Answer:
They are similar by the definition of similarity in terms of a dilation
Step-by-step explanation:
The given vertices of triangle ΔABC are;
A(1, 5), B(3, 9), and C(5, 3)
The vertices of triangle ΔDEF are;
D(-3, 3), E(-2, 5), and F(-1, 2)
Therefore, we get;
The length of segment, [tex]\overline{AB}[/tex] = √((9 - 5)² + (3 - 1)²) = 2·√5
The length of segment, [tex]\overline{BC}[/tex] = √((9 - 3)² + (3 - 5)²) = 2·√10
The length of segment, [tex]\overline{AC}[/tex] = √((5 - 3)² + (1 - 5)²) = 2·√5
The length of segment, [tex]\overline{DE}[/tex] = √((5 - 3)² + (-2 - (-3))²) = √5
The length of segment, [tex]\overline{EF}[/tex] = √((2 - 5)² + (-1 - (-2))²) = √10
The length of segment, [tex]\overline{DF}[/tex] = √((2 - 3)² + (-1 - (-3))²) = √5
∴ [tex]\overline{AB}[/tex]/[tex]\overline{DE}[/tex] = 2·√5/(√5) = 2
[tex]\overline{BC}[/tex]/[tex]\overline{EF}[/tex] = 2·√10/(√10) = 2
[tex]\overline{AC}[/tex]/[tex]\overline{DF}[/tex] = 2·√5/(√5) = 2
The ratio of their corresponding sides are equal and therefore;
ΔABC and ΔDEF are similar by the definition of similarity in terms of dilation.
When a number is increased by 23. the result is 42. What equation fits this statement?
Answer:
n + 23 = 42
Step-by-step explanation:
Well, let's see.
Let's name the number "n".
So, n + 23 = 42.
And there's your answer.
Hope this helped! :)
Answer:
y + 23 = 42
y = 19
Step-by-step explanation:
y + 23 = 42
Subtract 23 from both sides:
y + 23 - 23 = 42 - 23
y = 19
A number is divided into two parts, such that one part is 10 more than the other. If the two parts are in the ratio 5:3 find the number and the two parts.
Answer:
See below
Step-by-step explanation:
Given the above information, we can make the first part to be;
First part = y + 10
Then,
Second part = y
y + 10 : y = 5 : 3
(y + 10) / y = (5) / (3)
Cross multiply,
3y + 30 = 5y
Collect like terms
5y - 3y = 30
2y = 30
y = 15
Therefore, substituting the value of y,
First part = y + 10
First part = 15 + 10
First part = 25
Second part = y
Second part = 15
Number = First part + Second part
Number = 25 + 15
Number = 40
Solve the equation below. you must show all your work, and have the correct answer.
9x + 10 = 12x – 11
Answer:
x=7
Step-by-step explanation:
You need to bring 9x to the right side and bring '-ll' to the left side so it will be 11+10 = 12x-9x. Then you calculate 11+10, which is 21, then you subtract 12x to 9x. Then it will be 21 = 3x. Lastly, you divide 3 on both sides of the equation and get x to be 7!
Answer:
x=7
Step-by-step explanation:
9x+10=12x-11
-9x. -9x. subtract 9x from both sides
10 = 3x-11
+11 +11. add 11 to both sides
21 =3x
divide by 3x (21 ÷3=7) therefore x=7
The difference of two numbers is 74. Twice the first and thrice the Second sum up to 138. Find the two possible numbers . anyone??
Answer:
72 and -2
Step-by-step explanation:
x - y = 74
2x + 3y = 138
x - y = 74
y = x - 74
2x + 3(x - 74) = 138
2x + 3x - 222 = 138
5x = 360
x = 72
x - y = 74
72 - y = 74
-y = 2
y = -2
At the beginning of 2007, the population of a certain state was 55.4% rural and 44.6% urban. Based on past trends, it is expected that 15% of the population currently residing in the rural areas will move into the urban areas, while 21% of the population currently residing in the urban areas will move into the rural areas in the next decade. What was the population distribution in that state at the beginning of 2017
Answer:
New Rural Urban distribution = 56.4 , 43.4
Step-by-step explanation:
Let the total population be = 100
The rural urban distribution = 55.4% & 44.6% of 100 = 55.4 & 44.6 respectively
Given , 15% of rural population shifts to urban. So, 15% of 55.4 ie = 8.31 shift from rural to urban.
Also, 21% of urban population shifts to rural. So, 21% of 44.6 , ie = 9.36 shift from urban to rural.
So, New rural population = old rural - rural to urban shift + urban to rural shift = 55.4 - 8.31 + 9.36 = 56.39 ≈ 56.4
New urban population = old urban - urban to rural shift + rural to urban shift = 44.6 - 9.36 + 8.31 = 43.55 ≈ 43.4
So, the new distribution is = 56.4 , 43.4
ASAP
- WILL MARK BRIANIST
Now Mark me Brainiest
A rectangle has a perimeter of 6 feet.
Choose all the possible dimensions of the rectangle.
A. 1 foot by 2 feet
B. 1 foot by 5 feet
C. 2 feet by 1 foot
D. 2 feet by 4 foot
E. 3 feet by 3 feet
F. 4 feet by 2 feet
G. 5 feet by 1 foot
Option (A) 1 foot by 2 feet and option (C) 2 feet by 1 foot satisfy the perimeter given. Thus options A and C are correct.
What is a rectangle?"A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles".
For the above situation,
The length of the rectangle be 'l'
The breadth of the rectangle be 'b'
Perimeter of the rectangle, P = 2(l+b)
Option A : 1 foot by 2 feet
Here, l = 1 feet and b = 2 feet
⇒ [tex]P=2(l+b)[/tex]
⇒ [tex]P=2(1+2)\\[/tex]
⇒ [tex]P=6[/tex]
This perimeter is equal to the perimeter of the rectangle. Thus option A is correct.
Option B : 1 foot by 5 feet
Here, l = 1 and b = 5 feet
⇒ [tex]P=2(1+5)[/tex]
⇒ [tex]P=12[/tex]
This perimeter is not equal to the perimeter of the rectangle. Thus option B is not correct.
Option C : 2 feet by 1 foot
Here, l = 2 and b = 1 feet
⇒ [tex]P=2(2+1)[/tex]
⇒ [tex]P=6[/tex]
This perimeter is equal to the perimeter of the rectangle. Thus option C is correct.
Option D : 2 feet by 4 foot
Here, l = 2 and b = 4 feet
⇒ [tex]P=2(2+4)[/tex]
⇒ [tex]P=12[/tex]
This perimeter is not equal to the perimeter of the rectangle. Thus option D is not correct.
Option E : 3 feet by 3 feet
Here, l = 3 and b = 3 feet
⇒ [tex]P=2(3+3)[/tex]
⇒ [tex]P=12[/tex]
This perimeter is not equal to the perimeter of the rectangle. Thus option E is not correct.
Option F : 4 feet by 2 feet
Here, l = 4 and b = 2 feet
⇒ [tex]P=2(4+2)[/tex]
⇒ [tex]P=12[/tex]
This perimeter is not equal to the perimeter of the rectangle. Thus option F is not correct.
Option G : 5 feet by 1 foot
Here, l = 5 and b = 1 feet
⇒ [tex]P=2(5+1)[/tex]
⇒ [tex]P=12[/tex]
This perimeter is not equal to the perimeter of the rectangle. Thus option G is not correct.
Hence we can conclude that option (A) 1 foot by 2 feet and option (C) 2 feet by 1 foot satisfies the perimeter given. Thus options A and C are correct.
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Which expression is equivalent to?
-4(x + 2)-1/2(2x-6)
Answer:
-5x - 5
Step-by-step explanation:
distribute both -4 and -1/2
it should look like this...
-4x - 8 - x + 3 now add the like terms
-5x - 5
Final answer: -5x - 5
The circus admits children for $2 each and adults for $5 each. How many of each ticket were sold if 160 total tickets were sold for $476? Please I need an answer ASAP
Answer:
adults = 52
children = 108
Step-by-step explanation:
two equations can be derived from the question
x + y = 160 equation 1
2x + 5y = 476 equation 2
x = number of children
y = number of adults
multiply equation 1 by 2
2x + 2y = 320 equation 3
subtract equation 1 from 2
3y = 156
y =52
substitute for y in equation 1
x + 52 = 108
x = 160 - 52 = 108
i need help. i don’t understand
Answer:
26.4 (srr if incorrect)
Step-by-step explanation:
Select the two correct solutions of the inequality x + 8 > 14.
A. 6
B. 4
C. 8
D. 2
E. 10
Answer:
Step-by-step explanation:
So basically you’re asking if blank plus 8 is greater than 14 so the answers would be 8 and 10
2x + 9/3x + 16
X =
= [?]
3x/2-x=x/6-2/3 plz help
Answer:
= − 2
Step-by-step explanation:
Answer:
x = -2
Step-by-step explanation:
Trapezoid TRAP is shown on the grid below.
What is the length of the midsegment MN?
6
9
12
18
Answer:
18
Step-by-step explanation:
How do I graph -1, -4?
Answer:
Start at the origin and go to the left by one and go down by 4
Step-by-step explanation:
The x coordinate relates to the horizontal axis and the y axis refers to the vertical axis.
Before we start graphing we must always begin at the origin (0,0)
Since the x value is -1 we have to move left by 1 on the x axis
We would move to the left one value because negative is on the left side
For the y value, we would have to move 4 down on the y axis because this number is also negative.
So your graph should look like this
Hope this helps :)
pleas help due to night
Answer:
the answer is 33.4 because 33.4 x 2 is 66.8 and you add 1.2 + 1.2 that is 2.4. you add both and you get 69.2. Th answer is 33.4
Step-by-step explanation:
33.4 x 2 (1.2 x 2) + 69.2
brainliest pls.
Answer:
a = 33.4
Step-by-step explanation:
The short sides are both 1.2. You have to take them into account.
P = 2L + 2W
L is arbitrarily chosen to be the long side. The short side is W.
Givens
P = 69.2
L = a
W = 1.2
Solution
69.2 = 2 * 1.2 + 2a
69.2 = 2.4 + 2a
69.2 - 2.4 = 2a
66.8 = 2a
66.8/2 = a
a = 33.4
Find the common difference of the arithmetic sequence.
9, 13, 17, 21, . ..
Step-by-step explanation:
4 is the common difference
"The sum of negative two and nine times a number is less than ninety four."
Answer:
I believe you would write the answer is 7 * x is less than 94 (use actual less than symbol for answer).
Step-by-step explanation:
"The sum of negative two and nine" is saying -2 + 9.
"times a number" is saying the answer of -2 + 9 is multiplied by a number, or x.
"is less than ninety four." is saying that -2 + 9 * x is less than (use symbol) 94.
So the equation looks like this:
-2 + 9 * x is less than 94.
Now you can simplify the equation:
-2 + 9 = 7
7 * x is less than(use actual less than symbol) 94.
Could I get brainliest please?
What is
(7x-3) = (12x+12)
Answer:
x=-3
Step-by-step explanation:
Every dimension of a triangular pyramid is multiplied by 10 to produce a new figure that is geometrically similar. What effect does this have on
the surface area of the pyramid?
ОА
The surface area of the pyramid is multiplied by 10.
OB.
The surface area of the pyramid is multiplied by 50.
O C.
The surface area of the pyramid is multiplied by 100.
OD.
The surface area of the pyramid is multiplied by 1,000.
O E
The effect on the surface area cannot be determined.
PLEASE HELP ME I REALLY NEED THE ANSWER
1 tickets
2 tickets
3 tickets
4 tickets
Answer:
2 adult tickets
Step-by-step explanation:
we have two relations
[tex]a + c = 5[/tex]
[tex]9a + 4c = 30[/tex]
first rearrange the top equality for one of the variables
[tex]a = 5 - c[/tex]
now substitute into the second equation
[tex]9(5 - c) + 4c = 30[/tex]
perform the distribution and combine like terms
[tex]45 - 9c + 4c = 30[/tex]
[tex]45 - 5c = 30[/tex]
[tex] - 5c = - 15[/tex]
[tex]c = 3[/tex]
place this 3 into our first equation and solve for a
[tex]a + (3) = 5[/tex]
[tex]a = 2[/tex]
Uncle Eddie asked Mckenna and Lara to order 46 new wheels for 18 skateboards and bicycles in his repair shop. How many bicycles and how many skateboards are in Uncle Eddie’s shop?
Answer:
The Correct Answer is: 15 bicycles and 6 skateboards.
Step-by-step explanation:
I'm sure it is that one. No Doubts.
if the radius of circle is r cm.write domn the measurement of area of that circle
helpppppppppppppppppp
We can't see the container. You should ask again with a different picture so you can get the right answer.
X + 40
Х
Solve for x and find the measure of each angle using the space below.
Answer:
X = 70
Step-by-step explanation:
180 - 40 = 140
140/2 = 70
Please mark as brainliest if answer is right
Have a great day, be safe and healthy
Thank u
XD
What is the sum of ( 3 . 4 × 10 8 ) + ( 7 . 5 × 10 8 ) ?
A.
1
.
09
×
10
9
B.
1
.
09
×
10
8
C.
1
.
09
×
10
17
D.
1
.
09
×
10
16
A game has a deck of cards with 5 red cards and 3 blue cards. You randomly choose one card and without replacing it choose another card. What is the probability of choosing a red card and then a blue card?
A: 2/7
B:10/49
C:15/56
D:15/64
Answer: C (15/56)
Step-by-step explanation:
probability of red card: 5/8
probability of blue card (after): 3/7
5/8 times 3/7 = 15/56 so C
Round 91738 to the nearest ten thousand. Enter your answer in the box
below.
Answer here
Answer:
90,000
Step-by-step explanation:
5. Which statements describe supplementary angles?
SELECT ALL THAT APPLY
A Angles that add up to 90 degrees
B
Angles that add up to 180 degrees
C Opposite angles that are equal in measure
D Adjacent angles that form a line.
Answer:
B. Angles that add up to 180°
Step-by-step explanation:
I think that's the answer because supplementary angles add up to 180°
A toy machine has equal numbers of red, white, and blue foam balls which it releases at random. Ross wonders which color ball will be released next. Select the description of how you can use a standard number cube to model and predict this situation.
A.Let multiples of 2 represent red, let multiples of 3 represent white, and let the remaining numbers represent blue. Toss the cube 50 times to determine the experimental probability for each color. Predict that the next ball will be the color with the greatest experimental probability.
B.Since "red" has three letters and "one," "two," and "six" all have 3 letters, let these represent red. Since "blue" has 4 letters and "four" and "five" have four letters, let these represent blue. Since "white" has five letters and "three" has five letters, let this represent white. Toss the cube 50 times to determine the experimental probability for each color. Predict that the next ball will be the color with the greatest experimental probability.
C.Let 1 and 2 represent red, let 3 and 4 represent white, and let 5 and 6 represent blue. Toss the cube 50 times to determine the experimental probability for each color. Predict that the next ball will be the color with the greatest experimental probability.
D.Let even numbers represent red, let odd numbers represent white, and let prime numbers represent blue. Toss the cube 50 times to determine the experimental probability for each color. Predict that the next ball will be the color with the greatest experimental probability.
Answer:
Since there are three colors and a standard number cube has 6 sides, you can let the numbers 1 and 2 represent red, 3 and 4 represent white, and 5 and 6 represent blue. Then roll the number cube repeatedly, recording the results for each roll. After you have recorded a sufficient number of rolls, determine which color was rolled the most often.
RESULT
Let the numbers 1 and 2 represent red, 3 and 4 represent white, and 5 and 6 represent blue.
Option (C) predicts the probability of the above situation correctly is the correct answer.
What is probability?Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.
For the given situation,
A toy machine has equal numbers of red, white, and blue foam balls which it releases at random.
Ross wonders which color ball will be released next.
A standard number cube is used to model and predict this situation.
A standard number cube has six faces namely 1,2,3,4,5,6.
There are three foam balls. If we assign two numbers for each foam, then we can able to predict the probability of next foam by rolling it for number of times.
Thus from the given options, Let 1 and 2 represent red, let 3 and 4 represent white, and let 5 and 6 represent blue. Toss the cube 50 times to determine the experimental probability for each color. Predict that the next ball will be the color with the greatest experimental probability. This option determines the above situation.
Hence we can conclude that option (C) predicts the probability of the above situation correctly is the correct answer.
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