Answers
The values for x are:
question 15 ⇒x=8
question 16⇒x=19
question 17⇒x=14
Here you should apply your knowledge about regular polygons. The question asks the values of x that is a variable for some interior angles. Then, you will find x from the sum of interior angles of each regular polygon.
Sum of Interior Angles of Regular PolygonThere is a formula that relates number of sides polygon with its sum of interior angles. See below.
S=(n-2)*180°
S=sum of interior angles of regular polygon.
n=number of sides of regular polygon.
Exercise 15First, you should find the value for the sum of interior angles. Here, the regular polygon has 4 sides. Then,
S=(n-2)*180°
S=(4-2)*180°
S=2*180°=360°
Note that only 3 interior angles are shown in the figure. Nonetheless, the question gives an external angle (71°). Thus, the internal angle will be: 180-71=109°. This is because the interior and exterior angles are supplementary.
Next step, sum of interior angles for finding x
[tex]10x+6+13x-2+109+8x-1=360\\ \\ 31x=360-112\\ \\ 31x=248\\ \\ x=\frac{248}{31} =8[/tex]
x=8
Exercise 16
First, you should find the value for the sum of interior angles. Here, the regular polygon has 6 sides. Then,
S=(n-2)*180°
S=(6-2)*180°
S=4*180°=720°
Next step, sum of interior angles for finding x.
[tex]90+9x-19+7x+3+111+5x+8+128=720\\ \\ 21x=720-321\\ \\ 21x=399\\ \\ x=\frac{399}{21} =19[/tex]
x=19
Exercise 17
First, you should find the value for the sum of interior angles. Here, the regular polygon has 5 sides. Then,
S=(n-2)*180°
S=(5-2)*180°
S=3*180°=540°
The image of the question shows the sides are congruent, consequently, the angles are equal.
Next step, sum of interior angles for finding x.
[tex]9x-18+9x-18+9x-18+9x-18+9x-18=540\\ \\ 45x=540+90\\ \\ 45x=630\\ \\ x=\frac{630}{45} =14[/tex]
x=14
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Related Questions
Help appreciated, thanks so much!
Answers
Answer:
r= -6
Step-by-step explanation:
Write 41/10 as a fraction
Answers
Answer:
41/10
Step-by-step explanation:
Answer:
Based on what you asked i think the answer would be 4 1/10
Step-by-step explanation:
Which equation represents a graph with a vertex at (1, -6)?
A. y=3x2+6x–3
B. y=3x2-6x-3
C. y=3x2-8x-1
D. y=3x2-3x-6
Answers
Answer:
the answer is B
Answer:
its b
Step-by-step explanation:
Help????? Pls?????????
Answers
Answer:
20 men in the dance recital.
Step-by-step explanation:
tt
Jordan went shopping last weekend and bought a pair of shoes. The shoes were originally priced at $124.00, but are now on sale for 30% off the regular price. The sales tax is 7%.
What is the sales tax?
Answers
Answer:
8.68
Step-by-step explanation:
just multiply 124.00 times 0.07 and that's it
what is. the value of x in the equation 2.5(6x-4)=10+4(1.5+0.5x)?
Answers
Answer:
x=2
Step-by-step explanation:
We first distribute this. So we have 15x-10 = 10 + 6 +2x.
Then we move the variable to one side and have 13x= 10+10+6
Simplify to get 13x = 26.
x=2
Is the following relation a function?
Answers
Answer:
yes
Step-by-step explanation:
A function is any graph that the x values do not repeat.
You can check this by using this vertical line test
Run your finger or a pencil down a specific vertical (top to bottom) line on the graph, if you can see that it intersects into the graph more than once, then it's not a function.
La Distribuidora Industrial Dulzura va a seleccionar entre dos compañías para transportar su azúcar al mercado. La primera compañía cobra 49,430.00 por alquilar los camiones más 2,480.50 adicionales por cada tonelada de azúcar. La segunda compañía cobra 60,500.00 por alquilar los camiones más 1,927.20 adicionales por cada tonelada de azúcar.
Answers
Answer: La cuenta de Milla ganaría $63 más que la cuenta de Gion después de 1 año.
In a shopping district with a variety of stores, 9 of the stores sell jewelry. The jewelry stores make up only 3% of the shopping district. How many stores are in the shopping district?
Answers
Answer:
When I did this in middle school, the teacher made it unnecessarily difficult (-_-), so here`s my own method for you.
Finding 1%:
If 9 is 3%, then 3 is 1%. This method only works when the sides are divisible.
You can use the 1% to find the total, which is 100%.
3 stores (or 1%) x 100 = 300.
There are 300 stores in the shopping district.
Hope that helps
what is the slope of y= -1/6x - 3/2
Answers
Answer:
-1/6
Step-by-step explanation:
Answer: -1/6
Step-by-step explanation:
Use the slope-intercept form y=mx + b to find slope m
b
-
27 =43
I would really appreciate your help
Answers
Answer:
B = 70
Step-by-step explanation:
Answer:70
Step-by-step explanation:
Whats the reciprocal for -4
Answers
Answer:
It is n-1. Does this help any or not?
Answer:
1/4
Step-by-step explanation:
so -4 is basically -4/1, you flip that and change the negative symbol to positive, making it 1/4.
mga solusyon sa epektibong komunukasyon sa pamilya
Answers
Answer:
Translation: Solutions to effective family education
Step-by-step explanation:
HELLLLLLP’!!!!
Suppose f(x)=2x-3 describe how the graph of g compares with the graph of f G(x)=f(x)+11
Answers
Answer:
Step-by-step explanation:
g(x) = 2x - 3 + 11
= 2x + 8.
The graph of g is parallel to the graph of f but f is translated upwards by 8 units.
Write an equivalent fractions for 3/7 and 1/3 using 21 as the common denominator
Answers
Answer:
9/21 & 7/21
Step-by-step explanation:
Equivalent fraction for [tex]\frac{3}{7}[/tex] and [tex]\frac{1}{3}[/tex] using 21 using as the common denominator are [tex]\frac{9}{21} ,\frac{7}{21}[/tex].
What are equivalent fraction?"Equivalent fraction is fraction with different numerator or denominator
that represents the same value or proportion of the whole."
What is common denominator?"Common denominator is the same denominator of all the fraction"
We have to write an equivalent fractions for [tex]\frac{3}{7}[/tex] and [tex]\frac{1}{3}[/tex] using 21 as common denominator.
As we know when we multiply [tex]7[/tex] by [tex]3[/tex] to get [tex]21[/tex]
and we have to multiply [tex]3[/tex] by [tex]7[/tex] to get [tex]21[/tex]
⇒[tex]\frac{3}{7}=\frac{3}{7}[/tex]×[tex]\frac{3}{3}=\frac{9}{21}[/tex]
⇒[tex]\frac{1}{3}=[/tex][tex]\frac{1}{3}[/tex]×[tex]\frac{7}{7}=\frac{7}{21}[/tex]
Hence, Equivalent fraction for [tex]\frac{3}{7}[/tex] and [tex]\frac{1}{3}[/tex] using 21 as common denominator are [tex]\frac{9}{21} ,\frac{7}{21}[/tex].
Learn more about Equivalent fraction and common denominator here
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determine the equation of the line
Answers
Answer:
y=5x-12
Step-by-step explanation:
the slope is 5 and y int. is -12
In the equation y=2X+7 which
number is the slope?
Slope (m)
Answers
Answer:
2 is the slope
Step-by-step explanation:
the equation is y=mx+b so if it is
y= 2x+7 that means the slope is 2
Answer:
2
Step-by-step explanation:
This equation is in y=mx+b form.
Slope = m
Y-intercept = b
This will give you the slope of 2 :)
Write in y=mx+b form
Answers
Step-by-step explanation:
b =-4 (y-intercept)
x =0
m = 0 (the line doesn't have a slope)
y = mx + c
y = 0(0) + (-4)
y = - 4
Kiesha and her classmates wrote proportions for the reduction of a triangle.
A larger and smaller triangle have corresponding heights and bases.
Which proportions are set up correctly? Select three options.
StartFraction original height over original base EndFraction = StartFraction reduction height over reduction base EndFraction
StartFraction original height over reduction height EndFraction = StartFraction original base over reduction base EndFraction
StartFraction original height over reduction base EndFraction = StartFraction reduction height over original base EndFraction
StartFraction reduction height over reduction base EndFraction = StartFraction original height over original base EndFraction
StartFraction original height over original base EndFraction = StartFraction reduction base over reduction height EndFraction
Answers
Answer: A, B, and D are correct!
Step-by-step explanation:
Hope this helps! :)
The three proportions that are set up correctly for the reduction of a triangle are:
original height / original base = reduction height / reduction base
original height / reduction height = original base / reduction base
original height / reduction base = reduction height / original base
Options 1, 2, and 3 are correct.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
The three proportions that are set up correctly for the reduction of a triangle are:
1)
original height / original base = reduction height / reduction base
This proportion represents that the ratio of the original height to the original base is equal to the ratio of the reduction height to the reduction base.
2)
original height / reduction height = original base / reduction base
This proportion represents that the ratio of the original height to the reduction height is equal to the ratio of the original base to the reduction base.
