Which is the best description of triangles ABC and DEF?
2 similar triangles labeled ABC and DEF are shown. Side AB is 3 centimeters, side AC is 5 centimeters, and side BC is 2 centimeters. Side DE is 4 point 5 centimeters, side DF is 7 point 5 centimeters, and side EF is 3 centimeters.
A. They are congruent, but not similar.
B. They are similar, but not congruent.
C. They are neither similar nor congruent.
D. They are both similar and congruent.
Answer:
B. They are similar, but not congruent.
Step-by-step explanation:
How do similar right triangles lead to the definitions of the trig ratios?
Answer:
The ratio of two sides of one right triangle is the same of the corresponding sides of any its similar triangles. ... Then a/b = A/B, which means that this ratio is a constant. The same for a/c = A/C, and b/c = B/C
Hope it helps
Please mark me as the brainliest
Thank you
We have derived the definitions of the three basic trigonometric ratios sin, cos, and tan using similar right triangles.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = Perpendicular / Hypotenuse
Cosec = Hypotenuse / Perpendicular
Cos x = Base / Hypotenuse
Sec x = Hypotenuse / Base
Tan x = Perpendicular / Base
Cot x = Base / Perpendicular
We have,
Similar right triangles can be used to derive the definitions of trigonometric ratios, which are commonly abbreviated as sin, cos, and tan.
Consider a right triangle ABC, where angle A is the right angle.
Let's draw another right triangle ABD where angle A is also the right angle and angle B is congruent to angle D.
We say that triangles ABC and ABD are similar, which means that their corresponding angles are congruent and their corresponding sides are proportional.
Let's label the sides of triangle ABC as follows:
The side opposite angle A is side a (the hypotenuse).
The side opposite angle B is side b.
The side opposite angle C is side c.
We can label the sides of triangle ABD as follows:
The side opposite angle A is side a (the hypotenuse).
The side opposite angle B is side x.
The side opposite angle D is side y.
Since triangles ABC and ABD are similar, we can write the following proportion:
b / a = x / y
Solving for b, we get:
b = (x / y) * a
Now, we can use the Pythagorean theorem to relate the sides of triangle ABC:
a² = b² + c²
Substituting b with its value, we get:
a² = ((x / y) a)² + c²
Simplifying, we get:
a² = (x² / y²) a² + c²
Multiplying both sides by y², we get:
a² x y² = x² a² + c² y²
Now, we can solve for x/y, which is equal to sin(B) and y/a, which is equal to cos(B):
sin(B) = x / y = sqrt(a^2 - c^2) / a
cos(B) = y / a = c / a
Similarly, we can consider another triangle ABE, where angle A is the right angle and angle B is congruent to angle E.
We say that triangles ABC and ABE are also similar.
Let's label the sides of the triangle ABE as follows:
The side opposite angle A is side a (the hypotenuse).
The side opposite angle B is side x.
The side opposite angle E is side z.
Using the Pythagorean theorem for triangle ABC, we get:
a² = b² + c²
Substituting b with its value from triangle ABE, we get:
a² = ((z / x) a)² + c²
Simplifying, we get:
a² = (z² / x²) x a² + c²
Multiplying both sides by x², we get:
a² x² = z² a² + c² x²
Now, we can solve for z/x, which is equal to tan(B):
tan(B) = z / x = √(a² - c²) / c
Therefore,
We have derived the definitions of the three basic trigonometric ratios sin, cos, and tan using similar right triangles.
Learn more about trigonometric identities here:
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an evergreen nursery sells a certain shrub
Find the area of the shaded sector
Answer:
Step-by-step explanation:
What is the slope of 4,17 and 1,8
Answer:
Slope (m)= 3
Step-by-step explanation:
m= (Y2-Y1)/(X2-X1)
m= (17-8)/(4-1)
m= 9/3
m=3
Independent Practice
Simplify the expression. 6 7 −4 7
A.
2 72 square root of 7
B.
2
C.
− 10 7
D.
10 710 square root of 7
Answer:
A.
2 72 square root of 7
Step-by-step explanation:
Combine the fractions by finding a common denominator.
Exact Form:
2
7
Decimal Form:
0.
¯¯¯¯¯¯¯¯¯¯¯¯
285714
Simplify the expression.
Exact Form:
2
√
7
Decimal Form:
5.29150262
…
what is the reason these triangles are congruent
A. SSS
B. SAS
C. not congruent
Answer:
SAS because their is 2 lines and 1 lines
use the distributive property to write an expression that is equivalent, show your work.
4(x+8)=
What date would be four months prior to January 31st?
No links, No free point's. Please just Fr answer.
1.Sept 20th
2.Sept 28th
3.Sept 30th
Which is the correct answer?
Answer:
sept 30
Step-by-step explanation:
I need to find the sum of this equation please help :)
Answer:
i think
-17x^2 +3x
.....
can someone help me please ❤️
Answer:314
Step-by-step explanation:
V=pi r squared
V= 3.14x10 squared
10 squared= 100
V=3.14x 100
V= 314
t/3+9=12 ?? no clue how to do
Answer:
t = 9
Step-by-step explanation:
t/3 = 12 - 9
t = 3 * 3
t = 9
Answer:
t=9
Step-by-step explanation:
t/3+9=12
t/3+9-9=12-9
t/3= 3
3xt/3 = 3x3
t=9
The function C(x)=−15x+2304 represents the cost to produce x items. What is the least number of items that can be produced so that the average cost is no more than $33?
Answer:
152
Step-by-step explanation:
Given the function :
C(x)=−15x+2304
The least Number of items, x that can be produced so that average cost does not exceed $33
C(x) = less than or equal to 33
33 = - 15x + 2304
33 - 2304 = - 15x
-2271 = - 15x
x = 2271 / 15
x = 151. 4
Hence, the least number of items that can be produced is 152
What is -5^-4 (my friend needs help)
Answer:
-0.0016
- 1/ 625
Step-by-step explanation:
Answer:
Step-by-step explanation:
-5 ^ - 4
= 1 / -5 ^ 4
= 1/625
hope it helps :)
What is the answer for cos(43) = sin(?)
Answer:
Step-by-step explanation:
cos 43=cos (90-47)=sin 47
Jordan wants to play a basketball game at a carnival. The game costs the player $ 5 $5dollar sign, 5 to play, and the player gets to take two long-distance shots. If they miss both shots, they get nothing. If they make one shot, they get their $ 5 $5dollar sign, 5 back. If they make both shots, they get $ 10 $10dollar sign, 10 back. Jordan has a 40 % 40%40, percent chance of making this type of shot. Here is the probability distribution of X = X=X, equals the number of shots Jordan makes in a randomly selected game, and M = M=M, equals the amount of money Jordan gains from playing the game. X = # of shots made X=# of shots madeX, equals, \#, start text, space, o, f, space, s, h, o, t, s, space, m, a, d, e, end text 0 00 1 11 2 22 M = money gained M=money gainedM, equals, start text, m, o, n, e, y, space, g, a, i, n, e, d, end text − $ 5 −$5minus, dollar sign, 5 $ 0 $0dollar sign, 0 $ 5 $5dollar sign, 5 Probability 0.36 0.360, point, 36 0.48 0.480, point, 48 0.16 0.160, point, 16 Calculate the mean of X XX. μ X = μ X =mu, start subscript, X, end subscript, equals shots made
The mean is the average of the numbers divided by the total number of variables, and the further calculation can be defined as follows:
Calculating the Mean of X:
[tex]= \sum X \times p(X)[/tex]
[tex]= 0\times 0.36 + 1 \times 0.48 + 2 \times 0.16\\\\= 0 + 0.48 + 0.32\\\\=0.80\\\\[/tex]
Therefore, the final answer is "0.8".
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Answer:
-1 dollars
Step-by-step explanation:
please help!! thank you
Answer: It would be E
Step-by-step explanation:
Mr. Powell has a box that weighs 16 pounds. What is the weight of this box in ounces? A. 1 oz. B. 16 oz. C. 64 oz. D. 256 oz.
Answer:
256oz
Step-by-step explanation:
D.
hope this helps have a nice day
Answer:
Option D) 256 oz.
Step-by-step explanation:
Passed the test on T4L 2023 :) Hope this helped
Write the rational number in decimal form, rounded to
the thousandths: -1/3 =_____
The average response time to a bank robbery is about 9 min. A local community wants to improve on this time, so they implement advanced training seminars. They find that the new response time for a sample of 36 police officers is 8+4.2 (M SD) min. Test whether this advanced training seminar reduced response time at a.05 level of significance. A. This advanced training seminar significantly reduced response time, t(35) 11.43,p <.05 B. This advanced training seminar significantly reduced response time, (35)1.43, p < .05 C. This advanced training seminar did not reduce response time, t(35)--1.43, p> .05. D. There is not enough information to answer this question.
Answer:
The correct option is;
C. This advanced training seminar did not reduce response time, t(35) = -1.43, p > 0.05
Step-by-step explanation:
The given parameters are;
The population mean response time, μ = 9 minutes
The number of police officers in the sample, n = 36
The mean response time after the training, [tex]\overline x[/tex] = 8 minutes
The standard deviation of the response time after the training, s = 4.2 minutes
The level of significance, α = 0.05
The null hypothesis; μ ≥ 9
The alternative hypothesis; μ < 9
The test statistic for the t-test is [tex]t=\dfrac{\bar{x}-\mu }{\dfrac{s}{\sqrt{n}}}[/tex], therefore, we get;
[tex]t=\dfrac{8-9 }{\dfrac{4.2}{\sqrt{36}}} \approx -1.42857142857[/tex]
The degrees of freedom, df = n - 1 = 36 - 1 = 35
The critical-t at 0.05 level of significance is critical-t = 1.69, p(t < -1.43) > 0.05
and, we fail to reject the null hypothesis, therefore, the advanced training did not reduce the response time
Ryan garden is 20 yards wide. there are about 0.914 meters in 1 yard. About how many meters wide is Ryan's garden? (Decimal number only)
Answer:
the answer would be 18.28
Step-by-step explanation:
if you times 0.914 x 20
which would make 20 yards
because 0.914 is only 1 yard
What is the equation of the line that passes through the point (- 1, 5) and is parallel to the line y = - 3x + 5
Answer:
y - 5 = -3(x + 1)Step-by-step explanation:
Parallel lines has the same slope.
The equation of a line that passing through point (x₁, y₁) with a slope of m is:
y - y₁ = m(x - x₁)
m = -3
(-1, 5) ⇒ x₁ = -1, y₁ = 5
Therefore the equation:
y - 5 = -3(x + 1)
find the value of x..
Answer:
The answer is 116
Step-by-step explanation:
Because this shape is a quadrilateral, so the sum of the angles of a quadrilateral is a total of 360 degrees. So i added 90 + 90 + 64 = 244. And 360 - 244 = 116.
Answer:
116°
Step-by-step explanation:
There are 2 right angles so we add them:
1 right angle = 90°
2 right angle: 90° + 90° = 180°
As we can we have another value which is 64° so we add that as well:
180° + 64° = 244°
Since it is a 4-sided shape all the values will add up to 360°
Subtract 360 and 244
360° - 244° = 116°
x = 116°
Hope this helps
Please help me quickly! During spring, every three days there is usually 1 rainy day. In a 30 day month, how many days would you expect to be rainy? _______ rainy days
____________________________________
On average, for every 15 points scored by his basketball team, Riley scores 4 of them. About how many points would you expect Riley to score in a game where his team had a final score of 90 points _________ points
____________________________________
Use a proportion to convert 32 fluid ounces to cups. [ hint: use the conversion factor fl oz = 1 c.] __________ cups
Thanks so much!
Answer:
1. 10 rainy days
2. 24 points
3. 4 cups
Explanation:
Divide thirty by three to get ten rainy days.
Divide 15 by 90, then multiply the product by four to get 24 points.
divide the volume value by 8.
2x +3 =x
solve for x
Answer:
x = -3
Step-by-step explanation:
2x+3=x
=2x=x-3
=2x-x= -3
= x = -3
i hope this helps :)
Answer:
X=3
Step-by-step explanation:
2x-3=x
Where my marvel gang at tho?
Answer:
DC where it at chief, not starting nun just my opinion have a good day
Step-by-step explanation:
here queen/king
yeah I'll do you one better who's Gamora
Sasha makes $5.00 an hour. She needs to make $150 dollars. She
can use this equation to find the number of hours, h, that she needs
to work to earn $150.00.
Answer:
5h = $150
Step-by-step explanation:
Answer:
150 = 5h
Step-by-step explanation:
h = amount of hours
solve to find amount of hours she needs to work to earn $150
Dumisani earns R42480 per month. He splits his earnings in the ratio 7:5 and then saves the lesser amount. How much does he save?
Answer:
R17700
Step-by-step explanation:
Dumsani earns R42480 per month. He splits his earnings in the ratio 7:5 and then saves the lesser amount. How much does he save?
First step
We are given the ratio 7:5
The sum of the proportion = 7 + 5 = 12
We are told that he saves the lesser amount
The lesser ratio = 5
Therefore, the amount he saves is
= 5/12 × R42480
= 5 × 3540
= R17700
Therefore, he saves R17700
HELP ASAP WILL GIVE BRAINLYIST IF RIGHT AND EXTRA POINTS
List the simple shapes and to which you divided shape c and Measure their signs right all the measurements in inches
Kenny went shopping with Ali and purchased an iPhone that was on sale for 10% off. If he paid $270, what was the original price?
Answer:
$2700
Step-by-step explanation: