[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.
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There is a cookie jar in Julio's kitchen filled with 7 cookies. His mother bakes some more cookies. Now there are 14 cookies. How many cookies did Julio's mother bake.
your paper airplane is launched from 25ft. it descends at a rate of 5ft per second. write an equation that represents the height y of your airplane after x seconds
Answer:
y= -5x + 25
Step-by-step explanation:
y = mx + b
m(slope) = descending 5ft/sec means the height will decrease so the slope must be negative
b(y-int) = starting height of 25 ft added
13,22,31,...
Find the 31st term.
Find the 31st term.
Answer: 283
Step-by-step explanation:
To do this, it is helpful to get an equation you can use to solve any term.
This equation is:
[tex]13 + 9(n-1)[/tex]
So simply plug in 31 for n to get
[tex]13+9(31-1)[/tex]
[tex]=13+270[/tex]
[tex]=283[/tex]
Answer:
283
Step-by-step explanation:
9x+4=9(31)+4=283
13+9=22
22+9=31
9x
9(1)=9 9+4=13
9x+4
PLEASEEEE HELP!DUE IN 1 HOUR! A housing contractor has subdivided a farm into 100 building lots. She has designed two types of homes for these lots: colonial and ranch style. A colonial requires $30,000 of capital and produces a profit of $3000 when sold. A ranch-style house requires $40,000 of capital and provides an $7000 profit. If the contractor has $3.8 million of capital on hand, how many houses of each type should she build for maximum profit?
Answer:
Step-by-step explanation:
A housing contractor has subdivided a farm into 100 building lots. She has designed two types of homes for these lots: colonial and ranch style. A colonial requires $30,000 of capital and produces a profit of $2000 when sold. A ranch-style house requires $40,000 of capital and provides an $8000 profit. If the contractor has $3.2 million of capital on hand, how many houses of each type should she build for maximum profit?
? colonials
? ranches
For maximum profit, the contractor should build 80 colonial houses and 20 ranch-style houses. The maximum profit achievable is $740,000.
Let x be the number of colonial houses built.
Let y be the number of ranch-style houses built.
Now, we can set up the objective function, which represents the total profit:
Total Profit (P) = 3000x + 7000y
The total cost of the houses built cannot exceed the available capital, which is $3.8 million (or $3,800,000):
30,000x + 40,000y ≤ 3,800,000
The number of building lots used cannot exceed the total number of lots available, which is 100:
x + y ≤ 100
Also, we need to consider that the number of houses (x and y) must be non-negative:
x ≥ 0
y ≥ 0
Now, we have the linear programming model with the objective function and constraints.
We need to find the values of x and y that maximize the total profit (P).
Graph the feasible region determined by the constraints (x + y ≤ 100, x ≥ 0, y ≥ 0, 30,000x + 40,000y ≤ 3,800,000), and then evaluate the objective function (P = 3000x + 7000y) at each corner point of the feasible region to find the maximum profit.
The feasible region is a polygon with vertices at the following points:
(0, 0)
(0, 95) (Intersection of x = 0 and y = 95)
(80, 20) (Intersection of x = 80 and y = 20)
(100, 0) (Intersection of x = 100 and y = 0)
Now, evaluate the objective function (P) at each corner point:
(0, 0): P = 0
(0, 95): P = 665,000
(80, 20): P = 740,000
(100, 0): P = 300,000
The maximum profit of $740,000 occurs when the contractor builds 80 colonial houses and 20 ranch-style houses
Hence, for maximum profit, the contractor should build 80 colonial houses and 20 ranch-style houses.
To learn more on Linear programming click here:
https://brainly.com/question/30763902
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y=x^2 translate 4 units down and 3 units left
Answer: Hello! When a graph is translated 4 units down you are moving all of the y values. This makes it the easiest translation that we do, other than no translation! All you have to do is subtract 4. Your equation is y=x2 - 4. If you wanted to move the graph up it is addition and if you want to move it down it is subtraction. When you translate right to left it is more complicated! Hope this helps. :))
PLZ HURRY IT'S URGENT!!!
What is the value of x? Leave answer in **simplest radical form.***
options:
4
4√3
8
8√3
The length of a rectangle is times the width. If the perimeter is 32 inches, what is the width of the rectangle
Answer:
11
Step-by-step explanation:
DIRECTION: Solve each proportion.
1. 6/15 = n/25
2. 3/5 = 21/n
3. n/12 = 15/30
4.3/n = 12/24n
5. 6/12 = n/72
plss help me :(
Answer:
1. n=10
2. n=35
3. n=6
4. n=0 ? not sure for this one. two variables in the proportion
5. n=36
Step-by-step explanation:
set each set of proportion equal to each other and do cross multiplication
hope this helps !
how are you ?
Answer:
10356636Step-by-step explanation:
Please take a look of the attached photo for the solution.
Write each verbal expression as an algebraic expression.
The product of a number, b, and nine =
A number, x, raised to the fifth power =
Twelve divided by the product of number, y, and three =
Seven added to the difference of one and a number, k =
16. Use the vertical line test to determine whether the relation is a function.
Answer:
neither of them are
Step-by-step explanation:
Between which two integers does 7/3 lie?
Answer:
2 and 3
Step-by-step explanation:
7/3=2 1/3
So it lies between 2 and 3
2 1/3 is lesser that 3 but more than 2.
The position of a scuba diver relative to the water surface was −22 1/3 feet. He saw something interesting beneath him and increased his depth by 12 1/2 feet.
What is the position of the scuba diver now relative to the water surface?
Enter your answer as a mixed number, in simplified form, in the box.
Answer:
-34 5/6
Step-by-step explanation:
Hope this helps
Have a blessed day
Ten men and ten women are to be put in a row. Find the number of possible rows if Beryl, Carol, and Darryl want to stand next to each other in some order (such as Carol, Beryl, and Darryl, or Darryl, Beryl and Carol).
Answer: 6 possibilities.
Carol, Beryl, and Darryl
Carol, Darryl, and Beryl
Darryl, Carol, and Beryl
Darryl, Beryl, and Carol
Beryl, Darryl, and Carol
Beryl, Carol, and Darryl
Hope this helps :)
How long it would it take to spread a rumor in a town of 90,000 people if each person who heard the rumor told it to 3 new people every 15 minutes?
Answer:
it would take 30k minutes, equivalent to 500 hours/almost 21 days/almost 3 weeks
Step-by-step explanation:
Can someone pls help me!! And if u can explain how u do it I will very thankful for that..
Answer:
For the first question is 8y, and the second question would be 80
Step-by-step explanation:
The perimeter of a shape is calculated by adding it's sides together, and 2y+2y+2y+2y=8y. If y=10, we can substitute y for 10 in which 8*10 is 80.
a carpet cleaning service charges a one-time service fee of $100 with an additional $15 per hour for their business. write a linear equation that represents the total cost (y) for the hours work (x)
Answer:
The answer is y= 100 +15x
Step-by-step explanation:
You start with a service fee of $100
$15 per hour
x because the amount of hours can vary
y which is the total cost
y= 100+ 15x
What are the first five terms of the arithmetic progression with the first term 8 and common difference 7 , then find the 17th?.
Step-by-step explanation:
a1 = 8
a2 = 8 + 7 = 15
a3 = 15 + 7 = 22
a4 = 22 + 7 = 29
a5 = 29 + 7 = 36
an = an-1 + 7 = a1 + 7×(n-1)
a17 = 8 + 7×16 = 8 + 112 = 120
Is 0.136 greater or least to 0.23?
Answer: least
Step-by-step explanation: because 0.23 is closer to 1
Least
If you removed the last term from 0.136, it would become 0.13
Compared to 0.25, it is lower.
Graph the solution to the following system of inequalities.
-7x + 5y < -10
5x + 4y > 8
Then give the coordinates of one point in the solution set.
Graph attached
Solution is (1.6,0)1) Order this list from smallest to largest. 0.3 15% 2 1/2
Help help help help help
Answer:
100°
Step-by-step explanation:
Answer:
∡5=100°
Step-by-step explanation:
∡5 is perpendicular to the 100° above, therefore your answer is ∡5=100°.
Brainliest would be appreciated! :-)
How many 1/4 inch cubes does it take to fill a box with width 1 inches, length 3 3/4 inches and height 1 1/2inches?
Step-by-step explanation:
we need to see how many cubes fit into every dimension.
we can fit 4 cubes along the 1 in width. as 4×1/4 = 1 in.
we can fit 15 cubes along the 3 3/4 in length :
3 3/4 = 12/4 + 3/4 = 15/4
15/4 / 1/4 = 15/4 × 4/1 = 4×15 / 4×1 = 15
we can put 6 cubes on top of each other fit the height of 1 1/2 in
1 1/2 = 2/2 + 1/2 = 3/2 = 6/4
6/4 / 1/4 = ... = 6 (as above - simply 1/4 fits 6 times into 6/4).
so, we have
4 × 15 × 6 = 360
we need 360 cubes to fill the box.
45% of the people in the stadium are men, 23% of them are woman and the rest are children. What fraction of the people are children?
Answer:
8/25 of the people in the stadium are children.
Step-by-step explanation:
45 + 23 = 68
100 - 68 = 32%
32/100 simplified is 8/25
need help with math probelm
[tex]28+24=4(7)+4(6)=4(7+6)[=4(13)=52][/tex]
The answer: 4(7+6)
ok done. Thank to me :>
which of the following angle measure combinations will form a triangle?
A. 47° degrees, 63 degrees, and 70 degrees
B. 160 degrees, 50 degrees, and 150 degrees
C. 90 degrees, 1 degrees, and 88 degrees
D. 182 degrees, 1 degrees, and 2 degrees
6 wholes and 1/3 converted into decimal?
Answer:
6 is a whole number.
[tex]\frac{1}{3}[/tex] is approximately equal to 0.333, but this is a repeating decimal.
write 164/100 as a mixed number in simplest form.
Answer:
1 16/25
Step-by-step explanation:
I just recently learned this kind of stuff!
Answer:
1 16/25
Step-by-step explanation:
164-100=64
Common factors of 64 and 100:
1, 2, 4
Greatest common factor: 4
64/4=16
100/4=25
16/25
1 16/25
please help i only have a few minutes!! what are the measurements for 1 and 2?
Answer:
8 tablespoons1/2 cup4 ounces10 tablespoons plus 2 teaspoons2/3 cup5.2 ounces12 tablespoons3/4 cup6 ounces16 tablespoons1 cup8 ounces
Is 3x - y = -6 an equation for this graph? EXPLAIN how you know. Hint: try a test point like the the y-intercept to see if it makes a true statement.
You didn't provide any graphs.
write me 2 equivalent fractions of 1/3=_=_