Suppose a triangle has a side lengths AB, BC, and x where AB=2 • BC. Find the possible range for x in the terms of BC.

Answers

Answer 1

The possible range for x, in the terms, of BC is BC < x< 3BC.

Triangle Inequality Theorem

In mathematic, there is a rule for triangle side lengths. This rule says that the sum of the lengths of any two sides of a triangle is greater than the length of the one side (third side).  Therefore,

                                           [tex]L1+L2 > L3\; (1)\\ \\ L1+L3 > L2\; (2)\\ \\ L2+L3 > L1\; (3)[/tex]      

     

The question gives three sides: AB (L1), BC (L2) and x (L3). Also, you know that AB=2 BC.

Applying the equation (1) of rule for triangle side lengths, you have:

L1+L2> L3

AB+BC > x

2BC+BC > x

3BC > x

x< 3BC

Applying the equation (2) of rule for triangle side lengths, you have:

L1+L3 > L2

AB+x >BC

2BC+x > BC

x > -BC

Applying the equation (3) of rule for triangle side lengths, you have:

L2+L3 > L1

BC + x > AB

BC + x > 2BC

x > BC

The intersection of the inequalities results is the solution of this problem.  Then, the possible range for x, in the terms, of BC is BC < x< 3BC. See the attached image.

Read more about the triangle inequality theorem here:

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Suppose A Triangle Has A Side Lengths AB, BC, And X Where AB=2 BC. Find The Possible Range For X In The

Related Questions

Which is a TRUE statement about slope?

please help me with this

When a line increases as you read it from left to right, the slope of the line is negative.

When the slope of a line is negative, the y-values decrease as the x-values increase.

The slope of a line is always positive.

The slope of a line is never 0.

Answers

Answer:

when a line increases as you read it from left to right,the slope of the line is negative

Answer:

When a line increases as you read it from left to right, the slope of the line is negative.

Step-by-step explanation:

mark me as brainliest please

Start a 4 create a pattern that multiplies each number by 2 and subtracts 1. Stop when you have 5 number

Answers

Answer:

(0 x 2) - 1 = -1

(1 x 2) - 1 = 1

(2 x 2) - 1 = 3

(3 x 2) - 1 = 5

when does it become more efficient to buy another ticket book instead of additional individual tickets

Answers

Answer:

Because it’s easier to be alone than without friends if ur a depressed emo like me

Please help will give brainliest

Answers

Answer:

for freeee

Step-by-step explanation:

What is 1 2/3x4= PLS HELP

Answers

6 2/3. 1 2/3 * 4 = 20/6 which simplifies to 6 2/3. hope that helped :)

f(x)= {x+4 if x<5
{8 if 5 < or equal to x<7
{2x-1 if 7 < or equal to x < or equal to 10

for f(x), evaluate the following:
A. f(0)
B. f(6)
show all of your work.​

Answers

Answer:

  A.  f(0) = 4

  B.  f(6) = 8

Step-by-step explanation:

When evaluating a piecewise function, the fist step is to determine the applicable domain. Then the function defined for that domain is the one that is used for the evaluation.

A.

x = 0 is in the domain x < 5, so the applicable function is f(x) = x+4.

  f(0) = 0 +4 = 4

__

B.

x = 6 is in the domain 5 ≤ x < 7, so the applicable function is f(x) = 8.

  f(6) = 8

Write a+b as a difference.

Answers

Answer:

I think a-b.

Step-by-step explanation:

Hope it's help you ✨

There is no difference. They both refer to “the open interval from a to b”


Part A
The number sentences show a pattern in the sum of the fractions from 0 to 1 for different denominators
NTS
(a)
a
0 1 2.
+ +
2 2 2
1
2
b.
0 1 2 3
+
3
+ +
3 3
3
2.
Seven
C
0 1 2.
7
+ +
7
7 7
+ ...
4
7
d.
0
1
+
10 10
-+
2
10
+...
10 10
5
10
Based on this pattern, which equation will have a sum that is a whole number? Select the correct answer.

wa
A 0 1 2
+
5 5
+
= 1
B
1 2 6
+ +
6
6 6
с
0 1
2 2 8
+
8
8 8 8
1 2
12
+ + +
12 12 12 12
DON on
- + +
160
on 16 ICOS
OIN
--
NIN
---

Answers

Answer:

A. 012.+22212

Step-by-step explanation:

A because you use that to add

The equation having a sum that is a whole number is 0/5 + 1/5 + 2/5 + .... + 5/5

What is an whole number?

A whole number means a number that does not include any fractions, negative numbers or decimals.

