The diagonal of a square is 8 cm.
What is the length of the side of this square?
Give your answer as an exact surd in its simplest form
Answers
the length of the side of this square is [tex]4\sqrt{2} \:or \:5.65[/tex]cm
Answer:
Solutions Given:
let diagonal of square be AC: 8 cm
let each side be a.
As diagonal bisect square.
let it forms right angled triangle ABC .
Where diagonal AC is hypotenuse and a is their opposite side and base.
By using Pythagoras law
hypotenuse ²=opposite side²+base side²
8²=a²+a²
64=2a²
a²=[tex]\frac{64}{2}[/tex]
a²=32
doing square root on both side
[tex]\sqrt{a²}=\sqrt{32}[/tex]
a=±[tex]\sqrt{2*2*2*2*2}[/tex]
a=±2*2[tex]\sqrt{2}[/tex]
Since side of square is always positive so
a=4[tex]\sqrt{2}[/tex] or 5.65 cm
Answer:
Given :
↠ The diagonal of a square is 8 cm.
To Find :
↠ The length of the side of square.
Using Formula :
Here is the formula to find the side of square if diagonal is given :
[tex]\implies{\sf{a = \sqrt{2} \dfrac{d}{2}}} [/tex]
Where :
➺ a = side of square ➺ d = diagonal of squareSolution :
Substituting the given value in the required formula :
[tex]{\dashrightarrow{\pmb{\sf{ \: a = \sqrt{2} \dfrac{d}{2}}}}}[/tex]
[tex]{\dashrightarrow{\sf{ \: a = \sqrt{2} \times \dfrac{8}{2}}}}[/tex]
[tex]{\dashrightarrow{\sf{ \: a = \sqrt{2} \times \cancel{\dfrac{8}{2}}}}}[/tex]
[tex]{\dashrightarrow{\sf{ \: a = \sqrt{2} \times 4}}}[/tex]
[tex]{\dashrightarrow{\sf{ \: a = 4\sqrt{2}}}}[/tex]
[tex]{\dashrightarrow{\sf{\underline{\underline{\red{ \: a = 5.65 \: cm}}}}}}[/tex]
Hence, the length of the side of square is 5.6 cm.
[tex]\underline{\rule{220pt}{3pt}}[/tex]
Related Questions
The computer monitor to the right has a length of 44 inches and
a width of 38 inches. Find the length of the diagonal. Round your
answer to the nearest hundredth.
Answers
Answer:
58.14 inches
Step-by-step explanation:
Pitagoras:
Diagonal² = length² + width²
Diagonal² = 44² + 38²
Diagonal² = 1936 + 1444
Diagonal² = 3380
√Diagonal² = √3380
Diagonal = 58.137 = 58.14inches
While Jayden was at school, his house lost electrical power. By
the time the electrical power came back on the temperature inside the
house was 86°F. The air conditioner immediately started to cool the
house.Let f(x) represent the temperature, in degrees Fahrenheit, of
Jayden's house x minutes after the air conditioner started to cool the
house.What is the meaning of the statement f(25)=78?
Answers
Answer:
after 25 minutes the temperature was at 78 degrees
Step-by-step explanation:
The mean length of time, per week, that students at a certain school spend on their homework is 24.3 hours, with a standard deviation of 1.2 hours. Assuming the distribution of study
imes is normal, what percent of students spend more than 25 hours per week on homework?
Round
your answer to the nearest hundredth.
Answers
Answer:
21.1%
Step-by-step explanation:
(25 - 24.3) / 1.2 = 0.5833 z score = 78.9%
You need the percent that spend more than 25 hrs per week, so 100 - 78.9 = 21.1%
Harry spends $7.83 on 3 bags of walnuts. The bags all cost the same amount. What is the cost of each bag?
Answers
Answer:
i think the cost of each bag is $2.61
Step-by-step explanation:
suppose the cost of each bag is $x
7.83 = 3x
7.83/3 = x
2.61 = x
so the cost of each bag is $2.61
Kinsey adds -1 7/8 and it's opposite
Answers
Answer:
0
Step-by-step explanation:
the opposite is 1 -7/8 when you add them together they cancel out to zero
Haley is the head nurse at a hospital and must order supplies. If 1 4 of a package of bandages lasts 1 8 of the month, how many packages of bandages are needed for the entire month?
Answers
Answer:
2 Packages
Step-by-step explanation:
To last the whole month, we would need to multiply 1/4 by 8.
1 *8 = 8
4 * 1 = 4
8/4 = 2
How about: 37×13×78. Simplify this, if you please.
Answers
Answer:
37518
Step-by-step explanation:
Clear your calculator. Enter 37, followed by ×, and then 13, followed by ×, and then 78 and the ENTER key. Result: 37518.
Determine which number is greater and tell how many times as great. 7×1012 and 3.5×109
Answers
At a local print shop, 4 copies can be made for $2. At this rate, how how many copies could be made for $12?
Answers
Answer:
24
Step-by-step explanation:
$2 divided by 4 equals 50 cents
50 cents per copy
$12 will get you 24 copies
Answer:
24 copies
Step-by-step explanation:
$2 ----- 4 copies
$1 ----- 4 ÷2= 2 copies
$12 ----- 2(12)= 24 copies
Alternatively, we can present our working this way:
For every $2, 4 copies can be made.
Number of sets of $2 in $12
= $12 ÷$2
= 6
Since there are 6 sets of $2 and each set of $2 can make 4 copies,
number of copies
= 6(4)
= 24 copies
Iqbal and Sachin have bookshelves of the same size and holding books of the same sizes. Iqbal's shelf is 7/8 full and Sachin's shelf is 12/15 full. If 351 more books of the same size are distributed among them, then they can fill their shelves completely. How many books does Sachin have now?
a)
864
b)
865
c)
800
d)
850
Answers
Answer:
540 books
Step-by-step explanation:
It is given that Iqbal's shelf is 7/8 full ..
→ That Means we can say that, iqbal's shelf is (1 - 7/8) = 1/8 is Empty .....
Similarly,
Sachin's shelf is 12/15 full.
→ That Means we can say that, sachin's shelf is (1 - 12/15) = 3/15 is Empty.....
→ Both total Empty = (1/8 + 3/15)
Taking LCM of denominator ,
→ (15+24 /120)
→ 39/120
→ 13/40 part is Empty in both .
Now, it has been said that, when 351 more books are distributed among them , both shelves filled completely .
So, we can say that :----
→ 13/40 part ---------------- 351
→ 1 part ---------------------- 351*40/13 = 1080 = Total Books in Both Selves .
__________________
Now, since bookshelves of the same size and holding books of the same sizes ,,
→ Both have Books in Each = 1080/2 = 540 books .
A feather blew out of a bird nest 10 feet in the air. It drifted to the ground at a constant rate of 2 feet per second. Write an equation that shows the relationship between the elevation of the feather, y, and the number of seconds it has been falling, x
Answers
The question is an illustration of a linear function, and the equation that represents the function is [tex]y =-2x +10[/tex]
A linear function is represents as: y = mx + c, where:
m represents the slope or rate c represents the y-interceptIn this case, we have:
[tex]m = -2[/tex][tex]c = 10[/tex]So, the equation becomes
[tex]y =-2x +10[/tex]
Hence, the equation of the function is [tex]y =-2x +10[/tex]
Read more about linear functions at:
https://brainly.com/question/14323743
Pieter owns a currency conversion shop. Last Monday, Pieter changed a total of 20 160 rand into a number of different currencies. He changed 3/10 of the 20 160 rand into euros. He changed the rest of the rands into dollars, rupees and francs in the ratios 9:5:2 Pieter changed more rands into dollars than he changed into francs. Work out how many more.
Answers
Answer:
6,174
Step-by-step explanation:
in total we have 20,160 rand.
3/10 of that is = 6048.
6048 rand is euros.
we now have a remaining 14,112 rand.
the rest of the rands is split up into 9:5:2
to find out how much one part equals we add 9, 5 and 2 together.
9 + 5 + 2 = 16.
We then divide the remaining 14,112 rand by 16 to find out one part.
14,112 / 16 = 882.
1 part = 882.
(dollars) 9 parts = 882 x 9 = 7,938 rand
(rupees) 5 parts = 882 x 5 = 4,410 rand
(francs) 2 parts = 882 x 2 = 1,764 rand
to find out how many more rands pieter changed into dollars than he changed into francs we need to minus 1,764 from 7,938.
7, 938 - 1,764 = 6,174
Pieter changed 6,174 more rands into dollars than francs.
Hope this helped :)
finding the distance along a diagonal with the distance formula requires you evaluate a square root. true or false ?
Answers
Answer:
true
Step-by-step explanation:
Pythagoras is simply c² = a² + b².
so, it does not matter which side of the triangle we need, we will always have to solve a square root for the final result.
Can someone help me with these equation
Answers
Answer:
6
Step-by-step explanation:
i think this is correct answer
mark me
Why were people concerned with the East India Tea's Company monopoly over the
tea industry?
Answers
Answer:
You accedently put Mathematics I think you meant Social Studies haha
Step-by-step explanation:
please help me with this as soon as possible
Answers
Answer:
the answer is i dont know XD
Step-by-step explanation:
So if we want to do the first one it will be
Y = 4 x (1) - 3
Y = 4 - 3
Y = 1
For the second one we got x = 6
So we do the same thing but with 6 and say
Y = 4 x (6) - 3
Y = 21
It seems confusing at first but I’m sure you’ll get the hang of it
so easy read whats on the image
Answers
The answer is: J - 3.08 pounds
Option I ) 3.08 pounds
The reason being that it can't round up with the 2 so we just have that number to the hundredth
5+2x=2x+6
do anyone know the answer
Answers
Answer:
no solutions
Step-by-step explanation:
5+2x = 2x+6
Subtract 2x from each side
5+2x-2x = 2x+6-2x
5 = 6
This is not a true statement so there are no solutions
Find the indicated side of the
triangle.
10
459
a
b = [?]
Answers
Answer:
b=a
Step-by-step explanation:
Pythagorean Theorem:
b = 10/√2
Make x the subject of the formula: y=x^{2} + 5
Answers
First, multiply both sides by (x - 5), so you end up with:
(x-5)y = x + 2
Which can be expanded to give you:
xy - 5y = x + 2
Now add 5y to both sides to obtain:
xy = x + 2 + 5y
Now subtract x from both sides:
xy - x = 2 + 5y
Factorise x out:
x(y - 1) = 2 + 5y
Divide both sides by (y - 1):
x = 2 + 5y/y - 1There you go, x is now the subject.
A sporting event held at a high school had 135
attendees. The event earned a total of $930.
Admission to the event was $10 for adults and
$4 for students. How many adults (a) and how
many students (s) attended?
a + s = 135
10a + 4s = $930
[?] adults [ ] students
Answers
Answer:
65 adults and 70 students
The number of adults and students attendant the sporting event held at a high school are 65 and 70 respectively .
What is elimination method?In the elimination method, we eliminate any one of the variables by using basic arithmetic operations and then simplify the equation to find the value of the other variable. Then we can put that value in any of the equations to find the value of the variable eliminated.
According to the question
A sporting event held at a high school had 135 attendees.
In which adults and students are there .
Let adults be a
and students be s
Therefore,
The equation is
a + s = 135 ---------------------------(1)
Now,
The event earned a total of $930.
Admission to the event was $10 for adults and $4 for students.
i,e
10a + 4s = 930 ---------------------------(2)
Now , Using elimination method to solve both equations
a + s = 135 ---------------------------(1)
10a + 4s = $930 -------------------(2)
Step1: Multiplying equation 1 by 10
i,e
10a + 10s = 1350 -------------------(3)
Step2: Subtract equation (2) from (3)
10a + 10s = 1350 -------------------(3)
-10a - 4s = -930 -------------------(2)
6s = 420
s = 70
Now , Substituting the value of s in equation (1)
a + s = 135 ---------------------------(1)
a + 70 = 135
a = 65
Hence, The number of adults and students attendant the sporting event held at a high school are 65 and 70 respectively .
To know more about elimination method here:
https://brainly.com/question/12090959
#SPJ2
please help asap
ty :)
Answers
Answer:
y = 3x + 6
Step-by-step explanation:
Since the line is parallel, it has the same slope -- 3
y = 3x + b, sub point (1, 9)
9 = 3(1) + b
9 = 3 + b
b = 9 - 3
b = 6
y = 3x + b -- y = 3x + 6
The slope remains the same as it’s parallel. Then replace the x and y with the coordinates (1,9) —> 9=3(1)+b and solve for b. B will equal to 6 and you just put it in y=Mx+b format.
I really really really need help with this
Answers
Answer:
404
Step-by-step explanation:
Simplify = 8 + 30 x 13 + 6
Left to right = 8 + 390 + 6
Result = 404
Leave a brainliest if this helped.
Answer:
404
Step-by-step explanation:
do the equation inside the brackets first (BIDMAS) - 5 x 6 = 30
48 / 6 = 8
8 + (30 x 13) + 6 = 38
30 x 13 = 390
8 + 390 + 6 = 404
FINAL PART OF MY HW!!! PART 6!!! IT IS STILL UNIT RATE!!!!!
Answers
Answer: Answer is on first screenshot
Step-by-step explanation:
Casey's grandmother sent her an $80 bookstore gift card for her birthday last year. This year, she sent her a $110 bookstore gift card. Which proportion can be used to find the percent of last year's gift that this year's gift is, if n represents the unknown percent?
A 100/110 = 80/n
B 80/110 = n/100
C 110/80 = n/100
D 101/100 = 80/n
Answers
ANS WER AS SOON AS POSSIBLE
AND I WILL MARK U AS BRAINLIST
Answers
Take RHS = 6 x 105 + 6 x 102 = 6 x 100000 + 6 x 100 = 600000 + 600 = 600600 ≠ LHS Hence, RHS ≠ LHS
Hoped that helped!
Answer:
False
Step-by-step explanation:
use PEMDAS.
since there is no perenthesis you start with exponents.
10^5=100000
10^2=100
6*100,000+6*100
Next, you go to multipliation
600,000+600
Finally, you move on to addition
600,600
Krista's snow fort has an area of 6228 sq inches if it is 72 in long what is the width
Answers
Answer:
86.5 inches
Step-by-step explanation:
6228 / 72 = 86.5
Question Is In The Picture
Answers
Answer:
30
Step-by-step explanation:
Pythagorean theorem states that a^2 + b^2 = c^2
this theorem only works on triangles with an angle of 90 degrees or a right triangle.
18^2 + 24^2 = 900
the square root of 900 is 30
I did the square root of 900 because the square root is the 'opposite' of squaring which is what you need to do in order to find 'c' is the Pythagorean theorem. 'a' is 18, and 'b' is 24
Answer is 30
There is 46% hard working Elfs in the North Pole. there is 300 elfs in north pole. How many elfs are hard working
Answers
Answer:
138 hard working elfs
Step-by-step explanation:
the 46% of 300 is 138
Answer:
There is 138 Hard working Elves at the North Pole.
Step-by-step explanation:
300× 0.46= 138
How much does the state spend in tax dollars altogether?
a. 20 million dollars
b. 12 million dollars
c. 24 million dollars
d. 48 million dollars
Answers
Answer:
24 mill
Step-by-step explanation:
Answer:
24
Step-by-step explanation: