Identity the triangle congruence postulate (SSS,SAS,ASA,AAS, or HL) that proves the triangles are congruent. I will mark brainliest!!!
Answers
SSS, or Side Side Side
SAS, or Side Angle Side
ASA, or Angle Side Side
AAS, or Angle Angle Side
HL, or Hypotenuse Leg, for right triangles only
Side Side Side Postulate
A postulate is a statement taken to be true without proof. The SSS Postulate tells us,
If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
Congruence of sides is shown with little hatch marks, like this: ∥. For two triangles, sides may be marked with one, two, and three hatch marks.
If △ACE has sides identical in measure to the three sides of △HUM, then the two triangles are congruent by SSS:
Side Angle Side Postulate
The SAS Postulate tells us,
If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
△HUG and △LAB each have one angle measuring exactly 63°. Corresponding sides g and b are congruent. Sides h and l are congruent.
A side, an included angle, and a side on △HUG and on △LAB are congruent. So, by SAS, the two triangles are congruent.
Angle Side Angle Postulate
This postulate says,
If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
We have △MAC and △CHZ, with side m congruent to side c. ∠A is congruent to ∠H, while ∠C is congruent to ∠Z. By the ASA Postulate these two triangles are congruent.
Angle Angle Side Theorem
We are given two angles and the non-included side, the side opposite one of the angles. The Angle Angle Side Theorem says,
If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
Here are congruent △POT and △LID, with two measured angles of 56° and 52°, and a non-included side of 13 centimeters:
[construct as described]
By the AAS Theorem, these two triangles are congruent.
HL Postulate
Exclusively for right triangles, the HL Postulate tells us,
Two right triangles that have a congruent hypotenuse and a corresponding congruent leg are congruent.
The hypotenuse of a right triangle is the longest side. The other two sides are legs. Either leg can be congruent between the two triangles.
Here are right triangles △COW and △PIG, with hypotenuses of sides w and i congruent. Legs o and g are also congruent:
[insert congruent right triangles left-facing △COW and right facing △PIG]
So, by the HL Postulate, these two triangles are congruent, even if they are facing in different directions.
Proof Using Congruence
Proving Congruent Triangles 5
Given: △MAG and △ICG
MC ≅ AI
AG ≅ GI
Prove: △MAG ≅ △ICG
Statement Reason
MC ≅ AI Given
AG ≅ GI
∠MGA ≅ ∠ IGC Vertical Angles are Congruent
△MAG ≅ △ICG Side Angle Side
If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Related Questions
Enter the equation for the graph.АА- 112y = [?] cos([ ]x)Enter
Answers
A cosine function has the form.
[tex]y=A\cos (Bx)[/tex]Where A refers to the changes of the y-coordinate along the curve, that is, the amplitude. And B refers to the period, that is, the repetition period of the curve.
According to the graph, the amplitude is 1, so A = 1.
Notice that from 0 to 2(pi) the function completes two cycles, which means B = 3.
Therefore, the function is [tex]y=1\cdot\cos (3x)[/tex]solve the absolute value inequity lx-5l>_ 1
Answers
We are given the following the following inequality:
|x - 5| >= 1
When we have a inequality in the format:
|f(x)| >= a
There are two possible solutions.
Either f(x) <= -a or f(x) >= a
In this question:
|x - 5| >= 1
x - 5 <= -1
x <= -1 + 5
x <= 4
Or
x - 5 >= 1
x >= 1 + 5
x >= 6
In interval notation, the answer is:
[tex](-\infty,4\rbrack\cup\lbrack6,+\infty)[/tex]The solution on the number line is:
price of gas at store was 4.29 per gallon the next week it went up .55 and down .25 and back up 8.30 and finally it went down$.15 what is the price per gallon now
Answers
The final price of gas per gallon after number of reduction and increment is $12.74.
Given,
The price of gas at store = 4.29 per gallon
The increased amount of gas = 0.55
The new price of gas = 4.29 + 0.55 = 4.84 per gallon
Then decreased 0.25. So, the price of gas = 4.84 - 0.25 = 4.59 per gallon
Again the price increases 8.30 and the new price become, 4.59 + 8.30 = 12.89 per gallon
Then, the price of gas finally went down to .15.
