Answers
Answer:
See below.
Step-by-step explanation:
30.
E(1, 2), F(5, 6), G(3, -2)
a)
H, midpoint of segment EG
H( (1 + 3)/2, (2 + (-2))/2) = H(2, 0)
J, midpoint of segment FG
J( (5 + 3)/2, (6 + (-2))/2) = J(4, 2)
b)
Show that segment HJ is parallel to segment EF.
Parallel lines have equal slopes. We find the slopes of the two segments using the endpoints and show that the slopes are equal proving the segments are parallel.
slope of segment HJ:
slope HJ = (2 - 0)/(4 - 2) = 2/2 = 1
slope of segment EF:
slope EF = (6 - 2)/(5 - 1) = 4/4 = 1
slope HJ = slope EF = 1
Segments HJ and EF are parallel since their slopes are equal.
c)
Show HJ = (1/2)EF
We use the distance formula to find the lengths of segments HJ and EF.
length of HJ = sqrt[(4 - 2)^2 + (2 - 0)^2] = sqrt(4 + 4) = sqrt(8) = 2sqrt(2)
length of EF = sqrt[(5 - 1)^2 + (6 - 2)^2] = sqrt(16 + 16) = sqrt(32) = 4sqrt(2)
HJ = (1/2)EF
Substitute the lengths we found just above for HJ and EF:
2sqrt(2) = (1/2)[4sqrt(2)]
2sqrt(2) = 2sqrt(2)
The two sides are equal, so we have proved that HJ = (1/2)EF.
Related Questions
A mudslide left 42 acre-feet of mud in a valley. The mud is being
removed at the rate of 5 acre-feet per day.
Answers
Answer:
8.4 days
Step-by-step explanation:
I'm not sure what the question is, but if it's how many days it would take to remove all the mud, you divide 42 by 5 and get 8.4.
. Your friend claims that it is not possible to have a glide reflection if you have one translation followed by two reflections. Is your friend correct? Explain your reasoning.
Answers
Answer:
Yes my friend is correct
Step-by-step explanation:
You cannot have a glide reflection if you have one translation which is followed by two ( 2 ) reflections .
This is because Glide reflection is made up of one ( 1 ) reflection in line with a single translation along the same line
Glide reflection is known as an opposite isometry of the Euclidean plane
Glide reflection is a single operation that involves a reflection over a line and followed by a translation.
Your friend's claim is correct.
From the definition, we can deduce that glide reflection consists of:
1 reflection1 translationThis means that: 1 translation and 2 reflections is not a glide reflection
Hence, your friend's claim is correct.
Read more about glide reflection at:
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Find the slope of the line between the points (-2, 7) and (10, 3)
Answers
Answer:
m = -1/3
Step-by-step explanation:
10 x 10= 100
mbnv nmvbnhm
mb cvnmbnbn
Answers
Answer:
well your ans is right over there...
Step-by-step explanation:
thank you!!
Answer:
Yeah...10*10 = 100so what?What is the remainder when 2x^3−9x^2+11 is divided by x−6?
Answers
Answer:
119
Step-by-step explanation:
Given f(x) divided by (x - h) then the value of f(h) is the remainder, thus
f(6) = 2(6)³ - 9(6)² + 11
= 2(216) - 9(36) + 11
= 432 - 324 + 11
= 119 ← remainder
A man 2 m high observes the angles of elevation of the rops of house and a window on its sode are 45 and 60 respectively. If the top is at height of 12m above the ground , find the height.
Answers
Answer:
The height of the window = x + 2 = 4.23 + 2= 6.23m
Step-by-step explanation:
The angle of elevation of the top of the house and the window is 60 and 45 degree.
