1. 1080°
2. 36°
3. 27 diagonals
4. 140°
5. 7 sides
Step-by-step explanation:1. The sum S of the interior angles of a polygon is given by;
S = (n-2) x 180°
Where;
n = number of sides of the polygon.
Therefore, to get the sum of the interior angles of a polygon having 8 sides, we substitute n = 8 into equation (i) as follows;
S = (8 - 2) x 180°
S = 6 x 180°
S = 1080°
Therefore, the sum of the interior angles of a polygon having 8 sides is 1080°
2. The sum of interior angles of a polygon is given by;
S = (n - 2) x 180°
For a polygon which is a regular decagon where the number of sides n = 10, the sum is;
S = (10 - 2) x 180°
S = 8 x 180°
S = 1440°
Since the decagon is regular, then each of its interior angles is given by;
1440° / 10
=> 144°
Now, since we know that the sum of the interior angle and exterior angle will give 180°, then;
The exterior angle of a regular decagon is;
180° - 144° = 36°
Therefore, the exterior angle of a regular decagon is 36°
3. The number of diagonals N of a polygon with n sides is given by;
N = [tex]\frac{1}{2} n(n-3)[/tex]
So, for a nonagon which has 9 sides (i.e n = 9), the number of diagonals is;
N = [tex]\frac{1}{2}*9(9-3)[/tex]
N = [tex]\frac{1}{2}*9(6)[/tex]
N = 9(3)
N = 27
Therefore, a nonagon has 27 diagonals.
4. The sum of interior angles of a polygon is given by;
S = (n - 2) x 180°
For a polygon which is a nonagon where the number of sides n = 9, the sum is;
S = (9 - 2) x 180°
S = 7 x 180°
S = 1260°
Since the nonagon is regular, then each of its interior angles is given by;
1260° / 9
=> 140°
Therefore, the measure of each angle (interior angle) of a regular nonagon is 140°
5. The sum of the interior angles of a polygon is given by;
S = (n - 2) x 180°
So if the sum is 900, then to get the number of sides of the polygon, we substitute S = 900 into the equation;
900° = (n - 2) x 180°
Divide through by 180°
5 = (n - 2)
Solve for n;
n = 5 + 2
n = 7
Therefore, the regular polygon has 7 sides.
mathematics can uh solve this please
Answer:
[tex]a^3 + 1 = 0[/tex]
Step-by-step explanation:
We start with the equation:
[tex]a + \frac{1}{a} = 1[/tex]
We want to find the value of:
[tex]a^3 + 1 =[/tex]
We can start with our previous equation and multiply both sides by a:
[tex](a + \frac{1}{a})*a = 1*a\\a^2 + 1 = a[/tex]
Now we can rewrite our initial expression as:
[tex]a = 1 - \frac{1}{a}[/tex]
Replacing that in the right side, we get:
[tex]a^2 + 1 = a = 1 - \frac{1}{a}[/tex]
Now again, let's multiply both sides by a
[tex]a*(a^2 + 1) = a*(1 - \frac{1}{a} )\\a^3 + a = a - a/a\\a^3 + a = a - 1\\a^3 = -1\\a^3 + 1 = 0[/tex]
So we can conclude that:
[tex]a^3 + 1 = 0[/tex]
I need help quick it's urgent!
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
start by squaring both sides:
[tex](\sqrt{-8+3x} )^2=(2)^2[/tex]
squaring a square root cancels it out:
[tex]-8+3x = 4[/tex]
solve for x by first adding 8 to both sides:
[tex]3x=12[/tex]
then divide both sides by 3:
[tex]x=4\\[/tex]
If the scale factor of a figure is 6, what is the new length of the enlarged figure matched to the length of the orginal?
Original: 1 cm
Enlarged: 6 cm
Original: 7 cm
Enlarged: 42 cm
Original: 2.5 cm
Enlarged: 15 cm
Original: 5 cm
Enlarged: 30 cm
Answers:
Original = 1 ----> Enlarged = 6Original = 7 ----> Enlarged = 42Original = 2.5 ----> Enlarged = 15Original = 6 ----> Enlarged = 30It looks like you have the correct order. To get those answers above, we simply multiply the original length by the scale factor 6.
Example: 7*6 = 42
The PRODUCT of 25 and x.
Answer:
25x
Step-by-step explanation:
25•x is 25x.
Until you know what x is you cannot do anything
Once you find out what x is you can plug in the number in the x space to get 25•__
I hope this helped!
Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
C = 32π
Step-by-step explanation:
The circumference (C) of a circle is calculated as
C = 2πr ( r is the radius ) , then
C = 2π × 16 = 32π units
A garden table and a bench cost 816 combined. The garden table costs 84 less than the bench. What is the cost of the bench?
Answer:
366
Step-by-step explanation:
A garden table and bench cost 816 when combined together
The garden table cost 84 less than the bench
Therefore the price of the bench can be calculated as follows
x + (x+84)= 816
2x+84= 816
2x= 816-84
2x= 732
Divide both sides by 2
x= 732/2
= 366
Hence the price of the bench is 366
Here are the equations of two different graphs: y = x-7 and y = 3x - 7 Are the gradients of the graphs the same or different? Explain how you know.
help please
Answer:
this two graph is not same because they have different slopes for this they are not same
f(x)=2x^2−3x+5 Identify the quadratic term in the function.
Answer:
2×2-3×-5=0
Step-by-step explanation:
(2×2-3×)- 5=0
Help geometry ……………..
Answer:
Angle F
Step-by-step explanation:
=====================================================
Explanation:
We see that angle A = angle E as shown by the arc marking. The tickmark says that side AB is the same length as side EF.
In the letter sequences "AB" and "EF", erase the first letters A and E to be left with B and F. This is one way to show how angle B pairs with angle F, and that is enough to show the two angles are congruent.
Can someone please help me?the question is in the picture. Thank you
Answer:
It would be 9π
Step-by-step explanation:
(x-1)²π
(x-1)(2x-4)
Helppp me pleaseee ASAP
Answer:
$856.91 after 7 years
Step-by-step explanation:
Initial investment, P = 500
Interest rate, i = 8% (compounded once a year, i.e. annually)
Number of years, t = 7
Substitute in compound interest formula
Future value,
A = P (1 + 0.08/1) ^(1*7)
= 500 (1.08)^7
= 856.91 (to the nearest cent)
769 ÷ 30 in standard algorithm
plz i need asap
Answer:
it equal 25 and the remainder is 19. :)
Answer:
Step-by-step explanation:
exact form
769/30
decimal form
25.63
mixed number formed
25 19/30
Toby the poodle buries 9 sticks. Clifford the jack russel buries 7 times as the amount of sticks toby How many sticks did the dogs bury in all
Answer:
1√6
Step-by-step explanation
9+7=16
Can someone explain if this is correct. I’m unsure!
Answer:
Step-by-step explanation:
please help with 3 , 4 & 5 i mark Brian list
Answer:
see belowStep-by-step explanation:
Question-2:the square of x-5 given by
[tex] \displaystyle (x - 5) ^{2} [/tex]
use (a-b)²=a²-2ab+b² to simplify so we obtain:
[tex] \displaystyle {x}^{2} - 10x + 25[/tex]
hence
our answer is 2)
Question-3:to find:
[tex]f(x) - g(x)[/tex]
substitute the value of f(x) and g(x):
[tex] \rm \displaystyle{6x}^{2} + 8x - 5 - ( {2x}^{2} - 4x + 4)[/tex]
remove parentheses and change its sign:
[tex] \rm \displaystyle{6x}^{2} + 8x - 5 - {2x}^{2} + 4x - 4[/tex]
combine like terms:
[tex] \rm \displaystyle{6x}^{2} + 12x - 5 - {2x}^{2} - 4[/tex]
collect like terms:
[tex] \rm \displaystyle{4x}^{2} + 12x -9[/tex]
hence,
our answer is 3)
Question-4:given Polynomial:
[tex] \displaystyle {5x}^{3} + 2 {x}^{2} + 7[/tex]
substitute the value of x:
[tex] \displaystyle {5.(10}^{3}) + 2 ({10}^{2}) + 7[/tex]
simplify squares:
[tex] \displaystyle 5(1000) + 2 (100) + 7[/tex]
simplify multiplication:
[tex] \displaystyle 5000 + 2 00 + 7[/tex]
simplify addition:
[tex] \displaystyle 5207 [/tex]
hence our answer is 1)
Question-5:given:
12x³y⁶,8x⁴y,20x²y⁵notice that,
every time there's a GCF of 4x²y
hence our answer is 4)
Somebody really smart!!!?
Answer:Its the last one to the left up
Step-by-step explanation:
Answer:
78.5 square feet
option b
Step-by-step explanation:
area = pi*r^2
a = 3.14*5^2
a = 3.14*25
a = 78.5
A number cube is rolled once. What is the probability of rolling a three
Answer:
1/6
Step-by-step explanation:
A dies has six sides
1,2,3,4,5,6
There is 1 three
P(3) = number of threes/ total numbers
= 1 / 6
what is the result when this equation is solved for y?
Answer:
Ans:C
Step-by-step explanation:
4x^2+10x-2=6
4x^2+10x=6+2y
4x^2+10x-6=2y
(4x^2+10x-6)÷2=y
y=2x^2+5-3
Hope this is useful :)
prove that 9^3/2 -3 *5^0 -(1/81)^-1/2 = 15
Pls help, correct answer, I’ll mark as brainliest
Answer:
[tex]9^{3/2}-3\times 5^0-(\dfrac{1}{81})^{-1/2}=15[/tex]
Step-by-step explanation:
The given expression is :
[tex]9^{3/2}-3\times 5^0-(\dfrac{1}{81})^{-1/2}=15[/tex]
We need to prove that LHS is equal to RHS.
Taking LHS,
[tex]=9^{3/2}-3\times 5^0-(\dfrac{1}{81})^{-1/2}[/tex]
[tex]=(3)^{2\times\dfrac{3}{2}}-3-(\dfrac{1}{9})^{2\times \dfrac{-1}{2}}\\\\=27-3-9\\\\=15\\\\=RHS[/tex]
Hence, LHS = RHS.
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Answer:
x + y = 60
Step-by-step explanation:
[tex]2x + 2y + 60 = 180 \\ 2x + 2y = 180 - 60 \\ 2x + 2y = 120 \\ \frac{2x + 2y}{2} = \frac{120}{2} \\ x + y = 60 \\ [/tex]
Luke puts $35 in his savings account every month. Use a calculator to find how much money he will save in a year.
a lines y-intercept is -4, and it's slope is 2. what is its equation in slope-intercept form?
Answer:
2x-4
Step-by-step explanation:
2x-4
mx+b format
Find y.
Round to the nearest tenth:
29°
500 ft
у
X
y = [? ]ft
Y’all please help :,,,)
Answer:
Step-by-step explanation:
sin A = [tex]\frac{opposite side}{Hypotenuse}[/tex]
Sin 29 = [tex]\frac{y}{500}[/tex]
0.4848 * 500 = y
y = 242.4 ft
Answer:
Y=242.4
Step-by-step explanation:
due to the association property the angle at the bottom left is 29 degrees
since sine property is oposite over hypothesis we get
sine(29)=y/500
500sin(29)=y
Y=242.4
Where would the last point need to be in order to finish graphing a square using the points (1, 3), (5, 3), and (5, 7)?
A. (1, 5)
B.(5, 1)
C.(3, 7)
D.(1, 7)
SOMEONE HELP FAST PLEASE.
Answer:
f(0) = g(0)
Step-by-step explanation:
The functions intersect at x =0, which means they have the same y value at x=0
f(0) = g(0)
A roof is supported o 7 rafter each 6 1/2 feet long at 70 cents running foot how much did those rafters cost
Answer:
$31.85
Step-by-step explanation:
total cost of the rafters = total length of rafters used x cost per foot
total length of rafters used = number of rafters used x length of rafters
7 x [tex]6\frac{1}{2}[/tex]
to solve, convert [tex]6\frac{1}{2}[/tex] to an improper fraction
to convert to improper fraction, take the following steps :
1. Multiply the whole number by the denominator
2. Add the numerator to the answer gotten in the previous step
3. divide the number gotten in the previous step by the denominator
7 x [tex]\frac{13}{2}[/tex] = [tex]\frac{91}{2}[/tex]
cost per foot = 70 cents
100 cents = 1 dollar
70 cents = $0.70
total cost of rafters = $0.70 x [tex]\frac{91}{2}[/tex] = $31.85
can you please find the range of these numbers? 18, 16, 19, 15, 17. I will give 16 points
Answer: Hi the Range is 4
Step-by-step explanation: The range of a data set in statistics is the difference between the largest and the smallest values. While range does have different meanings within different areas of statistics and mathematics, this is its most basic definition, and is what is used by the provided calculator. Using the same example:
18, 16, 19, 15, 17
19,18,17,16,15
19-15= 4
ssignment-make sure I can open it.
Factor
6
2) Using SYNTHETIC Division, is “X = 2” a
solution of the polynomial 2x² + 3x2 - 11X – 6
*Show all work just below
How do you write an equivalent logarithmic equation for e^4=x
Answer:
4 = ln x
Step-by-step explanation:
e^4=x
Take the natural log of each side
ln(e^4)=ln(x)
We know ln a^b = b ln a
4 ln e = ln x
ln (e) =1
4 = ln x
standard form, degree, leading coefficient of 2x(2)-7x(4)+5x