Therefore, the price of gas now is:
12.89 - 0.15 = 12.74
That is, the final price of gas per gallon after number of reduction and increment is $12.74.
Learn more about price here:
https://brainly.com/question/14728538
#SPJ1
Aaquib can buy 25 liters of regular gasoline for $58.98 or 25 liters of permimum gasoline for 69.73. How much greater is the cost for 1 liter of premimum gasolinz? Round your quotient to nearest hundredth. show your work :)
Answers
The cost for 1 liter of premium gasoline is $0.43 greater than the regular gasoline.
What is Cost?This is referred to as the total amount of money and resources which are used by companies in other to produce a good or service.
In this scenario, we were given 25 liters of regular gasoline for $58.98 or 25 liters of premium gasoline for $69.73.
Cost per litre of premium gasoline is = $69.73 / 25 = $2.79.
Cost per litre of regular gasoline is = $58.98/ 25 = $2.36.
The difference is however $2.79 - $2.36 = $0.43.
Therefore the cost for 1 liter of premimum gasoline is $0.43 greater than the regular gasoline.
Read more about Cost here https://brainly.com/question/25109150
#SPJ1
the radius of a circle is 9 inches. what is the circumference?give the exact answer in simplest form.
Answers
Step 1
The circumference of a circle is given by;
[tex]2\pi r[/tex]where;
[tex]\begin{gathered} r=9in \\ \end{gathered}[/tex]Step 2
Find the circumference
[tex]\begin{gathered} C=2\times\pi\times9 \\ C=18\pi in\text{ches} \end{gathered}[/tex]Hence, in terms of π the circumference of the circle=18πinches
Tell whether the sequence is arithmetic. If it is what is the common difference? Explain.
{1, 5, 9, 13, …}
Answers
The sequence is arithmetic because the common difference is 4.
Answer:
the sequence is arithmetic. the cd is 4
Step-by-step explanation:
1 + 4 = 5
5 + 4 = 9
9 + 4 = 13
Charlie buys a new car with a sticker price of $9,684. For the down payment,he trades in his old car for $1,400. He finances the balance and makes36 monthly car payments of $253. What is the total amount paid for thecar, including interest?
Answers
The total amount = 36 x 253 + 1400 = 9108 + 1400 = $10508
Therefore,
the total amount paid with interest $10508
The given diagram shows the steps for constructing a parallel line to line AB and passing through point P, but an error has occurred in the construction
Answers
Given:
Constructing a parallel line to line AB and passing through point P.
To find:
The error occurred in the construction.
Explanation:
The procedure is,
The first arc must be drawn centred at C.
The second must be drawn centred at P.
Finally, the third arc must be drawn centred at F.
But here, the third arc is drawn centred at D. This is wrong.
Therefore, the correct step is that the third arc must be centred at F.
Final answer:
The third arc should be drawn centred at F.
the table shows a proportional relationship between the weight on a spring scale and the distance the spring has stretched. describe the scale you can use on X and Y axes of a coordinate grid that would show all of the distances and weights in the table
Answers
Here the values are proportional to each other.
Proportionality ratio is,
[tex]\frac{20}{28}=\frac{5}{7}[/tex]Then scale on X-axis representing weight in Newton is 1 unit is equal to 7 Newton
And on the the Y axis representing distance in cm is 1 unit is equal to 5 cm.
Which set of equations can be solved using the matrix equation:this is an online homework assignment I need help on for pre calculus
Answers
The given matrix equation is:
[tex]\begin{pmatrix}4 & -1 \\ -2 & -1\end{pmatrix}\begin{pmatrix}x \\ y\end{pmatrix}=\begin{pmatrix}-5 \\ -3\end{pmatrix}[/tex]To get the required equations, we will have to carry out the matrix multiplication, thus we have:
[tex]\begin{gathered} (4\times x)+(-1\times y)=-5 \\ (-2\times x)+(-1\times y)=-3 \end{gathered}[/tex][tex]\begin{gathered} 4x-y=-5 \\ -2x-y=-3 \end{gathered}[/tex]Hence, the correct option is option D
Determine the total number of roots of each polynomial function using the factored form. f (x) = (x + 1)(x - 3)(x - 4) 3 f (x) = (x - 6)2(x + 2)2
Answers
Answer:
(x + 1)(x - 3)(x - 4) 3 f (x) = (x - 6)2(x + 2)2
Step-by-step explanation:
A store manager or tshirts so that 15 out of every 35 are a medium. How many medium Tshirts would you expect to find when there are 126 T-shirt's on a rack?
Answers
Given:
Out of every 30 t-shirts, 15 are medium.
Let's find the number of medium t-shirts you expect to find when there are 126 t-shirts on a rack.
We have:
35 t-shirts = 15 medium
126 t-shirts = x medium
Now, let's solve for x.
Apply the proportioanlity equation:
[tex]\frac{35}{15}=\frac{126}{x}[/tex]Cross multiply:
[tex]\begin{gathered} 35x=126\times15 \\ \\ 35x=1890 \end{gathered}[/tex]DIvide both sides by 35:
[tex]\begin{gathered} \frac{35c}{35}=\frac{1890}{35} \\ \\ x=54 \end{gathered}[/tex]Therefore, there will be 54 medium t-shirts when there are 126 t-shirts.
ANSWER:
54
Probability knowledge check (this is math not chemistry I am looking at the tab correctly)
Answers
Given: The odds in favor of receiving a gift are 4/19.
Required: To determine the probability of receiving a gift.
Explanation: The probability of an event A that has an odd of happening as A/B can be calculated as
[tex]P(A)=\frac{A}{A+B}[/tex]Here A=4 and B=19. Putting the values, we get,
[tex]\begin{gathered} P(A)=\frac{4}{4+19} \\ =\frac{4}{23} \\ \end{gathered}[/tex]Final Answer: The probability of Brian receiving a gift is 4/23.
How do you write 94 in scientific notation?
Answers
By definition, Scientific notation has the following form:
[tex]a\cdot10^n[/tex]Where the coefficient "a" is a number from 1 to 10 (but not including 10), and the exponent "n" is an Integer.
In Scientific notation, the Decimal point must be after the first digit of the coefficient.
In this case, you have this number:
[tex]94[/tex]Notice that, in order to write it in Scientific notation, you must move the decimal point one place to the left. Therefore, the exponent of the base 10 will be 1:
[tex]94=9.4\cdot10^1[/tex]The answer is:
[tex]9.4\cdot10^1[/tex]The domain of a function is all whole numbers between 2.5 and 7.5. Can you represent the domain using set-builder notation in more that one way? Explain
Answers
The set builder notation of "The domain of a function is all whole numbers between 2.5 and 7.5" is Domain = {x: x∈W , 2.5<x<7.5 }.
In the Set Builder form , a statement or expression is used to represent all the elements of the set .
In the question ;
it is given that
the domain of the function is all whole numbers between 2.5 and 7.5 .
the set of whole numbers is represented by W.
Since the numbers between 2.5 and 7.5 are included , so "<" will be used .
The Set Builder notation is Domain = {x: x∈W , 2.5<x<7.5 } .
Therefore , the set builder notation of "The domain of a function is all whole numbers between 2.5 and 7.5" is Domain = {x: x∈W , 2.5<x<7.5 }.
Learn more about Set Builder Notation here
https://brainly.com/question/10294211
#SPJ1
When a scientist conducted a genetics experiments with peas, one sample of offspring consisted of 953 peas, with 746 of them having red flowers. If we assume, as the scientist did,
that under these circumstances, there is a 3 / 4 probability that a pea will have a red flower, we would expect that 714.75 (or about 715) of the peas would have red flowers, so the result
of 746 peas with red flowers is more than expected.
a. If the scientist's assumed probability is correct, find the probability of getting 746 or more peas with red flowers.
b. Is 746 peas with red flowers significantly high?
c. What do these results suggest about the scientist's assumption that 3 / 4 of peas will have red flowers?
a. If the scientist's assumed probability is correct, the probability of getting 746 or more peas with red flowers is
Answers
a. 74.99% probability of getting 746 or more peas with red flowers.
b. Since Z < 2, 746 peas with red flowers is not significantly high.
c. Since 746 peas with red flowers is not a significantly high result, we cannot conclude that the scientist's assumption is wrong.
Given,
953 peas in sample with 746 of them having red flower
Scientist's assumption;
Since there is a 3/4 chance that a pea will have a red blossom, we would anticipate 714.75 (or roughly 715) of the peas to do so; hence, the finding of 746 peas with red flowers is higher than we had anticipated.
Here,
Binomial distribution:
Probability of x successes on n trials, with p probability.
Normal distribution:
In a normal distribution with mean μ and standard deviation σ, the z-score of a measure X is given by:
Z = (X - μ) / σ
If np ≥ 10 and n (1 - p) ≥ 10 , the binomial distribution can be approximated to the normal with:
μ = np
σ = [tex]\sqrt{np(1-p)}[/tex]
Here,
n = 953 and p = 3/4 = 0.75
Lets see,
μ = np = 953 x 0.75 = 714.75
σ = [tex]\sqrt{np(1-p)}[/tex] = [tex]\sqrt{714.75 . (1 - 0.75)}[/tex] = √714.5 = 26.73
a. The probability of getting 746 or more peas with red flowers.
Using continuity correction, this probability is P(X ≥ 746 - 0.5) = P(X ≥ 745.5) , which is 1 subtracted by the p-value of Z when X = 745.5.
Then:
Z = (X - μ) / σ = (745.5 - 714.75) / 26.73 = 30.75 / 26.73 = 1.150
The p value of z score 1.150 is 0.2501
1 -0.2501 = 0.7499
0.7499 = 74.99% probability of getting 746 or more peas with red flowers.
b. Is 746 red-flowering peas noticeably high
Since Z < 2, 746 peas with red flowers is not significantly high.
c. What do these findings say about the researcher's prediction that 3/4 pea plants will have red flowers?
Since 746 peas with red flowers is not a significantly high result, we cannot conclude that the scientist's assumption is wrong.
Learn more about normal distribution here;
https://brainly.com/question/25082768
#SPJ1
You have $73.50. You earn additional money by mowing lawns. Then you purchase a new pair of shoes for $99.99 and have $23.51 leftmuch money do you earn mowing lawns?
Answers
The question provides the following information;
Money at hand = 73.50
Money earned = x
Purchases made = 99.99
Money left over = 23.51
These sets of numbers can be put into an equation as shown below;
(73.5 + x) - 99.99 = 23.51
This equation means what you had at the beginning plus what earned from mowing lawns is a total of 73.5 + x. Subtract the cost of shoes purchased from this total and you'll now have a balance of 23.51
We can now solve for the money earned from mowing lawns as follows;
(73.5 + x) - 99.99 = 23.51
Add 99.99 to both sides of the equation (in order to isolate the 73.5 + x on the left side of the equation). You now have;
73.5 + x = 123.5
Next you subtract 73.5 from both sides of the equation (in order to isolate the x on the left hand side)
x = 50
This means the money earned from mowing lawns is $50
Find the area of each figure. Round to the nearest 10th if necessary.
Answers
1.
First, divide the figure into 3 different figures.
Find the area of each figure, and then add them:
A1 is a rectangle:
Area of a rectangle: Lenght x width
A1 = 8 x 5.3 = 42.4 in2
A2 is also a rectangle:
Lenght = 4
width = 8 - 5.3 = 2.7
A2 = 4 x 2.7 = 10.8 in2
A3 is a triangle:
Area of a triangle = (base x height) / 2
base = 2.7
Height = 8-4 = 4
A3= ( 2.7 x 4 ) / 2 = 5.4 in2
Total area = A1 + A2 + A3 = 42.4 + 10.8 + 5.4 = 58.6 in2
Answer = 58.6 in2
If the rectangle below were to be enlarged by a scale factor of 5, what would the new size be? 2 10 x 15 10 X 6 8 X 15 Od 2 X 3
Answers
To dilate a shape by a determined scale factor, you have to multiply each side of the said shape by the scale factor.
