Which of the following sets of numbers could represent the three sides of a triangle?
Answers
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
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:
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
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:
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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
(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
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
What is the value of x?
HELP! Please
Answers
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.
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
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.
What is the awnser to that question
Answers
Answer:
C. 2 and 5
Step-by-step explanation:
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:
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]
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
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)
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°
PLEASE HELP, MARKING BRAINLIEST!!!!
What is the value of x? *Please show your work if you can.*
Answers
Answer:
I think 100..........
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]
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
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.
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
what percent is 30 of 20
Answers
Answer:
1.5
Step-by-step explanation:
Lmk if i need to explain!
CAN SOMEONE PLZ HELP
Answers
Answer:
(x, y, z) = (2, -1, 3)
Step-by-step explanation:
I solved it using the elimination method
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:
What is the result when the number 40 is decreased by 10%?
Answers
Answer:
it would be 36
Step-by-step explanation:
(please i'm taking a test) A fraction is never a rational number true or false
Answers
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
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.
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:
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?