[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:
Which group of numbers is listed from least to greatest?
0 -2,3,5,-8,9
0 -4, -6, -7,-8, -9
0 -2,-1, 0, 4,9
O 7,4, -6, -7, -9
Answer:
the third one
zero should always come after the negatives, and a whole number should always end the set.
Gary wants to buy a video game with a selling price of $48 on sale for 50% off. The sales tax in his state is 4.5%.
Answer:
$25.08
Step-by-step explanation:
$48 to which you apply the 50%
48/2= $24
then you add the sales tax:
24+4.5%= 25.08
What is the volume of a cylinder with a height of 13 and radius 6?
1470.27
v = pi r^2 (H)
v = 3.14 (6^2) (13)
v = 3.14 (36) (13)
v = 1470.27 (about)
Answer:
V = 1470
Step-by-step explanation:
V = πr²h
V = (3.14)(6²)(13)
V = (3.14)(36)(13)
V = 1469.52
if I set off for the market,a distance of 11km at 10am. And walk at an average speed of 3km per hour,At what time will I reach the market?
Answer:
At 1:40 pm you will reach the market.
Step-by-step explanation:
Distance (d) = 11 km
Average speed (v) = 3 km/h
Formula:
[tex] \rm Average \: speed = \dfrac{Distance}{Time} \\ \\ \rm 3 = \dfrac{11}{t} \\ \\ \rm t = \dfrac{11}{3} \\ \\ \rm t = 3 \frac{2}{3} \\ \\ \rm t = 3 hr \: 40min[/tex]
It will take 3 hours 40 minutes to reach the market.
So, if you set off for the market at 10 am you will reach market by 1:40 pm (10 am + 3hr 40min).
CAN SOMEONE HELP ME WITH THIS?
Answer:
d
Step-by-step explanation:
I WILL GIVE BRAINLEST HURRY PLEASE ITS DUE RIGHT NOW HURRY PLEASE plssss help me if your good at finding area in shapes plsss
07
Question 4
What is the 11th term of the geometric sequence
-1.5, -3, -6, -12, ...? /(5 pts)
Your Answer:
Answer:
-1536
Step-by-step explanation:
By taking the general formula for the geometric sequence, we substitute the variables with the values of our sequence, finding -1536 as the 11th term
Question 1: Whose percentage increased more from 1984 to 2014, males or females? By how much more did it increase?
My Answer: Between 1984 to 2014 males diagnosed with diabetes increased more than females. The number of males diagnosed with diabetes increased more than .9% compared to females.
Help my teacher said it was wrong
The percentage increase are applied to the number of male and female
from the previous period.
From 1984 to 2014, the percentage of females increased more than males.Reasons:
Let F represent the initial number of females and let M represent the initial number of males before 1984.
We have;
In 1984
Number of females = F × 1.026 = 1.026·F
number of males = M × 1.031 = 1.031·M
In 1994
Number of females = 1.026·F × 1.032 = 1.058832·F
Number of males = 1.031·M × 1.032 = 1.063992·M
In 2004
Number of females = 1.058832·F × 1.056 = 1.118126592·F
Number of males = 1.063992·M × 1.049 = 1.116127608·M
In 2014
Number of females = 1.118126592·F × 1.066 = 1.191922947072·F
Number of males = 1.116127608·M × 1.059 = 1.181979136872·M
Therefore, between 1984 and 2014, we have;
The percentage increase of females = 1.191922947072 × 100 - 100 ≈ 19.2%
The percentage increase of males = 1.181979136872 × 100 - 100 ≈ 18.2%
Therefore;
The percentage increase of the females is more than the males by (1.191922947072 × 100 - 100) - (1.181979136872 × 100 - 100) ≈ 0.994%
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Please look at picture for question.
Answer:
A 1.5
B -1/3
C -4/3
Step-by-step explanation:
I solved this by remembering...
numbers above 0 are positive
-1/3 is greater than -1
-4/3 means -1 AND 1/3 so this is less than -1
A = 1.5 (+ve value, upwards)
B = -1/3 (-ve value, downwards)
C = -4/3 (-ve value, downwards)
A = 1.5 (lies in between +1 & +2)
B = -1/3 (-0.33 lies in between 0 & -1)
C = -4/3 (-1.33 lies in between -1 & -2)
See the attached picture for more details.
______
Hope it helps ⚜
3(x+9)-4x=11x-13x+23
Answer:
[tex]\huge\boxed{x=-4}[/tex]
Step-by-step explanation:
[tex]3(x+9)-4x=11x-13x+23\\\\(3)(x)+(3)(9)-4x=(11x-13x)+23\\\\3x+27-4x=-2x+23\\\\(3x-4x)+27=-2x+23\\\\-x+27=-2x+23\qquad|\text{subtrsact 27 from both sides}\\\\-x=-2x-4\qquad|\text{add}\ 2x\ \text{to both sides}\\\\x=-4[/tex]
How do I solve this? 2(-2w-1.2+7x)
what is the area and perimeter of the figure with the given vertices? (7,8) , (-5, -8) , (7,-8) , (-5,8)?
Answer:
perimeter: 56 unitsarea: 192 square unitsStep-by-step explanation:
We assume you're interested in the convex polygon, so the given vertices are not listed in order around the figure.
The figure is 12 units by 16 units, so has a perimeter of ...
P = 2(L +W)
P = 2(16 +12) = 56 . . . . units
and an area of ...
