50 POINTS!!! In rectangle ABCD, AB = 6 cm, BC = 8 cm, and DE = DF. The area of triangle DEF is one-fourth the area of rectangle ABCD. What is the length in centimeters of segment EF? Express your answer in simplest radical form.
Answers
Answer:
[tex]EF=4\sqrt{3}[/tex]
Step-by-step explanation:
In rectangle ABCD, AB = 6, BC = 8, and DE = DF.
ΔDEF is one-fourth the area of rectangle ABCD.
We want to determine the length of EF.
First, we can find the area of the rectangle. Since the length AB and width BC measures 6 by 8, the area of the rectangle is:
[tex]A_{\text{rect}}=8(6)=48\text{ cm}^2[/tex]
The area of the triangle is 1/4 of this. Therefore:
[tex]\displaystyle A_{\text{tri}}=\frac{1}{4}(48)=12\text{ cm}^2[/tex]
The area of a triangle is half of its base times its height. The base and height of the triangle is DE and DF. Therefore:
[tex]\displaystyle 12=\frac{1}{2}(DE)(DF)[/tex]
Since DE = DF:
[tex]24=DF^2[/tex]
Thus:
[tex]DF=\sqrt{24}=\sqrt{4\cdot 6}=2\sqrt{6}=DE[/tex]
Since ABCD is a rectangle, ∠D is a right angle. Then by the Pythagorean Theorem:
[tex](DE)^2+(DF)^2=(EF)^2[/tex]
Therefore:
[tex](2\sqrt6)^2+(2\sqrt6)^2=EF^2[/tex]
Square:
[tex]24+24=EF^2[/tex]
Add:
[tex]EF^2=48[/tex]
And finally, we can take the square root of both sides:
[tex]EF=\sqrt{48}=\sqrt{16\cdot 3}=4\sqrt{3}[/tex]
Answer:
4\sqrt3
Step-by-step explanation:
we know that the area is 6 * 8 = 48 cm^2. because triangle DEF is one fourth of that, triangle DEF's area would be 12.
to find the hypotenuse of triangle DEF, we would first need to find the bases (which have equal lengths). 1/2 * b * b = 12, so b^2 = 24. using the pythagorean theorem, we have \sqrt24 + \sqrt24 = h^2 which means h is the sqrt of 48. simplified, we have 4\sqrt3.
Related Questions
If the lengths of the two legs of a right triangle are 12 and 16, what's the length of the hypotenuse?
Question options:
A)
14
B)
16
C)
20
D)
28
Answers
Someone pls help me
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Answer:
2. 8x
3. (12/2)*(10/2)
Step-by-step explanation:
ill mark brainlist plss help
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Answer:
345,512
Step-by-step explanation:
one liter is a thousand ml, so u just have to multiply
A man's income is increased in the ratio 47:40.find the increase percentage
Answers
Answer:
14.8%
Step-by-step explanation:
Given data
Initial income=47
Final income=40
The change= 47-40
=7
Hence the percent increase is
% increase= Change/ initial*100
% increase= 7/47*100
% increase=0.148*100
% increase=14.8%
What is the value of n?
Your answer in the box n=
5m 15m n 2m
Answers
Answer:
12.5
Step-by-step explanation:
because it's a progress
help me please help please
Answers
Answer:
x = 2
Step-by-step explanation:
there is no y intercept
Rosario is an ecologist who studies the change in the penguin population of Antarctica over time.
The relationship between the elapsed time t, in years, since Rosario started studying the population, and
the number of penguins, P(t), is modeled by the following function:
P(t) = 21,000 • (4/7)^t/3
Complete the following sentence about the rate of change in the penguin population.
The population of penguins loses 3/7 of its size every ____ years.
Answers
Answer: every 3 years
Step-by-step explanation:
If a 6 pack of sodas cost $2.40, then how much will one can cost?
Answers
Answer:
.40 cents
Step-by-step explanation:
Just simple divide 2.40/6 and when you get 0.4, add a 0 because it is money.
Answer:
0.40 cents
Step-by-step explanation:
You divide $2.40 by 6 and you get the answer 0.40 or 0.4
Write an expression for the area and perimeter for the figure shown.
I WILL GIVE THE BRAINLIEST IF YOU CAN ANSWER THIS
Answers
Area=(x-1)*(x-1)+(2x-1)*(x+3)
Hope it helps
PLEASE HELP I’M BEING TIMEDDDD
Answers
Answer:
1: 51.8°F
Step-by-step explanation:
2: 26.6
I'M NOT SURE IF I GOT THIS RIGHT I DID MY BEST.
A rectangle is shown.
What is the area of the rectangle?
Answers
Answer:
360
Step-by-step explanation:
15+15
12x15
ANSWER:
360
Step-by-step explanation:
15+15
12x15
please help meeeee and show your work :)
Answers
Answer:yes because the slopes od the lines are the same but the y intercepts are differen.
Step-by-step explanation:
when you connect (5,8) and (13,24) then (3,3) and (7,11) they insect what the the lines. so C yes because the slopes of the lines are the same but y intercepts are different
Roadsign cast of shadow that is 4 feet tall at the same time a 6 foot man standing next to the sign cast a shadow of those 2.4 feet long right and solve a proportion to find how tall the sign is
Answers
Answer:
10 feets
Step-by-step explanation:
Given that:
Road sign shadow (Rs) = 4 feets
Height of man (Hm) = 6
Man shadow (Ms) = 2.4 feets
Height of road sign (Hr) = x
Height of road sign / shadow of road sign = height of man / shadow of man
Hr/Rs = Hm / Ms
x / 4 = 6 / 2.4
Cross multiply :
4*6 = 2.4*x
24 = 2.4x
x = 24 / 2.4
x = 10 feets
Hence, height of road sign = 10 feets
Plz help me
Explation for both questions and tell what conceputal key you use.
Giving 35 points
1. Lizzy opened an ice cream parlor in her neighborhood selling homemade ice cream. She has a goal to create 80 new ice cream flavors. If she already created 37 flavors, how many more flavors does she still need to create?
2. A staples truck is delivering notebooks to CMS. There are 212 boxes with 198 notebooks in each box. How many total notebooks are there?
Answers
Step-by-step explanation:
2) 212*198 = 41 976
1) 80-37 = 43
9514 1404 393
Answer:
1. SCR (or PPW). 43 more flavors
2. GLT. 41,976 notebooks
Step-by-step explanation:
1. Conceptual key: SCR
Lizzy is starting with 37 flavors. She wants a result of 80 flavors, so the change can be computed from ...
37 + x = 80
x = 80 -37 = 43
Lizzy needs to create 43 more flavors.
__
Additional comment
This might also be considered to be using the PPW pattern, as both the number she has and the number she creates make up the whole number. The SCR key may better apply to cases where a "rate of change" is involved. There is no rate of change in this problem.
_____
2. Conceptual key: GLT
There are 212 groups of 198 notebooks, so the total is the number of groups times the number in each group.
(212 boxes)(198 notebooks/box) = 41,976 notebooks
Solve this problem???
Answers
The denominator of the first term is a difference of squares, such that
4a ² - b ² = (2a)² - b ² = (2a - b) (2a + b)
So you can write the fractions as
(4a ² + b ²)/((2a - b) (2a + b)) - (2a - b)/(2a + b)
Multiply through the second fraction by 2a - b to get a common denominator:
(4a ² + b ²)/((2a - b) (2a + b)) - (2a - b)²/((2a + b) (2a - b))
((4a ² + b ²) - (2a - b)²) / ((2a - b) (2a + b))
Expand the numerator:
(4a ² + b ²) - (2a - b)²
(4a ² + b ²) - (4a ² - 4ab + b ²)
4ab
So the original expression reduces to
4ab / ((2a - b) (2a + b))
or
4ab / (4a ² - b ²)
upon condensing the denominator again.
what tell the hardware what to do and and how to do it
Answers
Answer:
I am assuming you are telling me to tell a piece of hardware what to do and how so in that case, Hammer go hammer in that nail by hitting yourself on its head so I can hang this painting. LOL
Step-by-step explanation:
Which is the completely factored form of 4x3 + 10x2 – 6x?
2(x + 3)(2x – 1)
2x(x + 3)(2x – 1)
2x(x – 3)(2x – 1)
2(x – 3)(2x + 1)
Answers
Answer:
B. 2x(x + 3)(2x – 1)
Step-by-step explanation:
A. 2(x + 3)(2x – 1)
= (2x + 6)(2x - 1)
= 4x² - 2x + 12x - 6
= 4x² + 10x - 6
B. 2x(x + 3)(2x – 1)
= (2x² + 6x)(2x - 1)
= 4x³ - 2x² + 12x² - 6x
= 4x³ + 10x² - 6x
C. 2x(x – 3)(2x – 1)
= (2x² - 6x)(2x - 1)
= 4x³ - 2x² - 12x² + 6x
= 4x³ - 14x² + 6x
D. 2(x – 3)(2x + 1)
= (2x - 6)(2x + 1)
= 4x² + 2x - 12x - 6
= 4x² - 10x - 6
The completely factored form of 4x3 + 10x2 – 6x is 2x(x + 3)(2x – 1)
Answer:
The correct answer is B: 2x(x+3)(2x-1)
Step-by-step explanation:
I got it right on the quiz.
what is sqrt(405x ^ 7)?
Answers
Answer:
(405x ^ 7)²
405²x^14
164025x^14 is a square of 405x ^ 7
Step-by-step explanation:
Please answer help thank you
Answers
Slope = y1 - y2/x1 - x2
Slope
= 10-2 / 1-(-3)
= 8/1+3
= 8/4
= 2
The answer is m=2.
Convert 121
5
to mixed fraction.
Answers
Answer:
24 1/5
Step-by-step explanation:
I'm not sure if u meant 121/5 but I converted it and it's 24 as a whole number and 1/5 for the fraction
24 1/5
If the height of the aircraft is 5000metres,calculate the temperature outside
Answers
Answer:
222
Step-by-step explanation:
for sure 100%
gurantee at your own risk
Evaluate
12^2
1. 144
2. 24
3. 266
Answers
Answer:
The answer is 144
Step-by-step explanation:
12*12
12²
144
Mr. Smith is flying his single-engine plane at an altitude of 2400 feet. He sees a cornfield at an angle of depression of 30º. What is his horizontal distance to the cornfield?
Answers
Answer:
Height of the fighter plane =1.5km=1500 m
Speed of the fighter plane, v=720km/h=200 m/s
Let be the angle with the vertical so that the shell hits the plane. The situation is shown in the given figure.
Muzzle velocity of the gun, u=600 m/s
Time taken by the shell to hit the plane =t
Horizontal distance travelled by the shell =u
x
t
Distance travelled by the plane =vt
The shell hits the plane. Hence, these two distances must be equal.
u
x
t=vt
u Sin θ=v
Sin θ=v/u
=200/600=1/3=0.33
θ=Sin
−1
(0.33)=19.50
In order to avoid being hit by the shell, the pilot must fly the plane at an altitude (H) higher than the maximum height achieved by the shell for any angle of launch.
H
max
=u
2
sin
2
(90−θ)/2g=600
2
/(2×10)=16km
PLEASE HELP MY TEACHER ALWAYS IGNORES MY QUESTION AND I NEED HELP!
In the town of New Haven, the temperature at midnight was 1.2∘C. Which town was warmer at midnight, Princeton or New Haven? How many degrees warmer is it? If the point (3,-2.5) was also plotted on the diagram, what would it mean?
Answers
Answer:
For the first question it would be New Haven and it would be 4.7 degrees warmer. As for the second question it would be 3 hours after midnight the temperature is -2.5°C. Hope this helps!
Step-by-step explanation:
HELP ME PLEASE!! Thank you!!
Answers
Answer:
Step-by-step explanation:
so by "exact" they mean leave in the [tex]\sqrt{x}[/tex] parts.... sooo
they tell us the Hypotenuse ( Hyp) and one angle and want that side Opposite ( Opp) of the angle... sooo use the mnemonic
SOH CAH TOA
to help remember how the sin , cos, and tan functions fit on a triangle
there problems b/c easy A's when you get this. :P so learn it, know it, live it :D
Sin = Opp / Hyp
Cos = Adj / Hyp
Tan = Opp / Adj
now look at which one of the above formulas have the things we know and want to find
Sin looks like a good choice b/c it's got Opp, which we want to find, and Hyp which we know and also an angle which we can plug into the function
Sin(45) = Opp / 6
see how I got that?
[tex]\sqrt{2}[/tex] / 2 = Opp / 6
6 ( [tex]\sqrt{2}[/tex] / 2 ) = Opp
3[tex]\sqrt{2}[/tex] = Opp
the problem says leave it exact.. so don't try to reduce [tex]\sqrt{2}[/tex] just leave it
there is your answer
X = 3[tex]\sqrt{2}[/tex]
What is the square route of 16?
Answers
Answer:
the square route of 16=√4²=4
Answer:
4
Step-by-step explanation:
16/4 is 4 and they're both the same number
What is the smallest integer $n$ such that $5n + 3 > -10$?
Answers
Answer:
-2
Step-by-step explanation:
5n+3= -10
5n = -13
n = -13/5
= -2.6
question is integer
so answer is -2
The smallest integer n is -2
What is an integer?An integer is colloquially defined as a number that can be written without a fractional component.
What is Linear Inequality?In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality.
Given,
5n + 3 > -10
Consider
5n + 3 = -10
5n = -10-3
5n = -13
n = [tex]\frac{-13}{5} =-2.6[/tex]
Therefore the smallest integer n≅ -2
Hence, the smallest integer n is -2
Learn more about Integer and Linear inequality here
https://brainly.com/question/13006729
#SPJ2
Translate triangle ABC 4 units right and 5 units down H E L P
Answers
A (-2, 5)
B (0, 1)
C (2, 5)
Sry if my handwriting is hard to read but the following coordinates above is the same as the coordinates in the picture! I hope this help! Have a nice day!
I NEED HELP PLSSSS anyone that can help me out
Answers
a cylinder has a volume of 46 cubic inches. if all the dimensions are multiplied by 2.5, what would be the volume of the new cylinder?
Answers
Answer:
its v=720.52 in3
Step-by-step explanation:
