference of a circle
Right angles have a measure of 90°.
∵∠BOD=90°
Since ∠DC is 50°,
∠EBC = ∠BOD-∠DC
∠EBC = 90°-50° is 40°.
The angle measure of ∠EBC would be 40°.
learn more about arc of circle
https://brainly.com/question/1577784
#SPJ2
Gambarlah sebuah lingkaran dengan jari jari 2,5 cm. Lalu gambarlah 3 buah sudut keliling yg menghadap busur yang sama
Step-by-step explanation:
isidhxibdofeixeosgzifisvsoshzibdihddgd
A wire is attached to the top of a tower and to a point on the ground that is 35 m from the base of the tower. If the wire makes a 65 degree angle with the ground, how long is the wire? Round your answer to the nearest tenth.
Answer:
83
Step-by-step explanation:
The length of the wire is 83meter.
Given that,
A wire is attached to the top of a tower and to a point on the ground that is 35 m from the base of the tower.
If the wire makes a 65-degree angle with the ground.
We have to determine,
How long is the wire?
According to the question,
The computation of the length of the wire is shown below:
Let, the length of the wire be x,
There is 35m from the base of the tower,
And, the angle with the ground is 65 degree
Therefore,
The length of the wire is given by,
[tex]cos65 = \dfrac{35}{x}\\\\[/tex]
Substitute the value of cos65 in the equation,
[tex]cos65 = \dfrac{35}{x}\\\\x = \dfrac{35}{cos65}\\\\x = \dfrac{35}{0.42}\\\\x = 83.33 \ meter[/tex]
Hence, The length of the wire is 83meter.
To know more about Trigonometry click the link given below.
https://brainly.com/question/14418346
I dont understand the work my teacher gave me and I Have 45 pages to do
Answer:
just send them here , I will answer the ones I know .
3.5 m = ______cm
PLEASE HELP ME!!!!!!!
Answer:
Formula *10
Step-by-step explanation:
35
Determine which fraction is smallest given 21/64, 5/16, 11/32, 1,2
Find the measure of each angle in the angle pair described.
The measure of one angle is twice the measure of its supplement. What are the measures of the two angles?
Answer:
The best way to measure an angle is to use a protractor. To do this, you'll start by lining up one ray along the 0-degree line on the protractor. Then, line up the vertex with the midpoint of the protractor. Follow the second ray to determine the angle's measurement to the nearest degree
I REALLY NEED HELP!!! THIS IS DUE AT 12!!!
Jeremiah scored 32 points in yesterday’s basketball game. He made a total of 19 baskets.Some of the baskets were field goals (worth two points) and the rest were free throws (worth one point). Write and solve a system of equations to find the number of field goals and the number of free throws that Jeremiah made. Let x represent Field Goals and y represent Free Throws.
Answer:
x=16
y=3
Step-by-step explanation:
32÷2=16
19-16=3
x=16
y=3
The points L, M, N and O all lie on the same line segment, in that order, such that the ratio of LM:MN:NOLM:MN:NO is equal to 3:1:2.3:1:2. If LO=30,LO=30, find LN.LN.
Answer:
[tex]|LN| = 24[/tex]
Step-by-step explanation:
Given
[tex]LM:MN:NO = 3:1:2[/tex]
[tex]LO = 30[/tex]
Required
Find LN
[tex]LN = LM + MN[/tex]
From the ratio, LM = 3 and MN = 1
So:
[tex]LN = 3 + 1[/tex]
[tex]LN = 4[/tex]
LN and NO can be represented as:
[tex]LN : NO = 4 : 1[/tex]
The length of LN is then calculated as:
[tex]|LN| = \frac{LN}{LN+NO}*|LO|[/tex]
[tex]|LN| = \frac{4}{4+1}*30[/tex]
[tex]|LN| = \frac{4}{5}*30[/tex]
[tex]|LN| = \frac{4*30}{5}[/tex]
[tex]|LN| = \frac{120}{5}[/tex]
[tex]|LN| = 24[/tex]
Two siblings' ages have a sum of 64 years. The older sibling was born 6 years before their young sibling.
Write a system of 2 equations. Solve the system using substitution. Report your answer in the form of (older, younger).
Hi!
So we have to make a system of equations here.
Let sibling 1 be O and sibling 2 be Y (for older and younger)
So:
O + Y = 64
O = 64 - Y
(Either one works)
The older sibling is 6 years older.
O = Y + 6
Make everything in terms of Y.
64 - Y = Y + 6
Same to both:
58 = 2y
2y = 58
Divide by 2 on both sides:
y = 29
Since the older sibling is 6 years older:
29 + 6 = 35
Y = 29
O = 35
Let me know if you have any questions.
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket
Answer:
senior citizen tickets are $10 and child tickets are $8
Answer:
senior is 10 and child is 8
Step-by-step explanation:
5+5-66564+6367347646-4848
Answer:
6367276244 6367276244
6367276244 6367276244
Answer:
6367276244
Step-by-step explanation:
survey of a company's employees explored the relationship between employee status and support of a new workplace safety policy The results are displayed in the following two-way frequency table. Workplace Safety Policy For Against Total Part-Time
Employee 20 60 80 Full-Time Employee 100 20 120 Total 120 BO 200 used on the table above, which of the following statements are true? There are twice as many part-time employees against the workplace safety policy than full-time employees against the workplace safety policy IL There are more employees for the workplace safety policy than against the workplace safety policy There is an equal number of part-time employees and full-time employees.
Answer:
ll and lll
Step-by-step explanation:
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! ASAPPPP
DIVIDING EXPONETS
Answer:
[tex]-0.5n^{4}[/tex] or [tex]-\frac{1}{2} n^{4}[/tex]
Step-by-step explanation:
To simplify a dividing exponent, use the "Quotient of Powers" law: [tex]\frac{a^{m} }{a^{n} } = a^{m-n}[/tex]. In this situation, the equation would be: [tex]\frac{-9}{18} n^{6} -n^{2}[/tex] or [tex]-0.5n^{4}[/tex] (-0.5 is also [tex]-\frac{1}{2}[/tex]).
Hope it helps and is correct!
PLEASE HELP WILL MARK BRAINLY
Use a ratio box to solve this problem: Five hundred fifty students attended the assembly. If the ratio of boys to girls in the assembly was 6 to 5, how many girls attended the assembly?
Answer:
250 girls
Step-by-step explanation:
Please let me know if you want me to write an explanation for my answer :)
What’s 12 times 12divided by 58 ?
Answer:
2.48........is your answer
Step-by-step explanation:
12×12 =144
144÷58