Answers
Answer:
The two column proof is presented as follows;
Step [tex]{}[/tex] Statement Reason
1 [tex]{}[/tex] [tex]\overline {AC}[/tex] ≅ [tex]\overline {BD}[/tex] Given
[tex]{}[/tex] ∠CAB ≅ ∠DBA
2 [tex]{}[/tex] [tex]\overline {AB}[/tex] ≅ [tex]\overline {AB}[/tex] Reflexive property
3 [tex]{}[/tex] ΔABC ≅ ΔBAD SAS rule of congruency
Step-by-step explanation:
Given that we have;
Segment [tex]\overline {AC}[/tex] of ΔABC being congruent to (≅) segment [tex]\overline {BD}[/tex] on ΔBAD and angle ∠CAB on ΔABC is congruent to angle ∠DBA on ΔBAD, and also that the two triangles share a common side, which is segment [tex]\overline {AB}[/tex], we have;
Segment [tex]\overline {AB}[/tex] is congruent to itself by reflexive property, therefore;
Two sides and an included angle on ΔABC are congruent to the corresponding two sides and an included angle on ΔBAD, which by Side-Angle-Side, SAS, rule of congruency, ΔABC is congruent to ΔBAD
Related Questions
Find an equation of the line passing through the
point (6,5) and perpendicular to the line whose
equation is 2y + 3x = 6.
Answers
Answer:
In slope-intercept form:
[tex]\displaystyle y=\frac{2}{3}x+1[/tex]
Or, in standard form:
[tex]2x-3y=-3[/tex]
Step-by-step explanation:
We want to find the equation of the line that passes through the point (6, 5) and is perpendicular to the line whose equation is:
[tex]2y+3x=6[/tex]
Since the new line is perpendicular, its slope and the slope of the first equation will be negative reciprocals of each other.
So, find the slope of the first equation. Subtract 3x from both sides:
[tex]2y=-3x+6[/tex]
And divide both sides by two:
[tex]\displaystyle y=-\frac{3}{2}x+3[/tex]
So, the slope of the first equation is -3/2.
The slope of the new line is its negative reciprocal. So, the slope of the perpendicular line is 2/3.
Next, we also know that it passes through the piont (6, 5). We can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
Substitute:
[tex]\displaystyle y-(5)=\frac{2}{3}\left(x-6\right)[/tex]
And we have our equation!
If desired, we can simplify it into slope-intercept form:
[tex]\displaystyle \begin{aligned} y-5&=\frac{2}{3}x-4\\\\y&=\frac{2}{3}x+1\end{aligned}[/tex]
Or, into standard form:
[tex]\displaystyle \begin{aligned} y&=\frac{2}{3}x+1\\\\3y&=2x+3\\\\ 2x-3y&=-3\end{aligned}[/tex]
A ladder leans against the side of a house. The angle of elevation of the ladder is 68" when the bottom of the ladder is 16 it from the side of the house. Find the
length of the ladder. Round your answer to the nearest tenth
PLZ HELP ASAP!!!
Answers
Answer:
Length = 42.7 feet
Step-by-step explanation:
By considering it as right triangle we use trigonometric ratios to find the length of the ladder.
Given angle of elevation and adjacent side. We have to find the hypotenuse.
Trigonometric ratios
[tex]sin \theta = \frac{Opposite}{hypotenuse}\\\\cos \theta = \frac{adjacent }{hypotenuse }\\\\Tan \theta = \frac{opposite}{adjacent}\\ \\[/tex] [tex][ \ where \ \theta = 68^{ \circ} \ ][/tex]
To find length of ladder ( or hypotenuse ) :
[tex]cos \theta = \frac{16}{Length \ of \ ladder}\\\\Length \ of \ ladder = \frac{16}{cos 68} = 42.711\\\\[/tex]
Therefore, length of the ladder = 42.7 feet.
Why is the product of a rational number and an irrational number irrational?
A) because the product is always a non-terminating, non-repeating decimal
B) because the product is always a fraction
C) because the product is always a negative number
D) because the product is always a repeating or a terminating decimal
Answers
Answer:
A
Step-by-step explanation:
Answer:
✔ Because the product is always a non-terminating, non-repeating decimal.
Step-by-step explanation:
E 2021
3, 6, 9, 12, 15,
Tlie common difference " is
Answers
Answer:
The common difference is definitely 3. The common difference is the difference between the numbers in a sequence. In the sequence 3,6,9,12, and 15 the common difference is 3.
Lines RS, TV, and SW are shown.
On a coordinate plane, 3 lines are shown. Line R S goes through (negative 8, 6) and (2, 6). Line T V goes through (negative 6, negative 4) and (8, negative 4). Line S W goes through (2, 6) and (2, negative 8).
Which statements are true about these lines? Select three options.
Line RS has a slope of 6.
Line SW has an undefined slope.
Line TV has a slope of 0.
Lines RS and TV are parallel.
Line SW is perpendicular to line RS, but not to line TV.
Answers
9514 1404 393
Answer:
(b) Line SW has an undefined slope.
(c) Line TV has a slope of 0.
(d) Lines RS and TV are parallel.
Step-by-step explanation:
A horizontal line has 0 slope. Lines RS and TV are horizontal, hence are parallel and have 0 slope.
A vertical line has undefined slope. Line SW is vertical, hence has undefined slope.
Answer:
B,C,D
Step-by-step explanation:
Helpppppp pls
Find h.
h = [?] in
Answers
Answer:
h=rt.96=4 rt.6
Step-by-step explanation:
r=2 inches
therefore 100= root over h + 4
=>h=rt.96=4 rt.6
which linear inequality is represented by the graph
Answers
Answer:
Step-by-step explanation:
Convert 4cm to meters
Answers
Answer:0.04
Step-by-step explanation:
Answer:
0.04 meters
It's too simple
Help me out plz help me
Answers
Answer:
-15
Step-by-step explanation:
Step 1: Multiply 3 by both sides
3(2/3x)=3(-10)
Step 2: Simplify
2x=-30
Step 3: Divide both sides by 2
2x/2=-30/2
Step 4: Simplify
x=-15
Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?
A wire is in the shape of a rectangle Pentagon of side 12 centimetres. It is rebent into the shape of a rectangle whose length is 3 divided by 2 times it's breadth. Find the length and breadth of the rectangle
Answers
Answer
Total Length of Wire = Perimter of Pentagon
= 12 × 5 = 60 cm
Perimeter of Rectangle = 2 (l + b)
Given, l = 3/2 b
Therefore,
2(3/2 b + b) = 60
2 (5b/2) = 60
5b = 60
Breadth b = 12 cm
Length l = 3/2 × 12 = 18 cm
physics
Joseph Jogs from one end A to the other end B of a straight
300m road in 2 minutes 30 second then turns around and jogs 100 m back to point C in another minute. What are Josef's Average speeds and velocities in jogging from
a) A to B
and
b) A to C
pls give answer with explination do not send link
Answers
Answer:
a) Josef jogging from A to B;
i. speed = 2 m/s
ii. velocity = 2m/s
a) a) Josef jogging from A to C;
speed = 1.9 m/s
ii. velocity = 2.2 m/s
Step-by-step explanation:
One major difference between speed and velocity is that speed is a scalar quantity, while velocity is a vector quantity.
a) Josef jogging from A to B;
distance = 300 m
time = 2.5 seconds = 150 seconds
i. his average speed = [tex]\frac{distance}{time}[/tex]
= [tex]\frac{300}{150}[/tex]
= 2 m/s
ii. his average velocity = [tex]\frac{displacement}{time}[/tex]
= [tex]\frac{300}{150}[/tex]
= 2 m/s
b) Josef jogging from A to C,
distance = 300 + 100 = 400 m
time = 2.5 + 1 = 3.5 minutes
= 210 seconds
i. his average speed = [tex]\frac{distance}{time}[/tex]
= [tex]\frac{400}{210}[/tex]
= 1.9 m/s
ii. his average velocity = [tex]\frac{\sqrt{V_{1} ^{2} + V_{2} ^{2} } }{2}[/tex]
[tex]V_{1} ^{2}[/tex] = 4 m/s
[tex]V_{2} ^{2}[/tex] = 1.9 m/s
his average velocity = [tex]\frac{\sqrt{4^{2} + 1.9^{2} } }{2}[/tex]
= 2.2 m/s
Tori is cutting fabric squares to make a quilt. Her squares on average are 5 in. on each side with a standard deviation of 0.1 in. If her cuts are normally distributed, what percentage of her squares would be between 4.9 and 5.1 in?
Answers
Answer:
[tex]\approx 68\%[/tex]
Step-by-step explanation:
For normal distributions only, all data falls within approximately 68% of one standard deviation, 95% of two standard deviations, and close to 100% of three standard deviations. The standard deviation is far too small to represent two or three standard deviations, hence [tex]\implies \boxed{68\%}[/tex].
*Important: This problem would be unsolvable if the question did not say her cuts were normally distributed, because the information above is only applicable to normal distributions.
Answer:
68.26%Step-by-step explanation:
Given:
Mean μ = 5 inStandard deviation σ = 0.1 inThe squares between 4.9 and 5.1 represent:
x = 5 ± 0.1Relevant z- scores are:
z = (x - μ)/σz = (5.1 - 5)/0.1 = 1z = (4.9 - 5)/0.1 = -1From the z-score table we get:
z = 1 ⇒ 84.13% markz = -1 ⇒ 15.87% markThe data between these points is:
84.13% - 15.87% = 68.26%Help please...............................
Answers
Answer:
10cm+5cm+3cm+3cm+7cm+2cm=30cm
What is the value of D
Answers
Answer:
Value of what? There’s nothing
Step-by-step explanation:
The Naturally Made Bath and Body store pays $550 a month for rent and utilities. The average cost for its products to be manufactured is about $3.00 an item. If the average price for a product sold in the store is $5.50, what will the break-even point be?
Answers
Answer:
Break-even point is at quantity 220.
Step-by-step explanation:
Given the rent amount that is fixed cost for the store = $550
The average cost of the goods = $3
The average price of the goods = $5.50
Let the total number of break-even items = Q
Thus, total revenue = 5.50 x Q = 5.50Q
At break-even, TR = TC
5.50Q = FC + VC
5.50Q = 550 + 3Q
5.50Q - 3Q = 550
2.50Q = 550
Q = 550 / 2.50
Q = 220
Thus break-even point is at quantity 220.
Are lines l and k parallel
Answers
Answer:
yes both lines have a slope of 2, so they are parallel.
Question 7
1. Calculate and write your answer as a mixed number
1 4/5 + 2 2/3 - 16/15
Answers
Answer:
3 7/15
Step-by-step explanation:
1 4/5 + 2 2/3 - 16/15
9/5 + 8/3 - 16/15
27/15 + 40/15 - 16/15
52/15 = 3 7/15
Answer:
3 2/5
Step-by-step explanation:
STEP 1: Convert all fractions into improper fractions
9/5 + 8/3 - 16/15
Step 2: pass denominators
(9x3 + 8x5 - 16) / 15
=51/15
Step it into proper mixed number
3 2/5
PLZ HELP IF RIGHT I WILL THEN GIVE YOU BRAINLISET!!!!!!
Answers
Answer:
1, 4, 8, 10
16, 64, 96, 160
Hope it helps u
Thank You
Please mark as brainliest
Answer:
top row is 4 and 10 bottom is 96 and 128
Step-by-step explanation:
goo
Convert 14 into base 2
Answers
Answer: 0b1110
Step-by-step explanation:
what is the order of the numbers from least to greatest
Answers
Answer:
-3.7, -1.9, -1/2, 1 1/3, 1.6, 2 1/3
Step-by-step explanation:
I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if this answer is wrong.
Answer:
-3.7, -1.9, -1/2, 1 1/3, 1.6, 2 1/3
Step-by-step explanation:
hope this helps! have a great day!
which equation has the steepest graph?
A. y=7x+3
B. y=8x-1
C. y=-10x-4
D. y=-2x+6
Answers
A right rectangular prism has a square base and a height of 4 feet. Its volume, V, is 16 cubic feet. What are the lengths of the sides of the base?
A. 2 ft.
B. 4 ft.
C. 8 ft.
D. 16 ft.
Answers
This is because the volume is the base times the height
if you take the volume and divide it by the height than you get 4, which means the area of the base is 4
This means that when you multiply the side lengths together you should get 4 and since you know the base is a square (so both sides are the same length) the answer is 2
if a man died and left inheritance money$ 3990. As per his will this amount will be distributed in 15:18:17 ratio. Find the share of money each gets?
Answers
Answer:
The ratios are 15 18 and 17 which total 50
So one person will receive 15/50 = 30 per cent
Another person receives 18/50 = 36 per cent
The third person receives 17/50 = 34 per cent
1st Person 30% of 3,990 = 1,197.00
2nd Person 36% of 3,990 = 1,436.40
3rd Person 34% of 3,990 = 1,356.60
Step-by-step explanation:
Answer:
$1197 : $1436.4 : $1356.6
Step-by-step explanation:
15 + 18 + 17 = 50
3990 / 50 = 79.8
1st person : 79.8 x 15 = 1197
2nd person : 79.8 x 18 = 1436.4
3rd person : 79.8 x 17 = 1356.6
$1197 : $1436.4 : $1356.6
If this helps you, please mark brainliest!
HELP!!!
f(x) =x^2. What is g(x)?
Answers
Answer:
C. g(x) = 4x²
Step-by-step explanation:
we have one specific point on g(x) : (1,4)
so, for x=1 the functional value (y) has to be 4.
A. (4×1)² = 4² = 16 and not 4. => wrong
B. 1/4 × 1² = 1/4 and not 4. => wrong
C. 4×1² = 4 and that IS 4 => correct
D. 16×1² = 16 and not 4 => wrong
A car dealership has seven cars in the lot unfortunately the keys to the cars of been mixed up the manager randomly grab the key and tries to start a car salesman also randomly picks a different key and tries to start another car what is the probability that both cars start
Answers
To determine The probability of both of these occurring, you would multiply the probability of each together. So, there is a 1/7 chance of the first salesman getting the right key, and 1/6 chance of the second salesman getting the right key. 1/7 x 1/6= 1/42 chance of both occurring.
By what percent is 4.5 × 10^5 greater than 9 × 10^4
a) 200%
b) 400%
c) 500%
d) 600%
Answers
Answer:
C; 500%
Step-by-step explanation:
To get the percentage, we need to make a straight division, then multiply by 100%
We have this as;
(4.5 * 10^5)/(9 * 10^4) * 100%
= 5 * 100% = 500%
a.)Would the equation be sine or cosine if the situation was someone being on a roller coaster that starts 15 ft above ground level, goes up to 45 feet above ground level, and goes down 20 feet under ground level?
b.) What would the equation be? ford monition and the terminal is in the third quadrant
Answers
PLEASE HELP I’LL GIVE BRAINLIEST
What is the slope of the line shown below?
10+
(-6, 3) 5+
(12,6)
15
-10-
o A. - 1
O B. 6
O C.-6
OD
Answers
Answer:
B
Step-by-step explanation:
B
Answer:
the most likely answer is D 1/6
Step-by-step explanation:
Im not 100% sure
but hope this help if so can you mark me brainiest
thank you
Danessa is working with consecutive even numbers. If x is her first number, which expression represents her second number?
x + 1
x – 1
x + 2
2x
Answers
Answer:
x + 2
Step-by-step explanation: I believe that can help you!
What is the product of (a+b) (a-b)
Answers
Answer:
[tex]a^{2}+b^{2}[/tex]
Step-by-step explanation:
(a+b)(a-b)
[tex]a^{2}[/tex]-ab+ab-[tex]b^{2}[/tex]
[tex]a^{2} + b^{2}[/tex]