Mathematics High School

What is the side length of the smallest square plate on which a 30​-cm chopstick can fit along a diagonal without any​ overhang?

Answers

Answer 1

Answer:

21.2

Step-by-step explanation:

math xl said so

Answer 2

The side length of the smallest square plate is 21.2 units.

What is the Pythagoras theorem?

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given that, length of diagonal on the square is 30 cm.

Let the side of a square be x.

Now, x²+x²=30²

2x²=900

x²=450

x=√450

x=21.2 units

Therefore, the side length of the smallest square plate is 21.2 units.

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Related Questions

Solve the equation 1-|1/3q-5| = -6

Answers

q=1/36 or q=-1/6, for the question
q=36 hope this helps!!!

Find three consecutive integers with a sum of -36

Answers

The formula for this is:
 x + (x +1) + (x+2) = -36
3x + 3 = -36
3x  = -39
x = -13

-13,-12,-11

Hope this helps!

What is the equation of the line, in point-slope form, that passes through the points (-3, -1) and (-6, 8)? open study?

Answers

إ

Hello : let  A(-3,-1)    B(-6,8)
the slope is :   (YB - YA)/(XB -XA)
(8+1)/(-6+3)  =9/(-3)
the slope is: -3

the equation of the line, in point-slope form is : y - 8 = - 3(x +6)

The data set shows the weights of pumpkins, in pounds, that are chosen for a photograph in a farming magazine. 18 22 14 30 26 (a) What is the mean, x , of the data set? (b) What is the sum of the squares of the differences between each data value and the mean? Use the table to organize your work. (c) What is the standard deviation of the data set? Use the sum from Part (b) and show your work. (d) A second group of pumpkins, with weights of 32, 35, 33, 34, and 36 pounds, are chosen for another photograph. Will the standard deviation of these weights be greater or less than the standard deviation found in Part (c)? Answer this without doing a calculation and explain your reasoning.

Answers

(a) What is the mean of :   18, 22, 14, 30, 26    

 x = (18 +22+ 14+ 30+ 26)/5 = 22     

  (b) What is the sum of the squares of the differences between each data value and the mean: (data point - x)² or (data point - 22)²
(18-22)² = 16
(22-22)² = 0
(14-22)² = 64
(30-22)² = 64
(26-22)² = 16

Sum = 16+0+64+64+16 = 160

(c) What is the standard deviation 

s = √[(∑(x-22)²/(n-1)], where x is the data point, 20 the mean and n =5

√[(∑(x-22)² = 160 and n = 5 (5 data points) then s = 160(5-1) = 160/4 = 40

 d)     32, 35, 33, 34, and 36    
 Rewrite it from smaller to greater:
 32, 34, 34, 35 36.
We notice that the range is from 32 to 36  is only 4 (36-32), Where as the range of the 1st pumpkins is 30-14 = 16

Since the spread of the 1st one is by far larger than the 2nd, we can conclude that the standard deviation of the 1st is greater than the second
              

PLEASE HURRY!! 30 POINTS

Simplify
73+3(23−13)2

Answers

if exponent 2

73+3(23−13)^2
= 73 + 3(10)^2
= 73 + 3(100)
= 73 + 300
= 373

if not exponent 2, but multiply 2 then

73+3(23−13) 2
= 73 + 3(10)2
= 73 + 3(60)
= 73 + 180
= 253

Answer:

1976

Step-by-step explanation:

Find a equation for the line, in point-slope form, that contains (5,1) and is perpendicular to 6x − 3y = 2.

Answers

hello : 
let the slope : a    and ; b the slope of the line : 6x - 3y = 2
the line that is perpendicular to 6x-3y=2  so : a×b = - 1 
but : 
6x - 3y = 2...      y = 2x-2/3  when : b = 2
 in point - form form of the equation of the line that is perpendicular
 to 6x-3y=2 is : y = (-1/2)x +c
contains (5,1) : 1 =  (-1/2)(5) +c
c = 7/2
an equation is : y= (-1/2)x +7/2

How to write a standard form equation with an undefined slope?

