Answer:
The statements about arcs and angles that are true in the figure are;
1) ∠EFD ≅ ∠EGD
2) [tex]\overline{ED}\cong \overline{FD}[/tex]
3) mFD = 120°
Step-by-step explanation:
1) ∠ECD + ∠CEG + ∠CDG + ∠GDE = 360° (Sum of interior angle of a quadrilateral)
∠CEG = ∠CDG = 90° (Given)
∠GDE = 60° (Given)
∴ ∠ECD = 360° - (∠CEG + ∠CDG + ∠GDE)
∠ECD = 360° - (90° + 90° + 60°) = 120°
∠ECD = 2 × ∠EFD (Angle subtended is twice the angle subtended at the circumference)
120° = 2 × ∠EFD
∠EFD = 120°/2 = 60°
∠EFD ≅ ∠EGD
∠ECD = 120°
∠EGD = 60°
∴∠EGD ≠ ∠ECD
2) Given that arc mEF ≅ arc mFD
Therefore, ΔECF and ΔDCF are isosceles triangles having two sides (radii EC and CF in ΔECF and radii EF and CD in ΔDCF
∠ECF = mEF = mFD = ∠DCF (Given)
∴ ΔECF ≅ ΔDCF (Side Angle Side, SAS, rule of congruency)
[tex]\\ \overline{EF}\cong \overline{FD}[/tex] (Corresponding Parts of Congruent Triangles are Congruent, CPCTC)
∠FED ≅ ∠FDE (base angles of isosceles triangle)
∠FED + ∠FDE + ∠EFD = 180° (sum of interior angles of a triangle)
∠FED + ∠FDE = 180° - ∠EFD = 180° - 60° = 120°
∠FED + ∠FDE = 120° = ∠FED + ∠FED (substitution)
2 × ∠FED = 120°
∠FED = 120°/2 = 60° = ∠FDE
∴ ∠FED = ∠FDE = ∠EFD = 60°
ΔEFD is an equilateral triangle as all interior angles are equal
[tex]\\ \overline{EF}\cong \overline{FD}\cong \overline{ED}[/tex] (definition of equilateral triangle)
[tex]\overline{ED}\cong \overline{FD}[/tex]
3) Having that ∠EFD = 60° and ∠CFE = ∠CFD (CPCTC)
Where, ∠EFD = ∠CFE + ∠CFD (Angle addition)
60° = ∠CFE + ∠CFD = ∠CFE + ∠CFE (substitution)
60° = 2 × ∠CFE
∠CFE =60°/2 = 30° = ∠CFD
[tex]\overline{CF}\cong \overline{CD}[/tex] (radii of the same circle)
ΔFCD is an isosceles triangle (definition)
∠CFD ≅ ∠CDF (base angles of isosceles ΔFCD)
∠CFD + ∠CDF + ∠DCF = 180°
∠DCF = 180° - (∠CFD + ∠CDF) = 180° - (30° + 30°) = 120°
mFD = ∠DCF (definition)
mFD = 120°.
Answer:
1,3,5
Step-by-step explanation:
right on edge 2022
BRAINLIEST!!! PLEASE HELP! Find the number of four-digit numbers which are not divisible by 4
Answer
4141
4141/4=1035.25
Answer:
5234
Step-by-step explanation:
Simplify the question
10x /(divide) -2y
Answer:
-5x/y is the answer
Step-by-step explanation:
10x/-2y
Dividing by 2
=5x/-y
=-5x/y
I hope this will help you :)
Answer:
(-5x)/y
Step-by-step explanation:
I'm assuming you meant:
10x
---------
-2y
-5x
This reduces to ----------
y
y is inversely proportional to x.
when y=7 , x=9
a) work out an equation connecting y and x
b) work out the value of y x=21
Answer:
1. [tex]xy = 63[/tex]
2. [tex]y = 3[/tex]
Step-by-step explanation:
Given
Variation: inverse Proportion
y = 7, x = 9
Required
- Write an equation connecting y and x
- Find y when x = 21
Given that thee variation is inversely proportional;
This implies that
[tex]y\ \alpha\ \frac{1}{x}[/tex]
Convert variation to equation
[tex]y\ = \frac{k}{x}[/tex] ----------- Equation 1
Where k is the constant of variation
Substitute 7 for y and 9 for x in equation 1
[tex]7 = \frac{k}{9}[/tex]
Multiply both sides by 9
[tex]9 * 7 = 9 * \frac{k}{9}[/tex]
[tex]63 = k[/tex]
Substitute 63 for k in equation 1
[tex]y = \frac{63}{x}[/tex]
Multiply both sides by x
[tex]x * y = \frac{63}{x} * x[/tex]
[tex]xy = 63[/tex]
Hence, the equation connecting x and y is [tex]xy = 63[/tex]
Solving for when x = 21
Substitute 21 for x in the above equation
[tex]21 * y = 63[/tex]
Divide both sides by 21
[tex]\frac{21 * y}{21} = \frac{63}{21}[/tex]
[tex]y = 3[/tex]
A page in an average newspaper has 8 columns of print. Each column consists of 160 lines and each line averages 6 words. What's the average number of words on a full page?
Answer:
7,680
Step-by-step explanation:
A page has 8 columnsEach column consists of 160 lines.Each line averages 6 words.The average number of words on a full page
=Number of columns X Number of Lines X Number of words per line
=8 X 160 X 6
=7680
The average number of words on a full page is 7,680.
) We throw 9 identical balls into 7 bins. How many different ways are there to distribute these 9 balls among the 7 bins such that no bin is empty? Assume the bins are distinguishable (e.g., numbered 1 through 7).
Answer:
28 ways
Step-by-step explanation:
After placing 1 ball in each of the seven bins, there are two balls left.
If we place both balls in a single bin, there are 7 different ways to place the balls (place both on bins 1 through 7).
If we place each of the remaining balls in a different bin, the number of ways to place the balls is:
[tex]n_2=\frac{7!}{(7-2)!2!}=7*3=21[/tex]
The total number of ways to distribute those balls is 21 + 7 = 28 ways.
In the diagram, the measure of angle 6 is 98°. what is the measure of angle 7?
Answer:
7∠82°
Step-by-step explanation:
Well angle 6 and 7 are complementary angles, meaning they both add up to 180°.
So we do 180 - 98 which is 82°.
Answer: The measure of angle 7 is 82 degrees.
Step-by-step explanation:
Angle 6 and 7 lies on a straight line so they will add up to 180 degrees.
So if Angle 6 is 98 degrees then an a number plus 98 has to equal 180.
so we could generate an equation as x + 98 = 180
x + 98 = 180 solve for x
-98 -98
x= 82
Anyone know this one?
Answer:
(-3, 5), (1, 4), (-2, 3), and (0, 2).
Step-by-step explanation:
When a function is inverted, the x-values become y-values, and the y-values become x-values.
The ordered pairs for the function are (5, -3), (4, 1), (3, -2), and (2, 0).
After inversion, the ordered pairs will be (-3, 5), (1, 4), (-2, 3), and (0, 2).
Hope this helps!
what is 8 divided by 2 with 2+2 inn the parenthesis. I want to befriend the first person to get it. It's hard but have fun!!!
Answer:
16 or 1. There are 2 different answers depending on how you take the question as.
Step-by-step explanation:
8÷2(2+2)=
8÷2(4)=
4(4)=
16
OR
8÷2(2+2)=
8÷2(4)=
8÷8=
1
a container is 24m long ,9m wide and 8m high. How many books can it hold if each book is 20cm long, 16cm wideand 6cm thick
Answer:
900,000 books
Step-by-step explanation:
book is a three dimensional object there you need to find the ratio of the container to the book. ( units must be the same)
Vcontainer=length*width*height
Vcontainer=2400cm*900cm*800cm
Vcontainer=1,728,000,000cm^3
Vbook=length*width*height
Vbook=20cm*16cm*6cm
Vbook=1920cm^3
no books =Vcontainer/Vbook
no books =1,728,000,000cm^3/1920cm^3
no books=900,000 books
Please help me!!!!!!!!!!!!!
Answer:
-3.125 < -2.95 < 2.6 < 103.5
Step-by-step explanation:
1) [tex]5\frac{6}{15}- 2\frac{4}{5}[/tex]
=> [tex]\frac{81}{15} - \frac{14}{5}[/tex]
=> [tex]\frac{81-42}{15}[/tex]
=> [tex]\frac{39}{15}[/tex]
=> 2.6
2) -4.5 * -2.3
=> 103.5
3) [tex]\frac{5}{-1.6}[/tex]
=> -3.125
4) [tex]-\frac{33}{10} + \frac{7}{20}[/tex]
=> [tex]\frac{-66+7}{20}[/tex]
=> [tex]\frac{-59}{20}[/tex]
=> -2.95
Answer:
fourth, first, third, second,
Step-by-step explanation:
The first equals 2 9/15
The second equals 10.35
The third equals 3 1/8
The fourth equals -2 19/20
Can someone help me I really need help please help me thank you
Answer:60 degrees
Step-by-step explanation:
60 degress
43 + 167 + 90 = 300
360 - 300 = 60
<!> Brainliest is appreciated! <!>
Find all the missing elements:
B
A = 50°
a
C = 35°
A
с
b = 13
b
Å
B = 95° a = [?] C=
c = [ ]
Round to the nearest tenth.
Hope you understand :)
Answer:
B=95 a= 10 c= 7.5
Step-by-step explanation:
Simplify. 192−−−√ 83√ 643√ 106√ 824−−√
Answer:
192 - 4√291341371
Step-by-step explanation:
If your question is: 192 - √83(√643)(√106)(√824) - √0
Then you multiply all the √s together and then subtract it from 192. √0 is 0, so you don't have to worry about that.
If your question is to simplify 192 in √ form, then the answer is none of the above. To find the √ form of 192, square it: 192² = 36864. So to simplify 192 in √ form, it would be √36864.
the length of a rectangle is twice its width, the perimeter of it is 36cm. what is the are of it
Answer: 72 cm²
Step-by-step explanation: lets take the width as x and length as 2x as length is twice the width= perimeter of rectangle is 2*(l+b)=36cm
So, 2×(2x+x)=36cm
2×3x=36cm
6x=36cm
X=36/6:6cm( width, since width was taken as x)
Length= 2x: 2×6=12cm
So area of the rectangle is( l*b):
12×6= 72cm²
4.8x10^-3 as an ordinary number
Answer:
0.008.
Step-by-step explanation:
10^-3 basically tells you to move the decimal point to the left by three digits.
Right now, you have 8. If the decimal point were to move left by three digits, you can visualize 8 as 0008. Move left by three digits, and you get 0.008.
Hope this kind of helps!
Answer:
0.008.
hope this helps :)
Select an equation for this graph please help me.
A is the answer.
First, figure out all the coordinates for the points marked red( I Did this for all except first one, which was not on the right point)
They were:
-1,1
0,2
1,4
2,8
3,16.
Then, we must do trial and error for each of the options until we find one that fits perfectly. Luckily, the first option was right!
Hope this helps
Which relation defined by a graph is not a function?
Step-by-step explanation:Answer:a
Step-by-step explanation:horizonal line test can tell if it is a function or not.if we get more than one value of y for a value of x then it is not a function. In the option (a) we get +2and -2 for x=0
NEED MATH HELP NOW. Need help find the vertex and y intercept. Please show work.
Answer:
Vertex: ( 1 , 9 )
Y-intercept: ( 0 , 8 )
Step-by-step explanation:
y = - (x+2) (x-4)
y = -x² + 2x + 8
Find the vertex.
x = -b/2a
x = -2/2(-1)
x = -2/-2
x = 1
y = -(1)² + 2(1) + 8
y = -1 + 2 + 8
y = 9
Find the y-intercept.
Put x as 0.
y = -(0)² + 2(0) + 8
y = 8
what is the solution to this equation? 4X equals 32
Answer:
x = 8
Step-by-step explanation:
4x = 32
Divide each side by 4
4x/4 = 32/4
x = 8
The solution to the equation 4x = 32 is x = 8.
How to evaluate and solve the given equation?In order to evaluate and solve this equation, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right.
Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
Based on the information provided, we have the following mathematical equation:
4x = 32
By dividing both sides of the equation by 4, we have:
x = 32/4
x = 8
Read more on expression here: brainly.com/question/16729936
#SPJ6
Help help help please
Hey there! :)
Answer:
x = -7/12.
Step-by-step explanation:
Given:
[tex]x + \frac{5}{12} = -\frac{1}{6}[/tex]
Create a common denominator for each term:
[tex]\frac{12x}{12} + \frac{5}{12} = -\frac{2}{12}[/tex]
Disregard the denominator:
12x + 5 = -2
Subtract 5 from both sides:
12x = -7
Divide both sides by 12:
x = -7/12.
someone help me asap please/math 10
Answer:
Step-by-step explanation:
4. a) tan x=17/12=1.416
x=54.8≈55
b)sin b=78/132=0.59
b=36.2≈36
cos 28=x/82
x=82*cos 28=82*0.9=73.8
-3.42, 10.26, -30.78, 92.34, ___,... what is the next number
Answer:
-277.02
Step-by-step explanation:
Given series:
-3.42, 10.26, -30.78, 92.34,...We can see the series is a GP with common ratio of -3, as:
10.26/-3.42= -30.78/10.26= 92.34/-30.78= -3So the next term will be:
92.34 × (-3)= -277.02help help meeeee pls
8. The length of a side and the corresponding height
of a triangle are (x+3) cm and (2x – 5) cm respectively.
Given that the area of the triangle is 20 cm”, find
the value of x.
Answer:
x = 5
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here b = x + 3 and h = 2x - 5 , thus
[tex]\frac{1}{2}[/tex] (x + 3)(2x - 5) = 20 ( multiply both sides by 2 )
(x + 3)(2x - 5) = 40 ← expand factors on left using FOIL
2x² + x - 15 = 40 ( subtract 40 from both sides )
2x² + x - 55 = 0 ← in standard form
(x - 5)(2x + 11) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
2x + 11 = 0 ⇒ 2x = - 11 ⇒ x = - 5.5
But x > 0 , hence x = 5
Please can someone help with the question below
Answer:
The inequality shown here is
-3 ≥ x < 2
Hope this helps
What is the volume of the box if it is scaled down by a factor of 1/10?
Box Dimensions
7in Height
6in Length
2in Width
Answer:
8.4in²
Step-by-step explanation:
We are given the dimensions of a box as :
7in = Height
6in = Length
2in = Width
The volume of a box = Length × Width × Height
Volume of a box = 7in × 6in × 2in
= 84in²
We are also told in the question to find the volume of the box if it is scaled down by a factor of 1/10
Hence,the new volume = 84in² × 1/10
= 8.4in²
Therefore, the volume of the box if it is scaled down by a factor of 1/10 is 8.4in²
HELLO ME I NEED HELP SO BAD
Answer:
up 3 units
Step-by-step explanation:
y = f(x) + C C > 0 moves it up
We are moving the graph up 3 units
This can have more than one option answer this fast in two minutes
Answer:
Just QT and UX
Step-by-step explanation:
QT and TX intersect and are not parallel.
QU and ST are not parallel or intersecting.
QT and WX are not parallel or intersecting.
QT and UX are parallel.
What is the recursive formula for this arithmetic sequence?
-4, 3, 10, 17, ...
O A. (2= -4
Tan = 8-1-7
O B.
(a = 17
lan = an-1-7
= -4
O C.
la,
= 2n-1 +7
= 17
O D.
1 an = 2n-1 +7
Answer:
c
Step-by-step explanation:
The recursive formula for the given arithmetic sequence is a₁ = -4 and aₙ = aₙ₋₁+7
What is an arithmetic sequence?The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).
The arithmetic progression has wider use in mathematics for example sum of natural numbers.
Natural number = 1,2,3,4,5,6,7,8...
Given arithmetic sequence is -4, 3, 10, 17, ...
First term a₁ = -4
Common difference (d) = 3 - (-4) = 7
Now the nth term is given by :-
aₙ = aₙ₋₁+d
So according to our series, it will be
aₙ = aₙ₋₁+7
Hence, the recursive formula for this arithmetic sequence -4, 3, 10, 17, ...
will be a₁ = -4 and aₙ = aₙ₋₁+7
For more about Arithmetic progression
brainly.com/question/20385181
#SPJ7
a line has a gradient of 4 and passes through the post (1,7). what is the equation?
Answer:
y = 4x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 4, thus
y = 4x + c ← is the partial equation
To find c substitute (1, 7) into the partial equation
7 = 4 + c ⇒ c = 7 - 4 = 3
y = 4x + 3 ← equation of line
Answer:
The equation is y = 4x+3
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 4x + b
Substitute the x and y value into the equation
7 = 4(1)+b
7 = 4+b
Subtract 4
7-4 =b
3=b
The equation is y = 4x+3