Answer:
HL Postulate
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HL Postulate(Hypotenuse - Leg) or RHS theorem -> If any two right angles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.
AC ≅ DF , BC ≅ EF and ∠B ≅ ∠E ( both 90 0 )
∴ Δ ABC ≅ Δ DEF by RHS theorem
Theorem : Prove RHS theorem or postulate.
Given : AC = DF , BC = EF and ∠B = ∠E = 90 0
Prove that : ΔABC ≅ ΔDEF
Construction : Extend DE to G so that EG = AB. Join GF.
Statements
Reasons
1) AB = GE 1) Construction
2) ∠B = ∠FEG 2) Each 900
3) BC = EF 3) Given
4) ΔABC ≅ ΔGEF 4) By SAS postulate
5) ∠A = ∠G 5) CPCTC
6) AC = GF 6) If the two angles are congruent then angle opposite to them are equal
7) AC = DF 7) Given
8) DF = GF 8) By transitive property
9) ∠D = ∠G 9) Angles opposite to equal sides in ΔDGF are equal
10) ∠A = ∠D 10) From (5) and (9)
11) ∠B = ∠E 11) Given
12)∠A+∠B=∠D+∠E 12) Adding (10) and (11)
13) ∠C = ∠F 13) ∠A + ∠B + ∠C = 180
and ∠D + ∠E + ∠F = 1800
14) ΔABC ≅ ΔDEF 14) By SAS postulate and from (3) (7) and (13)
Step-by-step explanation:
Answer:
Step-by-step explanation:
HL is the the Hypothenuse Leg Postulate that sais that
If the hypotenuse and leg of one triangle are congruent
to the hypotenuse and leg of another triangle
then the triangles are congruent.
What value(s) of x in the relation below would
create a set of ordered pairs that is not a function?
Justify your answer.
{(0, 5) (1, 5) (2, 6) (x, 7)}
3 Answers: x = 0, x = 1, or x = 2
==================================================
Explanation:
The relation
{(0, 5) (1, 5) (2, 6) (x, 7)}
has points with x coordinates of: 0, 1, 2, and x.
If we repeated any of the x values listed so far, then we will not have a function.
So if we had the points (0,5) and (0,7), then the input x = 0 leads to multiple outputs. A function is only possible when any input x leads to exactly one output y.
This means that if x = 0, 1, or 2, then we won't have a function.
Side note: The y values can repeat, but if they do, then we won't have a one-to-one function. In this case, y = 5 repeats, so this function is not one-to-one (assuming x is not 0, not 1, and not 2).
Please help me on this
Answer:
PAGE 1
8.) d
9.) b
PAGE 2
6.) b
7.) d
PAGE 3
4.) c
5.) a
PAGE 4
1.) c
2.) c
3.) a
PAGE 5
10.) b
11.) d
Step-by-step explanation:
PAGE 1
8.) x - 20 + x + 10 = 180 (collect like terms)
2x - 10 = 180 (add 10 on both sides)
2x = 190 (divide by 2 on both sides)
x = 95
9.) 2y + y = 180 (collect like terms)
3y = 180 (divide by 3 on both sides)
y = 60
x = y ----> x = 60
PAGE 2
6.) 16x - 6 = 90 (add 6 on both sides)
16x = 96 (divide by 16 on both sides)
x = 6
7.) 5x + 30 = 7x (subtract 5x on both sides)
30 = 2x (divide by 2 on both sides)
15 = x
PAGE 3
4.) <8 and <16 are corresponding angles
5.) 180 - 130 = 50
PAGE 4
1.) HD and GE are skew lines
2.) AC, EG, and BD are parallel to FH
3.) EF, GH, and BF are perpendicular to FH
PAGE 5
10.) | and || only are the only ones correct
11.) l || m, by the Converse of the Consecutive Interior Angles Theorem.
b/c the two angles equal 180 together and one angle is on line l and the other is on line m. This shows they're parallel.
Hope this helps ya!!
Mackenzie built the small lego set it cost $5.49 Caleb built the large lego set how much do you think the large lego set cost
Answer:
Since there is no available data for the Lego set, it is safe to assume that the cost would be definitely higher than the small Lego set built by Mackenzie. For example, if the dimension of the small Lego set is 50 X 30 X 6 (length X breadth X height all in cm ) which cost Mackenzie $5.49.
On the other-hand, let assume that, the large Lego set built by Caleb is twice that of Mackenzie Lego set (that is 100 X 60 X 12 ), it could be found that, the cost for the large Lego set would cost minimum of $10.98
Step-by-step explanation:
whats the geometric mean of 1/2 and 8
Answer:
4
Step-by-step explanation:
1/2 of 8 is 4
please help me answer this ASAP if u view it then u'll see the question properly
[tex] \frac{1 + \sqrt{3} }{ \sqrt{12} } [/tex]
i will give brainliest answer if it the correct answers
Answer:
1/6 sqrt(3) + 1/2
Step-by-step explanation:
(1 + sqrt(3))
------------------
sqrt(12)
Multiply the top and bottom by sqrt(12)
(1 + sqrt(3)) * sqrt(12)
------------------
sqrt(12)*sqrt(12)
sqrt(12) + sqrt(3) * sqrt(12)
------------------
12
Simplify
sqrt(4)sqrt(3) + 6
------------------------
12
2 sqrt(3) +6
--------------------
12
1/6 sqrt(3) + 1/2
I can’t solve or bring myself to understand it :/ I’m having difficulties
Answer:
x = 50
Step-by-step explanation:
Since the output is 0, x^2 is 2500 but written differently.
Just take the square root of 2500, which is 50.
50^2 = 2500
2500 - 2500 = 0
write each percent as a fraction in simplest form
60%
Answer: 3/5 i hope this helps god bless
Step-by-step explanation:
At Samantha's Hats, there are 12 baseball caps and 4 other hats. What percentage of the hats are baseball caps?
Consider the expression 103 x 0.006. a) What is the exponent in the power of 10? [ Select ] b) How many factors of 10 are in 103? [ Select ] c) How do your answers to the last two questions relate to one another? [ Select ] d) What is the value of 103 x 0.006? [ Select ]
Solution :
Given that the expression is :
[tex]$10^3 \times 0.006$[/tex]
This can be written as,
[tex]$\Rightarrow 10^3 \times \frac{6}{1000}$[/tex]
[tex]$\Rightarrow 10^3 \times \frac{6}{10^3}$[/tex]
[tex]$\Rightarrow 10^0 \times 6$[/tex]
a). Therefore the exponent in the power of 10
= 0
b). Factors of 10 in [tex]$10^3$[/tex]
= 10 x 10 x 10
= 1000
= [tex]$10^3$[/tex]
So there are 3 factors of 10 in [tex]$10^3$[/tex]
c). If we compare the exponent of power of 10 in 1000 and factors of 10 in 1000, then both of them will be same.
But in part a), we are finding exponent in the power of 10 in the expression which is equal to 0. And in part b), we are finding the factor of 10 in 1000, which is equal to 3, as 10 x 10 x 10 = 1000.
d). The value of the expression [tex]$10^3 \times 0.006$[/tex] is 6.
Nicholas is buying shirts for his baseball team. He will pay $9.50 for each shirt plus a one-time fee of $22.50 for the design. Which equation can be used to find y, the total cost to buy x shirts?
(I mark Brainlist)
A. y = 9.5x + 22.5
B. y =22.5 + 9.5
C. y = 9.5x - 22.5
D. y = 22.5x - 9.5
Answer:
C or A
Step-by-step explanation:
I think that it is most likely C but you could try A to
Choose the number that is 5 more than a square number.
21
34
35
65
76
Answer:
21
Step-by-step explanation:
this requires practical assumption.
take 9 for example
5 more than 9 means 9 - 5 = 4
4 is a square number
21 = 21 - 5 = 16
16 is a square number
34 = 34 - 5 = 29
29 is not a square number
35 = 35 - 5 = 30
30 is not a square number
65 = 65 - 5 = 60
60 is not a square number
76 = 76 - 5 = 71
71 is not a square number
Gina tracks the low temperatures for a city over six days. Identify the days colder than -1.75°F.
Answer:
Its Monday and Tuesday
Step-by-step explanation:
Answer:
Monday and Tuesday
Step-by-step explanation:
"Days colder than -1.75 F."
Note that in negative numbers the greater negative number contains a lesser value:
Tuesday: -1.9 F < -1.75 F
Monday: -2.5 F < -1.75 F
Find the slope of each line.
the green shape is a dilation of the black shape.what is the scale factor of the dilation?
Answer: 5
Step-by-step explanation:
Scale factor = [tex]\dfrac{\text{ side length of image}}{\text{Side-length of original figure}}[/tex]
Given: Black triangle ( original) having perpendicular with length 4 units. [2 blocks above and 2 boxes below the x-axis ]
Green triangle ( image) having corresponding side as 20 units [10 blocks above and 10 boxes below the x-axis ].
Scale factor of dilation = [tex]\dfrac{20}{4}=5[/tex]
Hence, the scale factor of the dilation = 5
Peter is calculating the interest earned on a
deposit of $275 in an account that earns 8%
simple interest after 12 years.
Answer:
a) He substituted 0.8 instead of 0.08.
b) $264
Step-by-step explanation:
The full question is: a. What did Peter do incorrectly? b. What is the correct amount of interest?Using the equation [tex]I=prt[/tex], we can substitute the given values.I = 275 x 0.08 x 12I = 264How will the solution of the system y > 2x + Two-thirds and y 2x + One-third?
Sample Response: There is no solution to the system in its original form. There are no points in common. If the signs are reversed, the system has an intersection with an infinite number of solutions.
What did you include in your response? Check all that apply.
The shaded area would reverse on both inequalities.
The graphs do not overlap until the signs are reversed.
There are an infinite number of solutions in the system once the signs are reversed.
There are no solutions before they are reversed.
Answer:
all of them.
Step-by-step explanation:
Hope this helps!
<3
~nxmbus
Which triangles are similar A or b? I need help.