We can proceed as drawing a diagram as a man of height 2m and a building of total height 12m.
draw a horizontal line along the height of a man so that it touches building at height 2mtill the window height we assume its height as 'x' from the man's height.distance till the top from the window will be 'y'we don't know the distance between man and the building let it be 'b'
[tex]\frac{x}{b}=tan 45[/tex] =1
x=b .............(1)
total height of the building is given as 12m
x + y + 2=12
x + y = 10 .....................(2)
[tex]\frac{x+y}{b} =\frac{x+y}{x }[/tex] = tan 60
[tex]\frac{10}{x} = \sqrt{3}[/tex]
x = [tex]\frac{10}{\sqrt{3} }[/tex] ≈ 5.77m
y = 10 - [tex]\frac{10}{\sqrt{3} }[/tex]
y= 10(1-[tex]\frac{1}{\sqrt{3} }[/tex] ) ≈ 4.23m
The height of the window = x + 2 = 4.23 + 2= 6.23m
A pitcher ok a baseball team is practicing his fast ball trying to ensure he hits the strike zone. He consistently releases the ball 3.4 feet high while he is pitching. The pitcher must aim for the ball to hit the ground approximately 58.8 feet from the pitcher's mound in order to stay in the strike zone. At what angle of depression, to the tenth of a degree, must he release the ball
Answers
Answer:
3.3°
Step-by-step explanation:
The set up of the question will give a right angled triangle where the height covered by the bal is the opposite side.
The length at which the pitcher hit the ground is the hypotenuse.
Given
Opposite side = 3.4m
Hypotenuse = 58.8m
Required
Angle of depression
Using SOH CAH TOA trigonometry identity
According to SOH,
Sin(theta) = opposite/hypotenuse
Sin(theta) = 3.4/58.8
Sin(theta) =0.05782
theta = sin^-1(0.05782)
theta = 3.32°
Hence the angle of depression that he must release the ball to nearest tenth is 3.3°
Sum of Angles
Find the value of x and the measure of every angle.
It is Geometry
Answers
If the sum of a triangle equals 180 degrees we’ll go off of that by doing this.
(7x+8)+(5x+2)+(7x-1)=180
7x+8+5x+2+7x-1=180
19x+9=180
19x=180-9
19x=171
19x/19=171/19
x=9
With that let’s find each angle,
I’ll just label them A, B, C.
A: (7x+8)
7(9)+8
63+8=71
B: (7x-1)
7(9)-1
63-1=62
C: (5x+2)
5(9)+2
45+2=47
71+62+47=180
solve: -3 |x-3| = -6
Answers
Answer:
x = 5
Step-by-step explanation:
-3 * (x-3) = -6
3x+9 = -6 (divide by 3)
-x + 3 = -2 (minus 3)
-x = -5 (multiply by -1)
x = 5
Answer & Step-by-step explanation:
Answer the questions. All help needed.
Answers
1. Multiply all the x and y by 2
M (-6,4)
A (-4,6)
T (-2,4)
H (-4,2)
2. They stayed in the same quadrants. The x and y values shifted.
3. Scale factor of 1/2
4. .....mayhaps?
¿Cuántos enteros divisibles por 4 y por 9 hay entre 95 y 450?
Answers
Answer:
Hay 10 enteros divisibles por 4 y por 9 entre 95 y 450.
Step-by-step explanation:
Podemos reescribir esta pregunta como sigue: ¿Cuántos números entre 95 y 450 son divisibles por 36? Entonces, existe un conjunto de números enteros [tex]A[/tex] tal que cada elemento satisface la condición que:
[tex]A = \{x= \frac{n}{36}\,\land \,95\le n \le 450, n, x\in \mathbb{Z}\}[/tex] (1)
Sabemos que el entero más pequeño divisible por 36 es:
[tex]x_{min} = \frac{108}{36}[/tex]
[tex]x_{min} = 3[/tex]
Mientras que el entero más grande divisible por 36 es:
[tex]x_{max} = \frac{432}{36}[/tex]
[tex]x_{max} = 12[/tex]
La cantidad de enteros divisibles se obtiene a través de la siguiente expresión algebraica:
[tex]a = 1+(x_{max}-x_{min})[/tex] (2)
[tex]a = 1+(12-3)[/tex]
[tex]a = 10[/tex]
Hay 10 enteros divisibles por 4 y por 9 entre 95 y 450.
A circle has a diameter of 26 mm. What Is Its circumference?
Use 3.14 for 1, and do not round your answer. Be sure to Include the correct unit in your answer
Answers
The formula for circumference is 2 x pi x radius
In order to find the radius you need to divide 26 by 2
26 divide by 2 is equal to 13
2 x 3.14 x 13= 81.681 or 26pi
The drawing of the building, shown below, has a scale of 1 inch to 30 feet. What is the actual height, in feet, of the building?
Answers
Answer:
Actual height of the building is 37.5 feet
Step-by-step explanation:
Formula to be used to get the actual length of the building,
Scale used = [tex]\frac{\text{Dimension of image (on map)}}{\text{Dimension of actual}}[/tex] = [tex]\frac{1}{30}[/tex]
By this formula,
[tex]\frac{1.25}{\text{Actual height}}=\frac{1}{30}[/tex]
Actual height of the building = 1.25 × 30
= 37.5 feet
Therefore, actual height of the building will be 37.5 feet.
PLEASE ANSWER THESE 2 QUESTIONS!!!!!! THIS IS A MAJOR GRADE!!!!!!!!!!!!!!!!!
Answers
Answer:
I cant see the problems
Step-by-step explanation:
can anyone help me with this question?
Answers
Answer:
The answer is D, or 5/7
Answer:
The slope is 5/7
Step-by-step explanation:
From a point to get to the next point, you would need to go 5 up and 7 to the right in this graph.
complete the missing value in the solutuion to the equation
Answers
Answer:
Step-by-step explanation:
5x-2y=30
Given x=8
5×8-2y=30
-2y=30-40
y=5
Help me out here...........
Answers
Answer:
false cause if they both were added it would be 2/9ths
Step-by-step explanation:
answer:
JUST READ EXPLANATION!!!
Step-by-step explanation:
well, 1/3 divided by 3 =1/9
Combine and simplify the following radical expression. (2^3 square root 12)(3^3 square root 2)
Answers
Answer:
(2^3 square root 12)(3^3 square root 2)(32 square root)
Step-by-step explanation:
i lie
Answer:
432
Step-by-step explanation:
I checked it trust me
Rectangle ABCD is shown on the grid. What is the area of rectangle ABCD in square units? square units square units 17 square units 34 square units
Answers
Answer:
34sq. units
Step-by-step explanation:
The area of the rectangle shown is expressed as;
A = length *width
The length = AD = BC
Width = AB = CD
From the diagram, we will look for AD and AB using the formula for calculating distance between two points;
D = √(x2-x1)²+(y2-y1)²
For AB where A(-1,4) and B(3,3)
AB = √(3-(-1))²+(3-4)²
AB = √(4)²+(-1)²
AB =√16+1
AB = √17
For AD where A(-1,4) and D(-3,-4)
AD = √(-3-(-1))²+(-4-4)²
AD = √(-2)²+(-8)²
AD =√4+64
AD = √68
Hence area of the rectangle = √17*√68
Hence area of the rectangle = √1156
Hence area of the rectangle = 34
Hence area of the rectangle ≈ 34sq. units
Answer:
D.
Step-by-step explanation:
What shape is generated when AABC is rotated around the vertical line
through B and C?
Answers
The solution is, The shape that is generated is a Cone, when AABC is rotated around the vertical line through B and C.
What is a cone?A cone is a solid which tapers from a circular base to a point. A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex.
here, we have,
given that,
triangle ABC is rotated around the vertical line through B and C.
now, we have to find shape that is generated .
we know that,
A triangle, when rotated about one of it's side will generate a solid in a form of a Cone.
again, we have,
The cone could be a hollow one or a solid filled one, depending on the properties of the triangle being rotated.
Hence, The solution is, The shape that is generated is a Cone, when triangle ABC is rotated around the vertical line through B and C.
To get more about cone visit:
brainly.com/question/1082469
#SPJ7
The figure below shows the first 3 steps in the construction of a Sierpinski Triangle.
1 equilateral 3 congruent 9 congruent
triangle
equilateral equilateral
triangles
triangles
Which property explains why each of the 9 small triangles in step 3 is similar to the large triangle in step 1?
A. The side-side property of congruent triangles can be used because all the sides of an equilateral triangle are similar.
B. The side-side property of similar triangles can be used because all the sides of an equilateral triangle are congruent.
C. The angle-angle property of congruent triangles can be used because all the angles of an equilateral triangle are similar.
D. The angle-angle property of similar triangles can be used because all the angles of an equilateral triangle are congruent.
ок
Answers
Answer:
c
Step-by-step explanation:
Will mark Brainliest!!
Part A: An archer shoots an arrow into the sky where the motion of the arrow can be modeled by the equation
() = −16^2 + 80 where t is time in seconds and f(t) is height in feet. Find how long it will take the
arrow to hit the ground using an algebraic method. Show all of your reasoning/steps used with this algebraic
method.
Part B: Using the information in Part A, find how high the arrow will go at its maximum height, and how
long it takes for this to occur using an algebraic method. Show all of your reasoning used with this
algebraic method
Answers
Answer:
64 higene
Step-by-step explanation:
16 morderate 20 9 oxygen
HELP PLEASE PLEASE PLEASE!!The function f(x) = 4x – 8 is reflected across the y-axis, resulting in a new function, g(x). Write the EQUATION of g(x). Please show how you got it!!!
Answers
The minus makes the graph descend and therefore it's on the other site of the y-axis (sorry for my English haha...I'm not a native speaker)
If the function f(x) = 4x – 8 is reflected across the y-axis. Then the reflected function will be g(x) = – 4x – 8.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
It is the image of the line which is located in the opposite direction of a given line.
The function f(x) = 4x – 8 is reflected across the y-axis.
If the function f(x) = 4x – 8 is reflected across the y-axis, then replace x with negative x. Then the reflected function will be
g(x) = – 4x – 8
The graph of the function and reflected function is given below.
More about the function link is given below.
https://brainly.com/question/5245372
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Asha borrowed Rs.24000 from a moneylender at a rate of 4% per annum compounded semi annually ,what payment will she have to make after 1year and 6 months to the moneylender to clear her debt ?
Answers
Answer:
Rs. 25,468.8
Step-by-step explanation:
A = p(1 + r/n)^nt
Where,
P = principal = RS. 24,000
r = interest rate = 4%= 0.04
n = number of periods = 2
t = years = 1 year and 6 months = 1.5 years
A = p(1 + r/n)^nt
= 24,000(1 + 0.04/2)^2*1.5
= 24,000(1 + 0.02)^3
= 24,000(1.02)^3
= 24,000( 1.0612)
= 25,468.8
A = Rs. 25,468.8
Is y = 5x − 3 a linear function? If so, graph the function.
Answers
If you have a slope (which is before the x) then it’s a linear equation
what is negative 7 minus negative 2
Answers
Answer:
-5
Step-by-step explanation:
-7 - (-2)
-7 + 2
Example: If you owe someone $7, and you give them $2, how much do you still owe? You are owing him $7 so it's a negative and you give him $2 which is a negative as well since you are giving it to him. So, to answer how much do you still owe, you would add $2 to the $7 you owed, so now, you owe him $5, which is a negative since you OWE him.
Hope this helps:)
The product of a number and negative 7/10 is 1/2 what is the number
Answers
Answer:
5/7
Step-by-step explanation
The product of a number and negative 7/10 is 1/2 can be written as 1/2=(7/10)x, with this equation, multiply by the reciprocal, 10/7, to make the right side of the equation just x. On the left side, multiply 1/2 by 10/7 because when you do something on one side, you must do it on the other. 1/2 times 10/7 equals 5/7. Leaving you with x=5/7
Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = –8x + x2 + 7 ?
Answers
Answer:
the answer is 6x or by and ax6x 9x
Step-by-step explanation:
pleaseeee helpppppp asapppp
Answers
Answer:
30
Step-by-step explanation:
Which line is a linear model for the data?
Plz help ASAP
Answers
Answer:
the one you have clicked is correct just took that quiz
Step-by-step explanation: