Answer:
I prefer leaving the answer as √5 since it is a shorter form and exact form of the answer.
Here are reasons for leaving it as a radical form or a decimal approximation.
If you are looking for an exact answer, then you should leave it as √5. For example, if you are told a square has area 5 square units, then the exact length of the side is √5 units.
If √5 is the length of something that has to be made to that length, then you need an approximation. For example, if you are asked to make a square out of cardboard whose area is 5 square feet, then you need an approximation of √5 ft, such as 2.24 ft, so you can make each side of the cardboard square in the length of 2.24 ft.
We shall prefer to keep √5 in radical form, as it is an irrational number and will never give an exact value when converted to decimal form.
What are rational and irrational numbers?A rational number is any number that can be represented in the form p/q, where p and q are integers, q ≠ 0, and p, q are co-prime to each other, that is, they do not have any common factor except 1.
All terminating and non-terminating recurring decimals are rational numbers.
An irrational number is a real number that cannot be represented in the above form of a rational number.
All non-terminating non-recurring decimals are irrational numbers.
How do we solve the given question?We are asked, what would we prefer to do. Leave √5 in radical form or convert it into decimal form.
∵ √5 is an irrational number, we will never get a perfect value of it in decimal form, as irrational numbers are non-terminating non-recurring decimals. So, we shall prefer to keep √5 in the radical form.
Use of √5 in radical form: Gives the exact value in our calculations for equations.
Use of √5 = 2.236067977499........... in the decimal form: Used in trigonometry where we need to find the trigonometric ratio.
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a =5 b=7 ㅋ
What is
3 ab.
?
Answer:
Umm may be 105
Step-by-step explanation:
here a=5 b=7
3ab means 3×a×b
so,
3×5×7
=105
Answer:
[tex]\Huge \boxed{\mathrm{105}}[/tex]
Step-by-step explanation:
[tex]3ab[/tex]
The value of [tex]a[/tex] is given 5.
The value of [tex]b[/tex] is given 7.
[tex]\Rightarrow 3(5)(7)[/tex]
Evaluate the expression.
[tex]\Rightarrow 105[/tex]
Evaluate if x = 3, y = 4, and z = 5.*
6(r + y) =
I need help
Answer:
if y=4.then 6(r+4).
which is 6r+24.
and if it is equal to zero which is like this then it will be 6r+24=0.
which will be 6r=-24.
r= -24/6.
r= -4.
11. When you multiply two decimals less than 1, how does the product compare to the factors?
Illustrate with an example.
Answer:
The product is usually smaller than the two numbers multiplied
Step-by-step explanation:
When we multiply two decimals less than one, it is a certainty that the result of the multiplication would be less than the two decimals that were multiplied. An example is the multiplication of the decimals below;
0.958 * 0.325
which equals 0.31135
We can see from the example above that the result of the multiplication of the two decimals that are less than one, results in a product that is less than the factors that were multiplied.
Someone help me please
Answer:
4m^7y^2/-3
Step-by-step explanation:
what is the answer to 8^-2 =
Answer:
[tex]\huge\boxed{8^{-2}=\dfrac{1}{64}}[/tex]
Step-by-step explanation:
[tex]a^{-n}=\dfrac{1}{a^n}\Rightarrow 8^{-2}=\dfrac{1}{8^2}=\dfrac{1}{8\cdot8}=\dfrac{1}{64}[/tex]
other examples:
[tex]3^{-1}=\dfrac{1}{3^1}=\dfrac{1}{3}\\\\4^{-3}=\dfrac{1}{4^3}=\dfrac{1}{4\cdot4\cdot4}=\dfrac{1}{64}\\\\\left(\dfrac{1}{3}\right)^{-2}=3^2=3\cdot3=9\\\\\left(\dfrac{2}{5}\right)^{-3}=\left(\dfrac{5}{2}\right)^3=\dfrac{5^3}{2^3}=\dfrac{125}{8}[/tex]
Answer:
The answer is
Step-by-step explanation:
15/44
A boat traveled downstream a distance of 54 mi and then came back right back. If the speed of the current was 12 mph and the total trip took 6 hours, find the average speed of the boat relative to the water.
Answer:
18 mph.-
Step-by-step explanation:
This is 2*54 / 6
= 18 m p h.
2a=+2b=c solve for b
Step-by-step explanation:
pls make me as brainleist
addition of rational expressions using factoring. with step by step explanation please:)
Above picture are the steps
Answer:
2x
_______
x2−3x+2
or 2x/x2-3x+2
identify all the drawn radii of the circle created by the diameter and is perpendicular bisector
It’s a personal challenge
A rectangle has the following vertices. Find the area of the rectangle.
(9, – 1), (-1, 7), (-5, 2), (5,
6)
(1 point)
41 square units
123 square units
205 square units
82 square units
Answer:
D. 82 square units
Step-by-step explanation:
The area of the given rectangle is 82 square units. The correct option is (D).
How to use distance formula?The distance formula is used to find the distance between two points (x₁, y₁) and (x₂, y₂) as √((x₁ - x₂)^2 + (y₁ - y₂)^2).
By knowing the sides, the area of different polygonals such as parallelogram, trapezium and rectangles etc. canbe found.
The vertices of the rectangle are given as (9, – 1), (-1, 7), (-5, 2), (5, 6).
Suppose A, B, C and D are the corresponding vertices.
In order to find the area length and breadth is required.
Here, AB is the length and BC is the breadth which can be found using the distance formula as,
AB = √((-1 - 9)^2 + (7- (-1))^2)
= √(10² + 8²)
= 12.8
BC = √((-5 - (-1))^2 + (2 - 7)^2)
=√(-4² + -5²)
= 6.4
Thus, Area = AB × BC
= 12.8 × 6.4
= 81.92
Which is approximately 82.
Hence, the area of the rectangle is 82 square units approximately.
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Marcie found a shirt on sale for 35% off of $39.95.
How much will she pay for the shirt after the
discount?
Answer: Marcie will pay $25.97
Step-by-step explanation:
Goat on a Rope
Farmer Smith has a goat named Mel. He hasn’t had time to put up a fence to contain Mel, so he has Mel tied to a rope in his field. The rope is attached to a pole, allowing Mel to wander within a circular area. The rope is 10 feet long. Farmer Smith remembers that the formula for the area of a circle is A = r2 , and that “r” means the radius of the circle. He wants to know how much grass Mel can eat, so he uses 3.14 for , and calculates the area of the circle. How many square feet of grass can Mel reach while still on his rope? (It might help to draw a picture.)
Answer:
the area of grass is 314 square feet
Step-by-step explanation:
The radius of the circle the goat can reach is given by the length of the rope that ties the goat to the post (10 ft)
Then the area of the circle is: [tex]Area=\pi\,R^2=3.14\,(10\,\,ft)^2=3.14 * (100)\,ft^2=314 \,\,ft^2[/tex]
So the area of grass is 314 square feet
Which expression is equivalent to 2(m − 5) + 6?
Answer: 2m-4
Step-by-step explanation:
2(m-5)+6
=2m-10+6
=2m-(10-6)
=2m-4
Hope this helps!! :)
Please let me know if you have any question
Answer:
2m-4
Step-by-step explanation:
2(m-5)+6
=2m-10+6
=2m-4
You have two pieces for fabric. One piece is 6 feet wide and the other piece is 7.5 feet wide. You want to cut both pieces into strips of equal width that are as wide as possible. How wide should you cut the strips of fabric?
Answer:
Strips should be 1.5 ft wide.
Step-by-step explanation:
Given:
Width of 1st piece = 6 ft
Width of 2nd piece = 7.5 ft
To find:
To find the maximum width possible to make strips of equal size from both the pieces.
Solution:
This problem can be visualized as if we are given two numbers and we have to find the Highest common factor for both of them i.e. HCF of 6 and 7.5 will be our answer.
Let us try to factorize the given factors:
[tex]7.5 = 3 \times 2.5 = \underline {3 \times 0.5} \times 5[/tex]
[tex]6 = 3 \times 2 = \underline {3 \times 0.5 }\times 2[/tex]
The common factors are highlighted above as underlined.
Therefore, the answer is 3 [tex]\times[/tex] 0.5 = 1.5 ft
Strips should be 1.5 ft wide.
Simply each expression by combining like
terms. -7W + 2W - 12W-W
Answer:
answer is in the box. I hope that helps! :)
NEED HELP PLEASE !!!!
Answer:
It's the 3rd answer choice
You deposit $3000 in a savings account that earns 2.9% annual interest compounded monthly. You also save $80 per month in a safe at home. Write a function for the total amount of money saved C(t)=b(t)+h(t), where b(t) represents the balance of your savings account and h(t) represents the amount in your safe after t years. Round any decimals to three decimal places.
Answer:
C(t)=3000(1.002417)^12t+960t
if T=1 year then the saving will be : 4048.17
Step-by-step explanation:
3000 deposit amount, 2.9 compound monthly interest . save 80 dollars per month at home .
A=p(1+r)^t
A=3000(1+0.029/12)^12t
A=3000(1.002417)^12t dollars
for the amount saved at home=80*12t=960t dollars
C(t)=3000(1.002417)^12t+960t
if T=1 year then the saving will be :
C(t)=3000(1.002417)^12t+960t
=3088.17+960= 4048.17 dollars
Which are composite numbers?
Select all that are true.
49
35
32
41
47
Answer:
49, 35, and 32
Step-by-step explanation:
A composite number is one that may be generated by multiplying two smaller positive numbers. The correct options are A, B, and C.
What are Composite numbers?
A composite number is one that may be generated by multiplying two smaller positive numbers. It is a positive integer with at least one divisor other than 1 and itself.
Composite numbers are those numbers that are divisible by other numbers and form 1 and itself as well.
49
49 is divisible by 7, therefore, it is a composite number.
35
35 is divisible by 7, therefore, it is a composite number.
32
32 is divisible by 2, therefore, it is a composite number.
41
Since 41 is not divisible by any other number except 1 and itself, therefore it is not a composite number.
47
Since 47 is not divisible by any other number except 1 and itself, therefore it is not a composite numbers.
Hence, the correct options are A, B, and C.
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Simplify 15-10.24
Please help timed assignment!
Answer:
4.76
Step-by-step explanation:
Absolute Value. Show work...pls.
Answer:
10
Step-by-step explanation:
| 2+3(-4)|
Using PEMDAS, multiply first
| 2+-12|
Then add
| -10|
Then take the absolute value
10
Answer:
[See Below]
Step-by-step explanation:
Rewrite:
* |2 + 3 x -4|
Solve:
* 2 + 3 = 5
* 5 x -4 = -20
Now solve using absolute value:
* -20 = 20
(With absolute value it's just a short way of saying no negatives or fractions. It'd be the whole number of the number. Another example of this would be 8/1; the absolute value would be 8.)
the expanded fom of (a-b)²
Answer:
Step-by-step explanation:
[tex](a-b)^{2}[/tex] = [tex]a^{2}[/tex] - 2ab + [tex]b^{2}[/tex]
Hope this helps
plz mark as brainliest!!!!!
(BRAINLIEST QUESTION)
Pump it Up gym's daily revenue each can be modeled by R(x) = 5x where x represents the number of customers that visit the gym each day. The gym's daily costs can be modeled by the function C(x) = 2x + 150. Find the profit function P(x) if: P(x) = R(x) - C(x)
P(x) = 3x +150
P(x) = 7x - 150
P(x) = 3x - 150
P(x) = 7x +150
Answer:
P(x)=3x-150
Step-by-step explanation:
It is given that,
Daily revenue, R(x) = 5x, x is the number of customers that visit the gym each day
The daily cost pf the gym, C(x) = 2x+150
We need to find the profit function. It is given by :
P(x) = R(x) - C(x)
P(x) = 5x-(2x+150)
P(x) = 5x-2x-150
P(x)=3x-150
So, the correct option is (c) "P(x)=3x-150".
What is the inverse of the function f(x) = 2x + 1?
Answer:
1 + 2x = f(x) i believe
Step-by-step explanation:
Answer:
[tex]f^{-1}[/tex](x) = [tex]\frac{x-1}{2}[/tex]
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = 2x + 1 ( subtract 1 from both sides )
y - 1 = 2x ( divide both sides by 2 )
[tex]\frac{y-1}{2}[/tex] = x
Change y back into terms of x
[tex]f^{-1}[/tex](x) = [tex]\frac{x-1}{2}[/tex]
A wall of a building is 22 inches wide ten inches is concrete 8 inches is brick and 4 inches is limestone. What fraction of the wall is limestone?
Answer:
fraction of the wall is limestone is 4/22
or 2/11 as a reduced fraction
Step-by-step explanation:
fraction of the wall is limestone is 4/22
the width is 22 in total
10 inches concrete = 10/22
8 inches brick : 8/22
4 inches limestone : 4/22
10/22+8/22+4/22=22/22=1
which of the elements in set P are irrational
Answer:
-[tex]\sqrt{1}[/tex], [tex]\sqrt{2}[/tex], [tex]\frac{π}{2}[/tex]
Step-by-step explanation:
square roots and pie are irrational.
Need help with this the question is in the photo
Geneva's younger brother has a toy box that is 3.6 feet
long, 2.4 feet wide, and 1.5 feet high. What is the volume
of the toy box?
Answer:
12.96 ft ³
Step-by-step explanation:
The table below shows the number of minutes Morris practiced playing the trumpet during the past five weeks.
Week Minutes of Practice
1 30
2 40
3 52
4 66
5 82
6 ?
Answer:
6 100
Step-by-step explanation:
i found the answer because if you notice, once it gets to 3 52, 4 66, and 5, 82 it goes up 2 each time. So the answer would be 6 100!
Given that [tex]f(x)=\frac{3x+4}{5x-7} \\ g(x)=\frac{7x+4}{5x-3}[/tex] . Determine ([tex]g^{-1}[/tex]°[tex]f^{-1}[/tex])and the domain of their product.
Greetings from Brasil...
Solving the inverses of these functions and applying the composite we obtain:
(G⁻¹ о F⁻¹) = X
Note that (F⁻¹ о G⁻¹) also results in X (see second annex)
Complete the Equation.
6xy^-2/x^-3 = 6x [ ]^a0 /y^2
Answer:
a0 = 4
Step-by-step explanation:
6xy^-2/x^-3 =6xx^3/y^2 =6x^4/y^2a0 = 4