How can the triangles be proven similar by the sas similarity theorem? show that the ratios startfraction x y over v u endfraction and startfraction y z over v w endfraction are equivalent, and ∠u ≅ ∠x. show that the ratios startfraction u v over x y endfraction and startfraction w v over z y endfraction are equivalent, and ∠v ≅ ∠y. show that the ratios startfraction u w over z x endfraction and startfraction x y over w v endfraction are equivalent, and ∠w ≅ ∠x. show that the ratios startfraction x z over w u endfraction and startfraction z y over w v endfraction are equivalent, and ∠u ≅ ∠z.
Answers
All four conditions hold true, and therefore Triangle ABC ~ Triangle DEF by the SAS similarity theorem.
To prove that two triangles are similar using the SAS similarity theorem, we need to show that two pairs of sides are proportional and the included angle between these sides is congruent.
Let's assume that we have two triangles, Triangle ABC and Triangle DEF, such that ∠ABC ≅ ∠DEF and AB/DE = AC/DF.
To prove the similarity using the SAS theorem, we need to show the following:
startfraction xy over vu endfraction = startfraction yz over vw endfraction and ∠u ≅ ∠x
startfraction uv over xy endfraction = startfraction wv over zy endfraction and ∠v ≅ ∠y
startfraction uw over zx endfraction = startfraction xy over wv endfraction and ∠w ≅ ∠x
startfraction xz over wu endfraction = startfraction zy over wv endfraction and ∠u ≅ ∠z
Proof:
AB/DE = AC/DF and we are given that BC/EF = 1, which means that Triangle ABC ~ Triangle DEF by the SAS theorem. Thus, startfraction xy over vu endfraction = startfraction yz over vw endfraction and ∠u ≅ ∠x.
Using the same reasoning as above, we get that Triangle ABC ~ Triangle DEF by the SAS theorem. Thus, startfraction uv over xy endfraction = startfraction wv over zy endfraction and ∠v ≅ ∠y.
We know that AB/DE = AC/DF and BC/EF = 1. Multiplying these equations gives AB * BC = AC * DF. Dividing both sides by DE * EF, we get (AB/DE) * (BC/EF) = (AC/DF) * 1. Since we know that BC/EF = 1, we have AB/DE = AC/DF. Thus, Triangle ABC ~ Triangle DEF by the SAS theorem. Therefore, start fraction uw over zx end fraction = start fraction xy over wv end fraction and ∠w ≅ ∠x.
Using the same reasoning as above, we get that Triangle ABC ~ Triangle DEF by the SAS theorem. Therefore, start fraction xz over wu end fraction = start fraction zy over wv end fraction and ∠u ≅ ∠z.
Thus, we have shown that all four conditions hold true, and therefore Triangle ABC ~ Triangle DEF by the SAS similarity theorem.
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Related Questions
the answer is 1/2 trust me it is 1/2
Answers
Are you so sure
↓
These are just some
equivalent fractions of 1/2:
1/2 = 2/4 = 3/6 = 4/8
= 5/10 = 6/12 = 7/14 = 8/16
= 9/18 = 10/20 = 11/22 = 12/24
= 13/26 = 14/28 = 15/30 = 16/32
= 17/34 = 18/36 = 19/38 = 20/40
= 21/42 = 22/44 = 23/46 = 24/48
= 25/50 = 26/52 = 27/54 = 28/56
= 29/58 = 30/60 = 31/62 = 32/64
= 33/66 = 34/68 = 35/70 = 36/72
= 37/74 = 38/76 = 39/78 = 40/80
= 41/82 = 42/84 = 43/86 = 44/88
= 45/90 = 46/92 = 47/94 = 48/96
= 49/98 = 50/100 = 51/102 = 52/104
= 53/106 = 54/108 = 55/110 = 56/112
= 57/114 = 58/116 = 59/118 = 60/120
= 61/122 = 62/124 = 63/126 = 64/128
= 65/130 = 66/132 = 67/134 = 68/136
= 69/138 = 70/140 = 71/142 = 72/144
= 73/146 = 74/148 = 75/150 = 76/152
= 77/154 = 78/156 = 79/158 = 80/160
= 81/162 = 82/164 = 83/166 = 84/168
= 85/170 = 86/172 = 87/174 = 88/176
= 89/178 = 90/180 = 91/182 = 92/184
= 93/186 = 94/188 = 95/190 = 96/192
= 97/194 = 98/196 = 99/198 = 100/200
A university student completed courses worth 3 credits and some courses worth 4
credits. The student earned a total of 54 credits after completing 15 courses. How
many courses worth 4 credits did the student complete?
Answers
Use a system of equations. Let’s say that the number of courses worth 3 credits is X and the number of courses worth 4 credits is Y.
