Answer: Area of ΔABC is 2.25x the area of ΔDEF.
Step-by-step explanation: Because equilateral triangle has 3 equal sides, area is calculated as
[tex]A=\frac{\sqrt{3} }{4} a^{2}[/tex]
with a as side of the triangle.
Triangle ABC is 20% bigger than the original, which means its side (a₁) measures, compared to the original:
a₁ = 1.2a
Then, its area is
[tex]A_{1}=\frac{\sqrt{3} }{4}(1.2a)^{2}[/tex]
[tex]A_{1}=\frac{\sqrt{3} }{4}1.44a^{2}[/tex]
Triangle DEF is 20% smaller than the original, which means its side is:
a₂ = 0.8a
So, area is
[tex]A_{2}=\frac{\sqrt{3} }{4} (0.8a)^{2}[/tex]
[tex]A_{2}=\frac{\sqrt{3} }{4} 0.64a^{2}[/tex]
Now, comparing areas:
[tex]\frac{A_{1}}{A_{2}}= (\frac{\sqrt{3}.1.44a^{2} }{4})(\frac{4}{\sqrt{3}.0.64a^{2} } )[/tex]
[tex]\frac{A_{1}}{A_{2}} =[/tex] 2.25
The area of ΔABC is 2.25x greater than the area of ΔDEF.
Write a fraction equal to 1 with a numerator of 18
Answer:
18/18
Step-by-step explanation:
18 divided by 18 is one
Erica can paint her room 5 hours .If she had her friend Rachel help her , they can paint the room together in 3 hours .How long would it take for Rachel to paint the room alone , if Erica wanted to go play tennis for the afternoon ?
Answer:
7 hours 30min
Step-by-step explanation:
Step one :
Given data
We are told that Erica can paint 1 room in 5hours
Her work rate is 1/5 room per hour
And also with the assistance of her friend they can paint 1 room in 3 hours
Hence their combined work rate is 1/3 room per hour
Step two
The combined work expression is
1/A+1/B=1/T
Where A=Erica's work rate
B=Rachael's work rate
T=combined work
1/5+1/B=1/3
1/B=1/3-1/5
1/B=5-3/15
1/B=2/15
B=15/2
B=7.5 hours
It will take Rachel 7 hours 30min to paint the room
Which of the following would earn the same amount of interest as a $600 principal with 2.5%
interest for 6 years?
Answer:$225 at 10% for 4 years and $80 at 75% for 18 months
Step-by-step explanation:
The required interest earned is given as $90, as of the given condition.
Given that,
Principal = $600
Rate = 2.5% and time = 6 years
Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.
Here,
Simple interest = principal × rate × time /100
Simple interest = 600× 2.5× 6 /100
Simple interest = 90
Thus, the required interest earned is given as $90, as of the given condition.
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find the slope of the line through each pair of points. (9, 16) , (14, -12)
Answer:
slope = - [tex]\frac{28}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (9, 16) and (x₂, y₂ ) = (14, - 12)
m = [tex]\frac{-12-16}{14-9}[/tex] = [tex]\frac{-28}{5}[/tex] = - [tex]\frac{28}{5}[/tex]
Can you tell me the statements that are true?
Answer:
1=true
2=false
3=false
4=true
5=true
6=false
Step-by-step explanation:
hope this helps!:)
Graph the funtion f(x) = [tex]\sqrt[3]{x - 2}[/tex].
(I added a picture just in case you can't read the equation)
Struggling a lot could use a friend right about now thank you
This process is very simple. All you are doing is creating a table of values somewhere to help you graph this function. As you can see, the coordinates of [tex]\displaystyle [-6, -2], [1, -1], [2, 0], [3, 1],[/tex] and [tex][10, 2][/tex] are all touched on this graph, letting you know that this information is accurate.
I am joyous to assist you at any time. ☺️
Find the value of x. Round your answer to the nearest tenth.
Answer:
x=5.7
Step-by-step explanation:
sin(35=x/10
Xander is planning on building a house. The blueprints show a house that is 3 inches wide and 2 inches tall. The blueprints use a scale in which 14 inch represents 2 feet.
How wide and tall will the actual house be?
Drag and drop the height and width of the actual house into the boxes.
Answer:
16ft tall and 24ft wide
Step-by-step explanation:
Answer:
16ft 24ft
Step-by-step explanation:
i got the same qestion and its correct.
Simplify the expression below using laws of exponents.
Answer: 36/[tex]K^{2}[/tex]
Step-by-step explanation:
The k on top will cancel the k to the second power.
So the only number in the numerator is 1.
Then the 1 qill go away because you cant divide anything by 1.
The expoenet -2 that was at the top near K will become positive.
Then distribute
An item cost 460 before tax and the sales tax is 32.20 find the sales tax rate write your answer as a percentage
Answer:
7%
Step-by-step explanation:
Mrs Jonas has 35 students in her math class. If her class increases to 42 students next year what will be the percent of change?
A) 335
B) 93%
C) 75%
D) 20%
Answer:
D. because I did it
Step-by-step explanation:
got it right.
Answer:
20%
Step-by-step explanation:
well if the class would increase 35+35 it would be 50 % so its supposed to be a smaller percentage
What is the value of f(-1)?
O f(-1) = -3
Of(-1) = -1
O f(- 1) = 0
Of(-1) = 6
Answer: C: f(-1)=0
Step-by-step explanation:
To find f(-1), we look for the value under f(x) that corresponds to x=-1. This value is 0.
Question Three
What is the value of in the figure?
61
4 Ft
(5x)
(10x - 10)
6 ft
A
2
B
6.4
С
8
D 9.5
A complex number has a real part 4 and an imaginary part coefficient of -3. Which binomial is equivalent to this complex number?
Answer:
4-3i
Step-by-step explanation:
Here, we want to select the option that best correlate
The real and the complex part can be represented as;
a + bi
In this case, a is the real, b is the complex
So we have that;
Real part 4 and imaginary coefficient of 3
That will be
4 -3i
Answer:b
Step-by-step explanation:
i need help on my math how
Answer:
OK!!!!!!!!!!!!!!!1
Step-by-step explanation:
Answer: What do you need help with? I think if you put out you will try and help.
What value of x makes this equation true? 12x - 15 = 6 - 3x
Answer:
12x - 15 = 6 -3x (add 3x to both sides)
15x - 15 =6 (add 15 to both sides)
15x= 21 (divide both sides by 15 to get x alone)
x= 1.4 (the answer)
Answer:
1.4
Step-by-step explanation:
Which spacecraft tested the soil of Mars for signs of life?
Answer:
Viking landers
To date, the Viking landers (1976) were the only spacecraft to conduct experiments looking for life in the Martian soil.
Step-by-step explanation:
brainly?
start fraction 5.2 over 3.5 end fraction equals start fraction y over 7.5 end fraction
A. 7.25
B. 11.14
C. 5.05
D. 2.43
Answer:
A
jk its D hope this helps
21/35 as a decimal rounded to the nearest tenth
In the following table, y is a function of x. True or false: The table below represents a function.
Find the missing quantity in the double number line.
The missing quantity is 100 books in the double number line.
What is the proportion?A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other. Proportions are represented by the symbols "::" or "=".
Let the missing quantity be x in the double number line.
According to the given condition, we can write the proportion would be as:
40 books : 2 boxes = x books : 5 boxes
⇒ 40 / 2 = x / 5
Apply the cross-multiplication operation,
⇒ 40 × 5 = 2x
⇒ 2x = 200
⇒ x = 200/2
⇒ x = 100
Therefore, the missing quantity is 100 books in the double number line.
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what is 2x4(6.5x9.5) power of 12 show your work
Answer:
24.584...
Step-by-step explanation:
2x4(6.5x9.5) power of 12
2x4 x 61.75 power of 12
2x4 x 3.073...
8 x 3.073...
24.584...
What is the measure of the missing side?
A rectangle has an area of 135 ft 2 . What is the length, if the width is 9 ft?
Answer:
15 ft
Step-by-step explanation:
A=LxW
135 ft2 =m X 9ft
Divide 135 by 9
& that equals 15ft.
To check your answer, you multiply 15X9 and that equals 135. So the length of the rectangle is 15ft.
What is the unit rate depicted in the graph?
On a coordinate plane, a graph titled Lap Times has minutes on the x-axis and Laps on the y-axis. A line goes through points (4, 3) and (8, 6).
0.75 laps in one minute
1.25 laps in one minute
3 laps in 4 minutes
4 laps in 3 minutes
Answer:might be wrong but the answer is C
Step-by-step explanation:
The Unit Rate depicted in the graph will be 0.75 laps in one minute, i.e. Option A.
What is Unit Rate?The Unit Rate is defined as means a rate for one of something, i.e. ratios of two quantities.
We have,
Minutes on the x-axis,
And,
Laps on the y-axis.
And,
A line goes through points (4, 3) and (8, 6),
x₁ = 4, x₂ = 8, y₁ = 3, y₂ = 6
Now,
So,
Unit rate for x₁ and y₁,
i.e.
[tex]\frac{y_1}{x_1} =\frac{3}{4}=0.75[/tex]
Now,
Unit rate for x₂ and y₂,
i.e.
[tex]\frac{y_2}{x_2} =\frac{6}{8}=0.75[/tex]
So,
The unit rate is 0.75 laps in one minute.
Hence, we can say that the Unit Rate depicted in the graph will be 0.75 laps in one minute, i.e. Option A.
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Dolly and Willie's scores are shown. Dolly claims that she is the better student, but Willie
claims that he is the better student. What statistics make either Dolly or Willie seem like
the better student? Drag and drop the correct word into each box to complete the
explanation.
Answer:
I have attached a picture below. I hope this helps!
Is this graph a function? why or why not.
Answer:
The vertical line test can be used to determine whether a graph represents a function. ... If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x value has more than one output. A function has only one output value for each input value.
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
The diagram below represents the shape of the floor of a hotel lobby. The hotel plans on replacing the carpet in the lobby
12
1
1 14 11
1
1
1121
13 ft
! 11 ft
31 tt
Part A: What is the total area of the hotel lobby floor?
ft?
Part B: If the new carpet costs $1.75 per square foot, how much with the hotel spend on new carpet?
Answer:.
Step-by-step explanation:
URGENT!!!!!!!!!! PLEASE HELP!!!
Answer:
F' would be (5,2)
G' would be (0,2)
H' would be (0,6)
hope this helps!
Find the lateral area of this cone.
Round to the nearest tenth.
Hint: Lateral Area of a Cone = url
Where l = slant height
15in
12in
[?] in2
Answer:
565.5 in²
Step-by-step explanation:
Lateral area of a cone is represented by,
Lateral surface area = πrl
Here 'r' = Radius of the circular base
l = lateral height of the cone
By this formula,
Lateral area = π(12)(15)
= 565.49
≈ 565.5 square inch
Therefore, 565.5 in² is the answer.