Answers
Answer:
C. √2 - 1
Step-by-step explanation:
If we draw a square from the center of the large circle to the center of one of the small circles, we can see that the sides of the square are equal to the radius of the small circle (see attached diagram)
Let r = the radius of the small circle
Using Pythagoras' Theorem [tex]a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
to find the diagonal of the square:
[tex]\implies r^2 + r^2 = c^2[/tex]
[tex]\implies 2r^2 = c^2[/tex]
[tex]\implies c=\sqrt{2r^2}[/tex]
So the diagonal of the square = [tex]\sqrt{2r^2}[/tex]
We are told that the radius of the large circle is 1:
⇒ Diagonal of square + r = 1
[tex]\implies \sqrt{2r^2}+r=1[/tex]
[tex]\implies \sqrt{2r^2}=1-r[/tex]
[tex]\implies 2r^2=(1-r)^2[/tex]
[tex]\implies 2r^2=1-2r+r^2[/tex]
[tex]\implies r^2+2r-1=0[/tex]
Using the quadratic formula to calculate r:
[tex]\implies r=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\implies r=\dfrac{-2\pm\sqrt{2^2-4(1)(-1)}}{2(1)}[/tex]
[tex]\implies r=\dfrac{-2\pm\sqrt{8}}{2}[/tex]
[tex]\implies r=-1\pm\sqrt{2}[/tex]
As distance is positive, [tex]r=-1+\sqrt{2}=\sqrt{2}-1[/tex] only
Related Questions
hellllllllllllllllllllllp meeeeeeeeeeeeeeeeeeeee
Answers
Answer:
Number 1,2,3Low:10,200,8.5
High:55,260,9.3
Median:35,230,9.0
Lower Quantile:15,215,8.9
Upper Quantile:45,240,9.2
Interquantile Range:30,25,0.3
Some facts about powers of ten are shown. Use what you know about powers of ten to enter numbers that make the equation true.
Answers
Answer:
there are 4 before you can get 3.28.
As shown, 10^-1=1/10.
So, 1/10^-4 which makes it inverse,
10^4
Answer:
Step-by-step explanation:
there are 4 before you can get 3.28.
As shown, 10^-1=1/10.
So, 1/10^-4 which makes it inverse,
10^4
Wyatt is gathering box tops for his school. Last year he was able to collect 300 box
tops. Out of 300 box tops, 25 were already expired. He collected 400 box tops this
year. How many box tops will be expired this year if Wyatt can estimate the
number of box tops that will expire this year using the ratio from last year? Round
to the nearest whole number.
Answers
Answer:
Solution
Let last year and new year be L(y) and N(y)
Let last year Expired box and new year Expired box be L(E) and N(E)
Here,
L(y)=300 box
L(E)=25 box
N(y)=400 box
N(E)=x
We know,
N(y) / L(y) = N(E) / L(E)
400/300 = x/25
1.333333333 = x/25
x = 1.333333333 * 25
x = 33.333333333
So, the expire box this year is 33.333333333
The graph of the equation y=x²-2x-8 is a parabola. What is the equation of the axis of symmetry?
Answers
Answer:
x=1
Step-by-step explanation:
y=x²-2x-8
First, we solve for the vertex
The equation for the vertex is -b/2a
Substitution:
-b/2a
=-(-2)/(2*1)
=2/2
=1
Therefore the equation for the line of symmetry is x=1
Hope this helps!
Choose the best estimate for the length of a paperback book. A. 4 in. B. 8 in. C. 14 in. D. 18 in.
Answers
Answer:
A.4
Step-by-step explanation:
The average length of a paperback book is 4.25 inches in height and 6.87 in length. So the options you have here are 4,8,14, and 18 inches the closest number to 6.87 in 4 inches. I hope my answer helps you a lot.
I will give brainliest
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
I've labled all in red, hope this helps.
Answer:
I drew it for you.
Step-by-step explanation:
Pls give brainliest if I helped.
Answer the following about 437/7 estimating.
Answers
Answer:
a)- the first one, as 490 is farther than 420.
b)-underestimate
Answer:
A) FOR FIRST QUESQUESTION
B) FOR SECOND
Step-by-step explanation:
30 POINTS HELP ME-
(7.12) A group of students must collect at least $120 to organize a science fair. They have already collected $30. Which graph best represents all remaining amounts of money, in dollars, that the students should still collect to organize the science fair?
(A) Number line graph with closed circle on 120 and shading to the right
(B) Number line graph with closed circle on 90 and shading to the right.
(C) Number line graph with closed circle on 150 and shading to the right
(D) Number line graph with closed circle on 30 and shading to the right.
Answers
Answer:
Number line graph with closed circle on 30 and shading to the right
because you already have 30 dollars and they need at least 120 but if they get more then 120 they can still hold the science fair.
THIS ANSWER ISN'T MINE. I TOOK IT FROM AN ANSWER TO THE SAME QUESTION ANOTHER USER POSTED.
brainliest but please show work
Answers
3yd is the diameter of this circle so
3yd × pi= 9.42yd
In the diagram, lines r and s are parallel to each other and perpendicular to transversal line t. Line w is a transversal to lines r and s. Use properties of special angles, formed by parallel lines, perpendicular lines and their transversals, to describe the relationship between the angles. Choose all of the situations that correctly describe the relationship between the angles. Note: Figure is not drawn to scale.
s || r ; s ⊥ t ; r ⊥ t
line w is a transversal
m∠7=72°
10 and 14
(MULTIPLE CHOICE)
supplementary angles
The angles do not share a special relationship.
vertical angles
right angles
equal angles
alternate exterior angles
same side interior angles
alternate interior angles
corresponding angles
Answers
Answer:
Part 1)
Part 2)
Part 3)
Part 4)
Part 5)
Part 6)
Part 7)
Part 8)
Part 9)
Part 10)
Step-by-step explanation:
Part 1) Find the measure of angle 7
we know that
----> by corresponding angles
we have
----> given
therefore
Part 2) Find the measure of angle 4
we know that
----> by supplementary angles (form a linear pair)
we have
substitute
Part 3) Find the measure of angle 6
we know that
----> by alternate exterior angles
we have
therefore
Part 4) Find the measure of angle 1
we know that
----> by vertical angles
we have
therefore
Part 5) Find the measure of angle 16
we know that
----> by supplementary angles (form a linear pair)
we have
---> given
substitute
Part 6) Find the measure of angle 18
we know that
----> by alternate interior angles
we have
therefore
Part 7) Find the measure of angle 21
we know that
----> by alternate exterior angles
we have
therefore
Part 8) Find the measure of angle 10
step 1
Find the measure of angle 14
we know that
----> by supplementary angles (form a linear pair)
we have
substitute
step 2
we know that
---> sum of interior angles of a triangle
we have
substitute
step 3
Find the measure of angle 10
we know that
----> by vertical angles
we have
therefore
Part 9) Find the measure of angle 11
we know that
----> by supplementary angles (form a linear pair)
we have
substitute
Part 10) Find the measure of angle 12
see Part 8)
Step-by-step explanation:
last week you walked your dog 12.405 miles. this week you walked your dog 15 miles. how many fewer miles did you walk last week than this week?
Answers
= (15 - 12.405)miles = 2.595
The dog walked 3 miles less in last week than this week.
What is approximation?An approximation is anything that is similar, but not exactly equal, to something else. A number can be approximated by rounding.
Given that, last week you walked your dog 12.405 miles. this week, you walked your dog 15 miles.
The dog walked in last week approx = 12 miles
The dog walked this week = 15 miles
The fewer miles did he walked = 15-12 = 3
Hence, the dog walked 3 miles less.
For more references on approximation, click;
https://brainly.com/question/29669607
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For this item, enter the answer in the space provided. A college student earns $ 15, 000 working part-time at a bookstore. The student pays 1/10 of the earnings in taxes, spends 2/5 of the earnings on living expenses, and saves the remainder of the earnings. How much money does the student save?
Answers
Answer: 10,500
Step-by-step explanation:
How to calculate tax and earning
Given the following paramiters
Total amount earned by the student = $15000
Assume we have the following parameters
Earning paid off in taxes = $1500
Amount spent on living expenses = $3000
Amount she will have left = 15000 - (1500 + 3000)
Amount she will have left = 15,000 - 4500
Amount she will have left = 10,500
Hence the amount she will have left is $10,500
Answer:
$7,500
Step-by-step explanation:
First, find the amount he pays in taxes:
$15,000 x 0.1 = $1,500
Next, find the amount he pays in living expenses:
$15,000 x 0.4 = $6,000
Add the two amounts together:
$1,500 + $6,000 = $7,500
Subtract the combined amount from the original amount to find how much the student saved:
$15,000 - $7,500 = $7,500
Therefore, the college student saves $7,500.
ANSWER QUICKLY!!!
Which graph shows all real numbers closer to 0 than they are to 4?
Answers
Answer:
Graph A
Step-by-step explanation:
It’s the real numbers closer 0 then they are at 4.
I hope this helps
I'll give brainiest
-if u answer the question could you tell me how you got it tyy:)
The figure is the net for a rectangular prism.
What is the surface area of the rectangular prism represented by the net?
Enter your answer in the box.
Answers
Answer:184 cm^2
Step-by-step explanation:
10*6*2=120
6*2*2=24
2*10*2=40
120+40+24=184
Answer:
184 cm²
Step-by-step explanation:
You can find the surface area of this net by finding the area of each rectangle and adding them up.
The top rectangle has dimensions of 10 and 6. You multiply them to get 60. Add in the units and the area of the top rectangle is 60 cm².
The rectangle under the one we just found the area for has the dimensions 10 and 2. Find the area. A = 20 cm².
The two rectangles to the side of the second rectangle have the dimensions of 6 and 2. The area of one is 12 cm². This means the two rectangles added together are 24 cm².
The next rectangle has the same dimensions as the first rectangle we solved. Therefore, the area is the same, which is 60 cm².
The last rectangle has the same dimensions as the second rectangle we solved. Therefore, the area is the same, which is 20 cm².
We will add the numbers altogether to find the surface area.
60 + 20 + 24 + 60 + 20 = 80 + 24 + 80 = 104 + 80 = 184 cm²
Suppose the value 60 is added to the data set.
Answers
Probabilities! Can someone help me? 30 points for the right answer!
Answers
Answer:
Second and Last statements are true
Step-by-step explanation:
Probablity that it lands on red:-
1/5= 20
Probablity that it lands on green:-
2/4=40
Pls mark it as BRAINLIEST
Students are comparing the decimals 13.310, 13.28, and 13.301
Please put these numbers in order from least to greatest, enter the least value in answer spot 1.
________
________
________
Answers
Answer:
13.28
13.301
13.31
Step-by-step explanation:
13.28
13.301
13.310
PLEASE HELP ASAP ILL GIVE BRAINLIEST IF CORRECT
△ABC has interior angles with measures x°, 100°, and 70°, and △DEF has interior angles with measures y°, 70°, and 50°.
Using the given information, which statement is true?
The two triangles are not similar because x≠y .
The triangles are similar because they each have an interior angle with a measure 70°.
The two triangles are not similar because the interior angles are congruent but the side lengths are different.
The two triangles are not similar because y = 60 so it is impossible to have three congruent angles.
Answers
X= 10 degrees
Y= 60 degrees
Looking at the options, we see that the first statement is true. And if the angles are not equal, the triangles are not able to be similar.
A plastic bin in the shape of a cube contains 900 marbles, each with a volume of 8 in?. If the cube has side lengths of 2 feet, find the volume of the empty space in the bin (in cubic inches).
HELP QUICK ITS SO DIFFICULT
Answers
If on a scale drawing 5 inches represents 80 feet, then 3/4 inch would represent how many feet?
16 feet
8 feet
12 feet
4 feet
Answers
Answer:
12 feet
Step-by-step explanation:
80 / 5 = 16
1 inch = 16
16 / 4 = 4
4 * 3 = 12
A bakery made 9 cakes using 3 bags of flour. The bakery uses the same relationship
between cakes made and the amount of flour used to make all of their cakes. Which table of values shows the relationship between the number of cakes the bakery makes to the number of bags of flour the bakery uses?
Answers
Answer:
3/1 or 3:1 when simplified
so first number is three times larger then second number
The water glasses below are filled to the same height and have the same radius. How many times could you fill Glass B to equal the amount water in Glass A? Explain your reasoning.
Answers
Answer:
B
Step-by-step explanation:
%9 and 6 cm the glass ÷14
πcm }=. cm 9
thanks me later
The amount of water in Glass B to equal to 3 times of the amount water in Glass A
What is the volume?The volume is a measurement of three-dimensional space that is utilized.
Let r be the radius and h be the height of the cylinder and cone. Then the volume of the cylinder will be given as,
Volume of A = π r²h cubic units ...1
And the volume of the cone will be given as,
Volume of B = (1/3) × r²h cubic units ...2
From equations 1 and 2
Volume of B = 3 x volume of A
The amount of water in Glass B to equal to 3 times of the amount water in Glass A
More about the volume link is given below.
https://brainly.com/question/1578538
#SPJ2
WILL CHOOSE BRAINILEST!!! Find the midpoint of the line segment CD if C=(1,0) and D=(-7,2)
Answers
Answer:
m = (-3, 1)
Step-by-step explanation:
Midpoint formula: [tex]m = (\frac{x_{1} + x_{2} }{ 2},\frac{y_{1} + y_{2}}{2})[/tex]
[tex]m = (\frac{1 + -7 }{ 2},\frac{0 + 2}{2})[/tex]
[tex]m = (\frac{1 -7 }{ 2},\frac{0 + 2}{2})[/tex]
[tex]m = (\frac{-6}{ 2},\frac{2}{2})[/tex]
[tex]m = (-3, 1)[/tex]
Solve 5x-10=3x+2. Explain.
Answers
Answer:
6[tex] \: [/tex]
Step-by-step explanation:
It is given an equation and we are to find the value of x.
[tex] \: [/tex]
Given Equation :
[tex] \\ {\longrightarrow \qquad{ \sf{5x-10=3x+2}}} \\ \\ [/tex]
Subtracting 3x from both sides we get :
[tex]\\ {\longrightarrow \qquad{ \sf{5x-10 - 3x=3x - 3x+2}}} \\ \\ [/tex]
[tex] {\longrightarrow \qquad{ \sf{2x-10=2}}} \\ \\ [/tex]
Adding 10 to both sides we get :
[tex] \\ {\longrightarrow \qquad{ \sf{2x-10 + 10=2 + 10}}} \\ \\ [/tex]
[tex] {\longrightarrow \qquad{ \sf{2x=12}}} \\ \\ [/tex]
Dividing both sides by 2 we get :
[tex] \\ {\longrightarrow \qquad{ \sf{ \frac{2x}{2} = \frac{12}{2} }}} \\ \\ [/tex]
[tex] {\longrightarrow \qquad{ \frak{ \pmb{x=6}}}} \\ \\ [/tex]
Therefore,
The value of x is 6.Answer:
= 6-
Step-by-step explanation:
:-
5 + -10 = 3 + 2
ℜ :-
-10 + 5 = 3 + 2
ℜ :-
-10 + 5 = 2 + 3
-10 + 5 = 2 + 3
''.
, .
'-3' .
-10 + 5 + -3 = 2 + 3 + -3
ℭ : 5 + -3 = 2
-10 + 2 = 2 + 3 + -3
ℭ : 3 + -3 = 0
-10 + 2 = 2 + 0
-10 + 2 = 2
'10' .
-10 + 10 + 2 = 2 + 10
ℭ : -10 + 10 = 0
0 + 2 = 2 + 10
2 = 2 + 10
ℭ : 2 + 10 = 12
2 = 12
'2'.
= 6
= 6
Hopes this helps~
~~
help pls with this problem
Answers
Answer:
So, based on what I can see,
ON X FOR EACH
-from -7 to -3 (x) it is INCREASING
-from -3 to -1 it is INCREASING DRAMATICALLY
-from -1 to 1 it is DECREASING
-from 1 to 3 it is INCREASING
-from 3 to 5 it is DECREASING
-from 5 to 7 it is remaining CONSTANT.
Give the coordinates of each point.
please help thank you
Answers
d-4,6
b-9,6
c-11,6
Answer:
A = (1,6)
B = (4,6)
C = (9,6)
D = (11,6)
Since it is a strait line on six, all the points should have 6 as y. For the x's, just count how much it is away from the y-axis.
There is a proportional relationship between a volume measured in cups and the same volume measured in tablespoons. 48 tablespoons is equivalent to 3 cups, as shown in the graph.
A. What is the constant of proportionality for this relationship? (Type your answer as a fraction)
B. Write an equation representing this relationship. Use c for cups and t for tablespoons.
Answers
answer: 48 divided by 3 is equal to 16, so is 16/1 . for the b question is (1)c x (16)t
You are weighing 3 boulders. 1 weighs one-quarter of a ton, 1 weighs 8,112 ounces, and 1 weighs 505 pounds.
Which one is heaviest, and which is lightest?
Answers
Work:
Quarter ton= 500 lbs
8,112 oz=507 lbs
Can someone help me with this pls
Answers
Answer:
33.8
Step-by-step explanation:
1) Use Phythagoras theorem to get RS ↓
[tex]9.1 ^{2} + 6 ^{2} = 118.81 \\ \sqrt{118.81 } = 10.9[/tex]
2) RS = RQ
therefore, to get the perimeter, you'll have to total up the sides of the triangle ↓
[tex]rs + rq +qt + ts \\ = 10.9 + 10.9 + 6 + 6 \\ = 33.8[/tex]
Hope this helps =)
Answer:
33.8
**Brainliest would be appreciated**
Step-by-step explanation:
7th grade math i mark as brainliest
Answers
Answer: 64mi^2
Step-by-step explanation:
(2*5) +(6*8)+((3*4)/2) = 64mi^2