Answers
7a)
[tex]\frac{n(n - 3)}{2} = 665\\n(n - 3) = 665 \cdot 2\\n(n - 3) = 1330\\n^2 - 3n = 1330\\n^2 - 3n - 1330 = 0\\n = \frac{-(-3) \pm \sqrt{(-3)^2 - 4 \cdot 1 \cdot (-1330)}}{2 \cdot 1} = \frac{3 \pm \sqrt{9 + 5320}}{2} = \frac{3 \pm \sqrt{5329}}{2} = \frac{3 \pm 73}{2}\\n_1 = \frac{3 + 73}{2} = \frac{76}{2} = 38\\n_2 = \frac{3 - 73}{2} = \frac{-70}{2} = -35[/tex]
If n is the amount of sides then there's 38 sides in a polygon with 665 diagonals
7b)
We do the same as 7a) but with 406. We get that [tex]n_1 = 30.04[/tex] and [tex]n_2 = -27.04[/tex]. A polygon cant have 30.04 sides
Answer: A. 38 sides
B. When solved, you get -27.04 sides or 30.04 sides. Neither of these are possible because the number of sides cannot be negative or a decimal.
Step-by-step explanation: Part A:
If the polygon has 665 diagonals, set your original n-sided polygon equal to it.
n(n - 3)/2 = 665
Multiply both sides by 2 so it’s not in the denominator.
n(n - 3) = 1330
Distribute n and subtract 1330 from both sides so it is equal to zero.
n² - 3n - 1330 = 0
Factor it:
(n - 38)(n * 35) = 0
Solve for n by setting it equal to zero:
n = 38 & n = -35
The number of sides cannot be negative, therefore, the answer to Part A is 38 sides.
Part B:
Set your original n-sided polygon equal to 406 and solve to prove that a polygon cannot have 406 diagonals.
n(n - 3)/2 = 406
Multiply both sides by 2 so it’s not in the denominator.
n(n - 3) = 812
Distribute n and subtract 812 from both sides so that it is equal to zero.
n² - 3n - 812 = 0
This cannot be factored, so plug it into the Quadratic Formula. Here are the values you need for the Quadratic Formula based on the polynomial above:
a = 1
b = -3
c = -812
When you solve this, you will get:
n = -27.04 and n = 30.04
A polygon cannot have negative sides and it cannot have decimal sides. It has to be a positive integer (positive whole number).
Related Questions
The solution of a+b>12 is a>-3. What is the value of b?
Answers
Answer:
b>12-a
Step-by-step explanation:
Answer:
its b>12
Step-by-step explanation:
The first few steps in solving the quadratic equation 8x2 80x = −5 by completing the square are shown. 8x2 80x = −5 8(x2 10x) = −5 8(x2 10x 25) = −5 ______ which number is missing in the last step? −200 −25 25 200
Answers
The number is missing in the last step in the quadratic equation is 200. Then the correct option is D.
What is a factorization?It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.
The quadratic equation is 8x² + 80x = −5
On adding and subtracting 200 on both sides, we have
8x² + 80x + 200 = −5 + 200
8 (x² + 10x + 25) = −5 + 200
Thus, the number is missing in the last step in the quadratic equation is 200. Then the correct option is D.
More about the factorization link is given below.
https://brainly.com/question/6810544
The sand in an hourglass drops at a constant rate of 2.5 cubic millimeters ( mm3 ) every second. The amount of sand that drops, y , in mm3 , is a function of time, x , in seconds.
For the input values of 0 , 2 , and 6 , determine the matching outputs. Graph the inputs of 0 , 2 , and 6 and their corresponding outputs as ordered pairs, represented by points on the coordinate plane.
Keyboard Instructions
Initial graph state
The horizontal axis goes from -1 to 25 with ticks spaced every 1 unit(s).
The vertical axis goes from -1 to 18 with ticks spaced every 1 unit(s).
Created graph shapes
Point with coordinates (-1, 0).
Point with coordinates (-1, 0).
i Just need the graph points
Answers
Answer:
Step-by-step explanation:
In the graph, y is the amount of sand in mm^3 and x is time in seconds.
They are directly related as the sands drops at a constant rate of 2.5 cubic millimeters ( mm^3 ) every second.
So y = 2.5x
Input x=0, output is y=0
The first point is (0, 0)
Input x=2, y=2.5*2=5
The second point is (2, 5)
Input x=6, y=2.5*6=15
The third point is (6, 15)
Use a calculator to solve the following equation for θ on the interval [−90∘,90∘]. Sin(θ)=34
Answers
The value of θ from the given equation is 48.59degrees
Trigonometry identityGiven the trigonometry function
Sin(θ)=3/4
We are to find the value of theta that will make the expression true
Take the arcsin of both sides
arcsin Sin(θ)= arcsin(3/4)
θ = arcsin(3/4)
θ = 48.59
Hence the value of θ from the given equation is θ = 48.59 defense
Learn more on trig identity here:https://brainly.com/question/7331447
For the linear relation y= 2x + 5, the x-intercept is -2/5
True
False
Answers
Answer:
False
Step-by-step explanation:
Every linear equation in two variables can be written as y=mx+c.
Here, for each value of x there is a unique value of y.
Also, x & y are in direct variation.
Hence, xy will always remain constant.
Consequently, the graph will maintain a definite slope making it a straight line.
∴ The given statement is false.
Answer:
False
Step-by-step explanation:
=> y = 2x + 5
=> y - 2x = 5
=> - 2x + y = 5
=> (-2x + y) = 5
=> (-2/5)x + y/5 = 1
=> x/(-5/2) + y/5 = 1, it is in form of x/a + y/b = 1, a is intercept of x.
So, here, x intercept is -5/2.
Method 2;
=> y = 2x + 5
=> y = 2(x + 5/2)
=> y = 2{x - (-5/2)}, says, x intercept is - 5/2 & not - 2/5
HELP PLEASE!!!
If angle X and angle Y are a Linear Pair, what can be stated about the two angles?
A. Angle X and angle Y are both obtuse
B. Angle X and angle Y are complementary
C. Angle X and angle Y are supplementary
Answers
Answer:
C
Step-by-step explanation:
linear pairs equal up to 180°, so the 2 angles must be supplementary, meaning it adds up to 180°.
The product of two consecutive positive even integers is 24. Find the integers.
Answers
Answer:
The two consecutive even integers
:
(
4
,
6
)
or
(
−
6
,
−
4
)Step-by-step explanation:
n
and
n
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.
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.
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(
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×
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n
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n
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6
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:
(
4
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6
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(
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So,the two consecutive even integers
:
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What is the inverse of the equation y = 3x + 2?
Answers
Answer: y = (x-2)/3
This is equivalent to y = (1/3)x - 2/3
=================================================
To get this answer, we need to swap x and y in the original equation. Then solve for y to get the inverse.
y = 3x+2
x = 3y + 2 ... x and y swapped
x-2 = 3y
3y = x-2
y = (x-2)/3
y = x/3 - 2/3
y = (1/3)x - 2/3
This final equation has slope 1/3 and y intercept -2/3
Identify the cluster in the data
Answers
The one that has the most circles in a group :D
To hire a tutor, Abelia will pay $35 per hour plus a materials fee of $10. She will only pay the materials fee one time. The equation c = 10 + 35h can be used to represent this situation where c is the total cost and h is the number of hours Abelia hires the tutor.
Answers
Answer:
Yes! C=10+35h is correct!
Step-by-step explanation:
Yes, equation is correct!
$10 is fixed one time fee.$35 is hourly pay.
So, if she needs tutor for 'h' hours, the variable cost is $35h
So, total cost C =10+35h
Here’s an algebra problem 20 points will mark brainliest if correct!!!
Answers
Answer:
y = 12/7xStep-by-step explanation:
Given A graph with points A, B, C, D and ETo findEquation of the line through the points C and DSolutionWe'll get the coordinates of the points C and D first and find slope and y-intercept
As per the graph, the coordinates are:
C = (0, 0) and D (7, 12)Formula of the line
y = mx + bSlope is
m = (12 - 0)/(7 - 0) = 12/7y- intercept is 0 as per point CSo the line is
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Free points?!?! Sjisjsusdn disnsbsjd sjsjsjjsd dudjsjd sjsjsjjsd dhjdbsvsbssk usjsjdjdn sdudjsbdj dudjsjdjsobdud djsjdndbdun flight g g. Finding. Finding fouled. Dozen foams fouled hsjsjsjs we see s e e. E e e e e
Una dos tres Quattro cinco diese ceiento
1.
2.
3.
Choose all that apply
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Help please
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Explain your answer
Research paper
Thanks!
Thanks
thanks
History
African American
Experiences
Justice
Identify
Social
Women
Which factors push cultures to change over time
Population
Distribution
Trade
Growth
Technology
Properties of algebra
Find the sum of
I need this done before tomorrow please help
Answers
Answer:
If im not mistaken angle B nad D should have the same meausurement which would be 128°
Rewrite the following polynomial in standard form.
-2+1/3x^2-x
Answers
Step by step explanation
Evaluate.
781
1.8
2.10
3.11
4.9
Answers
Answer:
9 is the answer u are looking for square root
What is the exponential regression equation to best fit the data where the y values were rounded to the nearest integer.
Question 9 options:
y=3(1. 05)^x
y=2. 1(2. 05)^x
y=2. 17(2. 96)^x
y=2(2. 95)^x
Answers
Answer: y=2.17(2.96)
Step-by-step explanation: i took the test
PLZ HELP!!
Choose the best answer.
Solve the equation.
e – 8 = 22
Question 1 options:
e = 14
e = 30
e = -8
e = 22
Question 2 (1 point)
Choose the best answer.
Solve the equation.
n + 11 = –29
Question 2 options:
n = 18
n = 40
n = –17
n = –40
Question 3 (1 point)
Choose the best answer.
Solve the equation.
e – 14.4 = –20.8
Question 3 options:
e = –35.2
e = 6.4
e = –6.4
e = 35.2
Question 4 (1 point)
Choose the best answer.
Solve the equation.
t – (–16) = –13
Question 4 options:
t = –3
t = 29
t = –29
t = 3
Question 5 (1 point)
Choose the best answer.
On Wednesday, William wrote a check in the amount of $45.60. This brought his balance down to –$15.75. Suppose n represents William's balance before he wrote the check.
Which equation can be used to represent this situation?
Question 5 options:
n + 45.60 = –15.75
n – 45.60 = –15.75
n – 15.75 = –45.60
n – 15.75 = 45.60
Question 6 (1 point)
Choose the best answer.
Solve the word problem.
Luke mowed a lawn today to earn some extra money. He spent $2.10 on fuel and $4.45 on lunch. He charged $13.50 to mow the lawn.
What was his profit for mowing the lawn?
Question 6 options:
$20.05
$11.15
$15.85
$6.95
Question 7 (1 point)
What is the LCD of 12 and 35
?
Question 7 options:
2
7
10
20
Question 8 (1 point)
Choose the best answer.
Which statement correctly compares512 and 716
?
Question 8 options:
512>716
512=716
512<716
Question 9 (1 point)
Add.
23+58
Question 9 options:
724
711
3124
78
Question 10 (1 point)
Add.
−23+14
Question 10 options:
14
−512
17
37
Answers
Answer:
[tex]e = 30 \\ n = –40 \\ e = –6.4 \\ t = –29 \\ n – 45.60 = –15.75 \\ 6.95 \\ the \: LCD \: of \: 12 \: and \: 35 \: is \: 2 \\{ 512 < 716} \\ 81(not \: in \: the \: option) \\ - 9(not \: in \: the \: option)[/tex]
What is the square root of -1?
Answers
Answer:
i
Step-by-step explanation:
Zero has one square root which is 0. Negative numbers don't have real square roots since a square is either positive or 0. The square roots of numbers that are not a perfect square are members of the irrational numbers. This means that they can't be written as the quotient of two integers.
the answer is i
Step-by-step explanation:
for real this is true
Consider a post office with two clerks. Three people, A, B, and C, enter si- multaneously. A and B go directly to the clerks, and C waits until either A or B leaves before he begins service. What is the probability that A is still in the post office after the other two have left when
Answers
Answer:
0
Step-by-step explanation:
Linda pays $24.84 for 7.2 gallons of gas.
Find the unit price in dollars per gallon.
If necessary, round your answer to the nearest cent.
Answers
Answer:
3.45
Step-by-step explanation:
24.84/7.2 = 3.45
The unit rate is $3.45 per gallon
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: Linda pays $24.84 for 7.2 gallons of gas.
Thus unit rate ( dollars per gallon) = $24.84/7.2
=$3.45 per gallon
Hence, The unit rate is $3.45 per gallon
Learn more about the unitary method here:
https://brainly.com/question/22056199
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Jennifer drove 450 miles back home to Maine. If she drove this in 6 hours, what was her unit rate?
Answers
Answer:
the unit rate was 75
Step-by-step explanation:
i did 450 divided by 6 =75
she drove 75 miles per hour
Find the sum of the interior angles of a polygon with 20 sides
Answers
Answer:
3240°
Step-by-step explanation:
The sum of the interior angles of a polygon is found by (n-2)(180) where n is the number of sides so (20-2)(180) = (18)(180) = 3240°
CRIS 100 A hostel had rations for 60 days for 500 students. After 12 days, 300 more students join the hostel mess How long will the remaining ration last?
Answers
Answer:
30
Step-by-step explanation:
[tex]500\times\left(60-12\right)\div\left(300+500\right)[/tex]
Calculate
[tex]\frac{500\times\left(60-12\right)}{300+500}[/tex]
Calculate the sum or difference
[tex]\frac{500\times48}{300+500}[/tex]
Calculate the sum or difference
[tex]\frac{500\times48}{800}[/tex]
Cross out the common factor
[tex]\frac{5\times48}{8}[/tex]
Cross out the common factor
[tex]5\times6[/tex]
Calculate the product or quotient
[tex]30[/tex]
PLEASE HELP!!
(x+3)(x−2)/(x+7)² ≥0
Answers
Answer:
Step-by-step explanation:
The temperature in the morning was - 24
degrees. By the afternoon, the
temperature was 0.2 degrees. What was
the change in temperature?
Answers
Answer:
ΔT = -23.8°
Step-by-step explanation:
Given :-
T (initial) = 24°T (final) = 0.2°To Find :-
ΔTSolving :-
ΔT = T (final) - T (initial)ΔT = 0.2 - 24ΔT = -23.8°which is never visible on the graph of a sequence?
a. x-intercept
b. the first term
c. common difference
d. y-intercept
please help me :,(
Answers
The measures of the angles of a triangle are shown in the figure below . Solve for x
Answers
Which lunch box holds more? HELP image included
Answers
Answer:
lunch box a
Step-by-step explanation:
brainliest pls :3
I'm unsure of what the answer to this is.
Answers
Answer:
your answer is definitely B
Step-by-step explanation:
For each diagram below, write and solve an equation.
Answers
Answer:
A.x=3 C. n=10
Step-by-step explanation:
A.13-7=6
6/2=3
C.6x4=24
44-24=20
20/2=10
You want to test the effects of water aerobics on resting heart rate. You decide to test two different levels of exercise (water aerobics for 30 minutes twice a week and water aerobics for 60 minutes once per week.) You randomly find a group of 60 subjects (30 men and 30 women) for this study. What is an appropriate design for this study? A). Randomized block design B). Completely randomized design C). Matched pairs design
Answers
Answer:
The correct option is;
A). Randomized block design
Step-by-step explanation:
In a randomized block design the experimental units or subjects of the experiment are separated into subgroups known as blocks with the property that the the variability (difference) of the parameters within the blocks are lesser than the variability between block, such that the treatment of the research or experiment are assigned differently to each block
The groups can therefore comprise of the following;
Group 1
15 men and 15 women to perform water aerobics for 30 minutes twice a week
Group 2
15 men and 15 women to perform water aerobics for 60 minutes once a week
Therefore, the effect of the experiment will be much less attributed to gender than to the durations of the water aerobic exercise.