HELP, MARKING BRAINLIEST
How many compass settings are required to complete the construction?
Answers
Hint: if you don't know the answer you can count the number of arcs
Related Questions
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 115 grams of a radioactive isotope, how much will be left after 3 half-lives? Use the calculator provided and round your answer to the nearest gram.
Answers
2nd half-life: 57.5/2 = 28.75 grams
3rd half-life: 28.75/2 = 14.375 grams = 14 grams
After 3 half-lives, approximately 14 grams of the radioactive isotope will be left.
We have,
To calculate the remaining mass of a radioactive isotope after a certain number of half-lives, we can use the formula:
Remaining Mass = Initial Mass * (1/2)^(Number of Half-Lives)
Given:
Initial Mass = 115 grams
Number of Half-Lives = 3
Substituting the values into the formula, we get:
Remaining Mass = 115 * (1/2)^3
Calculating this expression:
Remaining Mass = 115 * (1/2)³
Remaining Mass = 115 * (1/8)
Remaining Mass = 14.375
Rounding to the nearest gram, the remaining mass is approximately 14 grams.
Therefore,
After 3 half-lives, approximately 14 grams of the radioactive isotope will be left.
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A. 6.2
B. 0.8
C. 12.3
D. 2.3
Answers
Let's x = the length of DE.
You would use the equation: tan (37) = x / 3
To isolate x, multiply each side by 3; you get x = 3(tan (37))
x ≈ 2.3 units
-6(14-7) healppppp plzzzz
Answers
-6 x 7=-42
-42 is your answer.
Hoped I helped!
Short answer: -42
Why?
So, we have a negative number: -6. Before we do anything with that yet, we have to do the parenthesis first. The equation inside the parenthesis is 14 - 7, which is 7. Now, we have to multiply it by -6. All you have to do is multiply regularly, or ignore the negative sign. -6 * 7 ==> -42. -42 is the final answer.
Hope this helped you! ♥
Alexis and tasha challenge each other to a typing test. Alex typed 54 words in one minute which was 123% of what tasha typed. how many words did tasha type in one mintue
Answers
Where: 'A' the number of words Alex typed in a minute and T is the number of words typed by Tasha in a minute.
[tex]A = (1.23)T \\ 54 = (1.23)T \\ \frac{54}{1.23} = T \\ T = 43.9 [/tex]
Therefore Tasha typed 43.9 words in one minute.
Hope this helps!
Which shows all the exact solutions of 2sec^2x-tan^4x=-1 ? Give your answer in radians.
Answers
You can use the fact that the range of tangent function is whole set of real numbers.
The solutions to the given equation are
[tex]x = \pm \dfrac{\pi}{3 }+ n\pi ; \: n \in \mathbb Z\\[/tex]
[tex]sin^2(\theta) + cos^2(\theta) = 1\\\\1 + tan^2(\theta) = sec^2(\theta)\\\\1 + cot^2(\theta) = csc^2(\theta)[/tex]
It is a fact that tangent ratio has range as all real numbers. We can use this fact along with the second Pythagorean identity to get to the solution of the given equation.
The given equation is [tex]2sec^2x-tan^4x=-1[/tex]
Using the second Pythagorean identity, we get the equation as
[tex]2\sec^2x-\tan^4x=-1\\\\2(1 + \tan^2x) - (\tan^2x)^2= -1\\\\(\tan^2x)^2 -2\tan^2x -3 = 0[/tex]
Assuming [tex]y = tan^2x[/tex], then we get [tex]y \geq 0[/tex]
The equation becomes
[tex](\tan^2x)^2 -2\tan^2x -3 = 0\\\\y^2 - 2y - 3 = 0\\y-3y + y - 3 = 0\\y(y - 3) + 1(y-3) = 0\\(y+1)(y-3) = 0\\y = -1, y = 3[/tex]
As we know that y is non-negative, so only valid solution is y = 3
Thus,
[tex]y = tan^2(x) = 3\\tan(x) = \pm \sqrt{3}\\x = \tan^{-1}(\pm \sqrt{3})[/tex]
Thus,
[tex]x = tan^{-1}(\sqrt{3}) = 60^\circ + n\pi ; \: n \in \mathbb Z\\\\x = tan^{-1}(-\sqrt{3}) = -60^\circ + n\pi ; \: n \in \mathbb Z[/tex]
Thus, the solutions to the given equation are:
[tex]x = \pm 60^\circ + n\pi ; \: n \in \mathbb Z\\[/tex]
Converting to radians,
[tex]x = \pm \dfrac{\pi}{3 }+ n\pi ; \: n \in \mathbb Z\\[/tex]
Thus,The solutions to the given equation are
[tex]x = \pm \dfrac{\pi}{3 }+ n\pi ; \: n \in \mathbb Z\\[/tex]
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The exact solutions of the equation 2sec^2x-tan^4x=-1 are x = 2nπ and x = (2n+1)π/2 for integer values of n.
