Can a triangle be constructed with sides 2.5 cm 3.0 cm and 6.5 cm give reason?

Answers

Answer 1

We cannot construct a triangle with side lengths 2.5 cm, 3.0 cm and 6.5 cm as they don't follow the Triangle Inequality Theorem.

It is not possible to construct a triangle using the given side lengths of 2.5 cm, 3.0 cm, and 6.5 cm. This is because of the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, if we take 2.5 cm and 3.0 cm as two sides, the sum of their lengths is 5.5 cm. But the length of the third side (6.5 cm) is greater than 5.5 cm, so these three side lengths cannot form a triangle.

It is important to note that this theorem applies to any triangle, whether it is acute, right or obtuse-angled triangle. It is also important to note that this theorem is necessary for the formation of a triangle, and without it, it would not be possible to form a triangle.

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Related Questions

mAFD=90 mAFB=31 Find mCFE

Answers

The value of angle CFE in the diagram attached is 51 degrees.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

From the diagram:

∠AFB = ∠CFD; ∠BFC = ∠DFE

Hence:

∠AFC = ∠CFE

∠AFD = ∠AFC + ∠CFD = ∠AFC + ∠AFB

90 = ∠AFC + 31

∠AFC = 51° = ∠CFE

The value of angle CFE in the diagram attached is 51 degrees.

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Match the vocabulary word with the correct definition.

1. a line segment where two faces meet
edge
2. a three-dimensional figure with one circular base
dimensions
3. to separate something into its basic parts
area
4. units used to measure the volume of a three-dimensional figure
cube
5. a three-dimensional figure with two parallel, congruent, circular bases and a curved surface
decompose
6. a three-dimensional figure made of six congruent squares
composite figure
7. a geometric figure that is made up of two or more basic shapes
base
8. the length of a plane figure; or, a special face of a solid figures
cone
9. the measurement of the space inside a plane figure
cylinder
10. measurements indicating the size and shape of an object, such as length and width
cubic units

Answers

Answer:

1. edge

2. cone

3. decompose

4. cubic units

5. cylinder

6. cube

7. composite figure

8. base

9. area

10. dimensions

can someone please help mee

Answers

Answer:

I think that this answer is 22

according to the graph, what is the value of the constant in the equation below?

Answers

Answer: B

Step-by-step explanation:

The product of height and width is constant.

If we take the point (0.5,1), we get the product to be 0.5.

During a pumpkin launching contest, two pumpkins are launched at the same time. the path of pumpkin a is modeled by the equation y = –0.01x2 0.32x 4. the path of pumpkin b is modeled by the equation y = –0.01x2 0.18x 5. if x represents the distance the pumpkin traveled in feet and y represents height of the pumpkin in feet, what does the intersection point of the equations represent?

Answers

The distance at which pumpkins are the same height.

What do you mean by X and Y coordinates?

The X and Y coordinates are an address that help locate a point in two dimensions of space. The coordinates (x, y) are used to represent any point in the coordinate plane. The x value indicates the point's position in regard to the x-axis, and the y value indicates its position in relation to the y-axis.

Solution

Both equations' graphs would be at an intersection, which would indicate that their x and y coordinates are identical. The same y coordinate would indicate being at the same height at that precise distance since y refers to the pumpkin's height.

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Answer:

D). the horizontal distance of the pumpkins from the launch site when their heights are the same

Step-by-step explanation:

I took the flipping test nickle

Graph the quadratic function by transforming the graph of f(x) = x^2. Give the minimum or maximum
vertex value and the equation for the axis of symmetry.

Answers

Answer: the maximum is (-2,5 )and the equation for the axis of symmetry is  x = -2

Explanation if you want:

for the min and max:  when a quadratic has a maximum point, that is the largest point that it will ever be at.  When it has a minimum, that is the smallest.

the +5 tells us that we have an upward movement of 5. The +2 means we actually move to the point -2.  bc: (x+2)=0 = -2so, from our initial function, those are the changes.

for the axis of symmetry: basically, this is the line that splits the graph into two equal parts.

it is the line that goes through the vertex (which we already know is (-2,5).

there u go

If 0 is greater than f but less than or equal to 90, and cos(22f-1) = sin(7f+4), what is the value of f?