The total number of courses the student took was 15, so X+Y=15.
Each X course was worth 3 credits each and each Y course was worth 4 credits each, for a total of 54, so 3X+4Y=54.
I’m going to take the first equation and solve it for X so I can plug it in to the second equation.
X=15-Y.
Now, plug it in to the second equation to solve for Y.
3(15-Y)+4Y=54
1. Distribute what’s inside the parenthesis.
45-3Y+4Y=54
2. Combine like terms.
45+Y=54
3. Subtract 45 from both sides.
Y=9
TRANSFORMING FUNCTIONS:
You have a coupon for an electronics store that allows you to deduct $50 when purchasing a new television. Additionally, the day you go shopping there is a 5% discount, storewide. If you are going to use the coupon, you need to apply it to the television set price before applying the 5% discount.
If a television costs x dollars, what expression represents what will you ultimately spend to purchase the television?
Answers
The expression 0.95x - 47.5 dollars represents what you will ultimately spend to purchase the television.
Let the television costs x dollars. After deducting $50 from the price, it will be (x - 50) dollars. On the day of shopping, there is a 5% discount. So, the price of the television will reduce by 5% of (x - 50).
Hence, the amount you need to spend will be equal to (x - 50) - 0.05(x - 50) dollars.
We can simplify the expression as follows;
(x - 50) - 0.05(x - 50)= x - 50 - 0.05x + 2.5= 0.95x - 47.5
Therefore, the expression that represents what will you ultimately spend to purchase the television is 0.95x - 47.5 dollars.
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Un equipo de futbol esta compuesto por 13 personas, contando el entrenador y el masajista. Tras jugar un partido, reciben para todos un cheque con 16_41 dolares. Sabiendo que en el lugar de "_" hay una cifra que no le queremos decir y que cada uno recibe una cantidad exacta igual¿a cuanto le tocara cada uno? que sean concretos pls
Answers
Answer:
Ok, tenemos que el cheque es de 16_41.
Y también sabemos que podemos dividir este numero entre 13 personas, de acá podemos concluir que este numero es un múltiplo de 13.
Sea el dígito faltan igual a x
Sabemos que un numero es divisible por 13 cuando la suma de los productos de las unidades, decenas, centenas,... De dicho número por los dígitos contenidos en la lista {1, –3, –4, –1, 3, 4 } (en ese orden) es 0 o múltiplo de 13.
Entonces, tenemos:
16x41:
1*1 + 4*(-3) + x*-4 + 6*-1 + 1*3 = 1 - 12 -4x - 6 + 3
=-14 - 4*x
entonces, -14 - 4*x tiene que ser igual a 0, 13 o algún múltiplo de 13.
Como ambos términos son negativos, no podemos tener esta igualdad igual a 0 o a 13, entonces apuntamos por el siguiente múltiplo de 13 después de -13 (es decir, 13*-2 = -26)
-26 = -14 - 4*x
-26 + 14 = -4*x
-12 = -4*x
-12/-4 = 3 = x
Entonces nuestro dígito es igual a 3, y nuestro numero es:
16341.
Ahora podemos probar:
16241/13 = 1257
Es decir, cada miembro recibe 1257.
At what point does the line given by the following equation cross the y-axis? y = (6/9)X + 9
A. (9,0)
B. (0,6/9)
C. (0,9/6)
D. (0,9)
Answers
Answer:
D
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = \(\frac{6}{9}\) x + 9 ← is in slope- intercept form
with y- intercept c = 9
then the line crosses the y- axis at (0, 9 )
Someone plz help me giving brainliest
Answers
Answer:
13/20
Step-by-step explanation:
Add up all the hours and then subtract by the total hours given.
Find the value of x.
Answers
Answer:
x=3
Step-by-step explanation:
BRAINLIEST plzzzzzzzzzzzzzzzzzz
The number 15/7 is graphed on a number line. Which number would be graphed at the same point?
A 1 2/7
B 2 1/7
C 2 3/7
D 7 1/2
Answers
15/7 as a mixed number will be equal to 2 1/7 so most likely B
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A white tail deer can sprint at speeds up to 30 mph American bison can run at speeds up to 3520 ft./min. which animal is faster and by how many miles per hour
Answers
Answer:
Bison, by 10 mph
Step-by-step explanation:
Convert ft/min to mi/hr.
3520 ft/min × (1 mi / 5280 ft) × (60 min / hr) = 40 mi/hr
The bison is faster than the deer by 10 mph.
a consumer affairs investigator records the repair cost for 44 randomly selected tvs. a sample mean of $91.78$91.78 and standard deviation of $23.13$23.13 are subsequently computed. determine the 90�% confidence interval for the mean repair cost for the tvs. assume the population is approximately normal.
