When you are given the side length and apothem of a regular polygon and asked for area, you are expected to use the formula
... A = (1/2)Pa
where P is the perimeter of the polygon, "a" is the apothem, and A is the area.
The only additional information you need is that a decagon has 10 sides, so its perimeter is 10×3.2 inches = 32 inches.
The area is ...
... A = (1/2)(32 in)(5 in)
... A = 80 in²
_____
Sometimes the dimensions of a problem like this don't quite add up. The geometry of a regular polygon means that the apothem can be found from the side length and vice versa. In this case, the side length of 3.2 inches means the apothem is about 4.92 inches; or the apothem of 5 inches means the side length is about 3.25 inches. Either way, the area is slightly different from that computed using the given numbers.
This is why I say you're expected to use the above formula. (You're not expected to think about it too much.)
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The product of (3 + 2i) and a complex number is (17 + 7i).
The complex number is ?
The product of (3 + 2i) and a complex number is (17 + 7i)
The product of (3 + 2i) and a complex number is (17 + 7i).
Let the complex number be a + ib
Product means we multiply
So (3+2i) * (a + ib) = (17+7i)
WE need to find a+ ib
Divie by 3 + 2i on both sides
a + ib = (17+7i) / (3+2i)
To divide multiply by the conjugate (3-2i)
[tex]a + ib = (\frac{ 17+7i)*(3-2i)}{(3+2i)(3-2i)}[/tex]
[tex]a + ib = (\frac{(17*3+7*2)+(7*3-17*2)i}{3^2-2^2}[/tex]
[tex]a + ib = (\frac{(65)+(-13)i}{13}[/tex]
[tex]a+ib = \frac{65}{13} - \frac{13}{13}[/tex]
a+ib = 5 - i
The required complex number is 5 - i
Answer:
37+55i
Step-by-step explanation:
The product of (3 + 2i) and a complex number is (17 + 7i) is expressed as shown below:
(3+2i)(17+7i)
Expanding the bracket,
= 51+21i+34i+14i²
= 51+55i+14i²
Note that in complex numbers i² = -1
Substituting this into the result, we have:
= 51+55i+14(-1)
= 51+55i-14
= 37+55i
The product of both complex number is 37+55i
Find the equation of the line in slope-intercept form.Slope is 3/5 and (0, −2)
Answer:
[tex]y = \frac{3}{5}x - 2[/tex]
Step-by-step explanation:
Using the point slope form of a line equation, substitute m = 3/5 and the point (0,-2).
[tex]y - y_1 = m(x-x_1)\\y --2 = \frac{3}{5}(x - 0)\\y + 2 = \frac{3}{5}x \\ y = \frac{3}{5}x - 2 [/tex]
Find the point, M, that divides segment AB into a ratio of 5:5 if A is at (0, 15) and B is at (20, 0).
A) (35, 10)
B) (20, 10)
C) (10, 7.5)
D) (17.5, 5)
C
a ratio of 5 : 5 simplifies to 1 : 1, which basically means we require the midpoint of the line segment
using the midpoint formula
M = [[tex]\frac{1}{2}[/tex] (0 + 20 ), [tex]\frac{1}{2}[/tex] (15 + 0)] = (10, 7.5 )
Answer:
Option C). (10, 7.5)
Step-by-step explanation:
We have to find the coordinates of point M that divides the segment AB into a ratio of 5:5.
Vertices A and B are (0, 15) and (20, 0)
Ratio 5:5 is simply the ratio 1:1 means point M is the midpoint of segment AB.
So x-coordinate of M will be [tex]\frac{(20+0)}{2}=10[/tex]
and y - coordinate will be = [tex]\frac{(15+0)}{2}=7.5[/tex]
Therefore Option C. (10, 7.5) are the coordinates of point M.
juan is saving money for a trip. he has already saved 100 he saves 50 each week what would be the rate of change of the situation?
Answer:
The rate of change would be 50
Step-by-step explanation:
The rate of change in any equation is simply the amount in changes for every value of x. Since it goes up by 50 for every increase of the week, it means that the rate of change is 50.
