1. Find the length of segment CD 2. Find the length of segment AD. 3. What is the similarity factor between △ABC & △CBD? 4. What is the ratio of the area of △ to the area of △CBD?
Answer:
1. CD = 6√3
2. AD = 18
3. ΔABC is an enlargement of ΔCBD by a scale factor of 2
4. 4 : 1
Step-by-step explanation:
The altitude of a triangle is the perpendicular line segment drawn from the vertex of the triangle to the side opposite to it.
Therefore, line CD is an altitude
If an altitude is drawn from the right angle of any right triangle, then the two triangles formed are similar to the original triangle and all three triangles are similar to each other.
If two objects are similar, their corresponding angles are congruent (the same) and their sides are proportional in length.
Therefore, if m∠B = 60° then m∠C of ΔADC = 60°
If m∠A = 30° then m∠C of ΔCBD = 30°
This means that all triangles are 30-60-90 triangles. 30-60-90 triangles are special right triangles as the angles of these triangles are in a unique ratio of 1:2:3. This means that the lengths of the sides is always in the ratio of 1 : √3 : 2 ⇒ y : y√3 : 2y
y: side opposite 30° angley√3: side opposite 60° angle2y: hypotenuse1. Using the 30-60-90 triangle formula for sides:
For ΔCBD: CD = y√3, CB = 2y, DB = y
We are told CB = 12 ⇒ 2y = 12 ⇒ y = 6
Therefore, CD = y√3 = 6√3
2. Using the 30-60-90 triangle formula for sides:
For ΔADC: CD = y, AC = 2y, AD = y√3
We know that CD = 6√3 ⇒ y = 6√3
Therefore, AD = y√3 = 6√3√3 = 18
3. Using the 30-60-90 triangle formula for sides:
For ΔABC: CB = y, AB = 2y, AC = y√3
We know that CB = 12 ⇒ y = 12
Therefore, AB = 24 and AC = 12√3
Therefore, ratio of ΔABC : ΔCBD using the lengths of their hypotenuse:
24 : 12 ⇒ 2 : 1
Therefore, triangle ΔABC is an enlargement of triangle ΔCBD by a scale factor of 2
4. Area of a triangle = 1/2 x base x height
⇒ Area ΔABC = 1/2 x BC x AC = 1/2 x 12 x 12√3 = 72√3
⇒ Area ΔCBD = 1/2 x DB x CD = 1/2 x 6 x 6√3 = 18√3
Therefore, Area ΔABC : Area ΔCBD ⇒ 72√3 : 18√3 ⇒ 4 : 1
Katie's mother has a large collection of shoes. She has 15 pairs of shoes, and 5 of them are
espadrilles.
If Katie's mother chose a pair of shoes at random, what is the probability that the shoes
would be espadrilles?
Answer:
1/3 or 5/15
Step-by-step explanation:
Tenisha solved the equation below by graphing a system of equations. Log Subscript 3 Baseline 5 x = log Subscript 5 Baseline (2 x 8) Which point approximates the solution for Tenisha’s system of equations? (0. 9, 0. 8) (1. 0, 1. 4) (2. 3, 1. 1) (2. 7, 13. 3).
Answer:
Its (1.0, 1.4)
Step-by-step explanation:
Cuz i said soo :3
Answer:
b
Step-by-step explanation:
just took the test : )
SOLVE THIS PROBLEM ASAP
Answer:
6,6
There are 8 spaces in bettween point a and b so 8/2 = 4 so 4 up from point a is 6,6
Step-by-step explanation:
brainiest promised if you help me
In training for a swim meet, Logan swam 750 meters in of an hour. His swimming partner, Mila, swam of Logan's distance in of an hour.
Fill in the blanks to compare Mila's and Logan’s swimming speeds.
1. What is Logan's average swimming speed? Show your work.
2. What is Mila's average swimming speed? Show your work.
3. Compare Mila's and Logan’s swimming speeds. Show your work.
Logan's swimming average is 2.25 kilometers per hour.
Mila's swimming average swimming speed is 34.44 m/min.
The distance swam by Logan = 750 m
The distance swam by Mila = of Logan's distance = × 750 = 2 × 250 = 500.
Which table represents a nonlinear function?
x y
−5 7
−2 6
1 5
7 3
x y
−2 −1
0 1
2 3
5 6
x y
−3 3
0 0
6 −6
10 −10
x y
−7 −3
−5 0
0 3
4 1
Answer:
the last one is non-linear
Step-by-step explanation:
the other 3 tables have all constant (the same) change rates of y change / x change for all their point intervals.
the first table shows for every increase of x by 3, y decreases by 1.
the second table shows for every increase of x by 2, y also increases by 2. that automatically means that this is also 1/1, 3/3, ...
the third table shows for every increase of x by 3, y decreases by 3.
but the fourth table shows a varying change rate from point interval to point interval :
x increases by 2, y increases by 3 : ratio 3/2
x increases by 5, y increases by 3 : ratio 3/5
x increases by 4, y decreases by 2 : ratio -2/4 = -1/2
they are all different.
but for a linear function they must be all equal.
mDWQNFIQnfwoeinfwejbfjewgb
Answiwafianignaasjkgniaswbn
Step-by-step explanation:
yooo im from k12 please help me rqqq!!!
Multiply 12x4(−56x3y2)
Question 9 options:
−10x12y8
10x7y2
10x12y8
−10x7y2
[tex]\\ \tt\hookrightarrow 12x^4(-56x^3y^2)[/tex]
[tex]\\ \tt\hookrightarrow -672x^{4+3}y^2[/tex]
[tex]\\ \tt\hookrightarrow -672x^7y^2[/tex]
None of the above
What is the slope of the line in this graph?
Answer:
the 2nd one
Step-by-step explanation:
Sketch the graph of each function.
1) y= 2
(9
X
20
18
to
12
te
-6
-2
2
4
6
x
Answer:
can yhu see the answer i put?
Step-by-step explanation:
Which of the following relations is a function?
A.
{(7,-2), (9,-1), (3,-2), (9,5)}
B.
{(8,4), (6,3), (6,2), (0,0)}
C. {(4, -1), (7,0), (6,0), (4,0)}
D. {(10,2), (5,3), (8,1), (3,2)}
keeping in mind that a function doesn't have any X-repeats, namely the x-values in the set aren't repeated, let's check the sets above.
Check the picture below.
Why is ≠ a condition for ()=?
Answer:
In the definition of a quadratic function the condition is always imposed because if the value of becomes zero, the degree of equation will be 1, and thus the quadratic function will become a linear function.
Step-by-step explanation:
I'm not quite sure, but I hope this answers your question
Help me please it would help me
======================================================
Explanation:
The x coordinate of the preimage point Q is x = 6.
The x coordinate of the image point Q' is x = 21.
The ratio of image over preimage is 21/6 = (3*7)/(3*2) = 7/2
You'll get this same value if you do the same steps with the y coordinates.
Therefore, the scale factor is 7/2 and the dilation rule is [tex](x,y) \to \left(\frac{7}{2}x, \frac{7}{2}y\right)[/tex]
Note: 7/2 = 3.5
PLS HELP I NEED TO FIND X!!!
Answer:
x =7.62
Step-by-step explanation:
Using Pythagoras Theorem:
a² + b² = c²
7² + 3² = x²
x² = 49 + 9
x = √58 .......in radical form
x =7.62 .....in 2 decimal form
x = 7.6 ......in nearest tenth place
Thank me I will give 15 points ,thanks!!
Talia grouped the terms and factored out the GCF of the groups of the polynomial 15x2 – 3x – 20x 4. Her work is shown below. (15x2 – 3x) (–20x 4) 3x(5x – 1) 4(–5x 1) Talia noticed that she does not have a common factor. What should she do? Talia needs to leave the polynomial as is because it is prime and cannot be factored. Talia needs to factor out a 3x from the first group and a 4x from the second group. Talia needs to factor out a negative from one of the groups so the binomials will be the same. Talia needs to apply the distributive property to get the expression (3x 4)(5x – 1).
Talia needs to factor out a negative from one of the groups so the binomials will be the same.
Given
Talia grouped the terms and factored out the GCF of the groups of the polynomial 15x^2 – 3x – 20x + 4.
What is GFC?The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers.
To find the GCF of the two terms, the continuous division must be done.
Talia needs to factor out a negative from one of the groups so the binomials will be the same.
She should do as follows:
[tex]\rm (15x^2- 3x) + (-20x + 4)\\\\3x(5x-– 1) + 4(-5x + 1)\\\\3x(5x - 1) - 4(5x - 1)[/tex]
Hence, Talia needs to factor out a negative from one of the groups so the binomials will be the same.
To know more about GFC click the link given below.
brainly.com/question/521142
Answer:
C. Talia needs to factor out a negative from one of the groups so the binomials will be the same.
Step-by-step explanation:
Aubrey ran 13 1/6 miles and walked 9 5/6 miles. How much farther did Aubrey run than walk?
Answer:
Aubrey ran 3 1/3 miles further than what she walked.
Step-by-step explanation:
This would be your basic subtraction problem. So, 13 1/6 - 9 5/6.
Since you can't subtract 5/6 from 1/6, let's borrow from 13. Now, instead of 13, it would be 12. Adding the whole (1) or 6/6 to the 1/6, you'll get 7/6. Now you can subtract. 7/6 - 5/6 = 2/6. Moving on, 12 - 9 = 3.
Therefore, your answer is 3 2/6. In simplified terms, it would be 3 1/3.
Hello I’m in algebra and I need help on questions I’ll give brainlist
Answer:
x=5
Step-by-step explanation:
50+50+80=180
you're welcome
On a coordinate plane, a curved line with minimum values of (negative 0. 44, negative 4. 3) and (3, negative 4), and a maximum value of (1. 7, 0. 7), crosses the x-axis at (negative 2. 5, 0), (1. 3, 0), (2, 0), and (3. 44, 0), and crosses the y-axis at (0, negative 4). Which interval contains a local minimum for the graphed function? [–4, –2. 5] [–2, –1] [1, 2] [2. 5, 4].
Answer:
The answer is D
Step-by-step explanation:
there's your thingy
Find the straight-time pay: $9.25 per hour, 35 hours.
Answer:
you will get paid $323.75 if you work 35 hours and get paid $9.25 per hour
Answer:
323.75
Step-by-step explanation:
$9.25 x 35 = 323.75
for certain positive integers a and b, 2/A+1/B=13/15. What is A+B
=====================================================
Explanation:
Simplify the left hand side to get
[tex]\frac{2}{A}+\frac{1}{B} = \frac{13}{15}\\\\\frac{2B}{AB}+\frac{A}{AB} = \frac{13}{15}\\\\\frac{2B+A}{AB} = \frac{13}{15}\\\\[/tex]
Compare the denominators AB and 15.
If AB = 15, then we could have,
A = 1, B = 15A = 3, B = 5A = 5, B = 3A = 15, B = 1Through trial and error, the only solution is A = 3 and B = 5 because 2B+A = 2*5+3 = 10+3 = 13 to match the numerator on the right hand side.
Therefore, A+B = 3+5 = 8
Please help me thank you so much
Ignore A please! I only need help on B and C Thank you!
I have the answer for c
61 dots will be in figure 20
1 x 20 = 20 (these are the dots that go up)
20 x 2 + 1 = 41 (these are tho dots that go to the right)
(the 1 is the first dot in figure one)
:) i need help with this, work not needed
Answer:
Negative leading coefficient
Step-by-step explanation:
The graphs goes up but eventually goes back down
4. The length of a rectangle is sixteen inches less
than three times its width. If the perimeter of
the rectangle is 192 inches, find the length of
the rectangle.
A. 28 inches
B. 54 inches
C. 68 inches
D. 72 inches
Answer:
68in
Step-by-step explanation:
l = 3w-16
l-3w = -16
l+w = 96
-4w = -112
w = 28 in
l = 96-28 = 68in
Please help asap shshshahahshaahha
5a-4b - c = 8 4a+2b - c = 2 3a + 4b +3c -16
Answer:
Step-by-step explanation:
5a - 4b - c = 8
4a + 2b - c = 2
3a + 4b + 3c = -16
by adding equation 1 and 2 we get
8a + 2c = -8
4a + c = -4
c = -4 - 4a
now substitute c in the 2nd equation
4a + 2b +4 + 4a = 2
8a + 2b = -2
4a + b = -1
b = -1 - 4a
we have b and c in terms of a, now let's find a
5a - 4(-4-4a) - (-1 - 4a) = 8
5a + 16 + 16a + 1 + 4a =8
25a = -9
a = -9/25
b = -1 - 4(-9/25)
b= -1+36/25=11/25
c=-4 -4a = -4 +36/25=-53/25
Three darts thrown at this dart board land in three different regions. If the order that the three darts are thrown does not matter, how many combinations of three different regions from the 10 possible regions would result in a sum of exactly 50 points
Since no specific method was stipulated the combinations of three different regions from the 10 possible regions that would result inexactly 50 points is Zero.
Possible ScoresThe possible scores are given below:
10 10 10, 10 10 5, 10 5 5, 5 5 5, 10 10 1, 10 1 1, 10 5 1, 5 5 1, 5 1 1 and 1 1 1.
The sum of each group of possible scores are:
3, 7, 11, 16, 12, 21, 15, 20, 25, 30
Examples of rudimentary addition:
1. 3+7+30 =40
2. 7+11+30=48
3. 11 + 16 + 30= 57
4. 16+12+30 =58
5. 12+21+30=63 etc
Again, using a rudimentary count, we can prove that no three categories all summed up, will add up to exactly 50 points.
Lean more about Combinations below:
https://brainly.com/question/1757772
please help, thank you
What is the value of x?
Enter your answer in the box.
x =
Answer:
x = 20
Step-by-step explanation:
The angles that are marked are called "vertical angles" (I think of a pair of scissors) The two angles are equal to each other. (They get bigger or smaller together, like a pair of scissors)
So, set them equal to each other and solve.
3x + 50 = 6x - 10
SUBTRACT 3x from both sides.
50 = 3x - 10
ADD 10 to both sides.
60 = 3x
DIVIDE both sides by 3.
20 = x
Answer:
x>20???
Step-by-step explanation:
am i right or wrong
Solve the equation. 20 = y + 8
Answer:
y = 12
Step-by-step explanation:
20 = y + 8
Subtract 8 from both sides:
20 - 8 = 12 ; 8-8 =0
12 = y
Switch it around:
y = 12
Side note - what plus 8 would give you 20? 12!
