triangle DEF is formed by connecting the midpoints of the sides triangle ABC. The lengths of the sides of DEF are shown. what is the length of AB
The requried length of the AB is given as AB = 16.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
Since triangle DEF is formed by connecting the midpoints of the sides of triangle ABC, the length of the sides of triangle DEF is half the length of the corresponding sides of triangle ABC. That is:
DE = 1/2 AB
EF = 1/2 BC
FD = 1/2 AC
We can use the information about the lengths of the sides of triangle DEF to find the length of AB.
Since DE = 8 and EF = 10, we can use the triangle inequality to find FD:
FD + DE > EF
FD + 8 > 10
FD > 2
Similarly, since EF = 10 and FD = 12, we can use the triangle inequality to find DE:
DE + EF > FD
DE + 10 > 12
DE > 2
Finally, since DE = 8 and FD = 12, we can use the triangle inequality to find EF:
EF + FD > DE
EF + 12 > 8
EF > -4
Since all sides of a triangle must have positive lengths, EF cannot be negative. Therefore, the inequalities we have found imply that:
2 < FD < 12
2 < DE < 8
0 < EF < 10
Since DE = 1/2 AB and EF = 1/2 BC, we can write:
AB = 2DE = 2(8) = 16
BC = 2EF = 2(10) = 20
Therefore, the length of AB is 16.
Learn more about triangles here:
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Evaluate the expression: -4a2 + 3ab - (2a + 3b) if a = 1/4 and b = -12
Enter answer as a decimal.
Answer:
Value of equation = 26.25
Step-by-step explanation:
Given:
Equation given
-4a² + 3ab - (2a + 3b)
Given value of a = 1/4
Given value of b = -12
Find:
Value of equation
Computation:
-4a² + 3ab - (2a + 3b)
By putting value of a and b
-4(1/4)² + 3(1/4)(-12) - [2(1/4) + 3(-12)]
-4(1/16) - (36/4) - [2/4 - 36]
-4/16 - 36/4 - [-142/4]
- 0.25 - 9 + 142/4
-0.25 - 9 + 35.5
Value of equation = 26.25
Which expression is equivalent to ?
Answer:
It's B or C, I can't see it clearly sorry!
Step-by-step explanation:
Suilin needed 7 dollars 13 cents to buy a book. In her wallet, she found 3 dollar bills, 4 dimes, and 14 pennies. How much more money does Suilin need to buy the book?
Answer:
$3.49
Step-by-step explanation:
Please help Due in 1 Min!
The answer is 16
Can i get brainliest please
What is the answer ? What value is missing from the table?
Answer A. 17
Step-by-step explanation: The cost, in dollars is increasing by $1.05 by 1’s. To get from 1.05 to 2.10 is 1.05. So to find the Gallons of Gas, you would keep adding 1.05 until you get 17.85 or you can multiply the numbers in the answer choice by 1.05 to get your answer.
A dress that is size x in France is equaivalent to size d(x) in the United States, where d(x)x32.
(a). Find a function that will convert U.S. dress size to French dress size.
(b) Use the inverse function to find the French size of a dress if it is U.S. size .
Answer:
[tex](a)\ d'(x) = x + 32[/tex] i.e. The inverse function
[tex](b)\ d'(10) = 42[/tex] i.e. The French size of a dress if it is U.S. size 10 is 42.
Step-by-step explanation:
Given
[tex]d(x) = x - 32[/tex]
Solving (a): The inverse function
[tex]d(x) = x - 32[/tex]
Replace d(x) with y
[tex]y = x - 32[/tex]
Swap y and x
[tex]x = y - 32[/tex]
Make y the subject
[tex]y = x + 32[/tex]
Replace y with d'(x)
[tex]d'(x) = x + 32[/tex]
Hence, the inverse function is: [tex]d'(x) = x + 32[/tex]
Solving (b): US size of 10
[tex]d'(x) = x + 32[/tex]
Substitute [tex]x =10[/tex]
[tex]d'(10) = 10 + 32[/tex]
[tex]d'(10) = 42[/tex]
What name is given to an angle that
measures 150°?
Answer:
Obtuse
Step-by-step explanation:
Since 150°>90°, it is an obtuse angle
Pam went to the mall one day, below shows what she bought and how much those items cost.
2 shirts - $31.45
Jeans - $18.50
Dress - $14.95
How much money did Pam spend in all?
Answer:
$96.35
Step-by-step explanation:
31.45 x 2 = 62.90
62.90 + 18.50 + 14.95 = $96.35
The number of pets owned by eight classmates is shown below:
1, 3, 2, 2, 1, 3, 3, 1
Part A: What is the mean of the data? Show your work. (4 points)
Part B: Use your answer from Part A to calculate the mean absolute deviation for the data. Show your work. (6 points)
Answer:
Part A: Mean = 2
Part B: 6
Step-by-step explanation:
Part A: Add all the data piece's and divide by total value
Part B: Subtract the mean from each piece of data in the dat set and find the absolute value of each answer. 1+1+0+0+1+1+1+1 = 6
The mean of the data of the number of pets owned by eight classmates is 2 and the mean absolute deviation for the data is 0.75.
What is mean of data set?The mean of the data is the average value of the given data. The mean of the data is the ratio of the sum of all the values of data to the total number of values of data.
The number of pets owned by eight classmates is shown below:
[tex]1, 3, 2, 2, 1, 3, 3, 1[/tex]
The total number of pets are 8. The mean is the ratio of sum of all the values to the total values. Thus,
[tex]m=\dfrac{1+ 3+ 2+ 2+1+3+3+1}{8}\\m=\dfrac{16}{8}\\m=2[/tex]
The mean absolute deviation (MAD), can be calculate by adding difference of each data from mean and then divided by number of terms.
[tex]\text{MAD}=\dfrac{(1-2)+ (3-2)+ (2-2)+ (2-2)+(1-2)+(3-2)+(3-2)+(1-2)}{8}\\\text{MAD}=\dfrac{6}{8}\\\text{MAD}=0.75[/tex]
Thus, the mean of the data of the number of pets owned by eight classmates is 2 and the mean absolute deviation for the data is 0.75.
Learn more about the mean here;
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1. Discriminate the solutions of the following quadratic equations.
(1) [tex]x^2+5x+3+a=0[/tex]
(2) [tex]x^2+(a+b)x+ab=0[/tex]
(Please show the steps if possible)
Help me .......is urgent ,,,,,The point-slope equation for a given line may look different than the slope-
intercept form, but they will simplify algebraically to the same equation.
A. True
B. False
Awnser- True
because the point slope is intercepted
rewrite each fraction with a denominator of 10 7/2=? 3/5=?
Lamont has 30 book pack in boxes. Each box holds 7 books. If he fills each box,how many books are left over?
Answer:
2 are left over
since 7 goes into 30 4 times which makes 28 books. Meaning 2 are going to be left over
Which two decimals are between 34.6 and 35.23? Please help I’ll give 15 points
34.75
35.15
You didnt give any choices so i just picked two random ones.
I really need help with this
Answer:
Oh Stop!!!! This is sooooooooooooo easy! If you would just pay attention in school and not spend all your time trying to buy the new ipad pro maybe you would not have to go to Branily to get a simple answer! Do you think your teacher would like you cheating like this???? I dont think so. So get of of Branily and start studying!!!!
Step-by-step explanation:
HELP ME SOMEONE PLEASE :(
Answer: The answer is A.
Step-by-step explanation:
The formula for the area of circles:
A = πr^2
Plug in the radius
A = π8^2
A = π64
A = 201.06192983/ 201 (rounded)
Answer:
A
Step-by-step explanation:
The formula for area of a circle is πr^2. the radius is 7 so pie time 7 times 2 square equal ≈201
If m=7 and r = 12, what is the value of the following algebraic expression
4m + 7r-5
The base of a triangle is 9/4 times of its height. If the area of triangle is 144 cm2. Find the height and the base.
Step-by-step explanation:
Given that the base of triangle is 9/4 times of its height . And area is 144 cm² . Let the height be h , then its base be 9h/4 .
• According to Question :-
[tex]\tt\to Area_{(\triangle)}=\dfrac{base\times height}{2}\\\\\tt\to 144cm^2 = \dfrac{9h\times h}{4\times 2 } \\\\\tt\to h^2 =\dfrac{12\times 12 \times 2 \times 2 }{3\times 3 }\\\\\tt\to h =\sqrt{\dfrac{12\times 12 \times 2 \times 2 }{3\times 3 }}\\\\\tt\to h =\dfrac{(12)(2)}{3} \\\\\tt\to \boxed{\orange{\tt h = 8 cm }}[/tex]
Therefore ,
Height = h = 8cm .Base ,= 9h/4 = 18cm .can u plz help me!? i need help
the answer is 4 buses
Step-by-step explanation:
because you multiply 30 times 4 and it gives you you the right answers
Please, my whole grade depends on this question!!!
Answer:
Y = 1/2 times -3 ( 1 x 5 )
Step-by-step explanation:
WILL GIVE BRAINLIEST!!!!!!!
A surveyor wants to find the distance between peaks A and B. He finds point C, 288 ft from peak A, so that ACB is a right angle. The measure BAC is 89. Find the distance AB
Hints on solving trigonometry problems:
If no diagram is given, draw one yourself.
Mark the right angles in the diagram.
Show the sizes of the other angles and the lengths of any lines that are known
Mark the angles or sides you have to calculate.
Consider whether you need to create right triangles by drawing extra lines. For example, divide an isosceles triangle into two congruent right triangles.
Decide whether you will need Pythagorean theorem, sine, cosine or tangent.
Check that your answer is reasonable. The hypotenuse is the longest side in a right triangle.
How to use the tangent ratio to find missing sides or angles?
Example:
PLEASE HELP!!
What value if m makes the equation true??
m+2m-6 =-12+2m
m=?????
I'm just doing this so I can see this on my phone (can't see images on computers)
Answer:
LOL
Step-by-step explanation:
└(^o^)┘└(^o^)┘└(^o^)┘└(^o^)┘└(^o^)┘└(^o^)┘└(^o^)┘└(^o^)┘└(^o^)┘└(^o^)┘
) 1 point 15) At the end of a game, the Wildcats have 2 points and the Lancers have 6 points. Cassie says the Lancers scored 4 more points than the Wildcats. Mark says the Lancers scored 3 times as many points as the Wildcats. Who is correct? * Cassie is correct Mark is correct Neither is correct Both are correct
What is the range?
The range is
2 3
4
4
5
6
7
8.
9 10
Answer:
8
Step-by-step explanation:
The expressions 3+y and 13(6+y) are equivalent
Answer:
below
Step-by-step explanation:
that is the procedure above
Laura goes to the carnival and receives 60 tokens to play games.
•each game required 4 tokens.
•At the end of the evening she used all of her tokens,how many games did laura play?
A.10
B.15
C.16
D.24
Answer: (B) 15
Step-by-step explanation:
Laura had 60 tokens to use and each game required 4 of them. By the end of the evening all of her tokens had been spent.
Let x represent the number of games Laura has played. Since Laura used up all of her tokens we can determine that for some integer x, 60 - 4x = 0
Solve for x
60 - 4x = 0
- 4x = - 60
x = [tex]\frac{60}{4}[/tex]
x = 15
Therefore, Laura played 15 games by the end of the evening
HELP! WILL GIVE BRANLIEST!
Answer:
ITS X=14 GURL TRUST
Step-by-step explanation:
Which is closest to the length of AB?
A. 3.5 in.
B. 2.9 in.
C. 2.4 in.
D 1.4 in
Answer:
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