What is the value of the expression? (5/2)2+3^3/4 Enter your answer in the box.
To evaluate the expression (5/2)^2 + 3^3/4, we simplify each part separately, then add the results. The final value of the expression is 13.
Explanation:To evaluate the expression (5/2)^2 + 3^3/4, we'll start by simplifying each part separately.
The first part, (5/2)^2, means we raise 5/2 to the power of 2. To do that, we multiply the numerator and denominator of 5/2 by itself:
(5/2)^2 = (5/2) x (5/2) = 25/4.
The second part, 3^3/4, means we raise 3 to the power of 3, and divide the result by 4:
3^3/4 = 27/4.
Now we can add the two simplified parts together:
(5/2)^2 + 3^3/4 = 25/4 + 27/4 = 52/4 = 13.
If 4x – 2y = 6, then y =
After solving the equation the value obtained for y will be equal to y = 2x - 3.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given equation in the question,
4x – 2y = 6
Let's solve the equation to find the value in terms of y.
2y = 4x - 6
y = (4x - 6)/2
y = 2x - 3
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Jerry measured and timed the descent of a diving bell spider in a large fish tank. The spider reached a position 4 1/2 inches below the surface of the water after descending at a constant rate for 1 1/2 seconds. Jerry recorded this as −4 1/2 inches. What is the position of the spider relative to the surface after 1 second? Enter your answer in the box.
-3 is the answer when you do this equation. Or it could be 300 depending.
Answer:
-3
Step-by-step explanation:
JK and JL in the xy-coordinate plane both have a common endpointJ(-4,11) and midpoints at M, (2,16) and M2(-3,5), respectively. What is the distance between M, and M2? Round to the nearest tenth.
okay so the coordinates are (2,16) & (-3,5) & what you have to do is use the distance formula. if you use it & solve your way through it, your answer should be 5 rounded to the nearest tenth
In a table do you have to list the x and y coordinates in order (largest to smallest)?
Answer:
No. (maybe)
Step-by-step explanation:
For expressing the corresponding values of x and y, any ordering will do. It is usually convenient for the user of the table if there is some recognizable order (so that a value can be found without searching the entire table). The usual expected order is by x-value, smallest to largest.
Some problem statements may specify that the table entries be listed in order. In those cases, yes, the table values must be listed as specified. (This accounts for the (maybe) answer, above.)
The difference between 72 and 16
72 - 16 = 56
-Nicole :) <3
72 - 16 = 56
If a question says "find the difference" it usually means that you can use subtraction :)
write an equation for a function , g(x), that is obtained by shifting the graph of f(x)= | x | three units to the left, reflecting that result over the x-axis, and then translating the graph up four unita.
g(x) =- | x + 3 | + 4
adding 3 units to x shifts the graph 3 units to the left
the negative reflects the function in the x- axis
adding + 4 translates the graph vertically up by 4 units
PLEASE HELP
Find the rectangular coordinates of the point with the polar coordinates (3, 3 divided by 2 pi).
Answer:
(0, -3)
Step-by-step explanation:
The terminal ray of the angle with measure 3π/2 radians is the negative y-axis. The point that is 3 units from the origin on that ray has x-coordinate 0 and y-coordinate -3. The point is (0, -3).
The president of a certain university receives a salary that is three times the salary of one of the department heads. The total of the two salaries is $190,000.
What is the salary of the department head?
3(X)+X=190000 is how you'd find the answer the answer is 47,500
What is 659.003 as a mixed number??
*Thanks*
Six hundred fifty-nine and three thousandths is ...
... 659 3/1000
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Andy and Samantha are performing an experiment in a science lab. The number of bacteria cells recorded by Andy in his experiment is represented by the equation below, where B represents the number of bacteria, x hours after beginning the experiment. The number of bacteria cells recorded by Samantha in her experiment is represented by the equation below, where B represents the number of bacteria, x hours after beginning the experiment. Using graphing technology, complete the statements. After hours, the total number of bacteria cells for both experiments will be the same. The total number of bacteria cells at that hour will be .
Answer:
after 5
time will be 35
Step-by-step explanation:
Joel is getting a dog, a cat, and a hamster. He goes to the pet store and can choose from 8 dogs, 12 cats, and 5 hamsters. How many different combinations can he get? A) 3 B) 25 C) 75 D) 480
The answer is B) 25
Option: B is the correct answer.
B) 25
Step-by-step explanation:Joel is getting a dog, a cat, and a hamster.
He goes to the pet store and can choose from 8 dogs, 12 cats, and 5 hamsters.
i.e. the total number of combinations that are possible could be calculated with the help of Combination as:
[tex]8_C_1+12_C_1+5_C_1[/tex]
We know that:
[tex]n_C_r=\dfrac{n!}{(n-r)!r!}[/tex]
Hence, the value of [tex]8_C_1\times 12_C_1\times 5_C_1[/tex] is:
[tex]=\dfrac{8!}{(8-1)!1!}+\dfrac{12!}{(12-1)!1!}+\dfrac{5!}{(5-1)!1!}\\\\\\=\dfrac{8!}{7!}+\dfrac{12!}{11!}+\dfrac{5!}{4!}\\\\=8+12+5\\\\=25[/tex]
Hence, the number of combinations is:
25
What is the answer to this? −4 1/2÷(−2 2/3) (it has to be a mixed number)
Here is you're answer:
In order to solve this equation you must first change the mixed numbers into improper fractions then use KCF. (Keep, Change, Flip)
[tex]-4\frac{1}{2} \div -2\frac{2}{3}[/tex]Change into improper fractions:[tex]-4\frac{1}{2} =\frac{-9}{2}[/tex][tex]-2\frac{2}{3} = \frac{-8}{3}[/tex][tex]\frac{-9}{2} \div \frac{-8}{3}[/tex]Apply KCF:[tex]\frac{-9}{2} \times \frac{-3}{8}[/tex]Now multiply: [tex]\frac{-9}{2} \times \frac{-3}{8} = \frac{27}{16}[/tex]Remember that a negative times a negative is a positive:[tex]= \frac{27}{16}[/tex]Change into a mixed number:[tex]\frac{27}{16} = 1\frac{11}{16}[/tex][tex]= 1\frac{11}{16}[/tex]Therefore you're answer is "1 11/16."
Hope this helps!
Lines AB and CD (if present in the picture) are straight lines. Find x. Give reasons to justify your solutions.
Answer:
x = 28°
Step-by-step explanation:
∠AOD and ∠BOC are vertical angles, hence congruent. That means the sum of ∠COE, ∠EOF, and ∠FOB is ∠BOC.
... 3x +x +(x+12°) = 152°
... 5x = 140° . . . . collect terms, subtract 12°
... x = 28° . . . . . . divide by 5
If line AB and CD are parallel to each other, hence the value of x from the given diagram is 39.2
To find the value of x from the given diagram, we will have to use the formula for finding the angle at a point.
The sum of all the angles at a point is 360 degreesTaking the sum of the angles and equating to 360 degrees is;152 + 3x + x + x + 12 = 360
152 + 12 + 5x = 360
164 + 5x = 360
5x = 360 -164
5x = 196
x = 196/5
x = 39.2
Hence the value of x from the given diagram is 39.2
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At a school concert the orchestra plays 8 songs that are 4.25 min long and 3 songs that are twice as long as each of the others. How long is the concert ?
Answer:
Total time of the concert = 59.5 min = 59 minute 30 seconds
Explanation:
At a school concert the orchestra plays 8 songs that are 4.25 min and 3 songs that are twice as long as each of the others.
Total length of 8 songs = 4.25*8 = 34 min
Length of 3 songs = 2*4.25 = 8.5 min
Total length of 3 songs = 3* 8.5 = 25.5 min
Total time of the concert = 34 + 25.5 = 59.5 min = 59 minute 30 seconds
The concert is 59.5 minutes long: 8 shorter songs at 4.25 min each and 3 longer songs at 8.5 min each.