Answers

an equation that has an undefined slope is a vertical line. A vertical line is represented by x = a number. You cannot write an equation for a vertical line in slope intercept form (because of the undefined slope)...but u can write it in standard form.

lets say u have a vertical line going thru (2,3).....since it is a vertical line, its equation would be x = 2

to write this in standard form, it would be : x + 0y = 2 <==


Find the values of x and y that make these triangles congruent by the HL Theorem

A. X=5, y=6
B. X= -5, y=6
C. X=5, y= -6
D. X=6, y=5

Answers

The correct answer is A. X=5, Y=6. Both triangles are right triangles. Each triangle has corresponding sides that are congruent which makes the triangles congruent. The answer A has the values that make each side of both triangles equal to the other triangle.

The sum of 2 consecutive numbers is 97. Find the numbers

Answers

For two consecutive numbers :

let the first number is a, and of course the next number to it would be a+1

adding these two numbers: (a) + (a+1) = 97

then solve for a:

a+a+1=97
2a+1=97
2a=96
a=48


so the first number is 48 and the second number is the next one to it (49)

The two numbers are  48 and 49

What is the reciprocal of 6 3/7?

Answers

I believe your answer is going to be -6 7/3. Reciprocals are the opposites of a number, so I switched the sign on the 6 and made it -. When dealing with fractions, the reciprocal is essentially just flipping the numerator and denominator, which is how I got 7/3. 

I hope I helped. Best of luck!

45/7 is the correct answer

Sydney read 50 pages and 40 minutes she reads at a constant rate how many pages can Sydney read per minute

Answers

The rate at which Sydney can read the pages of a certain book, article, or whatsoever write-up is given to be 50 pages per 40 minutes. This can be better expressed as,
                50 pages/40 minutes
The number of pages that she can read each minute is calculated by dividing both the numerator and the denominator of the ratio by 40, giving us,
                       (50/40) / (40 /40)
The new ratio is now 1.25:1

ANSWER: 1.25 pages per minute

Sydney can read 5/4 or 1.25 pages in one minute

Data;

number of pages = 50time taken = 40 minuterate = ?

What is Rate

This can be defined as the measure of one unit against another unit.

If it take Sydney 40 minutes to read 50 pages, let's calculate how many pages she will read in one minute to determine her rate.

[tex]40 pages = 50 minutes\\x pages = 1 minute[/tex]

Let's cross multiply both sides and solve for x

[tex]50 pages = 40 minute\\x pages = 1 minute\\x = \frac{50*1}{40}\\x = 1.25 page[/tex]

From the calculations above, Sydney can read 5/4 or 1.25 pages in one minute.

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Show work on simply 2+(3g-4)-(8g+3)

Answers

2 + 3g - 4 -8g - 3

2 - 7 -5g

-5g - 5 is your answer

hope this helps

The angle of elevation to the sun is 24°. What is the length of the shadow cast by a person 1.82 m tall?

Answers

Let AB is representing height of man which is 1.82 m tall.

The length of the shadow cast by a person 1.82 m tall is; 4.09m

Angle of Elevation

The angle of Elevation to the sub is 24°.

On this note, the shadow cast on the floor represents the adjacent of the angle of Elevation.

Hence, the length of the shadow cast can be calculated from Tangent identify as follows;

Tan 24° = 1.82/l

l = 1.82/Tan 24

l = 1.82/0.445

Length of shadow = 4.09m

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What is the total surface area of this composite solid ?

Answers

Each of the small 12 identical blocks has dimensions 4 by 5 by 7 inches.

Together they form a larger block of:

width w=5 in
length l = 7 in+7 in+7 in = 21 in 
height h = 4 in + 4 in + 4 in + 4 in=16 in

The total area of the block is:

(front face+back face)+("floor" face + "ceiling" face) + 2 side faces
=
16 * 21 + 16*21 + 5*21+ 5*21 + 5*16+5*16  (square inches)
=
336+336+105+105+80+80  (square inches)

= 672+210+160 (square inches)

=1,042 square inches


Answer: 1,042 square inches

5. 41°F equals how many degrees Celsius?

Answers

It would equal five degrees Celsius
A. 9°C 
B. 5°C 
C. 56°C 
D. - 5°C 
The answer is B

The plate is rotated 90° about the origin in the counterclockwise direction. In the image trapezoid, what are the coordinates of the endpoints of the side congruent to side FG?

Answers

[tex] (x, y) --\ \textgreater \ (-y, x) (-2, 5) --\ \textgreater \ (-5, -2)[/tex]
The answer to ur question is (x, y) --\ \ < \ (-y, x) (-2, 5) --\ \ < (-5, -2). Hope this helps you!!

solve for x. 3x-r=r(-3+x)

Answers

3x-r=r (-3+x)
3x-r=-3r+xr
3x-r+r=-3r+xr+r
3x=-2r+xr
3x-xr=-2r+xr-xr
3x-xr=-2r
x (3-r)=-2r
x (3-r)/(3-r)=-2r/(3-r)
x=-2r/(3-r)

the area of the a rectangular painting is 4902 cm squared. if the length of the painting is 86 cm, what is it’s width?

Answers

the width of the painting is 57 cm

Olivia's work and solution to the equation -6x + 11=43 is shown. Identify each error in Olivia,s work ad epxplian what she would have done instead.
-6x + 11=43
+11 +11
-6x = 54
-6x/6 = 54/6
X = 9

Answers

The correct solution algorithm for the equation -6x + 11 = 43 is give as follows:

-6x + 11 = 43

Subtract 11 from both sides to get:
-6x + 11 - 11 = 43 - 11
-6x = 32

Divide both sides by -6 to get:
-6x / -6 = 32 / -6
x = -5.33


Given Olivia's work as follows:

-6x + 11= 43
+11 +11
-6x = 54
-6x/6 = 54/6
X = 9

Therefore, Olivia's errors are:
1) She added 11 instead of subtracting 11.
2) She divided by 6 instead of -6.

Which expression is equivalent to 32⋅32⋅32⋅32 ? (Also All The 32s Are Fractions, The Lines Just Wont Come Up.)

Answers

Answer:

If this is 1/32 for all of them the answer would be (1/32)^4 or (1/32) to the 4th power. if this is 3/2 it would be (3/2)^4 or (3/2) to the 4th power.

Step-by-step explanation:

If this is 1/32 for all of them the answer would be (1/32)^4 or (1/32) to the 4th power. if this is 3/2 it would be (3/2)^4 or (3/2) to the 4th power. I hope this helps : )

Which equation illustrates the commutative property of addition?

Answers

the correct answer is A or the first one
yes answer is A.
first one

a + b = b +a
so in this case

12 + 6 + 15 = 12 + 15 + 6

Three eggs are required to make two dozen muffins. how many eggs are needed to make 12 dozen muffins using a proportion

Answers

18 eggs are required to make 12 dozen muffins
Amount of eggs needed to make 2 dozen muffins
= 3

Amount of eggs needed to make 1 dozen muffins
=3/2
=1.5

Amount of eggs need to make 12 dozen muffins
=1.5x12
=18

Write an equation of the line passing through point P(−8, 0) that is perpendicular to the line 3x−5y = 6

Answers

3x - 5y = 6
-5y = -3x + 6
y = 3/5x - 6/5.....the slope here is 3/5. A perpendicular line will have a negative reciprocal slope. All that means is " flip  the slope and change the sign. So our perpendicular line will need a slope of -5/3....see how I flipped the slope 3/5 and made it 5/3....then I changed the sign and made it -5/3.

y = mx + b
slope(m) = -5/3
(-8,0)...x = -8 and y = 0
now we sub and find b, the y int
0 = -5/3(-8) + b
0 = 40/3 + b
-40/3 = b

so ur equation is : y = -5/3x - 40/3 or 5x + 3y = -40
Final answer:

To find the equation of a line perpendicular to another line, we need to find the negative reciprocal of the slope. Substituting the values into the point-slope form, we can find the equation of the perpendicular line.

Explanation:

To find the equation of a line that is perpendicular to another line, we need to find the negative reciprocal of the slope of the given line. The given line has the equation 3x - 5y = 6, so its slope is 3/5. The negative reciprocal of 3/5 is -5/3, so the slope of the line perpendicular to the given line is -5/3.

Since we know a point on the perpendicular line is P(-8, 0), we can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting -8 for x1, 0 for y1, and -5/3 for m, we get y - 0 = -5/3(x - (-8)).

Simplifying the equation gives y = -5/3x - 40/3, which is the equation of the line passing through point P(-8, 0) and perpendicular to the line 3x - 5y = 6.

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Felicity's insurance company pays for 65% of her elbow surgery, after she pays a $500 deductible.
How much will Felicity pay for her elbow surgery if it costs $9400?

A. $3290
B. $3465
C. $3615
D. $3790

Answers

C

9400 – 500(deductible)

The remainder is 8900, and the company pays for 65% of that. That means Felicity pays 35%.

35% of 8900 is 3115. Add on the 500 deductible and she pays 3615 in total.
Its going to be D. $3790
Because you first have to take 9400•0.65= 6110
Then you subtract that from the total amount and the deductible like so:
9400-6110-500=3790
And that is how you come up with D as the answer

Simplify: (sin θ − cos θ) − (sin θ + cos θ)2 (5 points)

Answers

I'll use x instead of theta

(sin(x) - cos(x)) - (sin(x) + cos(x))^2
(sin(x) - cos(x)) - (sin^2(x) + 2*sin(x)*cos(x) + cos^2(x))
(sin(x) - cos(x)) - (sin^2(x) + cos^2(x) + 2*sin(x)*cos(x))
(sin(x) - cos(x)) - (1 + 2*sin(x)*cos(x))
sin(x) - cos(x) - 1 - 2*sin(x)*cos(x)
- 2*sin(x)*cos(x) - cos(x) + sin(x) - 1 

The final answer is choice D



Please help me out!! ☮✌

Answers

a linear pair would equal 180 degrees

so 180-28 = 152

16x^2 = 49 help find x.

Answers

x=1.75

16x^2=49
divide 16 from both sides
x^2=3.0625
square root on both sides
x=1.75

2007 divided by j = 223

Answers

j = 9 because 2007 / 223 = 9, and when you multiply 223 x 9, you get 2007

Study the products shown. Is there a pattern?

(x + 3)2 = x2 + 6x + 9

(x + 4)2 = x2 + 8x + 16

(x + 5)2 = x2 + 10x + 25

(x + 6)2 = x2 + 12x + 36

Each product is in the form ax2 + bx + c.

Which of the following describes the relationship between b and c?

c is 1.5 times that of b.

c is double b.

c is the square of half of b.

c is the square of b.

Answers

c is the square of half of b.

This is evident in all products,

(6/2)² = 3²
= 9
(8/2)² = 4²
= 16
(10/2)² = 5²
= 25
(12/2)² = 6²
= 36
(b/2)² = c

Answer:

The correct option is 3. c is the square of half of b.

Step-by-step explanation:

The given equations are

[tex](x+3)^2=x^2+6x+9[/tex]

[tex](x+4)^2=x^2+8x+16[/tex]

[tex](x+5)^2=x^2+10x+25[/tex]

[tex](x+6)^2=x^2+12x+36[/tex]

These are the perfect square. According to this pattern,

[tex](x+y)^2=x^2+2xy+y^2[/tex]           .... (1)

Each product is in the form

[tex](x+y)^2=ax^2+bx+c[/tex]         .... (2)

From (1) and (2), we get

[tex]b=2y[/tex]

[tex]c=y^2[/tex]

[tex]c=(\frac{b}{2})^2[/tex]                    [tex][\because b=2y][/tex]

It means c is the square of half of b.

Therefore the correct option is 3.

Determine the relationship between the lines that pass through the given points: line
a.(-3, 5) and (0, 7) line
b.(6, 2) and (9, 4)

Answers

a. (-3,5)(0,7)
    slope = (7 - 5) / (0 - (-3) = 2/3

y = mx + b
slope = 2/3
(0,7)...x = 0 and y = 7
sub and find b, the y int
7 = 2/3(0) + b
7 = b....this is ur y int (0,7)
so ur equation for this line is : y = 2/3x + 7

b. (6,2)(9,4)
    slope = (4 - 2) / (9 - 6) = 2/3

y = mx + b
slope(m) = 2/3
(6,2)...x = 6 and y = 2
sub and find b, the y int
2 = 2/3(6) + b
2 = 4 + b
2 - 4 = b
-2 = b...this is ur y int (0,-2)
so this equation is : y = 2/3x - 2

so " a " has a slope of 2/3 and a y int of 7 and " b " has a slope of 2/3 and a y int of -2.

ur lines are parallel lines.....parallel lines will have the same slope and different y intercepts <===

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