Based on the given segment lengths, determine whether the segments can form a triangle.
11.5,10.5, 6.1
9.5, 3.5, 4.5
8, 6.7, 1
8, 6.7, 9.8
5, 6, 8
9.5, 7.5, 8.5
Answers
For 3 sides to form a triangle two sides added together need to be greater then the 3rd side. You need to check all 3 combinations:
1. 11.5 + 10.5 = 22, 22> 6.1
11.5 + 6.1 = 17.6 17.6 > 10.5
10.5 + 6.1 = 16.6, 16.6 > 11.5
This one can make a triangle.
2. 9.5 + 3.5 > 4.5
9.5 + 4.5 > 3.5
4.5 + 3.5 < 9.5
Cannot make a triangle.
3. 8 + 6.7 > 1
6.7 + 1 < 8
Cannot make a triangle.
4. Can make a triangle
5. Can
6. Can
Can form triangle : 11.5,10.5, 6.1 & 8, 6.7, 9.8 & 5, 6, 8 & 9.5, 7.5, 8.5
Can not form triangle : 9.5, 3.5, 4.5 & 8, 6.7, 1
What is triangle inequality theorem ?
If sum of any two line segments is greater than the third line segment, then we can say that, they can make a triangle.
How to know which sets form triangle ?1st problem,
The given line segments are 11.5, 10.5, 6.1
Now, 11.5+10.5 = 22 > 6.1
10.5+6.1 = 16.6 > 11.5
11.5+6.1 = 17.6 > 10.5
So, this three segments can form triangle.
2nd problem,
The given line segments are 9.5, 3.5, 4.5
Now, 9.5+3.5 = 13 > 4.5
9.5+4.5 = 14 > 3.5
4.5+3.5 = 8 < 9.5
Here triangle inequality rule isn't applicable.
So, it can not form triangle.
3rd problem,
The given line segments are 8, 6.7, 1
Now, 8+6.7 = 14.7 > 1
8+1 = 9 > 6.7
6.7+1 =7.7 < 8
Here triangle inequality rule isn't applicable.
So, it can not form triangle.
4th problem,
The given line segments are 8, 6.7, 9.8
Now, 8+6.7 = 14.7 > 9.8
8+9.8 = 17.8 > 6.7
6.7+9.8 = 16.5 > 8
So, this three segments can form triangle.
5th problem,
The given line segments are 5, 6, 8
Now, 5+6 = 11>8
5+8 = 13 > 6
6+8 = 14 > 5
So, this three segments can form triangle.
6th problem,
The given line segments are 9.5, 7.5, 8.5
Now, 9.5+7.5 = 17 > 8.5
9.5+8.5 = 18 > 7.5
7.5+8.5 = 16 > 9.5
So, this three segments can form triangle.
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Related Questions
Simplify the expression.
(3x\y)^-3
Answers
(y/3x)^3
(y^3)/(3x)^3
(y^3)/27x^3
Which loan or loans listed below are awarded based on the financial need of the student?
I. Perkins loan
II. subsidized Stafford loan
III. unsubsidized Stafford loan
a.
I only
b.
I and II
c.
II and III
d.
I, II, and III
Answers
Answer:
B.
I and II
Step-by-step explanation:
The loan or loans listed below are awarded based on the financial need of the student are the Perkins loan and subsidized Stafford loan. Option B. This is further explained below.
What is loan?Generally, a loan is simply defined as a borrowed object, especially a quantity of money that is anticipated to be repaid with interest.
In conclusion, The Perkins loan and subsidized Stafford loan are two loans that are provided depending on the student's financial need.
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Assuming that the heights of college women are normally distributed with mean 63 inches and standard deviation 3 inches, what percentage of women are taller than 60 inches?
Answers
Answer:
cs.a,C|"< dl\vds
Step-by-step explanation:
2 1/2 =1 2/3 ÷y
i need help please
Answers
An alternative is 0.6
Answer:
Step-by-step explanation:
2*1 /2 = 1*2 / 3 / y
2/2=2/3 / y
1=2/3 x 1/y
1=2/3y
3y=2
y=2/3
Find the verte of the quadratic function given below f(x) = (x-4) (x+2)
Answers
Answer:
Vertex at (1,-9)
Step-by-step explanation:
Expand the equation by using foil method.