Answer:
A!
Step-by-step explanation:
Evaluate f(x)=x-5 when x=-5,x=0,and x=5
Answer:
f(x) = x - 5
f(-5) = -5 - 5
= -10
f(0) = 0 - 5
= -5
f(5) = 5 - 5
= 5
Hope this helps!
Zoey has a bag that contains orange chews, apple chews, and watermelon chews. She
performs an experiment. Zoey randomly removes a chew from the bag, records the
result, and returns the chew to the bag. Zoey performs the experiment 57 times. The
results are shown below:
A orange chew was selected 39 times.
A apple chew was selected 6 times.
A watermelon chew was selected 12 times.
Based on these results, express the probability that the next chew Zoey removes from
the bag will be apple chew as a decimal to the nearest hundredth.
Answer: 54%
Step-by-step explanation:
A truck moves 3 km in 30 min and and returns at same distance in 20 min find average speed
Answer:
Step-by-step explanation:
the truck mover 3 km one way, 3 km back, so he moves 6 km
one way the truck needs 30 min, on the way back 20 min
so we have 6 km in 50 min
v=distance/time
v one way=3km/30 min=0.1 km/min
v on the way back=3 km/20min=0.15 km/min
v average =0.1+0.15=0.125 km/min
or 7.5 km/hour
what is 7.0893 as a decimal but in word form.
Answer:
seven and eight hundred ninety-three ten-thousandths
Step-by-step explanation:
If 7 pounds cost $5.46, find the cost of 3 pounds.
Answer:
$2.19
Step-by-step explanation:
7 divided by 3 is 2.5
5.46 divided by 2.5 is 2.184
round it and get 2.19
PLEASE HELP FAST!! WILL MARK AS BRAINLIEST IF GIVEN GOID ANSWER....
Answer:
x = 36
y = 37.95
Step-by-step explanation:
By geometric mean property:
[tex] {12}^{2} = 4 \times x \\ \\ 144 = 4 \times x \\ \\ x = \frac{144}{4} \\ \\ x = 36 \\ \\ [/tex]
By Pythagoras Theorem:
[tex] {y}^{2} = {12}^{2} + {x}^{2} \\ \\ {y}^{2} = {12}^{2} + {36}^{2} \\ \\ {y}^{2} = 144 + 1296 \\ \\ {y}^{2} = 1440 \\ \\ y = \sqrt{1440} \\ \\ y = 37.95[/tex]
solve for x
3(x - 2) = 6x - 12
Answer:
The answer is 2
Step-by-step explanation:
Here's how I got it:
3(x - 2) = 6x - 12
Multiply 3 times x and 3 times 2, this is what you would get
3x - 6 = 6x - 12
Then, subtract the lowest x with the bigger X, this way you would have x on one side:
3x - 6 = 6x - 12
-3x -3x
This is what you should have after this:
-6 = 3x - 12
Now, to get the variable (letter that represents a number) by itself, you have to add 12 to both sides like this:
-6 = 3x - 12
+12 +12
You would get this:
6 = 3x
Finally, you have to get x by itself, so you have to divide 3 on both sides like this
6/3 = 3/3 x
That's why, your answer is 2
Please help! I think of a number, I double it, and then add 3. The result is 19. Write this in the form of an equation and then solve the equation to find the number I was thinking of.
Answer:
8
Step-by-step explanation:
Y×2+3=19
19-3=16
16÷2=8
You subtract the 3 first to get what the number was when doubled. After getting that number you would divide it by 2 to get the number that you thought of.
Of the four choices given, which two, when written as a system, have a solution of (-4,5)?
Answer:
The answer is A. The first one.
I hope this helps. ;)
Answer:
It is A on edge 2020
Step-by-step explanation:
Savannah and Reagan both work in a grocery store. They each stocked the same number of shelves last Saturday, but it took Reagan less time. They've been told that they'll spend their entire 4-hour shifts next Saturday stocking shelves. If their average speeds are consistent, who will likely stock more shelves next Saturday?
HELP!
Answer:
Reagan
Explanation:
Since Reagan is able to stock the same number of shelves as Savannah while spending less time to do so, it means that Reagan is able to stock shelves faster than Savannah, thus Reagan is able to stock more shelves than Savannah given that their average speeds are constant and that they both work under 4-hour shifts.
Hope this helps :)
There are 82 chairs at a birthday party. The chairs need to be lined up in equal-sized rows. How many possible ways can the chairs be lined up
Answer:
2 rows of 41
Step-by-step explanation:
i had the same question
The number of possible ways can the chairs be lined up is 2 rows of 41.
Given that,
There are 82 chairs at a birthday party. The chairs need to be lined up in equal-sized rows.Based on the above information, the calculation is as follows:
[tex]= 2 \times 41[/tex]
= 82 chairs
Here 2 denotes the rows.
Therefore we can conclude that the number of possible ways can the chairs be lined up is 2 rows of 41.
Learn more: brainly.com/question/13549064
what is 3/5 divided by 1/2 as a reduced fraction
Look at this angle, what are the sides?
Answer:
Both of the arrowed ones are the sides