3)
original height / reduction base = reduction height / original base
This proportion represents that the ratio of the original height to the reduction base is equal to the ratio of the reduction height to the original base.
Thus,
original height / original base = reduction height / reduction base
original height / reduction height = original base / reduction base
original height / reduction base = reduction height / original base
Learn more about triangles here:
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10/3 = x divided by -5/2
x = ?
Answers
Answer:
-4/3
have a nice day/night
Answer:
x = -25/3
Step-by-step explanation:
x divided by -5/2 is equal to x multiplied by -2/5
therefore, proportion is [tex]\frac{10}{3}[/tex] = [tex]\frac{-2x}{5}[/tex]
cross-multiply: -6x = 50
x = -50/6 or -25/3
PLEASE HELLPPPPP
A population, P, of birds is doubling in size every year, according to the model P=100(2^t), where T represents years. What was the initial population size? Show work.
Answers
Answer: The above Table 1 will calculate the population size (N) after a certain length of time (t). All you need to do is plug in the initial population number (No), the growth rate (r) and the length of time (t). The constant (e) is already entered into the equation. It stands for the base of the natural logarithms (approximately 2.71828). Growth rate (r) and time (t) must be expressed in the same unit of time, such as years, days, hours or minutes. For humans, population growth rate is based on one year. If a population of people grew from 1000 to 1040 in one year, then the percent increase or annual growth rate is 40/1000 x 100 = 4 percent. Another way to show this natural growth rate is to subtract the death rate from the birth rate during one year and convert this into a percentage. If the birth rate during one year is 52 per 1000 and the death rate is 12 per 1000, then the annual growth of this population is 52 - 12 = 40 per 1000. The natural growth rate for this population is 40/1000 x 100 = 4%. It is called natural growth rate because it is based on birth rate and death rate only, not on immigration or emigration. The growth rate for bacterial colonies is expressed in minutes, because bacteria can divide asexually and double their total number every 20 minutes. In the case of wolffia (the world's smallest flowering plant and Mr. Wolffia's favorite organism), population growth is expressed in days or hours.
Each wolffia plant is shaped like a microscopic green football with a flat top. An average individual plant of the Asian species W. globosa, or the equally minute Australian species W. angusta, is small enough to pass through the eye of an ordinary sewing needle, and 5,000 plants could easily fit into thimble.
See Straight Pin & Sewing Needle Used In Wayne's Word Articles
There are more than 230,000 species of described flowering plants in the world, and they range in size from diminutive alpine daisies only a few inches tall to massive eucalyptus trees in Australia over 300 feet (100 m) tall. But the undisputed world's smallest flowering plants belong to the genus Wolffia, minute rootless plants that float at the surface of quiet streams and ponds. Two of the smallest species are the Asian W. globosa and the Australian W. angusta. An average individual plant is 0.6 mm long (1/42 of an inch) and 0.3 mm wide (1/85th of an inch). It weighs about 150 micrograms (1/190,000 of an ounce), or the approximate weight of 2-3 grains of table salt. One plant is 165,000 times shorter than the tallest Australian eucalyptus (Eucalyptus regnans) and seven trillion times lighter than the most massive giant sequoia (Sequoiadendron giganteum).
See Photo Of Massive Giant Sequoia Tree
See Photo Of The Australian Wolffia angusta
See Photo Of The Indian Wolffia microscopica
See Additional Color Images Of Wolffia Species
The growth rate for Wolffia microscopica may be calculated from its doubling time of 30 hours = 1.25 days. In the above population growth equation (N = Noe rt), when rt = .695 the original starting population (No) will double. Therefore a simple equation (rt = .695) can be used to solve for r and t. The growth rate (r) can be determined by simply dividing .695 by t (r = .695 /t). Since the doubling time (t) for Wolffia microscopica is 1.25 days, the growth rate (r) is .695/1.25 x 100 = 56 percent. Try plugging in the following numbers into the above table: No = 1, r = 56 and t = 16. Note: When using a calculator, the value for r should always be expressed as a decimal rather than a percent. The total number of wolffia plants after 16 days is 7,785. This exponential growth is shown in the following graph where population size (Y-axis) is compared with time in days (X-axis). Exponential growth produces a characteristic J-shaped curve because the population keeps on doubling until it gradually curves upward into a very steep incline. If the graph were plotted logarithmically rather than exponentially, it would assume a straight line extending upward from left to right.
Sixteen days of exponential growth in Wolffia microscopica.
Wolffia plants have the fastest population growth rate of any member of the kingdom Plantae. Under optimal conditions, a single plant of the Indian species Wolffia microscopica may reproduce vegetatively by budding every 30 hours. One minute plant could mathematically give rise to one nonillion plants or 1 x 1030 (one followed by 30 zeros) in about four months, with a spherical volume roughly equivalent to the size of the planet earth! Note: This is purely a mathematical projection and in reality could never happen!
Step-by-step explanation:
Find the equation of the line that is perpendicular to y = –3x + 1 and passes though the point (6, 3).
A) y =
1
3
x + 1
B) y = –
1
3
x + 1
C) y = 3x – 5
D) y = –3x – 5
Answers
Answer:
A. y=1/3x+1
Step-by-step explanation:
When finding a line that is perpendicular to another line, all you have to do is find the "opposite reciprocal" of the slope. In this case that means writing the slope as the fraction -3/1, and then flipping the fraction over (1/-3) and taking away the negative sign which gets you 1/3 for the slope of your new line. Now, all you have of your new equation is the slope. You need to take your new equation (y=1/3x+b) and plug in the x and y coordinates to that equation, and then solve for the last variable which is b. That solving process goes as follows:
3=1/3*6+b
3=2+b
1=b
now you can replace the b with 1 in your equation to get your final answer of y=1/3x+1
b -2 = 9/b-2
Answer ?
Answers
Step-by-step explanation:
I don't know if it's correct
b=9/b-2+2
b=9/b
b^2=9
b=3 or b=-3
Y=|x+2|-3 find the axis of symmetry
Answers
if (x ➖ y)2=441 and xy=46 find the value of x2+y2
Answers
PLEASE HELP I HAVE A TIME LIMIT I WILL GIVE BRAINLIEST AND 5 STARS show your work rex mixed x liters of fruit syrup with y liters of water to make fruit punch three times the number of liters of water he used is equal to 6 more than twice the number of liters of fruit syrup he used the total number of liters of syrup and water he mixed was 7 liters what is the number of liters of fruit syrup and water that rex added to make the fruit punch
Answers
graph of lines 3 y equals 2x plus 11 and y equals minus x plus 7. Lines intersect at ordered pair 2, 5
graph of lines 3 y equals 2 x minus 4 and y equals minus x plus 7. Lines intersect at ordered pair 5, 2
graph of lines 3 y equals 2 x plus 6 and y equals minus x plus 7. Lines intersect at ordered pair 3, 4
graph of lines 3y equals 2x plus 1 and y equals minus x plus 7. Lines intersect at ordered pair 4, 3
I don't know if it's right tho :C
Answer:
The amount of fruit syrup Rex added is: 3 liters
and the amount of water he added is: 4 liters.
Step-by-step explanation:
3y = 2x + 6
x + y = 7
y = 7 - x
3(7 - x) = 2x + 6
21 - 3x = 2x + 6
21 - 6 = 2x + 3x
15 = 5x
15/5 = x
3 = x
x + y = 7
3 + y = 7
y = 7 - 3
y = 4
Solution is (3,4)
20z-8 please helpppp
Answers
Answer: 4(5z−2)
Step-by-step explanation: Brainliest pls
Diego cut 7 smaller boards of equal length from a board that is 9 and one-third feet long. How long is each of the 7 smaller boards?
Answers
Answer:
1 1/3 feet long
Step-by-step explanation:
Answer:
Each of the seven smaller boards will be 1.3 feet long
Step-by-step explanation:
We must divide 9 1/3 by 7
9 1/3 / 7 = 1.333286
We now have to round to the nearest tenth which would give us:
1.3
So our final answer would be 1.3
Can someone please help
Answers
The linear combination method gives a solution of (–4, 2) for which of these systems of linear equations? 3 x + 13 y = 14. And 6 x + 11 y = -2. 4 x + 5 y = 12. And 8 x + 3 y = -4. 5 x + 4 y = 12. And 7 x + 8 y = 12. 10 x + 3 y = 8. And 17 x + 6 y = 10.
Answers
Answer:
A. [tex]3x + 13y = 14[/tex] and [tex]6x + 11y = -2[/tex]
Step-by-step explanation:
Required
Determine which system of equation satisfy (-4,2)
To do this, we simply substitute -4 for x and 2 for y in the given functions.
A.
[tex]3x + 13y = 14[/tex] and [tex]6x + 11y = -2[/tex]
[tex]3x + 13y = 14[/tex]
[tex]3(-4) + 13(2) = 14[/tex]
[tex]-12 + 26 = 14[/tex]
[tex]14 = 14[/tex]
[tex]6x + 11y = -2[/tex]
[tex]6(-4) + 11(2) = -2[/tex]
[tex]-24 + 22 = -2[/tex]
[tex]-2 = -2[/tex]
The above shows that the given linear combination has a solution of (-4,2).
Hence, this option answers the question and there is no need to check other options
Answer: the answer is A
Step-by-step explanation: