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
on a coordinate plane, triangle a b c is shown. point a is at (negative 1, 1), point b is at (3, 2), and points c is at (negative 1, negative 1)if line segment bc is considered the base of triangle abc, what is the corresponding height of the triangle?
Answers
Answer:
The corresponding height of the triangle is [tex]1.2[/tex]
Step-by-step explanation:
We have[tex]\Delta ABC[/tex]
Here [tex]AD[/tex] is the height
We need to draw perpendicular from [tex]A[/tex] to [tex]BC[/tex]
The distance from the point [tex](m, n)[/tex] to the line [tex]A x+B y+C=0[/tex] is given by:
[tex]d=\frac{|A m+B n+C|}{\sqrt{A^{2}+B^{2}}}[/tex]
First let us calculate equation of [tex]BC[/tex]
[tex]y-y_1=m(x-x_1)\\\\y-2=\frac{2--1}{3--1} (x-3)\\\\y-2=\frac{3}{4} (x-3)\\\\4y-8=3x-9\\\\3x-4y=1[/tex]
Now distance from [tex](-1,1)[/tex] to [tex]3x-4y-1=0[/tex] is
[tex]d=\frac{|A m+B n+C|}{\sqrt{A^{2}+B^{2}}}\\\\=\frac{|3 \times1+-4\times-1-1|}{\sqrt{3^{2}+(-4)^{2}}}\\\\=\frac{6}{5}\\\\=1.2[/tex]
A store sells tents,sleeping bags,and campstools.A customer buys a tent, 2 sleeping bags, and 3 campstools for 212$.the price of the tent is 5 times the cost of a campstool.the cost of a sleeping bag is 6$more than the cost of a campstool.find the cost of was just item
Answers
The cost of each campstools, tent and sleeping bag is $20, $100 and $26
let
tent = 1
sleeping bags = 2
campstools = 3
Total cost = $212
tent = t
sleeping bags = s
campstools = c
If
t = 5c
s = c + 6
Total = t + 2s + 3c
212 = 5c + 2(c + 6) + 3c
212 = 5c + 2c + 12 + 3c
212 = 10c + 12
212 - 12 = 10c
200 = 10c
c = 200/10
c = 20
t = 5c
= 5 × 20
= 100
s = c + 6
= 20 + 6
= 26
Therefore, the cost of each campstools, tent and sleeping bag is $20, $100 and $26
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Kelly has a scarf that is 22 inches long. She folds the scarf in half
three times. How long is the scarf now?
Answers
Answer:
2.75 inches or 2 3/4 inches
Step-by-step explanation:
22 / 2 = 11
11 / 2 = 5.5
5.5 / 2 = 2.75
Find m angle O Y X in the diagram above.
URGENT!!
Answers
Answer:
• Angle OYW or Angle WYO is 90°
• Angle OYX or Angle XYO is 90°
• Angle WYX is 180° [ A straight line ]
Step-by-step explanation:
Line WYX is a perpendicular bisector of radius lind of the circle.
[tex]{}[/tex]
4. A donut shop bakes 4 dozen donuts every 18 minutes. How long did it take for the bakery to complete its
order of 144 donuts?
Answers
Answer:
54 minutes
Step-by-step explanation:
4 Dozen is 48
So we will need to know how many 18 minutes it takes to back 144 donuts
So divide 144 by 48
Which is 3
So you will need 3, 18 minutes to make 144 donuts
Now multiply 18 by 3 which is 54
So it takes 54 minutes to bake 144 donuts
Hope this helps!
Step-by-step explanation:
4 Dozen = 4 x 12 = 48 every 18 minutes
144/48 = 3
3 x 18 = 54 minutes
Erin made cookies in the shape of animals. Out of the 40 cookies she made, 16 of them were shaped like a giraffe. What percent of the cookies were shaped like giraffes?
Answers
Answer:
40
Step-by-step explanation:
16/40×100
= 1600/40
= 160/40
= 40
2b-3(1+b)=-3(b+7) whats the answer? and how do you do it??
Answers
Answer:
B=-9
Step-by-step explanation:
Technically, I didn't solve it. I used an algebra calculator online called m a t h w a y. It helps a lot but if you really need to know how to solve it on pencil and paper I cannot help you.
I had to space out the website so it let me submit this answer btw
Answer: -9
Step-by-step explanation:
2b-3(1+b)=-3(b+7)
2b-3+3b=-3b+-21
5b-3=-3b+-21
-21+3=-18
2b=-18
-18/2=-9
EWFrtujyhytgrfeds.DFGFDS
Answers
Answer:
Reese's puffs Reese's puffs
How many solutions does this equation have?
4h + 2 = 2 + 4h
Answers
should be 4
Step-by-step explanation:
The length of a certain rectangular prism is 3 less than twice the width. The height of the same prism is 4 more than
the width. Write an expression to represent the volume of the rectangular prism in terms of width (w).
V=2w? + 5w-12
V= -2w3 + 11w2 + 12w
V=2w3 +5w? - 12w
В.
С.
D
V=4w + 1
Answers
Answer:
it is c
Step-by-step explanation:
me big brain
Lena was playing a card game. She placed the cards in 2 rows of 26 cards each. In which other way can Lena place all of the cards?
Answers
Answer:
4 raws of 13 each
Step-by-step explanation:
The total number of cards =2×26=52we can divide 52 by 4 which is 13PLEASE HELP!!!!! 100 points!!!
The angle of elevation from an anchor to the top of a flag pole is 22 If the pole is
10 meters high, how long does the wire connecting the anchor to the pole must be?
(Round answer to the 1st decimal place.)
Answers
Answer:
26.7 mStep-by-step explanation:
The 22 degree angle is opposite to the 10 m side of the right triangle.
We need to find the length x of the hypotenuse.
Use trigonometry:
sine = opposite/hypotenusesin 22° = 10/xx = 10 / sin 22° x = 26.7 m (rounded)Answer:
PLEASE HELP!!!!! 100 points!!!
The angle of elevation from an anchor to the top of a flag pole is 22 If the pole is
10 meters high, how long does the wire connecting the anchor to the pole must be?
(Round answer to the 1st decimal place.)
Which equation matches the given points? (0, 7.6), (1, 6.2), (2, 4.8), (3, 3.4), (4,2)
Answers
The equation that matches the given points is g(x) = -1.4x + 7.6
The standard form of a linear equation is expressed as [tex]g(x)=mx + b[/tex]
m is the slope of the lineb is the y-intercept:Using the coordinate points (3, 3.4), (4,2)
[tex]m=\frac{2-3.4}{4-3}\\m=\frac{-1.4}{1}\\m=-1.4[/tex]
Substitute m = -1.4 and the coordinate (4, 2) into the formula:
[tex]2=4(-1.4)+b\\2=-5.6+b\\b=2+5.6\\b=7.6[/tex]
Get the required equation:
[tex]g(x)=mx+b\\g(x)=-1.4x+7.6[/tex]
Hence the equation that matches the given points is g(x) = -1.4x + 7.6
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Can someone plz help Me?
Answers
Answer:
C.
Step-by-step explanation:
Dont quote me but im pretty sure it's C here's why:
2/3 is .667 which means the trash compactor crushes the trash .01 kilo per 1 second 3/8 minutes being closest .25 means that it can crush it roughly in 22 second or 3/8 minutes.
which is a better deal? 5 pens for $1.85 OR 8 pens for $3.12 ? find the unit rate
Answers
Answer:
5 pens
Step-by-step explanation:
1.85 divided by 5 is .37
3.12 divided by 8 is .39
so 1.85 is a better deal
Round 1.09 to the nearest whole number.
Answers
Answer:
1
Step-by-step explanation:
1.09 is in between the whole numbers 1 and 2. it is closer to 1 since the tenths digit (0) is less than 5. if it were 5 or greater, then we would round up to 2.
Answer:
1
Step-by-step explanation:
1.09 is closer to 1 than 2, therefore the whole number is 1.
If you were counting people or objects, well you can't have 9/100 as a person so you'd round to 2. But in this case, round to 1!
I hope this helped :)
Kali earns $8 per hour. She worked x hours on both Monday and Tuesday. She also worked 5 hours on Thursday. The expression that represents Kali’s earnings for the week is shown.
2 (8 x) + 5 (box)
Which number should go in the box to complete the expression?
2
5
6
8
Answers
Answer:
8
Step-by-step explanation:
8 will go in the box
Select all of the tables that show a proportional relationship between x and y.
Answers
Answer:
The First Table
Step-by-step explanation:
All values can be said to be directly proportional to one another being multipled by 3.
a desk costs $145. what is the total cost of 23 desks?
Answers
Answer:
145*23=3335$
by multiplying cost by sum of desk
Research suggests that high school students could benefit from later school starting times. A school administrative team is considering a proposal to move the starting time of the local high school one hour later than the current start time. To measure interest in the proposal, members of the team randomly select subjects attending a large soccer tournament played on the high school grounds on a Saturday morning. The team finds that 58% of those surveyed support a later high school start time. Which type of bias is most likely to be present in the survey results?
This is undercoverage bias because adults with children are more likely to be included in the sample.
This is question wording bias because the phrasing of the later start times question may be confusing to some subjects.
This is nonresponse bias because some of those selected may choose to not provide their opinion on later start times.
This is voluntary response bias because vocal supporters of later start times will be more likely to offer their opinion.
Answers
Answer:
This is voluntary response bias because vocal supporters of later start times will be more likely to offer their opinion.
Step-by-step explanation:
Answer:
undercoverage bias
Step-by-step explanation:
All 150 eighth grade students at a local middle school were asked how many hours they studied during the week. Each row of the table represents one sample from the population. Find the mean Of each sample
Which row has the greatest mean?
1
2
3
4
Answers
The answer is 2...
It's row 2
Answer:
Row 2 (B)
Step-by-step explanation:
We can find out the answer just simply by adding up each of the rows seperately and finding out which one has the highest value, since all of the rows have the same amount of spaces that you need to divide by. Row 2 has the highest value with 23.
Use the diagonals to determine whether a parallelogram with vertices A(2, 7), B(7, 9), C(5, 4), and D(0, 2) is a rectangle, rhombus, or square. Give all the names that apply.
Answers
Step-by-step explanation:
A and B have among each other the same distance relation as D and C : +5 in x, and +2 in y direction
and D and A have among each other the same distance relation as C and B : +2 in x, and +5 in y direction.
that means the slope of the first pair of sides is 2/5, and the slope of the second pair of sides is 5/2.
and that means that these 2 pairs of lines are not perpendicular (for this not only would we need to have the ratio upside down but also the sign would need to be flipped). there are no 90° angles.
so, there is no rectangle or square.
but because the sums of x and y coordinate differences are the same, we have the same distances between neighboring points.
and that makes it a rhombus.
can some pls help me ☹?
Answers
Answer:
????????????????
Step-by-step explanation:
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Challenge An airplane is preparing to land at an airport. It is 36,000 feet above the ground and is descending at the rate of 3,200 feet per minute. At the same airport, another airplane is taking off and will ascend at the rate of 2,800 feet per minute. When will the two airplanes be at the same altitude and what will that altitude be? Use pencil and paper. Use two other methods to solve the problem. Explain which methods are easier to use and which are more difficult to use for the situation
They will be at the same altitude in _ minutes, when their altitude will be _ feet.
Answers
Answer:
6 seconds., 16800 feet
Step-by-step explanation:
The first plane is going y = -3200x + 36000
The second plane is going y = 2800x
Substitute the second equation for y into the first one:
2800x = -3200x + 36000
6000x = 36000 (Add 3200x to both sides)
x = 6 (Divide each side by 6000)
That means they will be the same altitude at 6 minutes.
To find how high, put your answer into one of the equations.
y = 2800 (6)
y = 16,800 feet
Find the measures of x and y
Answers
Answer:
x = 65°y = 25°Step-by-step explanation:
We can clearly see that 90 = x + 25. Let's solve for x.
=> 90 = x + 25=> x = 65°Since we found x, we can find y by substituting x in the equation 90 = x + y
=> 90 = x + y=> 90 = 65 + y=> y = 25°Conclusion:
Therefore, we found that:
x = 65°y = 25°Hoped this helped.
[tex]BrainiacUser1357[/tex]
Given the function f(x) x^2-2x/x^3 +9x^2-10x Find any holes, vertical asymptotes, and horizontal asymptotes there may be.
Answers
Answer:
See below
Step-by-step explanation:
I assume you mean [tex]f(x)=\frac{x^2-2x}{x^3+9x^2-10x}[/tex]:
Holes: Since [tex]f(x)=\frac{x^2-2x}{x^3+9x^2-10x}[/tex] reduces to [tex]f(x)=\frac{x(x-2)}{x(x^2+9x-10)}[/tex], then there is a hole at [tex]x=0[/tex] as [tex]x[/tex] exists in both the numerator and denominator (however, its limit as x approaches 0 is 1/5).
Vertical Asymptotes: If we further reduce [tex]f(x)=\frac{x(x-2)}{x(x^2+9x-10)}[/tex] to [tex]f(x)=\frac{x-2}{(x+10)(x-1)}[/tex], then we see that there are vertical asymptotes at [tex]x=-10[/tex] and [tex]x=1[/tex]
Horizontal Asymptotes: As the degree of the numerator is less than the degree of the numerator ([tex]2<3[/tex]), then there is a horizontal asymptote at [tex]y=0[/tex]
Find the slope of a line perpendicular to the given line. x = - 1
Answers
Consider the equation.
8x - 16y = - 14
The equation representing a line that is parallel to the line given and passing through the point (3, 0) is y= ___ x + ___
Answers
Answer:
[tex]y= \frac{1}{2}x+3[/tex]
Step-by-step explanation:
Rearrange equation to isolate y variable.
[tex]16y=8x+14[/tex]
Divide by 16 on both sides.
[tex]y=\frac{1}{2} x+7[/tex].
To make the line parallel to the given equation and pass through (3,0),
we will move the y intercept to 3.
[tex]y= \frac{1}{2}x+3[/tex]
ok the other one did not work so what 10 + 10 × 10 + 10 ÷ 10
Answers
Answer:
111
Step-by-step explanation:
it is correct 10 + 10 × 10 + 10 ÷ 10= 111
mark as brainliest
Which graph represents the solution set of the system of inequalities?
{y<2x+2x+y≥−3
Answers
Answer: the first graph (A)
Step-by-step explanation: are you actually low IQ or intellect this is the most easiest question I have ever seen I just finished this topic in my honor math class like last month in a week. BTW I am in the 9th grade
Now I got to tutor you so here you can use the process of elimination which you can see that < without the line below it means that the line is dotted and is the only one with a y-intercept of +2 is A and D are the only ligament answer now you dumc as i can't curse due to that i will get reported, so anyways go up 2 and go 1 to the right because it is 2x which is 2/1x rise/run and it is positive which means D is wrong because it has a negative slope which the only answer for this is A now get your (can't say) together and study.