A 51-foot wire running from the top of a tent pole to the ground makes an angle of 58° with the ground. If the length of the tent pole is 44 feet, how far is it from the bottom of the tent pole to the point where the wire is fastened to the ground? (The tent pole is not necessarily perpendicular to the ground.)
Answers
Answer:
35.11 ft
Step-by-step explanation:
This given situation can be thought of as triangle [tex]\triangle PQR[/tex] where PQ is the length of pole.
PR is the length of rope.
and QR is the distance of bottom of pole to the point of fastening of rope to the ground.
And [tex]\angle Q \neq 90^\circ[/tex]
Given that:
PQ = 44 ft
PR = 51 ft
[tex]\angle R = 58^\circ[/tex]
To find:
Side QR = ?
Solution:
We can apply Sine Rule here to find the unknown side.
Sine Rule:
[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}[/tex]
Where
a is the side opposite to [tex]\angle A[/tex]
b is the side opposite to [tex]\angle B[/tex]
c is the side opposite to [tex]\angle C[/tex]
[tex]\dfrac{PR}{sinQ}=\dfrac{PQ}{sinR}\\\Rightarrow sin Q =\dfrac{PR}{PQ}\times sinR\\\Rightarrow sin Q =\dfrac{51}{44}\times sin58^\circ\\\Rightarrow \angle Q =79.41^\circ[/tex]
Now,
[tex]\angle P +\angle Q +\angle R =180^\circ\\\Rightarrow \angle P +58^\circ+79.41^\circ=180^\circ\\\Rightarrow \angle P = 42.59^\circ[/tex]
Let us use the Sine rule again:
[tex]\dfrac{QR}{sinP}=\dfrac{PQ}{sinR}\\\Rightarrow QR =\dfrac{sinP}{sinR}\times PQ\\\Rightarrow QR =\dfrac{sin42.59}{sin58}\times 44\\\Rightarrow QR = 35.11\ ft[/tex]
So, the answer is 35.11 ft.
Related Questions
A bank is offering 5.5% simple interest on a savings account. If you deposit $15000, how much interest will you earn in six year?
What is this question asking for?
What Kinda Interest?
Answers
Answer:
a. $4,950
b. The question is asking us to calculate the simple interest that would be earned on the deposited amount for the given number of years at the given interest rate
c. Simple interest
Step-by-step explanation:
a. We want to calculate the amount of interest to be earned in six years
To calculate this, we use the formula for simple interest.
Mathematically;
Simple interest I = PRT/100
Where P is the principal which is the amount deposited = $15,000
R is the rate which is 5.5%
T is the time which is 6 years
Substituting these values in the simple interest formula, we have
I = (15,000 * 5.5 * 6)/100 = $4,950
b. The question is asking us to calculate the simple interest that would be earned on the deposited amount for the given number of years at the given interest rate
c. Simple interest
Someone pls help thank you sm ..
Answers
Answer:
15 lawns
Step-by-step explanation:
The Xbox costs $400 and his parents gave him $100. He needs to earn $300 more. $20 each lawn so $100 for 5 lawns. 5 lawns times three.
Xbox cost =400
Daniel's money =100
Xbox cost - Daniel money=300
yard cost =20
therefore 400 -100 /20
Daniel's need 15 yards to get the xbox
Need help pls will give you a good rating.
Answers
Answer:
x+4
.....................
Answer
[tex] \boxed{x + 4}[/tex]
Option C is the correct option
Step by step explanation
Let's find the expression which represents the length of the box:
[tex] \mathsf{length \times width \times height \: of \: prism \: = \: volume \: of \: prism}[/tex]
[tex] \mathsf{lengh \times \: (x - 1) \times (x + 8) = {x}^{3} + 11 {x}^{2} + 20x - 32}[/tex]
[tex] \mathsf{length = \frac{ {x}^{3} + 11 {x}^{2} + 20x - 32 }{(x - 1)(x + 8)} }[/tex]
Write 11x² as a sum
[tex] \mathsf{ = \frac{ {x}^{3} - {x}^{2} + 12 {x}^{2} + 20x - 32 }{(x - 1)(x + 8)} }[/tex]
Write 20x as a sum
[tex] \mathsf{ = \frac{ {x}^{3} - {x}^{2} + 12 {x}^{2} - 12x + 32x - 32 }{(x - 1)(x + 8)}}[/tex]
Factor out x² from the expression
[tex] \mathsf{ = \frac{ {x}^{2}(x - 1) + 12 {x}^{2} - 12x + 32x - 32 }{(x - 1)(x + 8)} }[/tex]
Factor out 12 from the expression
[tex] \mathsf{ = \frac{ {x}^{2}(x - 1) + 12x(x - 1) + 32x - 32 }{(x - 1)(x + 8)} }[/tex]
Factor out 32 from the expression
[tex] \mathsf{ = \frac{ {x}^{2}(x - 1) + 12x(x - 1) + 32(x - 1) }{(x - 1)(x + 8)} }[/tex]
Factor out x+1 from the expression
[tex] \mathsf{ = \frac{(x - 1)( {x}^{2} + 12x + 32) }{(x - 1)(x + 8)} } [/tex]
Factor out 12x as a sum
[tex] \mathsf{ = \frac{(x - 1)( {x}^{2} + 8x + 4x + 32) }{(x - 1)(x + 8)} }[/tex]
Reduce the fraction with x-1
[tex] \mathsf{ = \frac{ {x}^{2} + 8x + 4x + 32 }{(x + 8)} }[/tex]
Factor out x from the expression
[tex] \mathsf{ = \frac{x(x + 8) + 4x + 32}{(x + 8)} }[/tex]
Factor out 4 from the expression
[tex] \mathsf{ = \frac{x(x + 8) + 4(x + 8)}{x + 8} }[/tex]
Factor out x+8 from the expression
[tex] \mathsf{ = \frac{(x + 8)(x + 4)}{x + 8} } [/tex]
Reduce the fraction with x+8
[tex] \mathsf{ = x + 4}[/tex]
hence, x+4 is the expression that represents the length of a box.
Hope I helped!
Best regards!
Which term describes a time period marked by a change that begins a new period of development? century decade era millennium
Answers
Answer:
Era
Step-by-step explanation:
Century, Decade and Millennium have something in common and that which they have in common is that they are all measurement of time.
The keyword measurement implies that they are units of time just like seconds, minutes, hours, etc.
Century -> 100 years
Decade -> 10 years
Millennium -> 1000 years
However, era is used to describe events in history;
Take for instance; the era of the first generation of computer;
So, from the list of given options; Era best answers the question
An era describes a time period marked by a change that begins a new period.
An era :
begins with a significant eventgoes on for a period of time before it is replaced by another era. has distinct events from those of another eraExamples of eras include:
the Roaring Twenties the Progressive era The Cold War era The Age of EnlightenmentAll the eras mentioned above were distinct in how people behaved so in conclusion we can say that an era is a time period that begins a new period of development.
Find out more at https://brainly.com/question/20315058.
1: The best statement for reason 6 of this proof is -∠A ≅ ∠C
-∠B ≅ ∠D
-∠B and ∠D are supplements
-∠B ≅ ∠B
2.The best reason for statements 3.5. and 7 in this proof is
- Alternate interior angles are congruent.
-Corresponding angles are congruent.
-Alternate exterior angles are congruent.
-Interior angles on the same sides of a transversal are supplements.
3. The best statement for reason 8 of this proof is
-∠B ≅ ∠B -∠A and ∠C are supplements.
-∠B ≅ ∠D
-∠A ≅ ∠C
Answers
Answer:
1) -∠B ≅ ∠D
2) -Interior angles on the same side of a transversal are supplementary
3) -∠A ≅ ∠C
Step-by-step explanation:
1) Given that ∠A and ∠B are supplements and ∠A and ∠D are supplements, we have; ∠B ≅ ∠D
2) Given that ABCD is a parallelogram, therefore ∠A and ∠B, ∠A and ∠D and ∠B and ∠C are interior angles on the same side of a transversal and are therefore supplementary
3) Given that ∠A and ∠B and ∠B and ∠C are supplementary, therefore, ∠A ≅ ∠C.
Please help asap. I will give a thanks, rate your answer and mark the brainliest one too!
The formula v^2 - u^2 = 2as is used to model a moving object, where: u= starting speed (m/s) v = final speed (m/s) a = acceleration (m/s²) s = distance travelled (m) A car stops at some traffic lights. It then accelerates at 2.3 m/s² until it reaches a speed of 13.6 m/s. Find the distance, s, that it has travelled since stopping at the lights. Give your answer correct to 1 decimal place.
Answers
Answer:
s = 40.2 m
Step-by-step explanation:
It is given that,
Initial speed of the car, u = 0 m/s
Final speed of the car, v = 13.6 m/s
Acceleration of the car, a = 2.3 m/s²
We need to find the distance, s, that it has travelled since stopping at the lights. For this, we will use third equation of motion as :
[tex]v^2-u^2=2as[/tex]
s is distance
[tex]s=\dfrac{v^2-u^2}{2a}\\\\s=\dfrac{(13.6)^2-0}{2\times 2.3}\\\\s=40.2\ m[/tex]
So, the distance covered by the car is 40.2 meters.
I WILL GIVE BRAINLEST PLEASE HELP
Which of the following is an example of the difference of two squares?
A x2−9
B x3−9
C (x+9)2
D (x−9)2
I know the answer is either A or B i might be wrong tho pls help im not sure.
Answers
Answer:
A
Step-by-step explanation:
In this question, we are concerned with selecting which of the options best represents the difference of two squares.
Let’s have an exposition below as follows;
Consider two numbers, which are perfect squares and can be expressed as a square of their square roots;
a^2 and b^2
where a and b represents the square roots of the numbers respectively.
Inserting a difference between the two, we have;
a^2 - b^2
Now by applying the difference of two squares, these numbers will become;
a^2 - b^2 = (a + b)(a-b)
So our answer out of the options will be that option that could be expressed as above.
The correct answer to this is option A
Kindly note that;
x^2 -9 can be expressed as x^2 - 3^2 and consequently, this can be written as;
(x-3)(x + 3)
What is the slope of side AC?
Answers
Answer:
The slope is ( d-b)/ ( c-a)
Step-by-step explanation:
To find the slope we can use the slope formula
m = ( y2-y1_/(x2-x1)
= ( d-b)/ ( c-a)
Kameryn flips a coin, rolls a 6-sided die, and then spins an 8-section
spinner. How many possible outcomes are there?
Answers
Answer:
96 possible outcomes
Step-by-step explanation:
2 x 6 x 8 = 96
please please answer this question now
با )
Answers
Answer:
43/90
Step-by-step explanation:
We want to express 0.47777... as a ratio of two integers. To do so, we need to multiply by 10^n, where n is the number of repeating decimals. Only 7 is repeating so we multiply 0.47777... by 10. The trick to do this is to let x=0.47777... In other words, what we are doing is the following:
[tex]x=0.47777...\\10x=4.7777....\\\text{Subtract x}\\10x-x=4.7777...-x\\9x=4.7777...-0.4777...\\9x=4.3\\x=4.3/9=43/90=0.4\overline{7}[/tex]
The standard normal curve shown below models the population distribution of a random variable. What proportion of the values in the population does not lie between the two z-scores indicated on the diagram? z = -1.2 z = 0.85
Answers
Answer:
31.28%
Step-by-step explanation:
The z score is used in statistics to determine by how many standard deviations the raw score is above or below the mean. If the raw score is above the mean then the z score is positive while if the raw score is below the mean then the z score is negative. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Given the z score z = -1.2 z = 0.85. From the normally distribution table, the probability that a value falls between z = -1.2 and z = 0.85 = P(z < 0.85) - P(z < -1.2) = 0.8023 - 0.1151 = 0.6872
The proportion of values that do not fall between z = -1.2 and z = 0.85 = 1 - 0.6872 = 0.3128 = 31.28%
HELPP NEEDED ASAP PLEASE.
There are 20n members in the Trumpington marching band, and when they line up in rows of 26, there are 4 band members left over. If n is an integer and there are fewer than 1000 band members, what is the maximum number of people that could be in the Trumpington marching band?
Answers
Answer:
The maximum number of people that can be in the Trumpington marching band is 940 people
Step-by-step explanation:
The number of members = 20·n
The number per row = 26
The number left = 4
Therefore, we have;
If there are x rows of 26, we have;
26 × x = 20·n - 4
We have;
26 × x < 996
26 × x < 20·n
20·n < 996 therefore, 20·n ≤ 980
We check that 980/26 = 37 and some fractions
26 × 37 = 962 which will leave a remainder of 2
Therefore, we note that for 26 to have a remainder of 4, the last digit of the factor x must be 6 so has to get the last digit of the product 26 × x to be 6 while the digit of the product 20×n is 0 which will live 4 members out to get to the next 10 as follows;
26 × 36 = 936 while 20 × 47 = 940
We get 940 - 936 = 4 members
Therefore, the maximum number of people that can be in the Trumpington marching band = 940.
In the expression 3x2 + y -5, which of the following terms does not have a variable?
A.3x2
B. y
A
C. -5
D. None of these choices are correct.
Answers
Answer:
A, C
Step-by-step explanation:
Only B is containing a variable .
The -5 is not variable.
We have given that,
A.3x2
B. y
A
C. -5
In the expression 3x^2 + y -5
We have to determine which of the following terms does not have a variable.
What is the variable?
variable, In algebra, a symbol stands in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).
Only C contains a variable.
The -5 is not variable.
To learn more about the variable visit:
https://brainly.com/question/2804470
#SPJ2
please help me out
Answers
Answer:
81cm squared
Step-by-step explanation:
Area for triangle:
base x height x 1/2 =
5cm x 6cm x 1/2 =
30cm/2 = 15cm squared
Area for rectangle:
length x width:
11cm x 6cm = 66cm squared
Add the totals together = 66cm + 15cm = 81cm squared
Answer:
(triangle)
A. A= b × h ÷ 2
= 5cm × 7cm ÷ 2
= 35cm ÷ 2
= 17.5cm²
(rectangle)
B. A= L × W
= 11cm × 6cm
= 66cm²
(total of both area)
Total = A+B
=17.5cm² + 66cm²
=83.5cm²
Step-by-step explanation:
To find the area of a triangle, you must do the following formula:
Area= base × height ÷ 2
=x²
To find the are of the rectangle, you must do the following formula:
Area= Length × Width
= x²
Then you add the are of the first shape, A, with the second shape, B.
Total= A + B
=x²
I hope this helps! I'm sorry if it's wrong.
What collateral secures a mortgage?
O A.
5% of the purchase price of the house
B.
the house itself
C.
10% of the purchase price of the house
D.
none
Answers
Answer:
The House
Step-by-step explanation:
Help me figure this out, I don’t understand
Answers
Answer:
0,3
1,1
-1,1
-2.55, -10
2.55, -10
Step-by-step explanation:
It's asking for you to graph it and figure out points from the equation.
What you can do is subsitute values for X and solve for Y or use a graphing calculator. I used desmos, an online calculator and looked for coordinates. Also the +3 is the y intercept, which means y is 3 when x is 0.
Mark currently works part time with a salary of $8000 per year mark plans to quit working and attend college for four years if his college cost will total $64,000 how long will it take Mark to recover his investment assuming he has a salary of $32,000 upon graduating
Answers
The correct answer for this question is: If his college costs will total $64,000, it take Mark to recover his investment assuming he has a salary of $32,000 upon graduating for "2 years."
= 64,000 / 32, 000
= 2 years
Assuming that there'll be no additional costs in the middle of his college.
If you found this please brainliest it :)
Answer:
it is not 2 years
Step-by-step explanation:
Find the product of 0.3×0.23
Answers
Answer:
0.069
Step-by-step explanation:
0.3*0.23=0.069
Question. 7 Let abc be a three-digit number. Then, abc + bca + cab is not divisible by (a) a + b + c (b) 3 (c) 37 (d) 9
Answers
Answer:
D. 9
Step-by-step explanation:
Let
abc=100a+10b+c
bca=100b+10c+a
cab=100c+10a+b
abc + bca + cab=(100a+10b+c) + (100b+10c+a) + (100c+10a+b)
=100a + 10b + c + 100b + 10c + a + 100c + 10a + b
Collect like terms
=100a + a + 10a + 10b + 100b + b + c + 10c + 100c
=111a + 111b + 111 c
Factorise
=111(a+b+c)
abc + bca + cab = 111(a+b+c)
Factors of 111(a+b+c)= 1, 3, 37, 111, and (a+b+c)
abc + bca + cab is divisible by a+b+c because it is a factor of 111(a+b+c)
abc + bca + cab is divisible by 3 because 3 is a factor of 111(a+b+c)
abc + bca + cab is divisible by 37 because 37 is a factor of 111(a+b+c)
abc + bca + cab is not divisible by 9 because 9 is not a factor of 111(a+b+c)
Which of the following is a point-slope equation of a line that passes through the points (-1,4) and (8,2)
Answers
Answer:
y - 2 = -2/9( x - 8)
Step-by-step explanation:
hope this helps
let me know if u need more help
Answer:
y - 2 = -2/9(x - 8) or y - 4 = -2/9(x + 1)
Step-by-step explanation:
find slope first
(2 - 4)/(8 - -1) = -2/9
y - 2 = -2/9(x - 8)
55.5% repeating as a decimal
Answers
Answer:
55.5 ÷ 100 = 0.555
Step-by-step explanation:
When you ask, "What is 55.5 as a decimal?", we assume you want to know what 55.5 percent is as a decimal. In other words, 55.5 percent converted to decimal.
First, we will tell you why it is useful to know 55.5 as a decimal.
Normally, to calculate 55.5 percent, you would multiply a number by 55.5 percent and then you would take the product of that and divide it by 100 to get the answer.
Instead, you can simply multiply a number by 55.5 as a decimal to get the answer.
55.5 percent means 55.5 per hundred. Therefore, to get 55.5 as a decimal, all you have to do is divide 55.5 by 100 like so:
55.5 ÷ 100 = 0.555
Answer:
55.5% = 0.555
Step-by-step explanation:
55.5% = 55.5/100 = 0.555
Solve the following non-linear system of equations algebraically.
y = - 2x² - 4x + 5 and
y = 2x^2 + 4x + 5
Answers
Answer:
x = -2
Step-by-step explanation:
since y is common in both equations, you can equate them to be equal
-2x² - 4x + 5 = 2x² + 4x + 5
4x² + 8x = 0
factor out 4x
4x(x + 2) = 0
divide both sides by 4x
x + 2 = 0
x = -2
question : 4(3x + 2) -6 x 6
Answers
Answer:
x= 24
Step-by-step explanation:
open the bracket
4×3x =12x + 4 × 2 =8
12×+ 8-6×6
12×+ 12
x= 24
Answer:
12x - 28
Step-by-step explanation:
Because of PEMDAS you start with the parentheses and distribute the 4.
So,
(12x + 8) -6 x 6
Then, solve for the 6's
(12x + 8) -36
Remove the parentheses
12x + 8 - 36
Lastly, you get
12x - 28.
This is as far as you can go because there is no equals sign so you cannot actually solve for x.
Find the sum of 29,the product of 2 and 9 and the difference between 2 and 9
Answers
Step-by-step explanation:
Sum means adding of numbers
Product means multiplying the numbers
Difference means minus two numbers
First number is 2 and other number is 9.
Sum of 2 and 9 = 2+9 = 11
Product of 2 and 9 = 2×9 = 18
Difference between 2 and 9 = 9-2 = 7
Hence, this is the required solution.
A jar contains only red, white and blue marbles. The number of red marbles is 4/5 the number of white ones, and the number of white ones is 3/4 the number of blue ones. If there are 470 marbles in all, how any of them are blue?
•120
•200
•150
•184
Answers
Answer:
200
Step-by-step explanation:
i multiplied the answer choices by the fractions and 200 was the one that checked out
How many times larger is the value of
86,000,000 than 8,600?
Answers
Answer:
a 1000 times// just divide them
Answer:
10,000 times Larger
Step-by-step explanation:
To determine the multiple larger for 86,000,000 than 8,600, we simply will use the division operation and the result will be the multiple.
86,000,000 / 8,600 = 10,000
Hence, the number 86,000,000, is 10,000 times larger than 8,600.
Another method is simply to look at the additional zeroes that 86,000,000 has in comparison to 8,600. Since we can see that 86 is the only non-zero digit within the two numbers, we can use the properties of the decimal system to compare. Note that 86,000,000 has 6 zeroes, while 8,600 has two zeros. This means that we will need 4 zeroes as part of our tens multiple, so we can say that 10,000 is the multiple. Once again, we see that 86,000,000 is 10,000 times larger than 8,600.
Cheers.
An apartment complex has several 9-story buildings, and every apartment in the complex has a unique number. On the first floor of one of the buildings, you see four apartments numbered 109, 110, 111, and 112. In which building and on which floor is apartment 207?
Answers
Answer:
The apartment with the number 207 is in the second floor of the building that comes before the building with apartments numbered 109, 110, 111, and 112
Step-by-step explanation:
The given information of the naming of the apartments are;
The four apartments on the first floor of the building were numbered, 109, 110, 111, and 112
Therefore;
The first digit number, 1, which is consistent, represent the floor number (first floor)
The buildings in the complex are 9-story buildings, with 9 × 4 = 36 Apartments each
Therefore, for the numbers of the apartment to be from 9 to 12, on the floor, the numbering of the apartments is sideways such that the numbers of the apartment in the given building will be X09, X10, X11, and X12, where X is the floor number
The previous building apartment will be numbered X05, X06, X07, X08
Therefore, the apartment with the number 207 is in the second floor of the previous building to the one given.
Answer:
Apartment 207 is in 7th floor of the building number 6 .
Step-by-step explanation:
Given:
There are 9 floors in the building
The number of building and floor of apartment 207 .
Each floor in the building has four apartments
The number of apartment in a building = 4 * 9 = 36
Numbers on each floors are 01 to 36 after floor number
first floor of one of the buildings, we have four apartments numbered 109, 110, 111, and 112.
From the numbers, 1 is representing the floor number
9 , 10 , 11 & 12 are representing four apartments number
Recall,
Each floor has 4 apartments
207 = 36 * 5 + 4 * 6 + 3
36 * 5 = 5 buildings
4 * 6 = 6 floor of 6th building
180+24=204
205 - 208 =6th building 7th floor
Apartment 207 is in 7th floor of the building number 6 .
a piece of paper is 5.5 x 10^-4 inches thick. If jennifer has 35 such pieces,how thick is the whole stack? Write your answer in standard form.
Answers
Answer:
T = 0.01925 m
Step-by-step explanation:
It is given that,
Thickness of a piece of a paper is [tex]5.5\times 10^{-4}\ m[/tex]
Total number of pieces are 35
We need to find the thickness of the whole stack. It is simply a case of unitary method.
For 35 pieces, thickness is :
[tex]T=35\times 5.5\times 10^{-4}\\\\T=0.01925\ m[/tex]
So, the thickness of the whole stack is 0.01925 metres.
Bella is wrapping a cube-shaped gift box that measures 8.5 inches along each edge. How many square inches of wrapping paper is needed to cover the box completely without overlapping? A. 34 in.2 B. 72.25 in.2 C. 433.5 in.2 D. 614.125 in.2
Answers
Answer:
433.5 in²
Step-by-step explanation:
A cube has 6 sides
Area of 1 side = 8.5 x 8.5 = 72.25 in²
Area of 6 sides = 72.25 x 6 = 433.5 in²
Answer: c-433.5
Step-by-step explanation: A cube has 6 sides
Area of 1 side = 8.5 x 8.5 = 72.25 in²
Area of 6 sides = 72.25 x 6 = 433.5 in²
Answer: 433.5 in²
Select all of the numbers that are correctly written in scientific notation. 10.8\times10^{-3}10.8×10 −3 0.54\times10^60.54×10 6 1\times10^{-4}1×10 −4 7.6\times10^{2.5}7.6×10 2.5 9.8\times10^59.8×10 5
Answers
Answer:
1×10⁻⁴ and 9.8×10⁵Step-by-step explanation:
The standard form of writing a scientific notation is expressed as [tex]a.b*10^n[/tex] where a, b and n are integers. Note that a, b and n cannot be a fraction. When writing in scientific notation, the value of 'a' must not be equal to zero and it must not be a 'two digits values' but just 'a digit value'.
Based on the above conclusion, the following numbers are correctly written in scientific notation.
1×10⁻⁴ and 9.8×10⁵
- The expression 10.8×10 −3 is not correctly written because the value of a on comparison is a two digits number i.e 10.
- Also, 0.54×10^6 is not correctly written because a is zero on comparison
- 7.6×10 2.5 is not correctly written because the power is a decimal number i.e 2.5. We must only have an integer as the degree.