A = LW
A = (16)(12) = 192 . . . . square units
Suppose that you have $1500 to spend on fencing for your rectangular yard. The fence meets with your
house on one side, so you only need to fence three sides of the rectangle. The sides touching the house
will be equal in length, call these lengths x feet. And label the length of the third side y feet. Fencing
costs $57 per foot.
a. Write a function that expresses total fence cost as a function of x and y.
b. Write a function that expresses the total area as a function of x and y.
c. Write a function that expresses the total area as a function of x only. Assume that you want to
spend as much of that $1500 as you can.
d. Graph the result of c and past below. Be sure to include where the function reaches a maximum.
The cost function of the rectangular yard is 114x + 57y = 1500
Let x represent the length of the rectangular yard and y represent the width of the rectangular yard.
Since you need to fence only 3 sides, hence:
2x + y = Perimeter
Each foot cost $57 per foot and there is $1500 to spend, hence:
2x(57) + y(57) = 1500
114x + 57y = 1500
y = (1500 - 114x) / 57
The area (A) of the rectangular yard is:
A = x * y
A = xy
A = x[(1500 - 114x) / 57)
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If a rectangle has a base of 6' and a height of 4' its area would be what?
A= bxh
A= 6'x4'
A= 24 sq.ft.
I am confused, can someone help me
Answer:
bc=10
Step-by-step explanation:
12/bc=18/(33-18)
12/bc=18/15
18bc=12*15
18bc=180
bc=180/18
bc=10
A pianist charges $200 to perform at a restaurant. At the end of the night she collected her tips and left with a total earning of $310. Write an equation and solve for the amount she made in tips for the performance.
Answer:
310-200= T
Step-by-step explanation:
310 = 200 + x
Let’s break this down. 310 is their total earning, 200 is our set price for performing, and x represents how much she earned in tips.
310 = 200 + x
110 = x
Hope this helps!
A middle school had a school spirit day. In one class the ratio of students who wore school colors to the number of students who didn’t was 8 to 5. Ten students didn’t wear school colors
Answer:
Step-by-step explanation:
What multiplier would you use to decrease a value by 44%
Answer:
I think the answer is4k3+0 or 4
The instructions for mixing a powdered cleaner and water state that you should mix 3 ounces of powder in a 14 quart pal 3/4 full of water. To obtain a mixture of equal strength and a mop bucket containing 28 gallons of water requires how many ounces of powder
Answer:
this doesn't make sense
Step-by-step explanation:
Would I use subtraction for this problem ?
Answer:
Tim has 224 blue marbles.
Step-by-step explanation:
32 × 7 = 224
He has 7 times as many as Malanie (32)
I hope this helps!!!!
help me pls guys! im being timed and need some help!
Answer:
B.
Step-by-step explanation:
she only has $60 to spend therefore, she has the option of spending all of it, or less. However she cannot spend money she doesn't have.
Answer:
I think it's B
Step-by-step explanation:
(So far she has spent $45.95, plus the extra gift, and that has to equal less than or equal to $60) =
45.95 + extra gift (x) ≤ 60
How would I solve this algebra question? Step by step
3
Evaluate the function f(x) = (x + 2)2 for the given inputs.
a. f(5)=
b. f(-3) =
c. f (x+3) =
Answer:
a. 49
b. 1
c. x^2+10x+25
Step-by-step explanation:
Symply substitute the values (5, -3, x+3) in the equation (x+2)^2
Make the d subject of the formula c = kd^2 + e
[tex]c = k {d}^{2} + e \\ = > c - e = k {d}^{2} \\ = > {d}^{2} = \frac{c - e}{k} \\ = > d = \sqrt{ \frac{c - e}{k} } [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
The town of Winchester recently built an artificial body of Vater. This reservoir will store drinking water for the
town. Which of the following could cause contamination of the water and lead to human health-related problems
and loss of native species?
development of a water quality plan
B building a fence around the reservoir
C improvements to a water treatment facility
increased use of pesticides (chemicals) by farmers within the local watershed
Answer:
This reservoir, will store drinking water for the town. Which of the following could cause contamination of the water and lead to human health-related problems and loss of native species? ... Air pollution can affect human health and the health of other living things.
Step-by-step explanation:
Which relation is a function mastery test
Answer:
The relation which is a function is the one in which none of the first coordinates repeated.
Step-by-step explanation:
WHAT PERCENT OF 200 IS 28???? HELP MEEEEEE!!!!!!!!!
Answer:
14%
Step-by-step explanation:
Find the quotient of 29 and 200.
[tex]\frac{28}{200}=0.14[/tex]
Therefore, 28 is 14% of 200.
The number 28 is 14% of the number 200.
The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that the number is 200 and 28 is what percent of 200 will be calculated as:-
The percentage will be calculated as:-
200 x (X)% = 28
X% = ( 28 x 100) / 200
X% = 14%
Therefore, the number 28 is 14% of the number 200.
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co-efficint of (-xy²) in -5x³y²z⁴
[tex]-5x^3y^2 z^4 = 5x^2z^4(-xy^2)\\\\\text{The coefficient of}~ (-xy^2) ~\text{is }~ 5x^2 z^4.[/tex]
Does 28/4 have a remainder
Remainder=0
Quotient=7
Thanks!!
Nick drives 7 miles in ten minutes how many miles would nick drive if he drove at the same rate for 2 hours?
Answer 84 miles
Step-by-step explanation:
2hrs= 120min
7 miles/ 10 min = x miles/ 120 min
x = 84 miles