You should get X^2+2x-4x-8
And then add the like terms.
X^2-2x-8
And use this formula to find the vertex.
X=b/2a
plug in the values
X=-2/2(1)
you should get x=1
Thats the one value.
For another one you have to plug in you X= (value which is 1) in the f(x) which now becomes f(1)
the answer is f(1)=-9
what is the absolute value of 1
Answers
Answer:
1
Step-by-step explanation:
Since absolute value is the distance between zero, and the particular value, it is always positive! In this case, the distance between one and zero is exactly one!
A machine that drills holes for wells drilled to a depth of
–72 feet in one day (24 hours).
If the machine drilled at a constant rate, what was the
depth after 15 hours?
Answers
Answer:
depth of -117 feet
Step-by-step explanation:
24 hours 72 feet, so one hour 72/24 = 3 feet
after 15 hours, another 3*15 = 45 feet, so the depth become 72 + 45 = 117 feet
Please help. Systems of equations. Solve using elimination.
12X + 16y = 96
12X + 48y = 192
Answers
Answer:
x=4
y=3
Step-by-step explanation:
12X + 16y = 96--(1)
12X + 48y = 192---(2)
(2)-(1),
12x + 48y - (12x+ 16y)= 192- 96
12x + 48y - 12x - 16y = 96
32y = 96
y= 96÷32
y =3
substituting y=3 in (1),
12x +(16×3) = 96
12x + 48 = 96
12x = 96-48
12x = 48
x= 48÷12
x= 4
Hope this helps!
help me please I'm in a rush
Answers
Answer:
56
Step-by-step explanation:
616 divided by 11 equals the height
The Hornes buy a trampoline with a regular price of $495.00. It is on sale for 20% off the regular price. After calculating the sale price, they use a coupon for $35.00 off. The salesperson then adds a sales tax of 7%. What is the final price of the trampoline?
Answers
Answer:
$368.27
Step-by-step explanation:
495.00*0.20=$99
495-99=396
396-35=361
361*1.07=386.27
C, G, and D are collinear. E, G, and F are also collinear. The two lines
intersect at point G. Line EF bisects line CD. Find EG: if CG=5x-1, GD=7x-
13, EF=6x-4, and GF=13.
Answers
Answer:
EG is 19 units
Step-by-step explanation:
Let us solve the question
∵ Lines CD and EF intersected at point G
∴ CD = CG + GD
∴ EF = EG + GF
∵ Line EF bisects line CD
→ That means G is the midpoint of CD
∴ CG = GD
∵ CG = 5x -1
∵ GD = 7x - 13
→ Equate them to find x
∴ 7x - 13 = 5x -1
→ Add 13 to both sides
∴ 7x -13 + 13 = 5x - 1 + 13
∴ 7x = 5x + 12
→ Subtract 5x from both sides
∴ 7x - 5x = 5x - 5x + 12
∴ 2x = 12
→ Divide both sides by 2
∴ [tex]\frac{2x}{2}=\frac{12}{2}[/tex]
∴ x = 6
∵ EF = 6x - 4
→ Substitute x by 6 to find its length
∴ EF = 6(6) - 4 = 36 - 4
∴ EF = 32
∵ EF = EG + GF
∵ GF = 13
∴ 32 = EG + 13
→ Subtract 13 from both sides
∵ 32 - 13 = EG + 13 - 13
∴ 19 = EG
∴ EG = 19 units
Solve the inequality 4(k − 5) + 12k ≥ −4
Answers
Answer:
k ≥ 1
Step-by-step explanation:
Step 1: Write inequality
4(k - 5) + 12k ≥ -4
Step 2: Solve for k
Distribute 4: 4k - 20 + 12k ≥ -4Combine like terms: 16k - 20 ≥ -4Add 20 to both sides: 16k ≥ 16Divide 16 on both sides: k ≥ 1Inequality Form:
k
≥
1
k
≥
1
Interval Notation:
[
1
,
∞
)
[
1
,
∞
)
Wal-Mart buys paper plates for $3.25 and marks them up for 142%. How much do I buy them for?
Answers
Multiply the price by the percentage:
3.25 x 142% = 3.25 x 1.42 = 4.62
You pay $4.62
The height of a parallelogram is 5 feet The base is 7 feet the length is 9 1/2 feet what is the area of the parallelogram
Answers
Answer:
[10 ft.]
Step-by-step explanation:
It's being given that there is a paralleolgram.
Let the length of its base is x ft.
Therefore, length of height = (x+6) ft.
Also, area of paralleolgram = 160 sq.
ft.
Now, we know that,
Area of paralleolgram = base x height
Therefore, we will get,
=> x(x+6) = 160
=> x² + 6x - 160 = 0
=> x² + 16x - 10x - 160 = 0
=> x(x+16) - 10(x+16)=0
=> (x+16) (x - 10) = 0
=> x +16=0 or X- - 10-0
=> x=-16
or
X = 10
But, we know that, length can't ever be negative.
Therefore, x = 10
Hence, length of base = 10 ft.
Compute using long division: 342 ÷ 23
Answers
Start by setting it up with the divisor 23 on the left side and the dividend 342 on the right side like this:
2 3 ⟌ 3 4 2
Step 2:
The divisor (23) goes into the first digit of the dividend (3), 0 time(s). Therefore, put 0 on top:
0
2 3 ⟌ 3 4 2
Step 3:
Multiply the divisor by the result in the previous step (23 x 0 = 0) and write that answer below the dividend.
0
2 3 ⟌ 3 4 2
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (3 - 0 = 3) and write the answer below.
0
2 3 ⟌ 3 4 2
- 0
3
Step 5:
Move down the 2nd digit of the dividend (4) like this:
0
2 3 ⟌ 3 4 2
- 0
3 4
Step 6:
The divisor (23) goes into the bottom number (34), 1 time(s). Therefore, put 1 on top:
0 1
2 3 ⟌ 3 4 2
- 0
3 4
Step 7:
Multiply the divisor by the result in the previous step (23 x 1 = 23) and write that answer at the bottom:
0 1
2 3 ⟌ 3 4 2
- 0
3 4
2 3
Step 8:
Subtract the result in the previous step from the number written above it. (34 - 23 = 11) and write the answer at the bottom.
0 1
2 3 ⟌ 3 4 2
- 0
3 4
- 2 3
1 1
Step 9:
Move down the last digit of the dividend (2) like this:
0 1
2 3 ⟌ 3 4 2
- 0
3 4
- 2 3
1 1 2
Step 10:
The divisor (23) goes into the bottom number (112), 4 time(s). Therefore put 4 on top:
0 1 4
2 3 ⟌ 3 4 2
- 0
3 4
- 2 3
1 1 2
Step 11:
Multiply the divisor by the result in the previous step (23 x 4 = 92) and write the answer at the bottom:
0 1 4
2 3 ⟌ 3 4 2
- 0
3 4
- 2 3
1 1 2
9 2
Step 12:
Subtract the result in the previous step from the number written above it. (112 - 92 = 20) and write the answer at the bottom.
0 1 4
2 3 ⟌ 3 4 2
- 0
3 4
- 2 3
1 1 2
- 9 2
2 0
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 342 divided by 23 calculated using Long Division is:
14
The quotient after division is 322 and the remainder is 20.
What is long division?Long division is the mathematical method for dividing large numbers into smaller groups or parts.
Given that, 342 ÷ 23,
When we will divide 342 by 23, we will get,
The quotient 322 and the remainder is 20.
Hence, the quotient after division is 322 and the remainder is 20.
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Caroline surveyed 380 of the students in her school about their favorite color. 209 students said their favorite color was blue. What percentage of the surveyed students said their favorite color was blue?
Answers
Answer:
55% of the students surveyed said their favorite color was blue
Step-by-step explanation:
[tex]\frac{209}{380}[/tex] as a percent = 55%, or 0.55 in decimal form.
whats a better way to solve a polygon and what are the steps to it.
Answers
Hey there!
Calculating the exterior angles of regular polygons
To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°. The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where is the number of sides. All the interior angles in a regular polygon are equal.
Write an expression to b+b+b+b+b that is that a sum of two terms
Answers
Answer: 5b is your answer
Step-by-step explanation:
How many pounds are there in 2 3/4 tons? (1 ton = 2000 pounds)
Answers
Hello!
Answer:
There are 5500 pounds in 2 3/4 tons
Hope you luck!
What is the cf of 32 and 24?
Answers
Answer:
8
24 divided by 8 =3
32 divided by 8 =4
How can you solve the equation for 8(-3d+2)=88
Answers
Answer:
-3
Step-by-step explanation:
8(-3d + 2) = 88 divide both sides by 8
-3d + 2 = 11 rest 2 on both sides
-3d = 9 divide both sides by -3
d = -3
Answer:
i think D it's 110 cuz : 8×-3d and 8×2 = -24d+2=88 so D=88+24-2=110
2.4 Assignment 4
Alex has a job transporting furniture by truck. His truck is filled with tables that weigh 250 pounds each
and chairs that weigh 20 pounds each. There is a combined total of 300 tables and chairs in his truck.
Let x be the number of tables in his truck. Write an expression for the combined total weight (in
pounds) of the tables and chairs in his truck.
Choose one. 4 points
Total weight in pounds = 230.3 + 50
O
Total weight in pounds = -230.2 + 550
O
Total weight in pounds = -2302 + 75,000
O
Total weight in pounds = 2302 + 6000
Total weight in pounds = 230x + 75,000
Total weight in pounds = -230x + 50
O O
Total weight in pounds = -230x + 6000
Answers
Using a system of equations, it is found that the expression for the combined total weight is given by:
Weight = 250x + 20(300 - x).
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Number of tables in the truck.Variable y: Number of chairs in the truck.There is a combined total of 300 tables and chairs in his truck, hence:
x + y = 300 -> y = 300 - x
His truck is filled with tables that weigh 250 pounds each and chairs that weigh 20 pounds each, hence the total weight is:
Weight = 250x + 20(300 - x).
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What is the value of x? enter you answer in the box bellow.
Answers
If the same number is subtracted from both the numerator and the denominator of 13/17 , the result is 3/5 . Find the number.
Answers
Answer:
10/12?
Step-by-step explanation:
Mayela bought 3.4 pounds of almonds for 21.58. Approximately how many pounds of walnuts can mayela purchase for 1 dollar
Answers
Answer:
0.157
Step-by-step explanation:
She can buy 3.4 pounds for $21.58, so we will divide 3.4/21.58 to get 0.157 pounds per dollar.
What’s the Awnser cause I really don’t know
Answers
Answer:
Quest 1. is 5.5
Quest 2. is 48
Quest 3. is 7.5
Quest 4. is 6
Quest 5. is 8
Quest 6. is 9
Solve for x.
4x - 36
3x + 10
Answers
Answer:
x = 46
Step-by-step explanation:
Since the angles are equal to each other, make the equations equal to each other.
4x - 36 = 3x + 10 and simplify
x - 36 = 10
x = 46
Hope this helps!
The value of x is 46.
Since the angles are equal to each other, make the equations equal to each other.
4x - 36 = 3x + 10
First, let's move the term with 3x to the left side by subtracting 3x from both sides:
4x - 3x - 36 = 3x - 3x + 10
Simplifying further:
x - 36 = 10
Next, let's move the constant term -36 to the right side by adding 36 to both sides:
x - 36 + 36 = 10 + 36
Simplifying further:
x = 46
Therefore, the value of x is 46.
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Which rule describes the function in the graph below?
10
9
8
7
(4.6)
10,6
5
4
3
(-2,2
2
1
3
4 5
B 7
8 9
-7 -6 -5 -4 -3 -2 -14
Ni-
X, XS-2
Save and Exit
Next
Submit
Mark this and retum
Answers
Answer:THE ANSWER IS B ON 55th STREET NIFTY
Step-by-step explanation:
Maura added 5/8 of a cup of walnuts to a batch of trail mix. Later, she added 3/4 of a cup of almonds. How many cups of nuts did Maura put in the trail mix in all? Write your answer as a fraction or as a whole or mixed number. cups
Answers
Answer:
1 3/8 cups
Step-by-step explanation:
the equation is 5/8 + 3/4
to figure it out we need the same denominator, we'll be choosing 8
3 (x2)/ 4 (x2) = 6/8
you would have to multiply 2 both on the top and bottem
then you would have to add
5/8 + 6/8 = 11/8
then make that into a whole fraction
11/8 = 1 3/8
Rassan invests a sum of money in a savings account, with an interest rate of 4%. After 3 years, the balance reaches $1799.78. What is the amount of the initial investment? Round to the nearest whole dollar.
Answers
Answer:
I believe it is $1,607 hope it helps