A Pythagorean spiral is constructed by drawing right triangles on the hypotenuse of the other right triangles. Start with a right triangle in which each leg is 1 unit long. Use the hypotenuse of that triangle as one leg of a new triangle and draw the other leg 1 unit long. A spiral has been started below, continue the pattern until a spiral with 12 triangles is formed. 1. Determine the Tangent of the angle at the centre of the spiral for each of the first five triangles. 2. Use this pattern to predict the tangent of the 100th triangle.
Answers
Answer:
The angle is determined by dividing 360 by the number of vertexes that it took to complete the circle. The tangent of the 100th triangle would be the same respectively.
Step-by-step explanation:
I remember learning this in kindergarten.
Related Questions
PLEASE HELP!!!
Rectangle EFGH is reflected across the origin and then rotated 90° clockwise about the origin, forming rectangle E″F″G″H″. What are the coordinates of rectangle E″F″G″H″?
(A.) E″ (1, –5), F″ (1, –1), G″ (4, –1), H″ (4, –5)
(B.) E″ (–1, –5), F″ (–1, –1), G″ (–4, –1), H″ (–4, –5)
(C.) E″ (–1, 5), F″ (–1, 1), G″ (–4, 1), H″ (–4, 5)
(D). E″ (5, 1), F″ (1, 1), G″ (1, 4),
H″ (5, 4)
Answers
Answer:
c.
Step-by-step explanation:
90 degrees clockwise is (x,y)-(y,-x)
Answer:
The answer is A
Step-by-step explanation:
Took the test
PLEASE HURRY I NEED HELP BAD
An equation is shown below:
5(2x – 3) = 5
Part A: How many solutions does this equation have? (4 points)
Part B: What are the solutions to this equation? Show your work. (6 points)
Answers
Answer:
One solution
2
Step-by-step explanation:
5(2x-3)=5
10x-15=5
10x=5+15
10x=20
x=2
Part A: 1
Part B: It has only one solution and it is 2.
Hope this helps ;) ❤❤❤
Answer:
I believe 1 solution
Step-by-step explanation:
divide both side of equation by 5= 2x-3)=1
add 3 to each side= 2x=1+3
2x=4
x=2
Identify which of these designs is most appropriate for the given experiment: completely randomized design, randomized blockdesign, or matched pairs design.
A drug is designed to treat insomnia. In a clinical trial of the drug, amounts of sleep each night are measured before and after subjects have been treated with the drug.
The most appropriate is (randomized block, matched pairs, completly randomized) design.
Answers
Answer:
Matched pairs design
Step-by-step explanation:
Looking at the options;
-It's not a completely randomized design because a randomized design will assign all individuals to a group which in this case it doesn't.
- It's not a randomized block design because randomized block design will group the subjects in question into 2 or more blocks which have a common characteristic and will then randomly assign subjects in each of the blocks.
-It's a matched pair because every individual/subject undergoes measurements both before and after being treated with the drugs.
Thus, the correct option is matched pairs design.
How many solutions does this system have? x-y=-4 3x+y=8 one two an infinite number no solution
Answers
Answer:
work is shown and pictured
Karissa begins to solve the equation StartFraction one-half EndFraction left-parenthesis x minus 14 right-parenthesis plus 11 equals StartFraction one-half EndFraction x minus left-parenthesis x minus 4 right-parenthesis.. Her work is correct and is shown below.
Answers
Answer:
0
Step-by-step explanation:
Answer: it's C. 0
Also Happy early Christmas
At a pond, there were 24 ducks swimming. The ratio of ducklings to adult ducks is 5:1. How many ducklings were swimming at the pond?
Answers
Answer:
Hey there!
The ratio of ducklings to adult ducks is 5:1.
This means for every six ducks, five are ducklings and one is an adult.
If there are 24 ducks, then 5 times 4 = 20 ducklings and 4 adults.
Thus, there are 20 ducklings.
Hope this helps :)
Answer:
20 ducklings.
Step-by-step explanation:
32. Mariah bought a shirt for $28.50 and a
belt. The total cost was $45.50. Which
of the following equations can be used
to find the cost of the belt?
A 28.50 +b=45.50
B 45.50 + b = 28.50
Cb= 28.50 - 45.50
D b= 28.50 x 45.50
Answers
Answer:
The correct answer is A because subtract 28.50 from 45.50 and you get the answer of 17$ for the belt
A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 higher than in the first. The tax in the first city was 4.5%, and the tax in the second city was 3.5% . The total hotel tax paid for the two cities was $317.50. How much was the hotel charge in each city before tax? First city: Second city:
Answers
Answer:
$3750 and $4250
Step-by-step explanation:
x + 500 = y
.045x + .035y = 317.50
.045x + .035(x + 500) = 317.50
.045x + .035x + 17.5 = 317.50
.08x = 300.00
x = 3750
y = 4250
Two similar cylindrical cans hold 2 litres and 6.75 litres of liquid. If the diameter of the smaller can is 16cm, find the diameter of the larger can.
Answers
Step-by-step explanation:
It is given that,
Volume of the cylindrical can 1 is 2 litres and that of cylindrical can 2 is 6.75 litres. The diameter of the smaller can is 16 cm. We need to find the diameter of the larger can.
The formula of the volume of a cylinder is given by :
[tex]V=\pi r^2h[/tex]
So,
[tex]\dfrac{V_1}{V_2}=\dfrac{r_1^2}{r_2^2}[/tex]
Diameter, d = 2r
[tex]\dfrac{V_1}{V_2}=\dfrac{(d_1/2)^2}{(d_2/2)^2}\\\\\dfrac{V_1}{V_2}=(\dfrac{d_1^2}{d_2^2})[/tex]
V₁ = 2 L, V₂ = 6.75 L, d₁ = 16 cm, d₂ = ?
[tex]\dfrac{2}{6.75}=(\dfrac{16^2}{d_2^2})\\\\d_2=29.39\ cm[/tex]
So, the diameter of the larger can is 29.39 cm.
f(x) = x^2 - 4x + 3 f(x) = 1/2x + p The system of equations above, when graphed in the xy-coordinate plane, intersects at the point (4, q). What is p?
Answers
Answer:
p = 1
Step-by-step explanation:
Given that the system intersect at (4, q) then this point satisfies both equations, that is
q = 4² - 4(4) + 3
q = [tex]\frac{1}{2}[/tex] (4) + p
Equating both gives
16 - 16 + 3 = 2 + p, that is
3 = 2 + p ( subtract 2 from both sides )
p = 1
Write each of the following expressions without using absolute value.
|a−7|−|a−9|, if a<7
PLEASE HELP!!!! D:
Answers
=======================================================
If a < 7, then |a-7| = -(a-7) = -a+7 based on how absolute value functions are constructed. We're using the idea that
[tex]|x-k| = \begin{cases}x-k \ \text{ if } \ x \ge k\\ -(x-k) \ \text{ if } \ x < k\end{cases}[/tex]
Also, if a < 7, then |a-9| = -(a-9) = -a+9. This is true whenever 'a' is less than 9 for similar reasoning as above.
---------
So we have,
|a-7| - |a-9| = -a+7 - (-a+9) = -a+7+a-9 = -2
As long as a < 7, the result of |a-7| - |a-9| will always be -2.
---------
As an example, let's say a = 0
|a-7| - |a-9| = |0-7| - |0-9|
|a-7| - |a-9| = |-7| - |-9|
|a-7| - |a-9| = 7 - 9
|a-7| - |a-9| = -2
I recommend you try out other values of 'a' to see if you get -2 or not. Of course only pick values that are smaller than 7.
dentify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A researcher selects every 890 th social security number and researcher selects every 890th social security number and surveys surveys that the corresponding corresponding person.person. nothing nothing nothing Which type of sampling did the researcher researcher use
Answers
Complete Question:
Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below;
A researcher selects every 890th social security number and surveys the corresponding person. Which type of sampling did the researcher use?
Answer:
Systematic sampling.
Step-by-step explanation:
In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.
There are various types of sampling used by researchers and these are;
1. Random sampling.
2. Convenience sampling.
3. Stratified sampling.
4. Cluster sampling.
5. Systematic sampling.
A systematic sampling is a type of probability sampling method which involves the researcher selecting or collecting data from a larger population.
Under systematic sampling method, samples are selected from an ordered (fixed) sample population at periodic interval. Therefore, numbers are assigned to every member of the population and then, the "nth" member are selected by the researcher after choosing a fixed starting point.
In this scenario, the researcher selects every 890th social security number and surveys the corresponding person.
Hence, the type of sampling used by the researcher is systematic sampling.
A lead ball weighs 326 grams. Find the radius of the ball to the nearest tenth of a centimeter. the lead=11.35g/cm³
Answers
Answer:
3.14
Step-by-step explanation:
ratio
simplify
4x:9=7:3
Answers
Answer:
4x:9=7:3 can be written as
[tex] \frac{4x}{9} = \frac{7}{3} [/tex]
Cross multiply
We have
4x(3) = 9 × 7
12x = 63
Divide both sides by 12
[tex]x = \frac{21}{4} \: \: \: \: \: or \: \: \: 5 \frac{1}{4} [/tex]
Hope this helps you
Answer:
[tex]\boxed{x=\frac{21}{4}}[/tex]
Step-by-step explanation:
[tex]4x:9=7:3[/tex]
Turn ratios to fractions.
[tex]\frac{4x}{9} =\frac{7}{3}[/tex]
Cross multiplication.
[tex]4x \times 3 = 9 \times 7[/tex]
Simplify.
[tex]12x=63[/tex]
Divide both sides by 12.
[tex]x=\frac{63}{12}[/tex]
[tex]x=\frac{21}{4}[/tex]
Please help.............
.
Answers
Answer:
The length of arc is (7/12)π cm.
Step-by-step explanation:
Given that the formula to find the length of arc is Arc = (θ/360)×2×π×r where θ represents degrees and r representa radius. Then you have to substitute the following values into the formula :
[tex]arc = \frac{θ}{360} \times 2 \times \pi \times r[/tex]
[tex]let \: θ = 30 \\ let \: r = 3.5[/tex]
[tex]arc = \frac{30}{360} \times 2 \times \pi \times 3.5[/tex]
[tex]arc = \frac{1}{12} \times 7 \times \pi[/tex]
[tex]arc = \frac{7}{12} \pi \: \: cm[/tex]
Lines L and K are parallel to each other. Measure of angle A= 120 degrees, and measure of angle C= 80 degrees. What is the number of degrees in measure of angle B? Please answer ASAP! Thanks!
Answers
Answer:
160°
Step-by-step explanation:
The way I am doing it may not be the correct way but it works. What I did was take 90° away from 120° to make it 30° as if there is a line. I did this so I could make a triangle. Using the triangle addition postulate, I Added 30 to 80 to get 110 than subtracted that from 180 to get 70. Lastly, i added 90° to 70° to get 160°
Hope this helped you get the answer :)
The measure of angle B in Parallel lines will be 160°.
What are parallel lines?
Parallel lines are those lines that never intersect at any point and always maintain a constant distance.
We have,
Lines L and K are parallel to each other.
And,
The measure of angle A = 120°
The measure of angle C = 80°
Now,
Draw a straight line from A to B,
So, that ∠BAl = 90° and
∠ABk = 90°
We get,
ΔABC,
Now in ΔABC,
∠C = 80°
∠A = 120 - 90 = 30°
So, Using Tringle angle sum property,
80° + 30° + ∠ABC = 180°
⇒
∠ABC = 180° - 110°
∠ABC = 70°,
Now,
Adding ∠ABC and ∠ABk, to get ∠CBk,
i.e.
∠CBk = ∠ABC + ∠ABk = 70° + 90°
∠CBk = 160°
Hence we can say that the measure of angle B will be 160°.
To learn more about Parallel lines click here,
https://brainly.com/question/16701300
#SPJ2
A combination lock has 6 different numbers. If each number can only be used ONCE, how many different combinations are possible?
Answers
There are ten options for each number.
If there are 6 numbers, there are 10^6 different combinations.
Answer:
151200 possible combinations
Step-by-step explanation:
There are 10 digits 0 - 9 ( 0,1,2,3,4,5,6,7,8,9)
There are 10 choices for the first digit
10
There are 9 choices for the second digit
9
There are 8 choices for the third digit
8
and so on since we can only use each digit once
10 *9*8 *7 *6*5
151200 possible combinations
Need help quick quick quico
Answers
Answer:
7 batches
Step-by-step explanation:
PLEASE HELP ME! I will mark you as BRAINLIEST if you answer this correctly.
Answers
Answer:
0.92
Step-by-step explanation:
Each year, the value declines. This eliminates choices A and D.
The decline from 33000 to 30360 is slightly less than 10%, so the multiplier from one year to the next is slightly more than 1 -10% = 90%. The only choice in range is ...
0.92 . . . . the third listed choice
Need help with these last two questions, tysm if you do :D
Answers
Answer:
D.
A. x ≤ 1
Step-by-step explanation:
Well for the first question we need to simplify the inequality.
4x + 3 < x - 6
-x to both sides
3x + 3 < -6
-3 to both sides
3x < -9
Divide 3
x < -3
So if x is less than -3 than it goes to the left starting at -3.
So D. is the answer.
So to solve the floowing inequality we simplify, distribute, and combine like terms.
3(2x - 5) + 3 ≤ -2(x + 2)
6x - 15 + 3 ≤ -2x -4
6x -12 ≤ -2x - 4
8x - 12 ≤ -4
+12
8x ≤ 8
8/8
x ≤ 1
Hence the answer is A. x ≤ 1
The line’s graphed below are perpendicular. The slope of the red line is -1/3. What is the slope of the green line?
Answers
Answer:
C. 3
Step-by-step explanation:
Perpendicular lines have slopes that are negative inverses of the other.
This inverse of -1/3 is -3. The negative of -3 is 3.
The slope of the perpendicular line is 3.
Angle 6 and 7, are complementary angles?
Answers
Answer:
Hey there!
Angle 6 and angle 7 are actually supplementary angles, which are angles that add to 180 degrees.
Complementary angles are angles that add to 90 degrees.
Hope this helps :)
Answer:
∠6 & ∠7 are not complementary angles
Step-by-step explanation:
∠6 & ∠7 are supplementary angles on a line
The perimeter of a rectangle is 141 feet, and the length is twice the width. What are the dimensions ?
Answers
Answer:
The width is 23.5 ft and the length is 47 ft
Step-by-step explanation:
The perimeter of a rectangle is given by
P = 2(l+w)
141 = 2(l+w)
The length is twice the width
l = 2w
141 = 2 ( 2w+w)
141 = 2( 3w)
141 = 6w
Divide each side by 6
141/6 = 6w/6
23.5 = w
l = 2w = 2(23.5) = 47
The width is 23.5 ft and the length is 47 ft
Answer:
[tex]\boxed{Width = 23.5 \ feet}[/tex]
[tex]\boxed{Length = 47 \ feet}[/tex]
Step-by-step explanation:
Let Length be l and Width be w
Perimeter = 2(Length) + 2(Width)
Condition # 1:
2l+2w = P
=> 2 l + 2 w = 141
Condition # 2:
=> l = 2w
Putting the second equation in the first one
=> 2(2w)+2w = 141
=> 4w + 2w = 141
=> 6w = 141
Dividing both sides by 6
=> Width = 23.5 feet
Given that
=> l = 2w
=> l = 2(23.5)
=> Length = 47 feet
Workers in an office of 40 staff were asked their favourite type of take-away. Pizza 9 Curry 6 Fish & chips 11 Kebab 10 Other 4 How many degrees represent 1 person?
Answers
Answer:
Hey there!
In total, there are 360 degrees. If there are 40 staff members, then each member has 360/40=9 degrees.
Hope this helps :)
Answer:
9 degrees
Step-by-step explanation:
There are 360 degrees in a circle
There are 40 people
360 / 40 = 9
Each person gets 9 degrees
if 12 1/2% of a sum of money is $40, what is the TOTAL sum of money?
Answers
Answer:
$320
Step-by-step explanation:
Let the total sum of money be $x.
Therefore,
12 1/2% of x = 40
25/2% * x = 40
0.125 * x= 40
x = 40/0.125
x = $320
Thus, total sum of money is $320.
Helpppppppppp pleasessssss
Answers
Answer:
A.
Step-by-step explanation:
When it says (x + 7), that means the graph will be shifting to the right (so parallel to the x-axis.
Please answer this in two minutes
Answers
Answer: 1080 degrees
Hoped this helped :)
A student stands 20 m away from the footof a tree and observes that the angle of elevation of the top of the tree, measured from a table 1.5 m above the ground, is 34°28'. Calculate the height of the tree tothe nearest metre.
Answers
Answer:
6 to the north
Step-by-step explanation:
mark as brainliest
3/x-2, i'm confused as to what the horizontal asymptote is. The resources I found online conclude that it has a horizontal asymptote of y=0. I know that in order for a horizontal asymptote to be y=0, the denominator has to have a greater degree than the numerator. Im confused because doesn't the numerator have the same degree as the denominator (degree of 1)?
Answers
Answer:
y = 0
Step-by-step explanation:
Given
f(x) = [tex]\frac{3}{x-2}[/tex]
The degree of the numerator is zero 0 ( 3[tex]x^{0}[/tex] )
The degree of the denominator is 1
Since the degree of denominator > degree of numerator.
Then there is a horizontal asymptote at y = 0
7 - 5x > 3x + 31
A.X2-3 (all numbers greater than or equal to -3 will satisfy the inequality)B.xs-3 (all numbers less than or equal to -3 will satisfy the inequality)
C.X26 (all numbers greater than or equal to 6 will satisfy the inequality)
D.xs 6 (all numbers less than or equal to 6 will satisfy the inequality)
Answers
Answer: B. (all numbers less than or equal to -3 will satisfy the inequality)
Step-by-step explanation:
Hi, to answer this question we have to solve the inequality for x:
7 - 5x > 3x + 31
7-31 > 3x +5x
-24 > 8x
-24/8 > x
-3 > x
x < -3
So, the correct option is:
B. (all numbers less than or equal to -3 will satisfy the inequality)
Feel free to ask for more if needed or if you did not understand something.