Explanation:The given equation is 2sec^2x-tan^4x=-1.
Let's simplify the equation:
2(1/cos^2x)-(tan^2x)^2 = -1
2/cos^2x - tan^4x = -1
Now, substituting sec^2x = 1/cos^2x and tan^2x = (sinx/cosx)^2, we get:
2(1/cos^2x)-((sinx/cosx)^2)^2 = -1
2/cos^2x - sin^4x/cos^4x = -1
Now, let's substitute sin^2x = 1 - cos^2x:
2/cos^2x - (1-cos^2x)^2/cos^4x = -1
Now, solving for cos^2x:
2/cos^2x - (1-2cos^2x+cos^4x) = -1
2 - 2cos^2x + cos^4x - cos^2x = -cos^2x
cos^4x - 3cos^2x + 2 = 0
Now, we can solve for cos^2x by factoring the quadratic equation:
(cos^2x - 2)(cos^2x - 1) = 0
cos^2x = 2 or cos^2x = 1
Since the range of cos^2x is [0,1], we can discard the solution cos^2x = 2.
Therefore, cos^2x = 1.
Which means, cosx = ±1.
Since the required range is [0,2π], we can take two solutions:
cosx = 1, implies x = 2nπ, where n is an integer.
cosx = -1, implies x = (2n+1)π/2, where n is an integer.
Hence, the exact solutions of the equation 2sec^2x-tan^4x=-1 are x = 2nπ and x = (2n+1)π/2 for integer values of n.
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Evaluate 8- m/n+p ^2 when m=8 n=2 p=7
Answers
(8-8)/2+7^2 Exponents
(8-8)/2+49 add the denominators together
(8-8)/60 subtract 8-8
0/60 is the answer (which doesn't seem right to me)
Answer: 53.
Step-by-step explanation:
The given expression : [tex]8-\dfrac{m}{n}+p^2[/tex]
To find : The value of the above expression for the values m=8, n=2 and p=7.
For that , we just substitute the gives values m=8, n=2 and p=7 in the above expression by using Substitution property , we get
[tex]8-\dfrac{8}{2}+(7)^2[/tex]
Simplify,
[tex]=8-4+49[/tex]
[tex]=4+49=53[/tex]
Hence, the correct value of the given expression when m=8 n=2 p=7 is 53.
The equation of the line through ab *write your answer in slope-intercept form
Answers
But we can assume that A:(a,b) and B:(c,d), find the slope and then write the equation of the line thru points A and B:
d - b
m = -----------
c - a
d - b
then the equation of the line is y-d = ----------- (x-c)
c - a
Please ensure that you are sharing all of the info given (e. g., the coordinates of the points A and B).
The domain of {(x, y): y = 2x² + 1 is
Answers
Answer:
Domain: (- ∞, ∞)
Explanation:
The equation y = 2x² + 1 is a somewhat narrow parabola translate up 1 unit on the y-axis from the origin (0, 0). The domain of a graph indicates which x-values the diagram can potentially reach, or how far it can travels on the x-axis.
Because it is a parabola, it goes infinitely in both directions of the x-axis. Therefore, its domain is (-∞ ,∞)
Final answer:
The domain of the function y = 2x² + 1 is all real numbers, which is expressed as [tex]\( (-\infty, +\infty) \)[/tex]
Explanation:
The domain of a function refers to the set of all possible input values for which the function is defined. In the case of the function [tex]\( y = 2x^2 + 1 \)[/tex], it is a quadratic function, meaning it is defined for all real numbers [tex]\( x \).[/tex]
The function[tex]\( y = 2x^2 + 1 \)[/tex] involves squaring [tex]\( x \)[/tex], which can result in any real number. Since there are no restrictions on the values that[tex]\( x \)[/tex] can take, the domain of this function is all real numbers. Mathematically, we denote this domain as[tex]\( (-\infty, +\infty) \)[/tex].
This implies that for any real number you substitute in for [tex]\( x \)[/tex], the function [tex]\( y = 2x^2 + 1 \)[/tex] will produce a corresponding real number for [tex]\( y \).[/tex] There are no values of [tex]\( x \)[/tex] for which the function becomes undefined or non-existent.
Graphically, this function represents a parabola that opens upwards, covering all real values of [tex]\( x \)[/tex] along the x-axis. Therefore, the domain encompasses the entire real number line without any gaps or exclusions.
A regular pentagonal prism has 9-cm base edges. A larger, similar prism of the same material has 36-cm case edges. How does each indicated measurement for the larger prism compare to the same measurement for the smaller prism? A)volume B) weight
Answers
volume scale factor=(linear scale factor)³
the linear scale factor of the prism is:
(length of larger prism)/(length of smaller prism)
=36/9
=4
thus the volume scale factor will be:
4³=64
hence the volume of the larger prism is 4 times that of the smaller prism.
Simplify the square root of 48 ( this can be expressed as √48)
Answers
root (48)
We can rewrite this number as follows:
root (16 * 3)
Then, by properties of roots we have:
4 * root (3)
Answer:
The simplified expression for root (48) is:
4 * root (3)
Which graph represents the function g(x)=x−1−−−−−√+1 ?
Answers
Value under √ should be positive.
x-1≥0
x≥1.
Correct answer is A.
Answer:
First graph
Step-by-step explanation:
Given function,
[tex]g(x)=\sqrt{x-1}+1[/tex]
∵ The point from which the graph of the function passes through will be satisfy the function,
In the first graph,
Graph is passing through (1, 1), (5, 3) and (10, 4),
[tex]1=\sqrt{1-1}+1[/tex]
[tex]3=\sqrt{5-1}+1[/tex]
[tex]4=\sqrt{10-1}+1[/tex]
So, all points (1, 1), (5, 3) and (10, 4) satisfy the function,
In the second graph,
Graph is passing through (-1, -1), (3,1) and (8,2),
Since,
[tex]-1\neq \sqrt{-1-1}+1[/tex]
So, all points of graph 2 do not satisfy the function,
In the third graph,
Graph is passing through (1, -1), (5, 1) and (10, 2),
[tex]-1\neq \sqrt{1-1}+1[/tex]
So, all points of graph 3 do not satisfy the function,
In the fourth graph,
Graph is passing through (-1, 1), (3, 3) and (8, 4),
[tex]1\neq \sqrt{-1-1}+1[/tex]
So, all points of graph 4 do not satisfy the function
Simplify 2y (3-x) + 7 (x-2y)
Answers
Let's simplify step by step.
[tex]2y(3 - x) + 7(x - 2y) = [/tex]
First we work out the parenthesis (for instance possible by using rainbow technique).
[tex] 2y \times 3 + 2y \times - x + 7 \times x + 7 \times - 2y = \\ 6y - 2xy + 7x - 14y = [/tex]
Finally we collect the common terms.
[tex] - 2xy + 7x - 8y[/tex]
~ Hope this helps you!
6y - 2xy + 7(x - 2y)
Now distribute 7 through the second set of parenthesis.
6y - 2xy + 7x - 14y
Lastly,, collect the like terms with y.
-8y - 2xy + 7x
Since we cannot simplify any further,, -8y - 2xy + 7x is the correct answer to your question.
Let me know if you have any further questions.
:)
A certain website averages 4.9 hours of downtime per month with a standard deviation of 0.5 hours. In April, it had 3.5 hours of downtime. What z-score does the 4.5 correspond to?
Answers
Factor the polynomial. 7x2 + 68xy - 20y2 A) (7x - 2y)(x + 10y) B) (7x - 10y)(x - 2y) C) (7x + 10y)(x + 2y) D) (7x + 2y)(x - 10y)
Answers
7x2 + 68xy - 20y2
Factoring we have:
(7x-2y) (x + 10y)
We verify the factorization:
7x2 + 70xy - 2xy - 20y2
Rewriting we have:
7x2 + 68xy - 20y2
Therefore, the factorization is correct.
Answer:
A) (7x - 2y) (x + 10y)
Use a coordinate grid to create a map of a town with at least five different locations, such as a house, a post office, a school, a library, and a mall. Each location must be plotted where two grid lines cross. In addition, no two locations can lie on the same vertical grid line or the same horizontal grid line.
A. Post your diagram.
B. Use the Pythagorean theorem to find the distance between two of your locations.
Answers
A group consists of 6 men and 5 women. three people are selected to attend a conference. in how many ways can 3 people be selected from this group of 11? in how many ways can 3 men be selected from the 6 men? find the probability that the selected group will consist of all men.
Answers
Women = 5
Total number = 6+5 = 11
First question:
This is a question of combination.
Total number of selecting 3 people from the group = 11C3 = 11!/[3!(11-3)!]= 165 ways
Second question:
This is question of combination where only men are considered.
Total number of collecting 3 men from 6 men = 6C3 = 6!/[3!*(6-3)!]= 20 ways
Third question:
The probability that the 3 people selected will all be men is given by:
1st selection: 6/11
2nd selection: 5/10
3rd selection: 4/9
The probability = 6/11*5/10*4/9 = 4/33
1.
[tex] \displaystyle
\binom{11}{3}=\dfrac{11!}{3!8!}=\dfrac{9\cdot10\cdot11}{2\cdot3}=165 [/tex]
2.
[tex] \displaystyle\binom{6}{3}=\dfrac{6!}{3!3!}=\dfrac{4\cdot5\cdot6}{2\cdot3}=20 [/tex]
3.
[tex] |\Omega|=165\\
|A|=20\\\\
P(A)=\dfrac{20}{165}=\dfrac{4}{33}\approx12\% [/tex]
A fountain on a lake sprays water in a parabolic arch modeled by the equation y = -0.3x2 + 3x. A beam of light modeled by the equation -2x + 5.5y = 19.5 passes through the fountain to create a rainbow effect. If the beam cuts the water spray at points A and B, such that point B is at a higher level than point A, what distance from the ground level is point A?
Answers
Water model ⇒⇒⇒ y = -0.3 x² + 3x ( blue graph )
Light model ⇒⇒⇒ -2x + 5.5 y = 19.5 ( red graph )
The intersection between the two models A and B
A = ( 1.657 , 4.148 )
B = ( 7.13 , 6.138 )
B is at a higher level than point A
The distance from the ground level to point A = y-coordinate of point A
= 4.148
If you were to add the length of all the 3/8 pieces which are 4 (number of pieces) what would be the total length
Answers
To find the total length of four 3/8-inch pieces, you multiply the length of one piece (3/8 inch) by the number of pieces (4), which equals 1.5 inches.
To calculate the total length of all the 3/8-inch pieces, we multiply the length of one piece by the number of pieces, which is 4. The mathematical expression for this is:
Total length = length of one piece x number of pieces
Total length = 3/8 x 4
To perform the multiplication, multiply the numerators and then the denominators:
Total length = (3 x 4)/(8 x1)
Total length = 12/8 inches
Now, simplify the fraction by dividing the numerator and the denominator by the greatest common divisor, which is 4:
Total length = (12/4)/(8/4)
Total length = 3/2 inches
And since 3/2 inches is equal to 1.5 inches, the total length of all four pieces is 1.5 inches.
If a borrower obtains an interest-only loan of $112,500 at an annual interest rate of 6%, what is the monthly interest payment (rounded to the nearest $1)?
Answers
Annual interest rate = 6% = 0.06
Interest per year = Principal amount * Annual interest rate = 112,500*0.06 = $6,750
Monthly payment interest = Annual interest/12 = $6,750/12 = $562.50
If x varies directly with y and x=3.5 when y=14 find x when y=18
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You deposit $3000 in an account that pays 5% annual interest. What is the balance after 2 years?
Answers
With the deposit of 3000, the balance after 2 years would be $3307.50
How do we find the compound interest for the deposit?
The formula is: A = P(1+r)ⁿ
A is the amount of money accumulated after n years, including interest.
P = $3000
r = 5% = 0.05 (as a decimal)
n = 2 years
A = 3000 × (1+0.05)²
A = 3000 × (1.05)²
A = 3000 × 1.1025
A = 3307.50
Therefore, when a deposit of $3000 is made, the balance after 2 years would be $3307.50
If f is a function such that f(b)-f(a)/b-a=2, then which of the following statements must be true?
Answers
(y2 - y1)/(x2 - x1) which is the slope formula, or the average rate of change. thus your answer would be C
20 POINTS!
Yes or No?
Answers
Drawing a vertical line will cross the graph at one point only.
Every x was assigned one y.
Answer:
yes it is
Step-by-step explanation:
Find the width of a rectangular patio with a length of 16 ft and an area of 200 square feet
Answers
length * width = area
So let's represent the width, the unknown number, as w:
w * 16 = 200
Let's divide both sides by 16 to isolate w:
w = 12.5
The width is 12.5 feet
WHERE MY MATH FOLK AT?!?!
A cylindrical container, which will be used to collect oil, has a circumference of 15.5 in. and a height of 8 in.
Which estimate best approximates the amount of oil the container can hold?
Answers
15.5 in
r = ------------ = 2.468 in.
2*pi
Then the vol. of this cyl. is V = pi*r^2*h = pi * (2.468 in)^2 * (8 in). Complete the arithmetric and you'll then have your answer.
Find the value of y that makes the equation y = -2x + 4 true when x = 1. Select one: a. 2 b. -2 c. 6 d. -6
Answers
plug in 1 for x
y=-2(1)+4
then solve from there
substitute the value of x = 1 to the equation:
y = -2 · 1 + 4 = -2 + 4 = 2
Answer: a. 2
What is the center of the circle with the equation x2 + y2 – 10x – 11 = 0 ?
Answers
x^2 - 10x + y^2 = 11
(x - 5)^2 - 25 + y^2 = 11
(x - 5)^2 + y^2 = 36
Center of circle = (5, 0) and radius = sqrt36 = 6
50 POINTS FOR ALGEBRA ANSWERS
1. What are the zeros of the function?
f(x)=x3−x2−6x
A. −3 , 0, and 2
B. −3 , 0, and 1
C. −2 , 0, and 3
D. −1 , 0, and 3
2. The equation h(t)=−16t2+19t+110 gives the height of a rock, in feet, t seconds after it is thrown from a cliff.
What is the initial velocity when the rock is thrown?
3. Factor.
x2−6x+8
x2−6x+8= ( )( )
4. What are the zeros of the function f(x)=x2+2x−35 ?
There are two.
5. Let f(x)=x2−6x+13 .
What is the vertex form of f(x)?
What is the minimum value of f(x)?
6. Let f(x)=4x and g(x)=4x+1−2 .
Which transformations are needed to transform the graph of f(x) to the graph of g(x) ?
7. What is the average rate of change of the function over the interval x = 0 to x = 4?
f(x)=2x−1/3x+5
Enter your answer, as a fraction.
8. Which function grows at the fastest rate for increasing values of x?
A. g(x)=19x
B. h(x)=2x
C. f(x)=8x2−3x
D. p(x)=5x3+3
9. The equation of the linear regression line represents the relationship between the score a student earned on an aptitude test, x, and their final score in a statistics class, y.
yˆ=1625x+24.9
What does the slope of the line represent?
A. For every 25 points earned on the aptitude test, the student earned 16 fewer points in the statistics class.
B. For every 16 points earned on the aptitude test, the student earned 25 fewer points in the statistics class.
C. For every 25 points earned on the aptitude test, the student earned 16 additional points in the statistics class.
D. For every 16 points earned on the aptitude test, the student earned 25 additional points in the statistics class.
Answers
2. UNKNOWN
3. (x-4)(x-2)
4. 5, -7
5. vertex=(3,4)
minimum value=4
6. UNKNOWN
7. 5/3
8. D
9. C
Please help! Vectors and angles
A ship is sailing through the water in the English Channel with a velocity of 22 knots along a bearing of 157° (knots being a unit used to measure the speed of aircrafts and boats). The current has a velocity of 5 knots along a bearing of 213°. Find the resultant velocity and direction of the ship. (Remember that bearing is measured clockwise from the north axis).
1) 25 knots at 166.5 degree
2) 27 knots at 350 degree
3) 166.5 knots at 25 degree
4) 350 knots at 27 degree
Answers
We have been given that a ship is sailing through the water in the English Channel with a velocity of 22 knots along a bearing of 157°.
Further we have been given that current has a velocity of 5 knots along a bearing of 213°.
Therefore, angle between the direction of ship and direction of current will be
[tex]\theta = 213 - 157 = 56^{0}[/tex]
We can find the magnitude of resultant by using parallelogram law of vectors.
[tex]R=\sqrt{P^{2}+Q^{2}+2PQcos(\theta)}[/tex]
Upon substituting [tex]P=22, Q = 5 \text{ and }\theta = 56[/tex] in this formula, we get
[tex]R=\sqrt{22^{2}+5^{2}+2\cdot 22\cdot 5cos(56)}\\ R=\sqrt{484+25+220\cdot0.55919}\\ R=\sqrt{632.0224}\\ R=25.14 \text{ knots}[/tex]
Therefore, resultant velocity of the ship is 25.14 knots.
We find the angle of resultant from P, that direction of ship using the formula
[tex]\alpha = arctan(\frac{Qsin(\theta)}{P+Qcos(\theta)})[/tex]
Upon substituting the values, we get
[tex]\alpha = arctan(\frac{5sin(56)}{22+5cos(56)})\\ \alpha = arctan(\frac{4.14518}{24.79596})\\ \alpha = arctan(0.16717)\\ \alpha = 9.49^{0}[/tex]
Therefore, bearing of the resultant is [tex]157+9.49 = 166.49^{0}[/tex]
Hence, option (A) is the correct choice!
Which equation could be used to calculate the sum of the geometric series? 1/4+2/9+4/27+8/81+16/243?
Answers
1/4, 2/9, 4,27, 8/81, 16/243
the common ratio is: 2/3
thus the sum of the series will be given by the formula:
Sn=[a(1-r^n)]/(1-r)
plugging the values we obtain:
Sn=[1/4(1-(2/3)^n)]/(1-2/3)
thus the equation that will be used to find the sum is:
Sn=3[1/4-1/4(2/3)^n]
=3/4[1-(2/3)^n]
Answer: Sum of the geometric series will be [tex]\frac{763}{972}[/tex]
Step-by-step explanation:
Since we have given that
[tex]\frac{1}{4}+\frac{2}{9}+\frac{4}{27}+\frac{8}{81}+\frac{16}{243}[/tex]
Here,
[tex]a=\frac{2}{9}\\\\r=\frac{a_2}{a_1}\\\\r=\frac{\frac{4}{27}}{\frac{2}{9}}=\frac{4}{27}\times \frac{9}{2}=\frac{2}{3}\\\\n=4[/tex]
As we know the formula for "Sum of n terms in geometric series ":
[tex]S_n=\frac{a(1-r^n)}{1-r}\\S_n=\frac{\frac{2}{9}(1-\frac{2}{3}^4)}{1-\frac{2}{3}}\\S_n=\frac{130}{243}[/tex]
So, Complete sum will be
[tex]\frac{130}{243}+\frac{1}{4}=\frac{520+243}{972}=\frac{763}{972}[/tex]
Hence, Sum of the geometric series will be [tex]\frac{763}{972}[/tex]