Given that, number sentences show a pattern in the sum of the fractions from 0 to 1 for different denominators,

1) 0/5 + 1/5 + 2/5 + .... + 5/5 =

1/5(0 + 1 + 2 + 3 + 4 + 5) = 1/5(15) = 3 [whole number]

2) 0/6 + 1/6 + 2/6 + .... + 6/6 =

1/6(0 + 1 + 2 + 3 + 4 + 5 + 6) = 21/6 = 7/2 [fraction]

3) 0/8 + 1/8 + 2/8 + .... + 8/8 =

1/8(0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) = 36/8 = 9/2 [fraction]

4) 0/12 + 1/12 + 2/12 + .... + 12/12 =

1/12(0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12) = 78/12 = 13/2 [fraction]

Hence, the equation having a sum that is a whole number is 0/5 + 1/5 + 2/5 + .... + 5/5

Learn more about whole number click;

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The complete question is attached

294 students went on a field trip. Five buses were filled and 14 students travelled in cars. How many students were in each bus?
Use algebra (variables) to solve this question.
Please do not skip steps

Answers

5x + 14 = 294

5x = 280

x = 280 / 5

x = 56

56 students per bus

The second angle of a triangle is 95 more than the first angle. The third angle is three times the first. Find the three angles.

Answers

Answer: hope this helped!

Step-by-step explanation:

the clues for set up are all right in front of you:

x= first angle's measurement

x+5 = second angle's measurement

3x = third angle's measurement.

Their sum is 180 degrees; thus you can add the three expressions to get an equation that you can solve.

Learn from this example, please.

A clock's minute hand travels one full circle each hour. A particular clock's minute hand is 10. 2 cm. What is the approximate area covered by that minute hand in 3 hours? Use 3. 14 for π. 192. 17 cm² 326. 69 cm² 980. 06 cm² I don't know.

Answers

In three hours, it will cover 3 full circles. Then the area of the circle covered in three hours is 980.55 cm².

What is a circle?

It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

A clock's minute hand travels one full circle each hour.

A particular clock's minute hand is 10.2 cm.

In one hour, it covers one full circle. Then in three hours, it will cover 3 full circles.

The area of the circle covered in three hours will be

[tex]\rm Area \ of \ circle \ in\ 3\ hours = 3 * area\ of\ one\ circle\\\\Area \ of \ circle \ in\ 3\ hours = 3*\pi r^2\\\\Area \ of \ circle \ in\ 3\ hours = 3*\pi*10.2*10.2\\\\Area \ of \ circle \ in\ 3\ hours = 980.55[/tex]

More about the circle link is given below.

https://brainly.com/question/11833983

2and2/3 divided by 2/3

Answers

Answer:

4

Step-by-step explanation:

[tex]2\frac{2}{3}\div \frac{2}{3}[/tex]

[tex]\mathrm{convert\;mixed\;numbers\;to\;improper\;fractions:2\frac{2}{3}=\frac{8}{3}}[/tex]

[tex]=\frac{8}{3}\div \frac{2}{3}[/tex]

[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]

[tex]=\frac{8}{3}\times \frac{3}{2}[/tex]

[tex]\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}[/tex]

[tex]=\frac{8\times \:3}{3\times \:2}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:3[/tex]

[tex]=\frac{8}{2}[/tex]

[tex]\mathrm{Divide\:the\:numbers:}\:\frac{8}{2}=4[/tex]

[tex]=4[/tex]

~Learn with Lenvy~

Find the inverse of the function.
Y = 2x2 4

Answers

Answer:

To find inverse functions, switch the two variable and solve for y:

Step-by-step explanation:

x=2y²-4

x+4=2y²

(x+4)/2=y²

√((x+4)/2)=y

Hope this helps!

Answer:

q1, b ;q2, c

Step-by-step explanation:

PLEASE HELP ASAP, WILL GIVE BRAINLIEST!

If the area of this circle is 12, what is the area of the colored sector?

Answers

Answer:6

Step-by-step explanation:

since it is A half circle it is the hhalf Value of the area of the full circle

6
Half of a circle which the whole value is 12 and half of 12 is 6

What model describes the relationship between the amount of money in an account and time, given that the money triples every month

Answers

An algebraic equation that has variables for money and time

A swimming pool has a length of 28 feet, a width of 16 feet, and a depth of 7 feet.

How much water can the swimming pool hold?

Answers

Answer:

The pool can hold 3,136 cubic feet of water

Step-by-step explanation:

To know how much water the pool can hold,  we need to find the volume of this swimming pool, because the volume is how much a container can hold.

The formula for volume is L*W*H (length times width times height)

Let's multiply!

28*16*7=3136

Wich is an equation of the line with a slope of 1/4 and a y-intercept of -2​

Answers

Answer: y = 1/4x -2.

Step-by-step explanation: The formula for these types of equations is y = mx + b, where m is the slope and b is the y-intercept.  The slope, in this case, is 1/4 and the y-intercept is -2.  The equation of the line for this problem is y = 1/4x - 2.

Hope this helps! :)

5.8×10^7 bacteria are measured to be in a dirt sample that weighs 1 gram. Use scientific notation to express the number of bacteria that would be in a sample weighing 18 grams.

Answers

if Ibacteria are measured to be in a dirt sample that weighs 1 gram, Then he sample of bacteria that would be in a sample weighing 18 grams t is mathematically given as

x=1.044×10^9

What is the sample of bacteria that would be in a sample weighing 18 grams?

Question Parameter(s):

5.8×10^7 bacteria are measured to be in a dirt sample that weighs 1 gram.

Generally, the equation for the statement  is mathematically given as

5.8×10^7=1g

x=18grams

Therefore

x=\frac{5.8×10^7*18}{1}

x=1.044×10^9

In conclusion,  the sample of bacteria is

x=1.044×10^9

Read more about mass

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Evaluate the expression.

4x−5 for x=10
Enter the correct answer in the box.

Answers

Step-by-step explanation:

Substitute the given value of x into the expression;

[tex]4(10)-5[/tex]

Multiply;

[tex]40-5[/tex]

Subtract;

[tex]35[/tex]

Evaluate. Answer has to be in scientific notation

(8 x 10^6) + (7.3 x 10^4)

Answers

Answer:

8.0730000*10^6

Answer:

8,073,000

=8.1 × 10⁶

Step-by-step explanation:

The answer is above

Start at (5, 4). Move 5 units east, 4 units south, 4 units west, 4 units north, and 1 unit west.
What is the ordered pair of the final point?

Answers

Using translation concepts, it is found that the ordered pair of the final point is given by:

D. (5,4).

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this situation, considering that we start at point (5,4), the translations are as follows:

5 units east, hence x = x + 5 = 10.4 units south, hence y = y - 4 = 0.4 units west, hence, x = x - 4 = 6.4 units north, hence y = y + 4 = 4.1 unit west, hence x = x - 5 = 5.

It ends at the starting point, hence option D is correct.

More can be learned about translation concepts at https://brainly.com/question/4521517

What does X equal in this 30-60-90 triangle?

Answers

Answer:

19/2, or 9.5

Step-by-step explanation:

It's half of the longest side (You can see by flipping the triangle on the side between the 30 and the 90 angle, and notice that you get two halves of an equilateral triangle). In our case, its [tex]\frac {19}2 = 9.5[/tex]

Gary bought a bond with a face value of $12,000 and a coupon rate of 6.5%. The bond will mature in 10 years.

How much interest will he receive semiannually?

A) $780
B) $650
C) $468
D) $390​

Answers

Answer:d

Step-by-step explanation:

12,000 x 6.5% = 780 divided by 2 =390

D. $390​

May I get brainliest please? :)

Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. A ze-0.822-121 The area of the shaded region is (Round to four decimal places as needed.)

Answers

The area of the shaded region is 0.1271 (12.71%).

What is the z score?

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean)/standard deviation

Given:

Mean 0 and standard deviation 1. Hence, for z=-1.14:

P(z < -1.14) = 0.1271

The area of the shaded region is 0.1271 (12.71%).

Find out more on z score at: https://brainly.com/question/25638875

2 more than the difference between 8 and h

Answers

8-h+2

hope this helped! :)

x+5÷2=1 how to solve it. ​

Answers

               my mistake wrong answer, sorry                                                            

                       

                                                       

50 is the same as the quotient of p
and 10.

Answers

Answer:

500 divided by 10 = 50

Step-by-step explanation:

quotient means the answer of a division problem 50 is the quotient of 500 being divided by 10

Answer:

Setting this up;

50 = p/10

Step-by-step explanation:

Using the keywords;

'same as'

'quotient of'

and 'of p', we can determine how to format this expression.

Terry has an investment account which compounds interest continuously at an annual interest rate of 1. 4%. After 3 years, he has $1700 in the account. How much money did he initially place in the account? Round your answer to the nearest dollar. Do NOT round until you've calculated the final answer

Answers

Answer:

  $1,630.08

Step-by-step explanation:

The value of an amount earning interest continuously compounded is given by the formula ...

  A = Pe^(rt)

The value of P can be found by dividing by its coefficient:

  P = A/(e^(rt)) = Ae^(-rt)

  P = $1700·e^(-0.014·3) ≈ 1630.0786

Terry placed $1,630.08 in the account.

CHALLENGE Randi and her sister made balloon animals and sold them for $0.50 each at
a school carnival. They made $48.00. If Randi made twice as many balloon animals as
her sister, how many balloon animals did each girl make? Show your work.

Answers

Just need to set up an equation.
List what we know Randi made twice what sister did.

So 2X = Randi balloons made
X= Sister balloons made
We also know they made 0.5 for each animal so sales made / price = number sold
2X + X = 48/0.5
3X = 96
X = 32
So Randi made 64 And her sister made 32.
Cause 2X = Randi and X = sister

Select all the following that describe the association in the scatter plot

Answers

Answer:

C) positive association

Step-by-step explanation:

draw a line if these points gather around a line there is a relationship . The slope of the line is positive .So graph positive correlation .

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