The AAA (angle-angle-angle) similarity theorem can be used to express it as follows: two triangles have equal corresponding angles if and only if their corresponding sides are proportionate.
The Angle-Angle-Angle (AAA) criterion for the similarity of triangles states that “If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar”.
Proof:
Consider two triangles ABC and DEF, such that ∠A = ∠D, ∠B = ∠E and ∠C = ∠F as shown in the figure.
Now, cut DP= AB and DQ= AC and join PQ. Hence, we can say that a triangle ABC is congruent to the triangle DPQ.
(i.e) ∆ ABC ≅ ∆ DPQ, which gives ∠B = ∠P = ∠E and also, the line PQ is parallel to EF.
Therefore, by using the basic proportionality theorem, we can write
DP/PE = DQ/QF.
(i.e) AB/DE = AC/DF. …(1)
Similarly,
AB/DE = BC/EF …(2)
From (1) and (2), we can write:
AB/DE = BC/EF = AC/DF.
Therefore, the two triangles ABC and DEF are similar.
Hence, AAA(Angle-angle-angle) is proved.
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Emma is taking a trip to the beach. So far, she has driven 58 miles in 1.25 hours.
Determine Emma's constant speed and simplify it to a unit rate.
Then write a linear equation in two variables that represents Emma's distance, d, she travels in any given time t.
Answer:
46.4miles/hour
d=46.4t
Step-by-step explanation:
Let's say d=at, where d = distance, a = the unit rate, and t = any given time.
We're given that Emma takes 1.25 hours to drive 58 miles. Plugging that into our formula of d=at, we get:
58 = 1.25a.
So, a = 46.4.
The formula now becomes d=46.4t.
what is the answer for this, I have to solve the proportion,
n/18 = 12/7.5
Answer:
n = 28.8
Step-by-step explanation:
[tex]\frac{n}{18} =\frac{12}{7.5}[/tex]
n × 7.5 = 18 × 12
7.5n = 216
7.5n ÷ 7.5 = 216 ÷ 7.5
n = 28.8
write an equation of the line that passes through 3,1 and 0,10
Answer:y = -3x + 10
Step-by-step explanation:
To find an equation of a line that passes through two points, we have to first find the slope between the two equation. We can do this by using the slope formula:
where (x₁, y₁) and (x₂, y₂) are the two points that we are finding the slope between.
Lets make (x₁, y₁) equal to (0, 10) and (x₂, y₂) equal to (3, 1). Now we plug them into the slope formula:
So the slope between the two points is -3.
From here, I would normally take one of the points given to us and plug in the point and slope into the point-slope form of a line and then simplify until we get it in slope-intercept form. But if you look carefully, the y-intercept is given to us as the point (0, 10). So we now know that the y-intercept of the line is 10. We can now take the y-intercept and the slope and plug it into the slope-intercept form of a line to get out equation:
y = mx + b
plug in -3 for m (the slope) and 10 for b (the y-intercept)
y = -3x + 10
So now we have our equation.
I hope you find my answer and explanation helpful. Happy studying. :)
find the gradient of the line AB
Answer:
⅙
Step-by-step explanation:
[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]
From the graph, coordinates of A and B are (-1, 1) and (5, 2) respectively.
Gradient of line AB
[tex] = \frac{2 - 1}{5 - ( - 1)} [/tex]
[tex] = \frac{1}{5 + 1} [/tex]
[tex] = \frac{1}{6} [/tex]
If a figure can be rotated n times, it has how many lines of rotational symmetry?
Answer: n + 1
Step-by-step explanation:
Pls I need to know!!
could anybody help me pls
Answer:
all of them are much larger except number 2 which is close to 1
Step-by-step explanation:
Pls help meeeee and thank you so so so much
Answer: 1/3 x + -1
Step-by-step explanation:
Answer:
y = 2x -1
Step-by-step explanation:
Use slope intercept. The line is rising by 2 points and the y-intercept lies at -1.
A camping store is having a summer sale. Stoves are being sold at 40% off. If the sale price is $57 what was the original price of the stove before the sale
Answer:
The original price was $142.5.
Step-by-step explanation:
40 ÷ 100 = 0.4
$57 ÷ 0.4 = $142.5
Therefore, $142.5 is our answer.
Answer:
142.5
Step-by-step explanation:
Let's say the original price of the store before the sale is x
so 40% x X = $57
40/100 (X ) =57
0.4 (X) = 57 ====> X = 57 / 0.4 = 142.5
The original price of the stove before the sale is $ 142.5
Sean is cutting construction paper into rectangles for a project. He needs to cut one rectangle that is 16 inches × 15 1/4 inches. He needs to cut another rectangle that is 10 1/2 inches by 10 1/4 inches. How many total square inches of construction paper does Sean need for his project?
Answer:
the total square inches of the construction paper is 351.63 square inches
Step-by-step explanation:
The computation of the total square inches of the construction paper is shown below;
= (16 × 15 1 ÷ 4) + (10 1 ÷2 × 10 1 ÷ 4)
= (16 × 61 ÷ 4) + (21 ÷ 2 × 41 ÷ 4)
= (16 × 15.25) + (10.5 × 10.25)
= 244 + 107.625
= 351.63 square inches
Hence, the total square inches of the construction paper is 351.63 square inches
We simply added these two
pls help
3(x+2)=3x < 2x+18
Answer:
Step-by-step explanation:
3x + 6 - 3x < 2x + 18
6 < 2x + 18
-12 < 2x
-6 < x
Solution Set = {-5,-4,-3,-2,-1,0......}
Please mark as brainliest for further answers :)
Solve the problem.
20) You have 340 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle
that maximize the enclosed area.
A) 87 ft by 83 ft
B) 170 ft by 42.5 ft
C) 170 ft by 170 ft
D) 85 ft by 85 ft
Answer:
QUADRATIC FUNCTIONS AND EQUATIONS
Danielle N. asked • 11/25/17
You have 356 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area.
(Hint: Write formula for area as a quadratic function of length and use the concept of maximum value of quadratic function)
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Michael J. answered • 11/25/17
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Effective High School STEM Tutor & CUNY Math Peer Leader
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Let length = x
Let width = y
Area = xy
Perimeter equation is
2(x + y) = 356
x + y = 178
Substituting the perimeter equation in the area formula,
Area = x(178 - x)
Area = -x2 + 178x
If the zeros of this quadratic are 0 and 178, then the median is where the maximum area occurs.
178 / 2 = 89
Therefore, the dimensions are
length = 89 feet
width = 178 - 89 = 89 feet
Maximize the enclosed area of the rectangle is 85 ft by 85 ft.
What is perimeter of rectangle?Perimeter of rectangle is defined as addition the lengths of the rectangle's four sides.
Let length = a
Let width = b
Area of rectangle = ab
Perimeter of rectangle equation is 2(a + b)
2(a + b) = 340
a + b = 170
Substitute the perimeter equation in the area formula,
Area = a(170 - a)
Area = -a² + 170a
If the zeros of this quadratic are 0 and 170, then the median is where the maximum area occurs.
170 / 2 = 85
Therefore, the dimensions are
length = 85 feet
width = 170 - 85 = 85 feet
The rectangle is a square.
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3 consecutive even numbers that add up to 3000
Answer:
998, 1000, 1002
Step-by-step explanation:
Self explanatory, if you add the three numbers the sum is 3000.
Mr. Frank has 1.08 kilograms of fertilizer for the plants in his nursery. He wants every plant to get 93 mg of fertilizer 4 times each year. What is the number of plants he could fertilize with that amount? How much fertilizer will he have left over?
Answer: See explanation
Step-by-step explanation:
First and foremost, we should know that: 1 kilogram = 1,000,000 milligrams
Therefore, 1.08kg will be converted to milligram and this will be:
= 1.08 × 1,000,000 milligrams
= 1,080,000 milligrams
Since every plant gets 93mg of fertilizer, the number of plants that can be fertilized will be:
= 1,080,000 / 93
= 11612.903
Therefore, 11612 plants can be fertilized.
The fertilizer left over will be:
= 1,080,000 - (11612 × 93)
= 1080000mg - 1079916mg
= 84 mg
Meredith went to an aquarium with some of her friends. The tickets cost $12.95 each, and they spent $38 on souvenirs. The total amount spent was $115.70. Which equation can be used to determine how many tickets, t, were purchased?
Answer:
12.95t+38=115.70
Step-by-step explanation:
Please help me with this problem!!
The vertices of a triangle MNP are M(5,6) , N(0,3) , and P(4,-2). What is the coordinate of the midpoint of the line connecting the midpoints of sides MN and MP
Answer:
(3.5, 3.25)
Step-by-step explanation:
Given the vertices of a triangle MNP as M(5,6) , N(0,3) , and P(4,-2).
Midpoint of MP is expressed as;
M(5,6) and P(4,-2).
Xmp = (5+4)/2
Xmp = 9/2
Xmp = 4.5
Ymp = (6-2)/2
Ymp = 4/2
Ymp = 2
Hence the midpoint of MP is at (4.5, 2)
Similarly for MN
M(5,6) , N(0,3)
Xmn = 5+0/2
Xmn = 5/2
Xmn = 2.5
Ymn = 6+3/2
Ymn = 9/2
Ymn = 4.5
Hence the midpoint of MN is (2.5, 4.5)
The coordinate of the midpoint of the line connecting the midpoints of sides MN and MP will be expressed as;
MN(2.5, 4.5) and MP (4.5, 2)
M = {(2.5+4.5/2, 4.5+2/2)}
M = (7/2, 6.5/2)
M = (3.5, 3.25)
Hence the required midpoint coordinate is (3.5, 3.25)
PLS HELP
Find (a) the perimeter and (b) the area of the figure. Use 3.14 or 22
for it. Round your answer to the nearest hundredth, if necessary.
-3 ft-
tep-by-step explanation: Ta
Can someone help me with this. Will mark brainliest.
diagonals of a parallelogram bisects each other making an angle of 90°.
so, your answer is True
Answer:
A. True
Step-by-step explanation:
The diagonals of a parallelogram do always bisect each other. However, they only form right angles if the parallelogram is a rhombus or a square.
If w = 6 units, x = 3 units, and y = 5 units, what is the surface area of the figure?
Figure is composed of a right square pyramid on top of a square prism. The sides of the square pyramid are equal to the sides of the square prism, the length and width of the square prism is w, the height of the square prism is x, and the height of the square pyramid, which forms a right angle with the center, is y.
Answer:
240 units^2
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
178^2 units
Geometry
I just don’t understand this easy math, someone help
Answer:
Point R: (-2,0)
Point A: (-6,-2)
Point N: (-1,-3)
Step-by-step explanation:
Reflecting a shape across the y-axis means that the y value of the coordinate of the points would reverse its sign, meaning for eg a negative number would turn into a positive one or a positive would turn into a negative.
So in this case, point R would stay the same because it's on the y-axis but the two points A and N would change. Point A is (-6,2) so if we change the y coordinate we would get (-6,-2) and point N is (-1,3) so it would become (-1,-3). Therefore the answer is:
Point R: (-2,0)
Point A: (-6,-2)
Point N: (-1,-3)
What is Find the range of the following data set:
52, 48, 57, 47, 49, 60, 59, 51, 60 plz lmk!!!!!!!!!!!!!!
Answer:
13
Step-by-step explanation:
60 - 47 = 13
16 gallons of water are used to completely fill 5 fish tanks. If each tank holds the same amount of water, how many gallons will each tank hold?
Find the length of a diagonal of a square with a perimeter of 16.
Answer:
4√2
Step-by-step explanation:
If a square has a perimeter of 16, then its side lengths are 4.
Use the pythagorean theorem to find the diagonal.
4^2+4^2=c^216+16=c^232=c^2c=√32√32 can be simplified to 4√2.
The length of the diagonal of the square whose perimeter is 16 is 4√2
What is diagonal of the square?
The length of a diagonal is equal to the length of a side multiplied by the square root of 2
Given data ,
Let d be the diagonal of a square
Perimeter of square = 16
Perimeter of square = 4 x A
16 = 4 x A
A = 4
Therefore , diagonal of square is = 4√2
Hence ,The length of the diagonal of the square whose perimeter is 16 is 4√2
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The Jacksons and the Simpsons were competing in the final leg of the Amazing Race, which was 240240240 kilometers long. In their race to the finish, the Jacksons immediately took off traveling at an average speed of vvv kilometers per hour. The Simpsons' start was delayed by an hour. When they eventually took off, they traveled at an average speed that was 404040 kilometers per hour faster than the Jacksons' speed. Sadly for them, that didn't help, and the Jacksons won. Write an inequality in terms of vvv that models the situation.
Answer:
240/(v+40) + 1 > 240/v
Step-by-step explanation:
Both parties traveled a distance of 240 km.
Simpsons took off at average speed of 40 km/h & 1 hour later: 240/(v+40) + 1
Jacksons took off at average speed of v km/h: 240/v
An inequality in terms of v that models the situation is; [240/(v + 40)] + 1 > 240/v
How to write an inequality?We are told that distance travelled by both Jackson and Simpson is 240 km each.
Jacksons took off at average speed of v km/h. Thus, their time taken is 240/v
The Simpsons took off at an average speed of 40 km/h faster than Jacksons Speed. Since their start was delayed by an hour, then;
Time taken = [240/(v + 40)] + 1
Thus, the inequality that models the situation is; [240/(v + 40)] + 1> 240/v
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3n^2+4m+5
A. 2
B. 3
C. 4
D. 5
Answer:
3?
Step-by-step explanation:
3n²+4m+5
3n²+(4m+5)
=3n²+9m
=3n²/9m;(3÷9)(n²÷m)
=1n²/3m
=n²/3m
50 points!!! Will mark brainliest if correct!! Pls help me!!
Answer:
3rd option is correct, give me brainiest
Worth five points! Will mark the first person who answered with an actual correct answer brainliest and i don't lie about brainliest!! Please no nonsense answers I just want help :(
Triangle DEF is an isosceles triangle.
DE = EF
m⦟D = 26°
What is m⦟F?
A. 26°
B. 64°
C. 77°
D. 128°
Answer:
The answer is 77 degrees
Coach Ellis surveyed a sample of students about their favorite sport. The circle graph below shows
some of the percents to represent the results. 100 students chose football.
How many students chose swimming as their favorite sport?
Answer:
C. 120 students
Step-by-step explanation:
10 + 15 + 20 +30 = 75%
100 - 75 = 25%
25% chose football which is 100 students
30% chose swimming
setup proportion:
25/100 = 30/x
25x = 100(30)
25x = 3000
x = 120
Help please :(
CROWN ???
Answer:
7&8 both true
9 is false
Step-by-step explanation:
tghdhfshj
Answer:
True
True
False
Step-by-step explanation:
2(7) -3 = 14 -3 = 11
2(8) -3 = 16 -3 = 13
2(9) - 3 = 15
The answer has to be less than 15