Answers
Answer:
A.1: ∠BAC ≅ ∠BDC ≅ ∠EDF, ∠ACD ≅ ∠ABD ≅ ∠BDE ≅ ∠CDF
A.2: ∠1 ≅ ∠4, ∠2 ≅ ∠3 ≅ ∠5 ≅ ∠6
A.3: ∠2 ≅ ∠3
B.1: ∠ACD ≅ ∠CAB, ∠CDA ≅ ∠ABC, ∠DAC ≅ ∠BCA
B.2: ∠1 ≅ ∠3 ≅ ∠5, ∠2 ≅ ∠4 ≅ ∠6
see "additional comment" regarding listing pairs
Step-by-step explanation:
There are a number of ways angles can be identified as congruent. In each case, the converse of the proposition is also true.
opposite angles of a parallelogram are congruentcorresponding angles where a transversal crosses parallel lines are congruentalternate interior angles where a transversal crosses parallel lines are congruentvertical angles are congruentany two angles with the same measure are congruentIn these exercises, pairs of angles need to be examined to see which of these relations may apply.
__
ALeft
ABCD is a parallelogram, so the congruent angles are opposite angles and any that are vertical or corresponding:
∠BAC ≅ ∠BDC ≅ ∠EDF ≅ 110° (3 pairs)
∠ACD ≅ ∠ABD ≅ ∠BDE ≅ ∠CDF ≅ 70° (6 pairs)
Center
∠1 ≅ ∠4 ≅ 66° (1 pair) . . . . vertical angles
∠2 ≅ ∠3 ≅ ∠5 ≅ ∠6 ≅ 57° (6 pairs) . . . . marked with the same measure, and their vertical angles
Right
Assuming that lines appearing to go in the same direction actually do go in the same direction, the only pair of congruent angles in the figure is ...
∠2 ≅ ∠3
__
BLeft
Corresponding angles in congruent triangles are congruent. Here, the congruent triangles are ΔACD ≅ ΔCAB. So, the pairs of congruent angles are ...
∠ACD ≅ ∠CAB (30°)
∠CDA ≅ ∠ABC (90°)
∠DAC ≅ ∠BCA (60°)
Right
The corresponding angles and any vertical angles are congruent. This means all the odd-numbered angles in the figure are congruent, and all the even-numbered angles in the figure are congruent. The marked 72° angles show the "horizontal" segments are parallel by the converse of the corresponding angles theorem.
∠1 ≅ ∠3 ≅ ∠5 (72°) (3 pairs)
∠2 ≅ ∠4 ≅ ∠6 (108°) (3 pairs)
_____
Additional comment
The question asks you to list pairs of congruent angles. When 3 things are congruent, they can be arranged in 3 pairs:
a ≅ b ≅ c ⇒ (a≅b), (a≅c), (b≅c)
Similarly, when 4 things are congruent, they can be arranged in 6 pairs:
a ≅ b ≅ c ≅ d ⇒ (a≅b), (a≅c), (a≅d), (b≅c), (b≅d), (c≅d)
In the above, we have elected not to list all of the pairs, but to list the set of congruences from which pairs can be chosen.
Related Questions
Simplify 5^2 • 5^4
O A. 5^8
O B. 5^6
O C. 5•8
O D. 5^2
Answers
Work:
You add 2 and 4 and get 6. Thus your answer is 5^6
Can someone help me with this question please
Answers
Answer:
10.3 cm
Step-by-step explanation:
There are a few ways to do this.
1)Using the law of cosines, you have ...
b² = a² +c² -2ac·cos(B)
b² = 11² +11² -2(11)(11)·cos(56°) = 106.67
b = √106.675 ≈ 10.3
AC = 10.3 cm
__
2)Using trig functions. When you draw an altitude in this isosceles triangle from B to AC, it divides AC in half, and it divides angle B in half. The sine relation can help here:
Sin = Opposite/Adjacent
sin(56°/2) = (AC/2)/(11 cm)
AC = (22 cm)sin(28°) ≈ 10.3 cm
__
3)Using a triangle solver, you can find the value of AC to be about 10.3 cm. Triangle solvers are available as apps and on the web. Your graphing calculator may have one. See attached for the results from a nice solver available on the web. Units are cm.
Which number is closest to 63(square root)?
A. 8.4
B. 7.2
C. 7.9
D. 6.7
Answers
Answer:
C-7.9
Step-by-step explanation:
Because the square root is actually 7.93
Answer:
C. 7.9
Step-by-step explanation:
Do the square root of 63.
[tex]\sqrt{63} = 7.93725[/tex]
Your answer isn't perfect, but it's asking for which number is the closest to the [tex]\sqrt{63}[/tex].
[tex]\sqrt{63}[/tex] ≈ [tex]7.9[/tex]
Find the value of X.
50°
90°
100°
Answers
Answer: 60 degrees
Step-by-step explanation:
add 90 50 and 100
= 240
Total of all interior angles should be 360
So 360-240=120
Straight line: 180 degrees
180-120=60
Six times a number increased by 4 is no less than 50
Answers
Answer:
Number>2
Step-by-step explanation:
If number is 1 then 6×1=6
6×4=24
which is less than 50
If number is 2 then 6×2=12
12×4=48
which is less than 50
.PLEASE HELP!!
Paul opens a savings account with $350. He saves $150 per month. Assume that he does not withdraw
money or make any additional deposits.
a. Write a linear model that represents the total amount of money Paul deposits into his account after m months.
b. After how many months will Paul have $2,000?
Answers
Answer:
350+150m=total money
11 months
Step-by-step explanation:
you just put in the number of months that have passed in for m and solve for total money.
After how many months will Paul have $2,000?
350+150m=2000
350-350+150m=2000-350
150m=1650
150m/150=1650/150
m=11
Please help me I'm really stuck and I can't get a red if I get this wrong I will
Answers
Answer:
-0.75
Step-by-step explanation:
(0 , 22) (12, 13)
=13 - 22/12 - 0
=-9/12
=-0.75
what does the maximum point represent in the function?
a. Y-Int
b. x=0
c. height
d.vertex
Answers
Y is the intercept: for example (0,7) intercept is 7 for y. The y intercept is always x=0 and y=number
x=0 could be a solution or a x intercept.
Height is always the y value in a graph
Vertex is the point at which a parabola changes direction.
Hope this helps please like and brainiest if good!
Each of 8 girls has
a button collection.
Each girl has 8
buttons in her
collection. How
many total buttons
are there in the 8
collections?
Answers
Answer: there are 64 buttons because 8*8=64
Fill in the table using this function rule.
y = 4x + 1
HELP PLEASE NOW!!! no links plz
Answers
Answer:
y=4x+1
for x=3
y=4(3)+1
y=12+1
y=13
for x=6
y=4(6)+1
y=24+1
y=25
for x=8
y=4(8)+1
y=32+1
y=33
for x=10
y=4x+1
y=4(10)+1
y=40+1
y=41
x y
3 13
6 25
8 33
10 41
please pick me brainliest.
I HOPE IT HELPED
Carlos designs the skateboard ramp shown in the diagram, 132in h? 22 degrees Enter the height of the ramp (h), in inches, Round your answer to the nearest whole inch.
Answers
The height of the ramp is 49.45in
Data;
Length of the skateboard = 132inAngle between the height and skateboard = 22 degreesheight of the skateboard rampTrigonometric RatioTo solve this problem, we can use trigonometric ratio SOHCAHTOA
Since we have the value of the angle and length of the ramp, this can be illustrated as hypotenuse and angle between the hypotenuse and opposite of the right-angle triangle.
From the information above, we have angle and hypothenuse but we need to solve for the opposite of the right-angle triangle. The sine angle can solve this problem.
[tex]sin \theta = \frac{opposite}{hypothenuse} \\sin 22 = \frac{x}{132} \\x = 132 sin 22\\x = 49.45 in[/tex]
The height of the ramp is 49.45in
Learn more on trigonometric ratios here;
https://brainly.com/question/12172664
How many solutions does the system have? x y = 5 x y = 6 none one two infinite.
Answers
Answer:
none
Step-by-step explanation:
{ x=5-y
{ x=y=6
substitute the given value of x into the equation x+y=6
5-y+y=6
the equation for y
y∈⊘
The angle of elevation of the sun is 39° from the ground. A business building downtown casts a shadow that is 89 m long. How tall is the building?
Answers
[tex]\tan 39 \textdegree = \displaystyle \frac{h}{89}\\\\89\tan 39 \textdegree = h\\\\h = 72[/tex]Answer:
72 m
Step-by-step explanation:
Hi there!
Using the given information, we can construct a diagram. Please see the attached image.
We need to solve for the height of the building, or the length of the side opposite the angle that measures 39°. Given the only other piece of information is the length of its adjacent side, which is 89 m, we can use the tangent ratio to solve for the height:
[tex]\tan \theta = \displaystyle \frac{opposite}{adjacent}[/tex]
Plug in the given values:
tan 39° = h/89
89 tan 39° = h
h = 72
Therefore, the height of the building is 72 m.
I hope this helps!
Pleaseee help me solve this and show work
Answers
Answer:
x
Step-by-step explanation:
The greatest common factor is x. This is the biggest term that each term can be divided by.
please I need help!!!!
Answers
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Slope: m
(-3,1) and (3,3)
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-1}{3-(-3)} =\frac{2}{6}=\frac{1}{3}[/tex]
Hope this helps!
Which 2 numbers have a mean of 10 and a range of 4?
Answers
Answer:
12 and 8
Step-by-step explanation:
basic knowledge of math i guess
hope that helps love
please help with a full explanation at the bottom i’ll mark brainliest
Answers
Answer:
240 employees or A
Step-by-step explanation:
12 employees : 2 instructors
or 6:1
so there are 40 instructor
so 6*40 equals 240 employees
pls help i forgot how to do this
Find the area of the parallelogram.
Answers
Answer:
3484 [tex]ft^{2}[/tex]Step-by-step explanation:
Given,
The figure is of a parallelogram
Height (h) of the parallelogram = 52 ft.
Since,
In a parallelogram opposite sides are equal so,
Corresponding base to the height of the parallelogram is = 67 ft.
Therefore,
Area of the given parallelogram
= base × height
[On substituting their values]= 67 ft. × 52 ft.
[On multiplying]= 3484 [tex]ft^{2}[/tex]
Hence,
The required area of the parallelogram is 3484 [tex]ft^{2}[/tex] (Ans)
I will give brainliest
Answers
Answer:
2,-5,-12,-19,-26
Step-by-step explanation:
-7n +9
-7(1) +9 = 2
-7(2)+ 9= -5
-7(3)+9 = -12
-7(4)+9 = -19
-7(5)+9 = -26
Help on Math I need answers As soon as possible if you can :) I will add you to brainlist thingy
Answers
Answer:
[tex]-5°F, 0°F, 2°F , 5°F , \\ 13°F, 20°F[/tex]
Hope it helps you<3Write an equation in slope-intercept form for the line with slope -6 and y-intercept 7. Then graph the line.
Answers
y= -6x + 7
Answer:
y = -6x + 7
Step-by-step explanation:
Slope-intercept form: y = mx + b
where:
m is the slopeb is the y-intercept (when x = 0)Given: a line with a slope of -6, and y-intercept of 7
Equation: y = -6x + 7
y-intercept: (0, 7)Randomly select x-values that will help you graph the equation:
when x = -2:
y = -6(-2) + 7 [multiply]
y = 12 + 7 [add]
y = 19
coordinate: (-2, 19)
when x = 1:
y = -6(1) + 7 [multiply]
y = -6 + 7 [add]
y = 1
coordinate: (1, 1)
when x = 2:
y = -6(2) + 7 [multiply]
y = -12 + 7 [add]
y = -5
coordinate: (2, -5)
These coordinates fall on the line for the linear equation. Graph them on a coordinate plane, and they should give you the line for the equation.
2 2/3 lbs of rice cost $5.52. What is the cost of 1lb
Answers
Answer: I'm not fully sure but I think its 2.07
Answer:
$2.07 per pound
Step-by-step explanation:
we can rewrite 2 2/3 as 8/3
now we can create a proportion from cost to pounds of rice
5.52 is to 8/3 pounds as 'c' is to 1:
(5.52 ÷ 8/3) = c/1
cross-multiply to get:
8/3c = 5.52
multiply each side by 3/8 to get:
c = 5.52(3/8)
c = 2.07
From the observation deck of a skyscraper, Bashir measures a 45^{\circ} the angle of depression to a ship in the harbor below. If the observation deck is 1057 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary.
Answers
Which function is linear?
Answers
Answer:
A,B,and D is a linear equation
Answer:
B. 4x - y + 2.5 = 0
Step-by-step explanation:
Its linear as it doesn't have any square or division.
ignore - ², division, xy being together. if so option D, C, A cancels out.
PLEASE HELP DO BOTH A AND B PARTS PLEASE :)
Answers
Answer:
Market (3, 8)
Park (2, 5)
Lily's house (4, 3)
School (7, 6)
Step-by-step explanation:
E2023
Answer:
see attached diagram
market = (3, 8)
Step-by-step explanation:
Park = (2, 5)
Find the number 2 on the x-axis, then count up 5 units
Park = (2, 5)
x-coordinate: 1 unit to the right = 2 + 1 = 3
y-coordinate: 3 units up = 5 + 3 = 8
Therefore, market = (3, 8)
As part of a community service project at your highshcool you are organizing a fund raiser at the neighborhood movie theater money raised will benefit a summer camp for children with special needs the admission charge is 10.00 per person, 5.50 of which is used to pay the movie theaters rental fee, the remainder is donated to the summer camp fund what are the two variables involved in this problem
Answers
Answer:
Yes it is a function. It passes the vertical line test. In other words, it is impossible to draw a single vertical line through more than one point on the V shaped graph. Any input leads to exactly one output.
The domain is the set of all real numbers. This is because we can plug in any x value leading to some specific y value. There are no holes or gaps or jumps to indicate we must restrict any given x value. The domain would not be the set of whole numbers only because values between the whole numbers (eg: decimal values like x = 2.75) work just fine.
The range is the set of y values such that y is either 0 or larger than 0. In short, the range is . Notice how any point on the V shaped graph has a y coordinate that is either 0 or larger than 0. It is impossible to get a y value that is negative.
Step-by-step explanation:
Please help matimatik 10 points
Answers
Answer:
0.03
Step-by-step explanation:
Hope I helped
-Hunter Cross
Please mark Brainliest if Correct
Ross says a $125.95 skateboard at 40% off is cheaper than a $169.95 skateboard at 60% off. Is he correct?
Answers
Answer:
Ross isn't right.
Step-by-step explanation:
Skateboard $125.95 at 40% off is $75.57
How I got the number:
125.95/100 = 1.2595
1.2595 x 40 = 50.38
125.95 - 50.38 = 75.57
Skateboard $169.95 at 60% off is $67.98
169.95/100 = 1.6995
1.6995 x 60 = 101.97
169.95 - 101.97 = 67.98
Therefore the skateboard that is 60% off is cheaper.
Which of the following sets of angles of a triangle represents an acute triangle?
30°, 60°, 90°
60°, 65°, 55°
40°, 40°, 100°
45°, 40°, 95°
I think it's B, but I think i am wrong. Please explain...
Answers
Answer: It's B, great job!
Step-by-step explanation: An acute angle measures less than 90 degrees. 60,65, and 55 are all under 90.
On Dec. 4, 1998, sunrise was at 6:58 and sunset was at 4:12.
The length of the daylight was:
O A. 8 hr 15 min
B. 9 hr 3 min
O c. 9 hr 12 min
OD. 9 hr 14 min
E. 10 hr 15 min
PLS HELP