Answers
Answer:
[tex]x = 145[/tex]
Step-by-step explanation:
1.Approach
To find the value of (x), one will have to take multiple steps. Since a straight line is (180) degrees, one can use this property. Subtract the measure of the exterior angle (the angle formed between the extension of the side of a triangle, and the side of a triangle) from (180) to find an expression to describe the measure of the angle inside the triangle.
Then one is given a regular octagon, using the sum of interior angles formula, find the measure of any interior angle. The vertical angles that when two lines intersect, the opposite angles are congruent. One can use this property to find the final unknown angle in the triangle.
It is known that the sum of angles in a triangle is (180). Use this to find the measure of (x).
2. Find the measure of two angles in the triangle
The degree measure of a straight angle is (180), therefore, when two angles form a straight line, their sum of (180). One can apply this here by stating,
[tex]x+(unknown)=180[/tex]
Solve for unknown,
[tex]unknown = 180 - x[/tex]
One can also state,
[tex]170+(unknown_2)=180[/tex]
Solve for the unknown,
[tex]unknown_2=10[/tex]
3.Find the degree measure of one of the angles in the octagon
The given octagon (eight-sided figure) is a regular octagon. By its definition, all of the sides in any regular polygon are congruent. This is indicated here, thus the octagon is a regular octagon. One property of a regular polygon is that all of the angles in the figure are cognrunet. This means that the sum of interior angles divided by the number of angles wil give one the measurement of each angle.
The formula to find the sum of interior angles in a polygon is as follows,
[tex]S=180(n-2)[/tex]
Where (n) is the number of sides. Since an octagon has (8) sides substitute this number into the formula and solve for the sum of angles,
[tex]S=180(n-2)\\\\S=180(8-2)[/tex]
Simplify,
[tex]S=180(8-2)\\\\S=180(6)\\\\S= 1080[/tex]
Now divide by the number of angles. The number of angles in an octagon is (8). Since this is a regular octagon, all of the angles are congruent, thus dividing the sum of angles by the number of angles will give on the measure of each angle.
[tex]1080[/tex] ÷ [tex]8 = 135[/tex]
4. Find the measure of the final angle in the triangle
The vertical angles theorem states that when two lines intersect, the angles opposite each other are congruent. Therefore, the final unknown angle in this triangle is equal to (135) degrees, because the angle opposite in the octagon is equal to (135) degrees.
5. Find the meausre of (x)
The sum of angles in any triangle is (180) degrees. Since one has found the measure or expression of the angle measure of each angle in a triangle, one can form an equation and solve for the unknown,
[tex](180-x)+(10)+(135)=180[/tex]
Simplify,
[tex]325-x=180[/tex]
Inverse operations,
[tex]325-x=180\\\\-x = -145\\\\x=145[/tex]
Related Questions
Solve for O pls and thank you
Answers
Answer:
a) 67.4°
Step-by-step explanation:
since this is a right triangle you can use the sine trigonometric ratio of opposite/hypotenuse
sin⁻¹(Ф) = 12/13 which equals 67.4°
Aina builds a cube model out of manila cards. If the volume of the constructed cube is (2+3p) ³ cm³, find the total surface area of the cube in terms of p.
HELPPPP
Answers
Given:
The volume of a cube = [tex](2+3p)^3\ \text{cm}^3[/tex]
To find:
The total surface area of the cube in terms of p.
Solution:
Volume of a cube is:
[tex]V=a^3[/tex] ...(i)
Where, a is the side length.
It is given that,
[tex]V=(2+3p)^3\ \text{cm}^3[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=2+3p\text{ cm}[/tex]
Now, the total surface area of a cube is:
[tex]A=6a^2[/tex]
Where, a is the side length.
Putting [tex]a=2+3p[/tex], we get
[tex]A=6(2+3p)^2[/tex]
Therefore, the total surface area of the cube in terms of p is [tex]6(2+3p)^2\ \text{cm}^2[/tex].
Franklin races bikes. In his city, there are 44 lengths of race tracks. The chart shows the race tracks and each track's length in miles. Race Track Length in Miles A \frac{1}{4} 4 1 B \frac{3}{2} 2 3 C 1\frac{3}{4}1 4 3 D \frac{4}{4} 4 4 Frankin races 33 laps in the same lane. The total distance he races is more than 4\frac{1}{2}4 2 1 miles. Which track does Franklin race on?
Answers
Answer:
51
Step-by-step explanation:
51 is elaginlent to 44 and 33 12 garde things
Please help me, Please
Answers
Answer:
7th graders in the school
Step-by-step explanation:
if she wants to know what 7th graders like, ask 7th graders since no one els would know as good as 7th graders themselves
Answer:
A.7th graders in the school
Step-by-step explanation:
Because she specifically wants to find the favorite activity of 7th grade students she should sample only 7th grade students to get the best and most accurate results.
1. Explain how to find the area of a complex figure. Draw an example to help illustrate
your understanding. Please help!
Answers
Answer:
Refer to the attached file
Hope it helps..
Context: You and your friends go to the state fair. It costs $6 to get into the fair and $2 each time you go on a ride. Where do you see the y-intercept in the table and in the equation?
Answers
Answer:
see below
Step-by-step explanation:
The y intercept is when x =0
The equation is y =2x+6
The equation is in the form y = mx+b. It is the constant added to the equation.
In the table it is the y value when x =0
Why was Elmo's Report Card All Wet?
Answers
Answer:
why was it ♂️
All of his grades were down below c level
hehe
=)
Answer this for me thanks
Answers
Answer:
The value of x is 15 inch.
Step-by-step explanation:
Area, A = 81 square inch
Perimeter, P = 48 inch
let the side is y.
[tex]y^2 = 81\\\\y = 9 inch[/tex]
Let the other side is d.
P = 4 d = 48
d = 12 inch
the length x is given by
[tex]x^2 = 9^2 + 12^2\\\\x^2 =81 + 144 = 225\\\\x = 15 inch[/tex]
So, x = 15 inch.
The manager of a home store is buying lawn
chairs to sell at his store. Each pack of chairs
contains 10 chairs. The manager will sell each
chair at a markup of 20% of the wholesale
cost, plus a $2.50 stocking fee.
Answers
Answer:
5$
Step-by-step explanation:
Figure VWYX is a kite.
3
(18x-2)
V
Y
(12x+2)
х
Answers
Answer:
18X-2+12X+2=360-180
30X=180
X=6
The value of the variable x is 6, in the given rhombus.
What are the properties of the rhombus?A quadrilateral having the following characteristics is called a rhombus:
The lengths of the four sides are equal.Parallel sides are situated next to one another.Angles that are opposite each other are equal (i.e., they have the same measure).The diagonals form a right angle split across one another.Each diagonal is the same length.From the properties of a rhombus,
The sum of all angles is 360°.
Thus, in the given case,
18x-2+12x+2+ 90° +90° = 360°
18x- 2 + 12x +2 = 180°
30x = 180
x = 6
Therefore, the value of the x is 6.
Learn more about Rhombus here:
https://brainly.com/question/27870968
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PLEASE HELP! NO SPAMMING! SHOW WORK!
The ratio of the dimensions of the model to the dimensions of the Great Pyramid is about 1 to 38. The surface area of the real pyramid is about how many times the surface area of the model.
Dimensions: a pyramid with a square base.
base sides: 6m
height: 4m
Answers
========================================================
Explanation:
Consider a square on paper that is 3 inches by 3 inches. It's area would be 3*3 = 9 square inches.
The ratio 1 to 38 means that 1 inch on paper corresponds to 38 inches in real life (assuming the "1 to 38" doesn't have any verbal units attached to it; if so, then refer to the note below). So a 3 by 3 square corresponds to a 114 by 114 square because 3*38 = 114.
The area of the second larger square is 114*114 = 12,996 square inches.
Now divide the two areas: (12,996)/(9) = 1444
It's probably not entirely obvious, but through a bit of playing around with various numbers, you should find that 38^2 = 1444. It's not a coincidence that this happens. The linear scale factor is 38 which means the area scale factor is 38^2 = 1444.
In short, the larger square in real life has area that is 1444 times that of its scaled down counterpart.
Or put another way:
large area = 1444*(small area)
------------------
Side note: This all assumes that the numbers in "1 to 38" are both the same unit. If we had a mixed ratio of units like "1 inch to 38 feet", then the answer would be different. You would need to convert from feet to inches, and then follow the steps above to get a different answer.
islah sold a shirt at sh 2000 making a loss of 9%, how much did islah paid for the shirt ?
Answers
Answer:
2,197.8
Step-by-step explanation:
5.
Which of the quadratic functions has the narrowest graph?
A. [tex]y=-2x^2[/tex]
B. [tex]y=\frac{1}{2} x^2[/tex]
C. [tex]y=\frac{1}{7} x^2[/tex]
D. [tex]y=-4x^2[/tex]
Answers
Answer:
C. y= 1/7x2
Step-by-step explanation:
The equation with the highest leading coefficient (the number before the x^2 term) will have the narrowest graph. Here, we have to choose between -1, 1/6, 2, and 1/8. The highest number out of all of those numbers is 2, so y = 2x^2 will have the narrowest graph.
I will mark you brainliest if you solve this
show your working as well
4) (4x2– x – 7) + (2x3+ 6x2– 11)
5)(2x3– x + 4) + (5x2– 6x – 5)
6)(3x2+ 2x + 1) – (x2– 3x + 4)
7)(2x2– 3x + 7) – (5x2+ 3x + 6)
Answers
Answer:
4) 2x3 + 10x2−x−18
5) 2x3+5x2−7x−1
6) 2x2+5x−3
7) −3x2−6x+1
Step-by-step explanation:
4) (4x2 - x - 7) + (2x3+ 6x2– 11)
Combine Like Terms:
=4x2+−x+−7+2x3+6x2+−11
=(2x3)+(4x2+6x2)+(−x)+(−7+−11)
=2x3+10x2+−x+−18
5) (2x3– x + 4) + (5x2– 6x – 5)
Combine Like Terms:
=2x3+−x+4+5x2+−6x+−5
=(2x3)+(5x2)+(−x+−6x)+(4+−5)
=2x3+5x2+−7x+−1
6) (3x2+ 2x + 1) – (x2– 3x + 4)
Distribute the Negative Sign:
=3x2+2x+1+−1(x2−3x+4)
=3x2+2x+1+−1x2+−1(−3x)+(−1)(4)
=3x2+2x+1+−x2+3x+−4
Combine Like Terms:
=3x2+2x+1+−x2+3x+−4
=(3x2+−x2)+(2x+3x)+(1+−4)
=2x2+5x+−3
7)(2x2– 3x + 7) – (5x2+ 3x + 6)
Combine Like Terms:
= (2x2 −5x2 )+(−3x−3x)+(7−6)
What is the measure of ZWX?
Answers
Step-by-step explanation:
180°+63°
=243°
holp it help
Gloria set aside $100 to buy school lunches for the year. Each school lunch cost $2. The inequality 100 – 2x < 20 can be used to find the number of school lunches Gloria can buy before she has less than $20 left. What is the solution to this inequality?
Answers
Answer:
she would be able to buy 40 lunches
Step-by-step explanation:
Subtract 100 from both sides of the inequality
Divide each term by −2 and simplify.
The solution to the inequality 100 – 2x < 20 is x > 40
How to find solution to an inequality?
She set aside $100 to buy school lunches for the year. Each school lunch cost $2.
Therefore, the inequality can be used to find the number of school lunches Gloria can buy before she has less than $20 left.
100 – 2x < 20
The solution of the inequality is as follows;
100 – 2x < 20
subtract 100 from both sides
100 - 100 - 2x < 20 - 100
-2x < - 80
divide both sides by -2
x > 40
learn more on inequality here: https://brainly.com/question/11872626
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Helpppp does anyone know
Answers
======================================================
Explanation:
We can apply the remote interior angle theorem. Some math books or teachers may refer to this as the "exterior angle theorem". They're the same idea just with different names.
According to that theorem, the interior angles x and 53 add up to the exterior angle 158
x+53 = 158
x = 158-53
x = 105
This theorem only works if neither interior angle is adjacent to the exterior angle. Hence the "remote" part.
----------
If you wanted a slightly longer approach, then let y be the missing angle that isn't marked in the diagram. Angle y is adjacent to the 158 degree angle.
We can find y by noting how 158 and y are supplementary
158+y = 180
y = 180-158
y = 22
Then we use the fact that adding three angles of any triangle always gets us 180 degrees
x+y+53 = 180
x+22+53 = 180
x+75 = 180
x = 180-75
x = 105
Effectively, this example helps reinforce why the remote interior angle theorem is true.
which function is nonlinear
Answers
Answer:
C, y=2x(x-4)
Step-by-step explanation:
All the other equations can be graphed as lines, but C is the only one that is a parabola (a curve).
Find the equation of the line parallel to y = 2/3x-7
passing through A(6,-1).
Answers
Answer:
y = 2/3x - 5
Step-by-step explanation:
If two lines are parallel, they have the same slope. This means the line we are looking for has a slope of 2/3. Since we are also given a point, we can start by writing the equation in point-slope form which is represented by
[tex]y-y_{1} =m(x-x_{1} )[/tex]
Where m is the slope and (x1, y1) is a point. We have both, so we can substitute the values and simplify:
y + 1 = 2/3 (x - 6)
y + 1 = 2/3x - 4
y = 2/3x - 5
FInd WY Given: Giving brainly.
Answers
Answers:
x = 2WY = 28===========================================================
Explanation:
The tickmarks show that WZ and XY are the same length. The arrows show that WX is parallel to ZY. This is an isosceles trapezoid.
For any isosceles trapezoid like this, the diagonals are the same length. We can prove it using the SAS congruence theorem.
So,
WY = XZ
15x-2 = 9x+10
15x-9x = 10+2
6x = 12
x = 12/6
x = 2 .... first answer
Use that value of x to find the length of each diagonal.
WY = 15*x - 2 = 15*2-2 = 30-2 = 28 .... second answerXZ = 9x+10 = 9*2+10 = 18+10 = 28Both diagonals are 28 units long, which helps confirm we have the right x value.
If ABC ~ DEF and the scale factor from ABC to DEF is 2, what are the lengths of , , and , respectively?
Answers
Answer:
4,8,12 hope that helps heeeeheheʘ‿ʘ
A company that makes hair-care products had 7,000 people try a new shampoo. Of the 7,000 people, 28 had a mild allergic reaction. What percent of the people had a mild allergic reaction?
Answers
Answer: 0.4%
Step-by-step explanation:
First, a porportion needs to be set up.
part/whole = percent/100
28/7,000 = x/100
Second, cross multiply.
2800=7,000x
x=0.4
Need help with this question
Answers
Find the equation of a line with slope - 5 passing through the point A(-3, 6).
Answers
Answer:
y=5x-9
Step-by-step explanation:
-5(-3)+b=6
15+b=6
B=-9
for freshman year Nick had 3.5 for a gpa. what gpa does Nick needs for sophomore, junior, senior year to get the average of at least 4.0?
Answers
Answer:4.0
Step-by-step explanation:
Keelie has a triangular-shaped card. The lengths of its sides are 4.4 cm, 5.5 cm, and 6.6 cm. Is the card a right triangle?
Answers
Answer:
No
Step-by-step explanation:
We can use the Pytaghorean theorem to verify it
4.4^2 + 5.5^2 = 6.6^2
19.36 + 30.25 = 43.56
49.61 = 43.56 (false)
A set of parents started a savings account for their newborn child. After 7 years, the
child's account had 900 dollars. The balance in the account continues to grow by a
factor of 5 in value every 7 years. Let n be the number of 7-year periods since the
account was started.
Which function, f(n), represents the value of the savings account?
Answers
Answer:
hsshshshwwbwbbs29oooo
Plz answer this question
Answers
Answer:
3,16,729
Step-by-step explanation:
PLZ HELP ITS URGENT
Answers
it is blurry so take it again
Dois triângulos semelhantes possuem razão entre suas áreas igual a 9. Se o perímetro de um deles é 10, o perímetro do outro deve ser:
Answers
Answer:
O perímetro do outro triângulo deve ser ou de 30 unidades de comprimento, ou de 3.33 unidades de comprimento.
Step-by-step explanation:
Dois triângulos semelhantes possuem razão entre suas áreas igual a 9.
O perímetro tem grau um, enquanto a área tem grau 2. Isto implica que a razão entre os perímetros é a raiz quadrada da razão entre as áreas, então a razão entre os perímetros é de 3.
Se o perímetro de um deles é 10, o perímetro do outro deve ser:
Ou 10*3 = 30, ou [tex]\frac{10}{3} = 3.33[/tex]
O perímetro do outro triângulo deve ser ou de 30 unidades de comprimento, ou de 3.33 unidades de comprimento.
