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.
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Answer:
C would be your answer
Step-by-step explanation:
a polygon has perimeter 15 units.it is dilated with a scale factor of 3/5.what is the perimeter of its image
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Given what we know, we can confirm that the perimeter of the image is 9 units.
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Aaron saw it was 86° Fahrenheit, F, in Australia in January. Aaron used the formula C=5/9(F−32) to find the temperature in degrees Celsius, C. What temperature, in degrees Celsius, did Aaron find?
Answers
Answer:
[tex]30^{\circ}\text{C}[/tex]
Step-by-step explanation:
The temperature that Aaron saw was [tex]86^{\circ}\text{F}[/tex]
The formula to convert Fahrenheit to Celsius is
[tex]C=\dfrac{5]{9}(F-32)[/tex]
[tex]\Rightarrow C=\dfrac{5}{9}\times (86-32)[/tex]
[tex]\Rightarrow C=30^{\circ}\text{C}[/tex]
The given temperature in Celsius that Aaron found would be [tex]30^{\circ}\text{C}[/tex].
The relationship between income (I), in dollars, and the time (h), in hours, for 2 different jobs is represented. Compare the hourly rates of Job A and Job B.
Answers
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete. However, I will solve using the following assumptions.
Job A:
[tex]y = 2x + 5[/tex]
Job B
[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} \ \\ y & {6} & {10} & {14} & {18} & {22} \ \end{array}[/tex]
The first step is to calculate the rate of Job B using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where:
[tex](x_1,y_1) = (1,6)[/tex]
[tex](x_2,y_2) = (2,10)[/tex]
So, we have:
[tex]m = \frac{10 - 6}{2 - 1}[/tex]
[tex]m = \frac{4}{1}[/tex]
[tex]m = 4[/tex]
So, the hourly rate of job B is $4/hr
For Job A:
[tex]y = 2x + 5[/tex]
A linear equation has the form:
[tex]y = mx + b[/tex]
Where m is the rate
By comparison:
[tex]m = 2[/tex]
So, the hourly rate of Job A is $2/hr
Comparing both rates, we can draw the following conclusions;
The hourly rate of Job A is greater than the hourly rate of Job BThe hourly rate of Job A is twice the hourly rate of Job B.HELLLLLP MEEEE IDENTIFY THE HEIGHT
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Answer:
11
Step-by-step explanation:
The height is 11 inches.
X to the fourth power minus Y to the fourth power
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Answer:
[tex](x - y) \times (x + y)( {x }^{2} + {y}^{2} )[/tex]
Step-by-step explanation:
[tex](x ^{2} - y ^{2} ) \times (x ^{2} + y ^{2} )[/tex]
[tex] ({x} - y) \times (x + y) \times {x }^{2} + y ^{2} )[/tex]
What is another way of writing 5(6+3) using to distribute property
Answers
Answer:
The multiplication of 5(6) and 5(3) will each be done before you add.
5(6) + 5(3) = 30 + 15 = 45. Note that the answer is the same as before.
Step-by-step explanation:
hope this helps...
have a nice weekend ヽ(ヅ)ノ
oh and if i was supposed to follow something sorry cuz i can't see the pic...
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Answer: B
Step-by-step explanation:
fish swims at an altitude of -20.2 meters. A bird flies at an altitude of 38.1 meters. Which of the following statements are true? PLZ HEPPO
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Answer:
D and e
Step-by-step explanation:
2. Find the missing side length.
Round answers to the nearest tenth.
13
29°
Х
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Answer:
50
Step-by-step explanation:
Since it's a right angle, it's automadically 90 degrees. Add 29 + 13 which gives you 42. 90 - 42 gives you 48. Rounded to the nearest 10th is 50. Here's what I explained in numerical form:
29 + 13 = 42
90 - 42 = 48
Five or more raise the score. For or less turn to zero:
48
8 is larger than 5 so you add "plus 1" to the next number:
50
Your employer tells you that the salary for your new job will be less than $484 per week but not less than $396 per week. Which inequality describes your salary, S?
Answers
I think the inequality is less than or equal to (here what the sign looks like ≤ )
(-1)^2 × (-1)^3 × (-1)^5
Answers
Answer:
1
Step-by-step explanation:
(-1)^2 = 1
(-1)^3 = -1
(-1)^5 = -1
(1) (-1) (-1) = 1
Kamogelo walks 1.25 km in 25 minutes and Masego walks 1.44 km in 30 minutes. If these are
their travelling times and distance to school then, who walks faster.
Answers
Answer:
Kamogelo walks Faster
Step-by-step explanation:
1.25 km is less distant and in twenty five minutes it is fast enough.
(a) All even numbers are divisible by 2.
Answers
All even numbers are divisible by 2
Find the distance between (5, 9) & (-7, -7). Round to the nearest tenth.
Answers
(-7,-7)-(5,9)=
(-7-5,-7-9)=(-12,-16)
(-12,-16) gives us the distance point coordinates. Now to find the magnitude we can take sqrt((-12)^2+(-16)^2)=20
So the distance between the two points is 20
I hope this helps
Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is 37%. If they have six children, what is the probability that at most one of their six children will have that trait? Round your answer to the nearest thousandth.
Answers
Answer:
Yes
Step-by-step explanation:
Answer:
Sum: 0.78619≈0.786
Step-by-step explanation:
n=4
r=1, 2, 3, 4
r=1,2,3,4
"At least" counts up.
p=32\%=0.32
p=32%=0.32
q=1-0.32=0.68
q=1−0.32=0.68
The chance a success does NOT occur.
_{n}C_{r}p^rq^{n-r}
The probability that at most one of their six children will have that trait is 0.68
How to determine the probability?From the question, the given parameters are
Number of children, n = 6
Probability of a child with the trait, p = 37%
The required probability that at most one will have that trait is represented as P(x ≤ 1)
This probability is calculated ;
P(x ≤ 1) = P(0) + P(1)
Where
P(x) = ⁿCₓ * pˣ (1 - p)ⁿ⁻ˣ
So, we have
P(x ≤ 1) = ⁷C₀ (37%)⁰ (1 - 37%)⁷⁻⁰ + ⁷C₁ (37%)¹ (1 - 37%)⁷⁻¹
Evaluate;
P(x ≤ 1) = ⁷C₀ * 1 * (63%)⁷ + ⁷C₁ * (37%) * (63%)⁶
So, we have;
P(x ≤ 1) = 1-0.32= 0.68
Hence, the probability is 0.68
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Trying again, but im attaching the screenshot this time!
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Answer:
the area of a triangle is 9 because 4.24 times 4.24 equals 17.9776 estimated is 18 divided by 2 is 9 times 4 is 36. Now we divide 36 by 2 so we know what the area of the two trapezoids so we know the top and the bottom which is 18. The area of the square in between the triangles is 4.24 times 6 which is 25.22 estimated is 26. Now we add 26 with 18 which is 34. Now we have to find the area of the rectangle to do this we need to multiply 7.24 and 2 we need to do this so we know the length of the rectangle which is 14.48 estimated is 14. Now that we know the length we multiply it with the height which is 6, 14 times 6 equals 84.
84 is the rectangles area and the area for the trapezoids is 36.
84 plus 18 plus 18 equals 120 squared
3y (3x - 1) - ( 3x - 1) tama "termino común"
Answers
Answer:
9xy-3x-3y+1
Step-by-step explanation:
3y(3x-1)-1(3x-1)
6. What percentage of the children in class 5 is a member of a sports club? 3
Result sports questionnaire
for: class 5
“Are you a member of a
sports club?
yes: 15
no:5”
Answers
Answer:
75%
Step-by-step explanation:
Let x be the percentage for sports club members.
x% of 20 = 15
x/100 x 20 = 15
x/5 = 15
x = 75
In a recent survey of 700 people, 15% said that red was their favorite color. How many people said that red was their favorite color?
Answers
Answer:
Answer: 105
Step-by-step explanation:
In a recent survey of 700 people, 15% said that red was their favorite colour. 105 people said read was their favorite colour.
Answer:
105
Step-by-step explanation:
There are two mystery numbers. The sum of 2 times the first number and 5 times the second number is -5. The sum of 3 times the first number and 10 times the second number is -5. What are the two numbers?
Answers
Answer:
the two numbers are -5 and 1
Step-by-step explanation:
Let x and y be the first number and second number respectively.
According to the question, we can find 2 equations:
2x + 5y = -5
3x + 10y = -5
On solving,
x = -5
y = 1
Answer:
X=-5,Y=1
Step-by-step explanation:
First equation: 2X+5Y=-5
Second equation:3X+10Y=-5
If we subtract the first from the second equation
(3X+10Y)-(2X+5Y)= 0 so, X+5Y= 0
So X= -5Y .then substitute in the second equation
So ,3(-5Y)+10Y= -5 , therefore -15Y + 10Y=-5 so, -5Y=-5 which means that Y=1
Then substitute with that in the first equation so 2X+5= -5
2X= -10 therefore X=-5
I NEED HELP PLZZ THE IS DUE TODAY PLZZ thank you
Answers
The height is 2 cubes, the length is 5 cubes, and the width is 3 cubes. Now you can just plug it into the formula.
V=lwh
V= 5x3x2
V=30
Hope this helps!! :)
Plsss help I have a couple min left plssss
Answers
Answer:
here is the answer
Step-by-step explanation:
the first one the slope is 2
the second one the slope is -3
the slope is always the one with the x and the second one without the x is the y axis
Side c on a right triangle is ALWAYS the longest.
O No answer text provided.
O No answer text provided.
O True
O False
Answers
Answer:
the answer should be false..
what are the values of x and y
Answers
Answer:
Y: 145
X: 35
Hope I was able to help you, have a wonderful day!
A fitness trainer sets the incline on a
treadmill to 7º. The walking surface is 5
feet (60 inches) long. Approximately how
many inches did the trainer raise the
end of the treadmill from the floor?
Answers
Answer:
Step-by-step explanation:
sin Ф equal the opposite leg of the triangle dividend by the hypotenuse
sin Ф = opp / hyp
the problem gave you the Ф (the angle 7°)
and the length of the hypotenuse (the walking surface 60 inches)
You want to use the inches since the question wants to know how many inches off the floor is the end of the walking surface
sin 7 = opp / 60 solve for opp
60 × sin(7) = opp use your calculator, I don't have one handy
Use special right triangle find the exact value of x.
X=?
Answers
Answer: 12
Step-by-step explanation:
PLEASE HELP I AM ABOUT TO FAILL
Suppose that a plano cost 5,000 and loses 20% of its value oach year. table shows the value, of a piano after years.
1. 5000
2. 4000
3. 3200
write an equation that can be used to find the value of the piano, v, after t years.
Answers
Answer:
Step-by-step explanation:
90
Based on the information, the value of the piano after 16 years is $140.74.
What is Compound interest?Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.
Using this formula to find the value of the piano, v, after t years.
CP = Principal(1-rate)[tex]^t[/tex]
Where:
Principal=$5,000
Rate=20%
Number of year = 16 years
Let plug in the formula;
=5,000(1-0.20)^16
=5,000(.80)^16
=$140.737
= $140.74 (Approximately)
Hence, the value of the piano after 16 years is; $140.74.
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Help pls for brainlest and extra points i need done soon
Answers
Answer:
5/6= 10/12
12/100<10/12