To find the total duration of the concert, we first calculate the duration of the 8 shorter songs and then the longer ones.
1. Shorter songs:
Duration of each shorter song = 4.25 minutes
Total duration of 8 shorter songs = 8 × 4.25 = 34 minutes
2. Longer songs:
Each longer song is twice as long as the shorter ones, so its duration is 2 × 4.25 = 8.5 minutes
Total duration of 3 longer songs = 3 × 8.5 = 25.5 minutes
Now, add the durations of both types of songs to find the total duration of the concert:
Total duration = Duration of shorter songs + Duration of longer songs
Total duration = 34 minutes + 25.5 minutes = 59.5 minutes
So, the concert is 59.5 minutes long.
please help! cube root
What is the value of the expression? (5/2)2+33/4 Enter your answer in the box.
Answer:
Step-by-step explanation:
its 43
The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 6.8% daily failure rate.
a. What is the probability that the student's alarm clock will not work on the morning of an important final exam?
nothing (Round to three decimal places as needed.)
b. If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam?
nothing (Round to five decimal places as needed.)
c. What is the probability of not being awakened if the student uses three independent alarm clocks?
nothing (Round to five decimal places as needed.)
d. Do the second and third alarm clocks result in greatly improved reliability?
A.
No, because total malfunction would still not be unlikely.
B.
No, because the malfunction of both is equally or more likely than the malfunction of one.
C.
Yes, because total malfunction would not be impossible, but it would be unlikely.
D.
Yes, because you can always be certain that at least one alarm clock will work.
Answer:
Step-by-step explanation:
let X be the random variable for number of times the clock fails .
X is Poisson with average = 6.8% = 0.0068
PDF of x = e^(-0.0068) 0.0068^x/x!
a) The probability that the student's alarm clock will not work on the morning of an important final exam = P(X=0) = 0.00675
b) If the student has two such alarm clocks, the probability that they both fail on the morning of an important final exam:
Since both clocks are independent prob for both failing is
P(x1 fails) *P(x2 fails) = 0.00675(0.00675) = 0.000455625
c) the probability of not being awakened if the student uses three independent alarm clocks = Prob for all 3 fails = 0.00675^3
= 0.00000307546
d) Yes. Because all three fail probability is almost zero.
D. Yes, because you can always be certain that at least one alarm clock will work.
What are the steps for using a compass and straightedge to construct a line through point P that is parallel to line m? A horizontal line m and a point P are drawn. The point P is above the horizontal line m. Drag the steps and drop them in order from start to finish.
Answer:
Here's the list of the following sequence in the right order for you (I took the test myself and got this whole sequence right)
1. Use the straightedge to draw a line n that passes through P and intersects line m. Label the point of intersection as point X.
2. Place the point of the compass on point X and draw an arc that intersects lines m and n. Label the intersections as points A and B.
3. Without changing the width of the compass opening, place the point of the compass on point P and draw an arc that intersects line n. Label the intersection as point C.
4. Place the point of the compass on point A and open it to width AB.
5. With the compass opening set to width AB, place the point of the compass on point C and draw an arc that intersects the arc that was drawn from point P. Label the intersection of the arcs as point Y.
6. Use the straightedge to draw line PY.
Answer:
Here, m is a line and we have to find the draw parallel line of line of m through a point P with the help of straightedge and compass,
The correct order of steps for constructing a line through point P that is parallel to line m are as follows,
Step 1 : Use the straightedge to draw a line n that passes through P and intersect line m, lebel the point of intersection as X,
Step 2 : Place the point of the compass on point X and draw an arc that intersect line m and n, label the intersection point A and B,
Step 3 : Without changing the width of the compass opening, place the point of compass on point P and draw an arc that intersect line n label the intersection point as C,
Step 4 : Place the point of compass on point A and open it to the width of AB,
Step 5 : With the compass opening set the width of AB, place the point of the compass On point C and draw an arc that intersects the arc that was drawn from point P lebel the intersection of arc as point Y,
Step 6 : Use the straightedge to draw PY
(-5,-7),(0,-5),(5,-3) Determine the intercepts of the line that passes through the following points.
x-intercept ( , )
y intercept ( , )
Answer:
x-intercept (12.5, 0)y-intercept (0, -5)Step-by-step explanation:
The slope of the line is ...
... (change in y)/(change in x) = (-3 -(-5))/(5 - 0) = 2/5
The y-intercept is given: (0, -5).
The slope-intercept form of the equation can be written from this information as ...
... y = (2/5)x - 5
Solving this for y=0 (to find the x-intercept), we have
... 0 = (2/5)x - 5
... 5 = (2/5)x
... 5·(5/2) = x = 12.5
So, the x-intercept is 12.5, and the y-intercept (given) is -5.
One US dollar is currently worth 0.79 euro (€). If you exchange $522 for euros, how many euros will you have?
I'm pretty sure you would have 412.38 (€) because the equation would be $522 × 0.79.
Answer:412.38
Step-by-step explanation:
What is the solution of the system of inequalities
Answer:
There are four (4) whole-number solutions to these inequalities:
... {(4, 1), (5, 0), (6, 0), (7, 0)}
Step-by-step explanation:
These are nicely solved by graphing. Whole numbers are non-negative integers, so x and y can be any values 0, 1, 2, .... The area of overlap on the graph clearly shows that y=0 and y=1 are the only viable choices for y, and that the values for x are limited in each of these cases.
Write an equation of the line passing through each of the following pairs of points. (−3, 1), (0, 3)
The 2-point form of the equation for a line is applicable. For points (x₁, y₁) and (x₂, y₂) that equation is ...
... y = (y₂ -y₁)/(x₂ -x₁)·(x -x₁) +y₁
Filling in your point values gives ...
... y = (3 -1)/(0 -(-3))·(x -(-3)) +1
This can be simplified to ...
... y = (2/3)(x +3) +1
... y = (2/3)x +3
what is an equation in point-slope form for the line that passes through the points (4,-1) and (-3,4)?
y - 4 = - [tex]\frac{5}{7}[/tex](x + 3 )
the equation of a line in point-slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
to calculate m use the gradient formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (4, - 1) and (x₂, y₂ ) = (- 3, 4)
m = [tex]\frac{4+1}{-3-4}[/tex] = [tex]\frac{5}{-7}[/tex] = - [tex]\frac{5}{7}[/tex]
use either of the 2 points as a point on the line
using (a, b) = (- 3, 4 ), then
y - 4 = - [tex]\frac{5}{7}[/tex](x + 3 )
a store is having a dealer close-out sale. A computer desk, originally priced at $83, is now on sale for $78.85. what is the close-out discount rate? This is a percent of decrease.
A computer desk, originally priced at $83, is now on sale for $78.85
originally priced at $83. After discount the price becomes $78.85
Discount amount = $83 - $78.85 = $4.15
Decrease rate = discount amount divide by original price
Decrease rate = [tex]\frac{4.15}{83}= 0.05[/tex]
Decrease rate = 0.05
To find percent of decrease we multiply by 100
0.05 * 100 = 5%
Decrease percentage = 5%
The school bookstore has 108 book covers. They will be equally distibuted among the students in the 2 sixth grade classes. Each class has 18 students. How many books covers does each student receive?
Each student will receive 3 book covers when 108 book covers are equally distributed among 36 students from two sixth-grade classes.
The question asks us to figure out how many book covers each student will receive if 108 book covers are distributed equally among students in two sixth-grade classes, with each class having 18 students.
First, calculate the total number of students by multiplying the number of classes by the number of students in each class: 2 classes * 18 students/class = 36 students.Then, divide the total number of book covers by the total number of students: 108 book covers / 36 students = 3 book covers per student.As a result, each student will receive 3 book covers.