Answers
To determine the 90% confidence interval for the mean repair cost for the TVs, we can use the formula:
Confidence Interval = Sample Mean ± (Critical Value * Standard Error)
Where:
Sample Mean = $91.78
Standard Deviation = $23.13
Sample Size = 44
Critical Value (z-value) for a 90% confidence level = 1.645 (obtained from a standard normal distribution table)
Standard Error = Standard Deviation / (\(\sqrt{Sample Size}\))
Standard Error = $23.13 / \(\sqrt{44}\)= $23.13 / 6.633 = $3.49 (rounded to two decimal places)
Confidence Interval = $91.78 ± (1.645 * $3.49)
Upper Bound = $91.78 + (1.645 * $3.49) = $91.78 + $5.74 = $97.52 (rounded to two decimal places)
Lower Bound = $91.78 - (1.645 * $3.49) = $91.78 - $5.74 = $86.04 (rounded to two decimal places)
Therefore, the 90% confidence interval for the mean repair cost for the TVs is approximately $86.04 to $97.52.
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At age 45 when the deferred payments from his current contract ends, all-star shortstop Alex Rodriguez plans to have $230 million in savings from his baseball playing days. He wants two things from his savings: a 40-year ordinary annuity and $500 million at age 60 in order to purchase majority ownership in his native Miami's Florida Marlins. How large can his annual annuity payment be based on this information and assuming his savings can earn 8% annually after age 45 ? $6,069,727 $5,620,118 $6,906,832 $6,395,215
Answers
Therefore, the annual annuity payment can be approximately $6,069,727.
To calculate the size of the annual annuity payment, we can use the present value formula for an ordinary annuity. The formula is given by:
PMT = PV / [(1 - (1 + r)⁻ⁿ) / r]
Where:
PMT = Annual annuity payment
PV = Present value of the annuity
r = Annual interest rate
n = Number of periods
Given:
PV = $230 million
r = 8% = 0.08
n = 40 years
Using the formula, we can calculate the annual annuity payment:
PMT = 230,000,000 / [(1 - (1 + 0.08)⁻⁴⁰) / 0.08]
PMT ≈ $6,069,727
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answers
Answer:
Step-by-step explanation:
f(x) = x^2 – 5x + 12
The value of f(–10) = 82? NO
f(-10) = (-10)^2 – 5(-10) + 12
f(-10) = 100 + 50 + 12
f(-10) = 162
NO
The graph of the function is a parabola. YES
See attached graph.
YES
The graph of the function opens down. NO
See attached graph.
The graph contains the point (20, –8). NO
See graph
----
Plus we can use x=20 in the function and see if it returns -8:
f(x)=x^2-5x+12
f(20)=(20)^2-5*(20)+12
f(20) = 400 - 100 + 12
f(20) = 312 It does not result in -8
The graph contains the point (0,0). NO
See graph
Kevin needs of a yard of fabric to make a pillow. He has 35 yards of fabric.
Answers
Answer:
Kevin can make 35 pillows.
Step-by-step explanation:
I assume that your question would be, "How many pillows can Kevin make?" If this is not the answer that you were looking for, you need to input your question.
Someone plz help me I’m on my last question for delta math. I added a screenshot below
Answers
Answer:
f(x) = -2x – 7 ; if x < -5
-(x + 2)² + 6 ; if -5 ≤ x < 0
√(x) – 1 ; if x ≥ 0
In an examination, Ram got 40 out of 50 in English and 49
out of 50 in Maths. Find the percentage of:
a) Marks in English
b) Marks in Maths.
Answers
Answer:
Fractions
Step-by-step explanation:
the first step would be to conveery 50 into 100. put 40/50 in a fraction and mutiply by two.
\(\frac{40}{50}\) x \(\frac{2}{2}\) = \(\frac{80}{100}\). convert this to a percent. therefore, mark's average in english is an 80%. do the same with his math .
B: 98%
:)) brainliest? :)
Graph the following function. -|2x-1|+3
Answers
Good evening,
Well I think that's what it is supposed to look like.
How many triangles can ASA have?
Answers
We have explained the ASA rule of congruency of the triangle
What is an ASA congruency of triangles?
ASA Congruence. Angle-Side-Angle. If two angles in one triangle are congruent to two angles of a second triangle, and also if the included sides are congruent, then the triangles are congruent.
If a triangle PQR is congruent to a triangle ABC, we write it as ∆ PQR ≅ ∆ ABC.
Note that when ∆ PQR ≅ ∆ ABC, then sides of ∆ PQR fall on corresponding equal sides of ∆ ABC and so is the case for the angles.