The figure is a rectangle with length l=3 and width w=2, to enlarge it using factor 5, you have to multiply both lengths by 5:
[tex]\begin{gathered} l=3\cdot5 \\ l=15 \end{gathered}[/tex][tex]\begin{gathered} w=2\cdot5 \\ w=10 \end{gathered}[/tex]After dilating the rectangle by scale factor 5, the new size will be 10 x 15
if a triangle has side lengths of 4x + 6, 6, and 5x; what is the perimeter
Answers
5. Use a number line to find the product: 5 x (-3)=
Answers
First, we solve the expression.
Since it is a negative number we have to place it 15 places to the left ( from zero)
Y=-4 graph each equation by making a table
Answers
The graph of the equation and the table is attached below.
Graph:
Graph means the pictorial representation of the given set of data or the equation.
Given,
Here we have the equation
y = -4.
Now, we need to plot the graph for this equation and we have also draw the table for that.
Here we have the equation y = -4. This one can't take any value for the calculation,
Which means it we take any value on the x coordinate, the given equation will result only the value of y as -4.
Which means, if we take x as -2, the value of y is -4.
If we take x as -1, it will also have the value of y as -4.
If we take x as 0, then again we will get the value of y as -4.
Therefore, it will continuous at infinity.
So, the table for this equation is look like the following.
And the graph of the equation is attached below.
To know more about Graph here.
https://brainly.com/question/17267403
#SPJ1
9 + 4 + (-1) +(-1) +...+ (-546) = 0X X80Σ (-3 + 10) = 0E=1
Answers
Answer
The sum of the sequence = -30072
Explanation
We are given a sequence of numbers and asked to find the sum of the terms up until the last term given. The sequence given is
9, 4, -1,.............., -546
On careful observation of this sequence, we can see that it is an arithmetic progression with a common difference of -5 between consecutive terms.
Common difference = (n + 1)th term - nth term
= 4 - 9 Or -1 - 4
= -5
For an arithmetic progression, the formula for the last term is given as
Last term = a + (n - 1)d
where
L = last term = -546
a = first term = 9
n = number of terms in the sequence = ?
d = common difference = -5
So, we can solve for the number of terms
-546 = 9 + (n - 1)(-5)
-546 = 9 - 5n + 5
-546 = 14 - 5n
14 - 5n = -546
-5n = -546 - 14
-5n = -560
Divide both sides by -5
(-5n/-5) = (-560/-5)
n = 112
We can now use the formula for the sum of an arithmetic progression to find the sum of this sequence.
[tex]\text{Sum of an A.P. = }\frac{n}{2}\lbrack2a+(n-1)d\rbrack[/tex]We know all of these parameters now
Sum of this AP = (112/2) [(2 × 9) + (112 - 1)(-5)]
= 56 [18 + (111 × -5)]
= 56 [18 - 555]
= 56 [ -537]
= -30072
Hope this Helps!!!
At a local market, 3 apples and 2 pears cost $2.70. Three apples cost the same as 4 pears. Type a system of equations to find the cost for one apple and the cost for one pear.
Answers
Data:
Apple: A
Pears: P
3A+2P=$2.70
3A=4P
to find the cost for one apple:
I need to use substitution to solve each system of equations then use ordered pairs
Answers
From the given question
There are given that the equation
[tex]\begin{gathered} 2x+5y=38\ldots(1) \\ x-3y=-3\ldots(2) \end{gathered}[/tex]Now,
From the equation (1)
[tex]\begin{gathered} 2x+5y=38 \\ 2x=38-5y \\ x=\frac{38}{2}-\frac{5}{2}y \\ x=19-\frac{5}{2}y\ldots(3) \end{gathered}[/tex]Then,
Put the equation (3) into the equation (2)
So,
[tex]\begin{gathered} x-3y=-3 \\ 19-\frac{5}{2}y-3y=-3 \\ 38-5y-6y=-6 \\ 38-11y=-6 \\ -11y=-6-38 \\ -11y=-44 \\ y=4 \end{gathered}[/tex]Then,
Put the value of y into the equation (3)
So,
[tex]\begin{gathered} x=19-\frac{5}{2}y \\ x=19-\frac{5}{2}(4) \\ x=19-\frac{20}{2} \\ x=19-10 \\ x=9 \end{gathered}[/tex]Hence, the value of x is 9 and y is 4.
A cell phone regularly sells for $210 is on sale for 30% off. With this discount, find the sale price. Round to the nearest cent if necessary
Answers
To know the price to
Answer each part. If necessary, round your answers to the nearest hundredth.х5?(a) At Hoffman's Bike Rentals, it costs $31 to rent a bike for 7 hours.How many dollars does it cost per hour of bike use?Il dollars per hour(b) A color printer prints 10 pages in 3 minutes.How many minutes does it take per page?minutes per pageCheck0 2021 McGraw Hill Education All Rights.
Answers
EXPLANATION
If it cost $31/7 hours, we can apply the unitary method to get the unit cost:
[tex]\text{unit price=}\frac{31\text{ dollars}}{7\text{ hours}}=4.42\text{ dollars/hours}[/tex]It will cost 4.42 dollars/hours
We can apply the same reasoning to the printer.
JACKSON WORKS AS A DISHWASHERAT A RESTAURANT DOWNTOWN. HEEARNS $8.56 PER HOUR. IF HEWORKED 25.5 HOURS LAST WEEK,HOW MUCH DID HE EARN?
Answers
Gathering the data
$8.56 h
25.5 per hour
2) Assuming Jackson does not get any tips or extra money for his job.
Let's calculate it.
M=8.56 (25.5)
M=218.28
So Jackson earned $218.28 last week for his 25.5 working hours, at the restaurant.
Need help asap thank you!
Answers
All potential solutions are covered by theoretical domains and ranges. The solution sets are constrained by actual domains and ranges to fit inside predetermined constraints. Make a function equation out of a word problem that specifies the domain and range of application. All potential solutions are covered by theoretical domains and ranges.
Domain and range: what are they?C = 9 + 7.34
One room costs = $7.34.
Charges of n room = Charges of one room × Number of Rooms
Charges of n room = 7.34 n
Reservation Room = $ 9
Total Cost (c) = Reservation Room + Charges of n room
C = 9 + 7.34
They only clean a maximum of 15 rooms.
Domain = { 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}
When n = 1 , C = 9 + 7.34 ×1 = 16.34
When n = 2 , C = 9 + 7.34 ×2 =23.68
When n = 3 , C = 9 + 7.34 ×3 =31.02
When n = 4, C = 9 + 7.34 ×4 =38.36
When n = 5 , C = 9 + 7.34 ×5 = 45.7
When n = 6, C = 9 + 7.34 × 6 = 53.04
When n = 7 , C = 9 + 7.34 ×7 = 60.38
When n = 8 , C = 9 + 7.34 ×8 =67.72
When n = 9 , C = 9 + 7.34 × 9 =75.06
When n = 10, C = 9 + 7.34 ×10 = 82.4
When n = 1 1, C = 9 + 7.34 ×1 1 = 89.74
When n = 12 , C = 9 + 7.34 ×1 2 = 97.08
When n = 13 , C = 9 + 7.34 ×1 3 = 104.42
When n = 1 4, C = 9 + 7.34 ×14 = 111.76
When n = 1 5, C = 9 + 7.34 ×15 = 119.1
C = 9 + 7.34
Domain = { 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}
Range = { 16.34,23.68,31.02,38.36,45.7, 53.04,60.38,67.72,75.06,82.4,89.74,97.08,104.42,111.76,119.1}
To Learn more About Domain and range, Refer:
https://brainly.com/question/2264373
#SPJ13
The measures of the angles of a triangle are shown in the figure below. Solve for x.
(x+9)°
42°
104°
Answers
Answer:
Step-by-step explanation:
first do 104 + 42 it should be 146
second since it is x+9 do 146 - 189, it should be 43.
third check your work by doing 43 + 146
if it equals 189 then do 43 - 9, you should get 34
so x = 34