Which of the following sets of numbers could represent the three sides of a triangle?​

Which Of The Following Sets Of Numbers Could Represent The Three Sides Of A Triangle?

Answers

Answer 1

Answer:

{5, 15, 19}

Step-by-step explanation:

According to the triangle inequality theorem, the sum of the lengths of any two sides of a ∆ must be greater than the length of the third side.

Thus, any of the given sets of numbers will represent the 3 sides of a ∆, if the following condition is satisfied:

a + b > c

b + c > a

a + c > b

Where a and b are the smaller side lengths, and c is the length of the longest side.

Let's check each set of numbers given to see if any satisfies this condition.

✍️Option 1: {6, 20, 28}

6 + 20 is not greater than 28

20 + 28 > 6

6 + 28 > 20

❌This set of numbers does not represent the sides of a ∆.

✍️Option 2: {4, 11, 15}

4 + 11 = 15

11 + 15 > 4

4 + 15 > 11

❌This set of numbers does not represent the sides of a ∆.

Option 3: {9, 19, 30}

9 + 19 is not greater than 30

19 + 30 > 9

9 + 30 > 19

❌This set of numbers does not represent the sides of a ∆

Option 4: {5, 15, 19}

5 + 15 > 19

15 + 19 > 5

5 + 19 > 15

✅This set of numbers does not represent the sides of a ∆

Only option 4, satisfied the condition stated earlier, therefore, based on the triangle inequality theorem, {5, 15, 19}, is the set of numbers that represents the 3 sides of a triangle.


Related Questions

You begin the week with 30 units of orange juice. You purchase 50 units. Your ending inventory for the week is 30 units. How many units did you sell?
a) 5
b) 15
c) 49
d) 50

Answers

Answer:

D

Step-by-step explanation:

30 from the beginning of the week plus 50 that you bought.

80-x=30

50=x

Answer is D

Answer:50

Step-by-step explanation:

30+50=80

80-30=50

So he sell 50

What is the value of x?
HELP! Please

Answers

D. 68
I don’t remember what formula this is called but the formula says that all angles in a triangle should add up to 180, so 75+37= 112, 180-112= 68

Answer:

a. 68

Step-by-step explanation:

You just have to subtract these two numbers from 180 because adding all the angles of a triangle the resulta is 180. Subtracting those numbers from 180 will give you the result.

What is the result when the number 40 is decreased by 10%?

Answers

Answer:

it would be 36

Step-by-step explanation:

Your bank pays 4% annual interest compounded quarterly on January 1, April 1, July 1, and October 1. You deposited $840 on April 1 and made no other deposits or withdrawals. Find your savings account balance on January 1 of the next year.
and
Your bank pays 4% annual interest compounded quarterly on January 1, April 1, July 1, and October 1. You deposited $840 on April 1 and made no other deposits or withdrawals. How much interest did you earn for these nine months?

Answers

Answer:

The interest earned in 9 months is $25.45284

Step-by-step explanation:

The interest rate given by the bank = 4%

The rate at which the interest is applied = Quarterly

The amount of money deposited = $840

The formula for compound interest is given as follows;

[tex]Compound \ interest = P \times \left [ \left(1 + \dfrac{r}{n} \right )^{t \times n} - 1\right ][/tex]

Where;

P = The principal = $840

r = The rate = 4% = 0.04

n = The number of times the interest is compounded per period  = quarterly = 4

t = The time duration in period = 9 months = 3/4 × 1 year

Substituting the values gives the Compound interest C.I. as follows;

[tex]C.I. = 840 \times \left [ \left(1 + \dfrac{0.04}{4} \right )^{\dfrac{3}{4} \times 3} - 1\right ] = 840 \times \left [ \left(1 + \dfrac{0.04}{4} \right )^{ 3} - 1\right ] = \$ 25.45284[/tex]

The interest earned in 9 months = $25.45284.

Clea estimates that a glass contains 250.55 mL of water. the actual amount of water in the glass is 279.48 mL. To the nearest tenth of a percent what is the percent error in Clea's estimate?

Answers

honestly anna made a scale drawing, in inches, of a building using a scale of 1:600. her scale drawing was 6 inches long. Greg made a scale drawing of the same building using a scale of 1:300. how long, in inches, was greg’s scale drawing.

Which one??? I need help. Be serious please

Answers

Answer:

c

Step-by-step explanation:

10+12=22

=22^2

=484

Answer:

I believe the answer is C or D.

Step-by-step explanation:

need rn! worth 13 ~ what is the equation of the parabola? 謝謝

Answers

Answer:

Its B.

Step-by-step explanation:

Emath.com- Parabola calculator

A rectangle has a length that is three feet more than twice it's width. The perimeter of the rectangle is 78 feet. State the value for the width.

Answers

Let the width of the rectangle be 'w'

According to the question length of the rectangle (l) is three feet more than twice it's width;

[tex] \longrightarrow [/tex] l = (2w + 3) ft

Perimeter of rectangle = 78 ft

Formula of perimeter of rectangle = 2(Length + Width)

So,

[tex] \rm \implies 2(Length + Width) = 78 \\ \\ \rm \implies 2(2w + 3 + w) = 78 \\ \\ \rm \implies 2(3w + 3) = 78 \\ \\ \rm \implies 2 \times 3(w + 1) = 78 \\ \\ \rm \implies 6(w + 1) = 78 \\ \\ \rm \implies w + 1 = \dfrac{78}{6} \\ \\ \rm \implies w + 1 = 13 \\ \\ \rm \implies w = 13 - 1 \\ \\ \rm \implies w = 12 \: ft[/tex]

[tex] \therefore [/tex] Width of the rectangle (w) = 12 ft

The ratio of red marbles to blue marbles in a bag is 2 to 3. Which of the following could be the number of red and blue marbles in the bag?

Answers

Answer:

4 red marbles and 6 blue marbles

Step-by-step explanation:

Multiply any numbers to 2 and 3 and you get another ratio.

(please i'm taking a test) A fraction is never a rational number true or false

Answers

The answer is false because a fraction can not be regional

The Giant Anteater can eat 70,000 ants in 2 days. It’s true

Answers

Answer:

cool

Step-by-step explanation:

is this a question?

I WILL GIVE BRAINLIEST FOR CORRECT ANSWER!!!

Jada fills the bathtub before taking a bath and then allows the water to drain when she is done. The graph below models the number of gallons of water, y, in the bathtub over time, t, in minutes. (look at graph)


Is the number of gallons of water in the bathtub a function of time?

A)Yes because each t value is paired with exactly one number of gallons.
B)Yes because the number of gallons is bounded between y = 0 and y = 36.
C)No because each number of gallons is paired with more than one t value.
D)No because from t = 5 to t = 20 the number of gallons of water is constant.

Answers

A.Yes because each t value is paired with exactly one number of gallons.

Step-by-step explanation:

Yes  the number of gallons of water in the bathtub a function of time because each t value is paired with exactly one number of gallons.

Option A

Given :

The graph below models the number of gallons of water, y, in the bathtub over time, t, in minutes.

The number of gallons of water in bathtub depends on the time taken to fill or drain water

For each minutes in x  there is one y value

There is no break in the graph . For each x  value there is only one value

From this graph we can say that , for each t value (minutes)  there is exactly one number of gallons (y value )

So, yes because each t value is paired with exactly one number of gallons.

Learn more :  brainly.com/question/19620324

What is the value of x in the equation Negative two-thirds x + 9 = four-thirds x minus 3?

Answers

Answer:the answer is x=6

Step-by-step explanation:

I alr did the quiz for this question on edg 2020

Answer:

x= 6

Step-by-step explanation:

LuAnn is playing a math game. She chooses three cards. The value of each of her cards is shown. • First card: -12 • Second card: 3 • Third card: -5 What is the sum of the values of LuAnn's three cards?

Answers

The sum of all the cards of Luann is -14.

One of the four fundamental operations for arithmetic on integers, decimals, fractions, real and complex numbers, as well as in algebraic expressions or on structures related to them, including vector spaces, is sum (also known as addition).

The terms, addends, or summands collectively refer to the numbers or objects that need to be added in general addition; this nomenclature also applies to the summation of several terms. This should be distinguished from multiplied factors.Addition or sum follows the commutative , associative and distributive properties.

The given numbers on the cards are given as - 12 , 3 and - 5 .

Therefore the addition or sum is equal to :

-12 + 3 + ( - 5 ) =  - 17 + 3 = - 14

Hence the sum of all the cards in LuAnn's card games is -14.

To learn more about sum visit:

https://brainly.com/question/537797

#SPJ1

CAN SOMEONE PLZ HELP

Answers

Answer:

(x, y, z) = (2, -1, 3)

Step-by-step explanation:

I solved it using the elimination method

negative four times the sum of a number and 3 is at least 28, translate.

Answers

Answer: [tex]-4 * (n+3) \geq 28[/tex]

Step-by-step explanation:

Negative four -> [tex]-4[/tex]

Times the sum of a number and 3 -> [tex]-4 * (n + 3)[/tex]

Is at least 28 -> [tex]-4 * (n+3) \geq 28[/tex]

What is mZCAD?
O 80°
O 20°
O 80°
O 100°
O 110°

Answers

Answer:

The angle of CAD is 100°.

Step-by-step explanation:

Given that total angles in a triangle is 180° so you will have to find the angle of CAB :

∠CAB + ∠ACB + ∠ABC = 180°

∠CAB + 80° + 20° = 180°

∠CAB + 100° = 180°

∠CAB = 180° - 100°

∠CAB = 80°

Next, you have to subtract it from 180° because straight line have a degree of 180°

∠CAD = 180° - 80°

∠CAD = 100°

what percent is 30 of 20

Answers

Answer:

1.5

Step-by-step explanation:

Lmk if i need to explain!

20points- Correct answer get Brainlest- Help please-Thank you- :)


Of all students, calculate the relative frequency for males who carpool.


Gender School Transportation Survey

Walk Ride Bus Carpool Total

Male 9 26 9 44

Female 8 26 24 58

Total 17 52 33 1



0.204

33

0.088

9

Answers

Answer:

0,204

Step-by-step explanation:

What is the awnser to that question

Answers

Answer:

C. 2 and 5

Step-by-step explanation:

WILL REWARD Christina has already spent 2 minutes on the phone, and she expects to spend 2 more
minutes with every phone call she routes. Write an equation that shows the relationship
between the phone calls routed p and the minutes on the phone t.
Write your answer as an equation with t first, followed by an equals sign.

Answers

Answer:

t=2x+ 2

Step-by-step explanation:

x is every phone call 2 is how many minutes she spends on each call The other 2 is the 2 minutes she already spended

Answer:

Step-by-step explanation:

t=2+2p

What is the correct answer? ​

Answers

The answer is Cccccccccccccccccccccc

Answer:

C)  y = 10/3x - 5

Step-by-step explanation:

Slope intercept equation is y = mx + b:

    m is the slope

    b is y-intercept

When you read slope you can also read it as rise over run. Rise is move up or down on the y axis depending if number is negative or positive. Run is move left or right on x axis depending if number is negative or positive.

Example: y = [tex]\frac{10}{3} x - 5[/tex]

Start at the y-intercept which is -5. On graph you can see the line crosses the y axis at (0, -5). From this point rise 10 then run 3 you'll end up at point (3, 5). Connect the dots of the two points and you'll see a line like the one in the problem.

help me plzzzz lzzzzzzzzzz

Answers

Answer:

2 to the 8th power

Step-by-step explanation:

When there are parenthesis, for exponents, you have to multiply the exponents. 2*4=8

In triangle DEF, segment DJ is a perpendicular bisector of side EF. If EJ is 3y-8 and JF is 7y-40, what is the length of JF?

Answers

Answer: The length of JF = 16 units.

Step-by-step explanation:

Given: In triangle DEF, segment DJ is a perpendicular bisector of side EF.

i.e. DJ is perpendicular to EF and DJ divides EF into two equal parts EJ and JF. [The perpendicular bisector is a line that is perpendicular to a line segment and splits it into two congruent segments.]

If  EJ is 3y-8 and JF is 7y-40.

Then, [tex]3y-8=7y-40[/tex]

[tex]\Rightarrow\ 7y-3y=40-8\\\\\Rightarrow\ 4y=32\\\\\Rightarrow\ y=8 \text{ [Divide both sides by 4]}[/tex]

JF= 7(8)-40 =56-40= 16 units

Hence, the length of JF = 16 units.

Answer:

plz giv brainlist

Step-by-step explanation:

PROBLEM SOLVING Find the value of k so that the graph of the equation has the given y-intercept.
y = -1/3x + 5/6k; b = - 10

K=?

Answers

Answer:

2k⋅(3k−7)⋅(k+4)

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

 ((6 • (k3)) +  (2•5k2)) -  56k

STEP

2

:

Equation at the end of step

2

:

 ((2•3k3) +  (2•5k2)) -  56k

STEP

3

:

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  6k3 + 10k2 - 56k  =   2k • (3k2 + 5k - 28)

Trying to factor by splitting the middle term

4.2     Factoring  3k2 + 5k - 28

The first term is,  3k2  its coefficient is  3 .

The middle term is,  +5k  its coefficient is  5 .

The last term, "the constant", is  -28

Step-1 : Multiply the coefficient of the first term by the constant   3 • -28 = -84

Step-2 : Find two factors of  -84  whose sum equals the coefficient of the middle term, which is   5 .

     -84    +    1    =    -83

     -42    +    2    =    -40

     -28    +    3    =    -25

     -21    +    4    =    -17

     -14    +    6    =    -8

     -12    +    7    =    -5

     -7    +    12    =    5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  12

                    3k2 - 7k + 12k - 28

Step-4 : Add up the first 2 terms, pulling out like factors :

                   k • (3k-7)

             Add up the last 2 terms, pulling out common factors :

                   4 • (3k-7)

Step-5 : Add up the four terms of step 4 :

                   (k+4)  •  (3k-7)

            Which is the desired factorization

Final result :

 2k • (3k - 7) • (k + 4)

Stephen ran a race that was 5 miles long . he ran 1/4 of a mile in 1/8 of an hour . he ran the same pace the entire race , how long , in hour did it take Stephan to run the entire race ?

Answers

Answer:

1/2 hour

Step-by-step explanation:

he ran 1.25 miles in 7.5 mins

so

1.25x=37.5

x=30 MINS

30 mins =.5 hours or 1/2 hours

PLEASE HELP, MARKING BRAINLIEST!!!!

What is the value of x? *Please show your work if you can.*

Answers

Answer:

I think 100..........

(I will give branliest please help me)
Which linear equation represents a line that is parallel to the line drawn and includes point P?
y = 42 - 4
4x + 3y = 15
y=-30 +3.25
-3. + 4y = -5

Answers

the second one I think

13) (-4.3) (2,-1)
slope formula

Answers

Answer:

[tex]3 - ( - 1) \div 2 - ( - 4) \\ 3 + 1 \div 2 + 4 \\ 4 \div 6 \\ = \frac{2}{3} [/tex]

7. What is the area of the shaded region?
5.6 cm
6.4 cm
5.8 cm
1.2 cm
0.8 cm

Answers

5.12+7.68+2.88 I’d say somewhere around 13.12cm I can’t see all the answers
Something around 13 or 14
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