This means that PQ covers AB, QR covers BC, and RP covers CA;
∠P, ∠Q, and ∠R cover ∠A, ∠B, and ∠C respectively.
Also, between the vertices, there is an existence of one-one correspondence.
That is, P corresponds to A, Q corresponds to B, R corresponds to C and it is written as
P↔A, Q↔B, R↔C
Under this condition, the correspondence ∆ PQR ≅ ∆ ABC is true but is not correct for the correspondence ∆QRP ≅ ∆ ABC.
Hence, we have explained the ASA rule of congruency of the triangle
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(Multiple choice)
Can I please have some help with this question, I will reward most Brainly to who ever gets it correct.
Answers
Answer:
Option c
Step-by-step explanation:
y-intercept is the point where the line crosses y axis. It is also his monthly savings
find the exact value of cos-1 (sqrt 3/2)
Answers
The exact value of cos^-1( √3/2) = 30°
What is trigonometric ratio?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
There are special angles in trigonometry, this angles have exact value and can be obtained without using calculator. Examples of this calculator are; 30°, 60°, 45°
sin30 = 1/2
cos 30 = √3/2
tan 30 = 1/√3
cos 60 = 1/2
sin 60 = √3/2
tan 60 = √3
Therefore, if cos^-1( √3/2) = x
cos x = √3/2
cos 30 = √3/2
cos x = cos 30
therefore x = 30
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Martha fue a una tienda de dulces a granel y compró 150 gramos de caramelos a $10.29 por cada 100 gramos y 220 gramos de chispas a $21.29 por cada 100 gramos. ¿Cuánto dinero gastó en total?
Answers
Answer:
62.273
Step-by-step explanation:
sorry it took me a little while to translate i speak only english
3
1
3
19 -3
to get 75 13)?
Which matrix post multiplies to
4
Answers
Answer:
Please dont delete
Explanation:
Hello. I am sorry that I can not answer your question but I am doing this so I can get answers of my own. I appreciate your understanding and I hope you get your answer soon. Good luck!
show that
\(3 \frac{3}{4} \div 1 \frac{1}{3 } = 5 \frac{1}{12} \)
write down all the steps in your working
Answers
Explanation:
3 3/4 ÷ 1*1/3
3 3/4 * 1/3
15/4 * 1/3
= 5 1/12
Please help asap!!!!!!!!
Answers
The y-coordinate for the solution to the system of equations is -3.
What is a system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations. The intersection of two lines represents the system of equations' solution.
Given system of equations are,
6x + 11y = -3
4x + y = 17
To solve these equations, we must first remove x or y terms.
To do this we must make the removing term's coefficients the same.
In this case, let's remove y.
We are multiplying the second equation by 11. Then,
6x + 11y = -3
44x + 11y = 187
Now we will subtract the second equation from the first.
- 38x = -190
x = 5
Now to find y, substitute x in any one of the equations.
6 * 5 + 11y = -3
11y = -33
y = -3
Hence the y-coordinate for the solution to the system of equations is -3.
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(3 3/4)÷(−2 1/2)
IM IN A TIME CRUNCH PLEZZZ HALPPPP
Answers
Answer:
-1.5
Step-by-step explanation:
(23 PTS) WILL GIVE BRAINLIST
Answers
Answer:
Step-by-step explanation:
g(x) would be
8
4
2
0
- 2
A loan of $740 is taken out a daily interest of 0.66%. How much will it cost to pay off the loan after 57 days?
Answers
Answer:
$1,018.39
Step-by-step explanation:
Interest formula is I = Prt/100
where P = principal
r = interest rate (in percent)
t = number of time periods
Here we have P = 740
interest = 0.66% per day
t = 57 days
I = 740 x 0.66 x 57 /100 = 278.39 (rounded)
Total amount to pay back = 740 + 278.39 = $1,018.39
3. There were 15,876 fans at the first MLS soccer game and 13,759 at the second game. How many more fans were at the first game?
Answers
Answer:
2117 more fans
Step-by-step explanation:
So, all you do is just subtract 15,876 from 13,759, which gives 2117 more fans.
Hope I helped !!!
Solve for the value of n.
Answers
Answer:
n= 27
Step-by-step explanation:
To solve first subtract the 90-degree angle:
180-90= 90
Then, convert into an equation:
3n+9= 90
Subtract 9 from both sides:
3n=81
Then divide by 3:
n= 27
Hope this helps!
if any two sides and any angle are congruent in two triangles, than the triangles must be congruent.
true or false
Answers
Answer:
true
Step-by-step explanation:
A class is taking a trip to the museum. The teacher finds that for every 3 students who brought a bag lunch, 2 students will buy lunch at the museum. Which line represents the problem situation?
Answers
Answer:
a
Step-by-step explanation: