Answer:
Option B is correct.
The approximate area of regular octagon is, 101 square ft.
Step-by-step explanation:
Given: A regular octagon has a radius of 6 ft and a side length of 4.6 ft.
To find the area of a regular octagon(A) of side length a is given by :
[tex]A=2\cdot(1+\sqrt{2})a^2[/tex]
Given the length of side, a= 4.6 ft
Substitute the value of a=4.6 ft in the given formula of area:
[tex]A=2\cdot(1+\sqrt{2})\cdot(4.6)^2[/tex] or
[tex]A=(2+2\sqrt{2})\cdot (21.16)[/tex] or
[tex]A=(2+2.828)\cdot(21.16)[/tex]
Simplify:
[tex]A=4.828\cdot 21.16 =102.16048[/tex] square ft.
therefore, the approximate area of regular octagon is, 101 square ft
Check all that apply: If cos theta = 15/17 then:
A. Sec theta = 17/15
B. Tan theta = 8/15
C. Sin theta = 15/8
D. Csc theta = 17/15
The options (A) and (B) are correct.
What is trigonometric Ratios?"Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. It is with respect to any of its acute angles are known as the trigonometric ratios of that particular angle".
For the given situation,
Cos θ = 15/17
By using Pythagoras theorem,
We know Cos θ = [tex]\frac{base}{hypotenuse}[/tex]
Sine θ = [tex]\frac{perpendicular}{hypotenuse}[/tex]
tan θ = [tex]\frac{perpendicular}{base}[/tex]
By Pythagoras theorem, [tex]Hypotenuse^{2}= base^{2}+perpendicular^{2}[/tex]
⇒[tex]17^{2}=15^{2}+perpendicular^{2}[/tex]
⇒[tex]perpendicular^{2}= 289-225[/tex]
⇒[tex]perpendicular=\sqrt{64}[/tex]
⇒[tex]perpendicular=8[/tex]
Thus, Sec θ = 17/15
Tan θ = 8/15
Sine θ = 8/17
Cosec θ = 17/8.
Hence we can conclude that the options (A) and (B) are correct.
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Answer:
tan and sec
Step-by-step explanation:
A amd B
A cylindrical metal can is to have no lid. it is to have a volume of 8Ï in3. what height minimizes the amount of metal used?
To solve this problem let us say that,
h = height of the can
r = radius of the can
We try to minimize the amount of metal used which is the surface area (SA), and the equation for a cylinder is:
SA = 2πrh + πr^2
To get the minima, we take the derivative of this function and set it equal to 0. But first, the function is in two variables so we must eliminate one of them. We use the extra information given in the problem which is volume:
V = 8π = πr^2 h
Therefore,
h = 8/r^2
Plug this into the SA function to have it in terms of one variable only:
SA = 2πrh + πr^2
SA = 2πr(8/r^2) + πr^2
SA = 16π/r + πr^2
Taking the 1st derivative of the function:
0 = −16π r^−2 + 2πr
0 = −16π/r^2 + 2πr
16π/r^2 = 2πr
r^3 = 8
r = 2 in
By obtaining r, we calculate for h:
h = 8/r^2
h = 8/(2)^2
h = 8 / 4
h = 2 in (ANSWER)
How many ways are there to place 5 basketball players on the court if you must place 2 guards, 2 forwards and a center, from a team of 12, consisting of 4 guards, 5 forwards and 3 centers?
Final answer:
There are 180 ways to place 5 basketball players on the court, selecting 2 guards, 2 forwards, and 1 center.
Explanation:
To determine the number of ways to place 5 basketball players on the court, we need to find the number of combinations of guards, forwards, and centers that can be selected from the available players. There are 4 guards, 5 forwards, and 3 centers in the team.
The number of ways to select 2 guards from 4 is C(4,2) = 6.
The number of ways to select 2 forwards from 5 is C(5,2) = 10.
The number of ways to select 1 center from 3 is C(3,1) = 3.
By the multiplication principle, the total number of ways to place the players on the court is 6 × 10 × 3 = 180.
Please Help!! Find the measure of angle 2. Image Attached
What is the slope of the line that passes through the points (4, -7) and (9, 1)?
(5/8)
(8/5)
(-6/12)
(-13/6)
Given the vertices of ∆ABC are A (2,5), B (4,6) and C (3,1), find the vertices following each of the
transformations FROM THE ORIGINAL vertices:
a. Rx-axis
b. Ry = 3
c. T<-2,5>
d. T<3,-6>
e. r(90◦, o)
In which expression should the exponents be multiplied?
a. (5^3)-4
b. (1/3)^4*(1/3)^7
c. 3^7/3^15
d. 4^5*4^2
Option b is the correct answer. Exponents should be multiplied in the expression (1/3)^4*(1/3)^7, resulting in (1/3)^11.
The expression where the exponents should be multiplied is Option b. (1/3)^4*(1/3)^7. This is because when you multiply two expressions that have the same base, you add their exponents. In this case, you have the base (1/3) raised to the 4th power and then to the 7th power, so you add the exponents 4 + 7, which equals 11. Therefore, (1/3)^4*(1/3)^7 simplifies to (1/3)^11.
Another case where you multiply exponents would be when raising a power to another power, like in (5^3)^4. Here the exponents 3 and 4 are multiplied, resulting in (5^12).
Which number line represents all of the values of x for the equation x2 = 36?
yes thats the corrects answer -6 and 6 on the number line.
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -4 + 5 cos θ
Answer:
x-axis
Step-by-step explanation:
Conjectures can always be proven true.
True or False
Solve 2x2 + 20x = −38.
a. −5 ± square root 14
b.−5 ± square root 51
c. −5 ±square root 6
d.−5 ± square root 13
Answer:
c
Step-by-step explanation:
−5 ±square root 6
Find f(x) and g(x) so that the function can be described as y = f(g(x)). y = eight divided by square root of quantity two x plus four.
A bicyclist travels 1 mile in 5 minutes. If m represents minutes, what does the expression m over 5 represent
Which of the following ordered pairs is represented by a point located on the x-axis?
Select one:
a. (6,-6)
b. (3,3)
c. (0,8)
d. (-5,0)
Graph the following piecewise function and then find the domain.
(6.04)The scatter plot shows the relationship between the number of hours spent jogging and the number of minutes spent stretching, by the students on a track team:
What is the y-intercept of the line of best fit and what does it represent?
1 minute; the number of minutes students stretch when they do not jog
1 hour; the number of hours students jog when they do not stretch
4 hours; the number of hours students jog when they do not stretch
4 minutes; the number of minutes students stretch when they do not jog
A rectangular patio is 9 ft by 6 ft. When the length amd width are increased by the same amount, the area becomes 88 sq ft. Ginger is using the zero product property to solve the equation (6+x)(9+x)= 88. What do her solutions represent?
The solutions represent the additional length and width that need to be added to the original dimensions to achieve the desired area of 88 sq ft.
Explanation:The equation is: (6+x)(9+x) = 88. Ginger is using the zero product property to solve for x. The solutions she finds represent the value of x that, when added to both the length and width of the original patio, will result in a patio with an area of 88 sq ft.
By solving the equation, Ginger will find the possible values of x that will make the area of the new patio equal to 88 sq ft. These values represent the additional length and width that need to be added to the original dimensions to achieve the desired area.
For example, if Ginger finds that x = 2, then the new patio dimensions would be 9+2 = 11 ft by 6+2 = 8 ft, resulting in an area of 11 * 8 = 88 sq ft.
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Solve log660 – log630. A. 5 B. log62 C. 2 D. log630
Answer:
Option B - [tex]\log_6 60-\log_6 30=\log_6 (2)[/tex]
Step-by-step explanation:
Given : Expression [tex]\log_6 60-\log_6 30[/tex]
To find : Solve the given expression?
Solution :
Step 1 - Write the expression
[tex]\log_6 60-\log_6 30[/tex]
Step 2 - Applying logarithmic property, [tex]\log a-\log b=\log(\frac{a}{b})[/tex]
[tex]\log_6 60-\log_6 30=\log_6 (\frac{60}{30})[/tex]
Bases are same.
Step 3 - Solve
[tex]\log_6 60-\log_6 30=\log_6 (2)[/tex]
Therefore, The solution of expression is
[tex]\log_6 60-\log_6 30=\log_6 (2)[/tex]
So, Option B is correct.
Which lines can you conclude are parallel given that m14 + m2 = 180? Justify your conclusion with a theorem.
Answer:
Option 2 is correct.
Step-by-step explanation:
Given the diagram and also the condition m∠14 + m∠2 = 180°
we have to tell which lines are parallel.
By the theorem of exterior angles
Same-side exterior angles which are formed outside of the parallel lines and on same side of transversal line.
The theorem states that when parallel lines are cut by a transversal line, the sum of the same-side exterior angles is 180° i.e these are supplementary.
∴ Lines a and b are are parallel by converse of same side exterior angle theorem.
What is the value of x in the equation 2(x – 3) + 9 = 3(x + 1) + x?
x =
James is four years younger than Austin. If 2 times James age is increased by the square of austins age, the result is 28. Find the 2 ages. Use an algebraic solution
The value of y varies jointly with the values of x and z. When x=4 and z=9, the value of y is 360. What is the value of y when x=5 and z=12?
The equation sec^2x-1=tan^2x is an identity true or false
A box with a square base and open top must have a volume of 32,000 cm3. find the dimensions of the box that mini- mize the amount of material used.
How do you simplify this problem?
1+tan^2(x) = sec^2(x)
sec^2(x) = 1/cos^2(x)
csc(-x) / 1/cos^2(x) =
cos^2(x) csc(-x)
Look at the formula for finding distance.
D=RT
Which of the following is the formula to find time (t)?
ANSWERS:
A-T=DR
B-T=R/D
C-T=D/R
D-T=D-R
The book Kathy is reading is 540 pages long. So far, she has read 405 pages. What percent of the book does she have left to read?
Answer: b
Step-by-step explanation: i got it right
A point where two or more rays or "arms" of an angle meet
Final answer:
The point where two or more rays meet in optics is known as the focal point, which is crucial in geometric optics. For a converging lens or mirror, it's where light rays converge, while for a diverging lens or mirror, it's where light rays appear to originate.
Explanation:
The point where two or more rays or 'arms' of an angle meet in the context of geometrical optics is known as the focal point. In terms of a converging lens or mirror, the focal point is where converging light rays intersect after passing through the lens or reflecting off the mirror surface. This is a fundamental concept in the study of geometrical optics, which deals with the ray aspect of light. A ray is a straight line that originates at a point and is used in geometric optics to represent the path along which light travels.
For a converging lens, which is also known as a convex lens, parallel light rays entering the lens will refract and converge at a single point on the opposite side of the lens. This single point is the focal point. Similarly, in concave mirrors, ray diagrams show the focal point as the point where reflected rays converge or appear to converge. The distance from the focal point to the mirror along the central axis is referred to as the focal length. Conversely, for a diverging lens or mirror, the focal point is the point from which diverging light rays appear to originate.
find the 5th term of the sequence in which T1=8 and Tn=3t n-1
A cell phone company charges a basic rate of $19.99 per month for 300 minutes of local usage. Any local usage over 300 minutes is charged at $.10 per minute. All long distance calls are charged at $.25 per minute. Write and simplify an expression that gives the total monthly bill if x is the number of local minutes and y is the number of long distance minutes. Evaluate the expression if local usage totals 375 minutes and long distance usage totals 54 minutes.
total = 19.99 + 0.10(x-300) + 0.25y
x = 375
y=54
total = 19.99 +0.10(375-300) +0.25(54)
total = 19.99 + 0.10(75) + 0.25(54)
total = 19.99 + 7.50 + 13.50
total = $40.99
The total monthly bill is $40.99 for 375 local minutes and 54 long distance minutes, given the cell phone company's rates.
The total monthly bill can be expressed as the sum of the basic rate, the extra charge for local minutes beyond the included 300, and the charge for all long distance minutes. The expression can be written as:
Total Monthly Bill = Basic Rate + (Local Extra Charge x Extra Local Minutes) + (Long Distance Rate x Long Distance Minutes)
Where:
Basic Rate = $19.99Local Extra Charge = $0.10 per minuteExtra Local Minutes = x - 300 (only if x > 300)Long Distance Rate = $0.25 per minuteLong Distance Minutes = yFor x = 375 local minutes and y = 54 long distance minutes, the total monthly bill is calculated as follows:
Total Monthly Bill = $19.99 + ($0.10 x (375 - 300)) + ($0.25 x 54)
Total Monthly Bill = $19.99 + $7.50 + $13.50
Total Monthly Bill = $40.99