Answers

The value of f from the given expression is 3

Sine and cosine function

Given the expression below

cos(22f-1) = sin(7f+4),

This can also be expressed

cos(22f-1) = cos(90-7f-4)

cos(22f-1) = cos(86-7f)

22f - 1 = 86 - 7f

Collect the like terms

22f+7f = 86 + 1

29f = 87

f = 3

Hence the value of f from the given expression is 3

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write the slope-intercept form of the equation of each line

1. 9x -7y = -7

2. 11x -4y = 32

3. 11x -8y =-48

Answers

Answers
1. y=9/7x +1
2. y= 11/4x -8
3. y= 11/8x +6
See work in attachment

A right-triangle has the hypotenuse length of 5 units long. One of the other sides of the triangle is 3 units. What is the length of the remaining side

Answers

Answer:

4

Step-by-step explanation:

[tex] {3}^{2} + {x}^{2} = {5}^{2} \\ \\ 9 + {x}^{2} = 25 \\ \\ {x}^{2} = 16 \\ \\ x = 4[/tex]

Which inequality can be used to explain why these three segments cannot be used to construct a triangle? ac ab > cb ac cb < ab ac cb > ab ac ab < cb

Answers

The response option that demonstrates why the three segments cannot be combined to form a triangle is AC + CB< AB.

What is triangle inequalities?

According to the triangle inequality, the length of any two sides of a triangle added together must be longer than the length of the third side. Since a straight line is the shortest distance between two places, this conclusion follows. If the triangle isn't degenerate, the inequality is strict (meaning it has a non-zero area).

Which inequality explains why a triangle cannot be made from the three segments?

Since the length of any two sides of a triangle added together is longer than the length of the third side, it follows from the triangle inequalities theorem that this is the case.

As a result, the necessary inequality is AC + CB AB because the sum of sides AC + CB is less than AB.

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I understand that question you are looking for is:

Which inequality can be used to explain why these three segments cannot be used to construct a triangle?

A. AC + AB > CB

B. AC + CB < AB

C. AC + CB > AB

D. AC + AB < CB

Which of the following parabolas has its vertex the furthest away from the x-axis
Oy
x² - 1
y = 3x² + 4
Oy
=
Y =
1/2x²
Oy = x² - 10
Question 12 (1 point)

Answers

Answer:

y=x^2-10

Step-by-step explanation:

URGENT, PLEASE ANSWER THESE QUESTIONS

Answers

Can send helicopter 3 but not helicopter 1 and 2.

What is distance formula?

Consider two points (x1, y1) and (x2, y2) in the two-dimension, then the distance between these two points is given by,

[tex]d=\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

We will solve given problem as shown below:

Let fire have coordinate F (-3,-5)

Let Helicopter 1 have coordinate H1(1,4)

Let Helicopter 2 have coordinate H2(-2,3)

Let Helicopter 1 have coordinate H3(4, -2)

A. Distance between helicopter 1 and fire

[tex]=\sqrt{(1-(-3))^2+(4-(-5))^2}[/tex]

[tex]=\sqrt{16+81}[/tex]

[tex]=\sqrt{97}=9.8[/tex]

No, cannot send helicopter 1

B. Distance between helicopter 2 and fire

[tex]=\sqrt{(-3-(-2))^2+(-5-3)^2}[/tex]

[tex]=\sqrt{1+64}[/tex]

[tex]=\sqrt{65}=8.06[/tex]

No, cannot send helicopter 2

Distance between helicopter 3 and fire

[tex]=\sqrt{(4-(-3))^2+(-2-(-5))^2}[/tex]

[tex]=\sqrt{49+9}[/tex]

[tex]=\sqrt{58}=7.6[/tex]

Yes, can send helicopter 3

Hence, can send helicopter 3 but not helicopter 1 and 2.

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The sum of two numbers is 140, and their difference is 20. What are the two numbers?

Answers

Answer:

60 and 80.

Step-by-step explanation:

If the numbers are x and y:

x + y = 140

x - y = 20     Adding:

2x = 160

x = 80

So y =  140 - 80 = 60.

Answer:

80 and 60

Step-by-step explanation:

Expressing the Word Problem mathematically.

Let the first number be X.

Let the second number be Y.

From the question,

[tex]x + y = 140 - - - - - (1) \\ x - y = 20 - - - - - (2) \\ From \: equation \: (2) \\ x = 20 + y - - - - - - (3) \\ Substitute \: equation \: 3 \: into \: 1 \\ 20 + y + y = 140 \\ 20 + 2y = 140 \\ 2y = 140 - 20 \\ 2y = 120 \\ Dividing \: bothsides \: by \: 2 \\ \frac{2y}{2} = \frac{120}{2} \\ y = 60 \\ Substitute \: y \: into \: quation \: 3 \\ x = 20 + 60 \\ x = 80 \\ Therefore, \: x = 80 \: and \: y = 60[/tex]

The two numbers are 80 and 60

An entomologist can model the number of mosquitos in a forest as a function of
rainfall. In a similar way, they can also model the number of bats in the forest.
The function f(x) = 5x
22
gives the number of mosquitos in the forest (in
millions), and the function g(x) = 3a 0.5a² gives the number of bats (in millions
-
In both equations z represents rainfall (in centimeters). Here are the graphs of f and
G

Answers

The interpretation of the point of intersection of the curves is (c) they give a solution to the equation 5x - x^2 = 3x - 0.5x^2

How to interpret the points of intersection?

The graph of the two functions alongside their equations are the given parameters of this question

The functions are given as:

f(x) = 5x - x^2

g(x) = 3x - 0.5x^2

When the graphs of two curves or lines intersect on a coordinate plane, it means that the point of intersection represents where the graphs have equal value

In this case, it represents

f(x) = g(x)

Substitute the known values in the above equation

5x - x^2 = 3x - 0.5x^2

So, the interpretation of the point of intersection of the curves is (c) they give a solution to the equation 5x - x^2 = 3x - 0.5x^2

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There are 24 students in a class. if 16 are boys, what fraction of the students are boys?

Answers

Answer:

2/3 is the fraction of students who are boys.

Step-by-step explanation:

First of all, a fraction consists of two parts: The denominator and the numerator. The denominator is the whole, while the number is a part of the whole (and sometimes above).

1. Since in your question, there are 24 students in total in the class, the denominator will be 24.

2. You said that 16 of them are boys, so 16 is the numerator.

3. In a fraction, it will be 16/24.

4. 16/24 can be simplified into 2/3 since both 16 and 24 can be divided by 8.

So our final answer is 2/3.

1 x/3 - 3/4 = 5/12
solve for x!

Answers

The value of x is 7/2

How to solve for x?

The equation is given as:

x/3 - 3/4 = 5/12

Multiply through by 12

4x - 9 = 5

Add 9 to both sides

4x = 14

Divide by 4

x = 7/2

Hence, the value of x is 7/2

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What is the solution to 9|x + 8| > 45?

Answers

The solution to the inequality is x > -3 or x < -13

How to solve the inequality?

The inequality is given as:

9|x + 8| > 45

Divide through  by 5

|x + 8| > 5

Split the inequality

x + 8 > 5 or x + 8 < -5

Solve for x

x > -3 or x < -13

Hence, the solution to the inequality is x > -3 or x < -13

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From Andys house to Billys hometown you can travel by 3 roads. And to get from Billys hometown to Willies's house you can travel by 5 roads. How many possible wats are there to travel from andys house to willies house?

From Dan's ranch one road is built to get to Andy's house and two roads are built to get to Willies house (see previous problem). How many way are there now to get from Andys house to willies house?

Answers

Andy to get to Willie's house = 15 ways

Andy to get to Willie's house = 45 ways

How to determine the ways

From the information given, we have that from

Andy's house to Billy's  hometown = 3 roads

Billy's hometown to Willies house = 5 ways

To travel from Andy's house to Willies house, we should multiply the number of ways

= 3 × 5

= 15 ways

Dan's ranch to Andy's house = 1 road

To Willie's house = 2 roads

For Andy to get to Willie's house, we have;

= 3 × 15

= 45 ways

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5[tex]5x-3y=34\\x-2y=4[/tex]

Answers

the correct answer is 4 as it is equaled when added

#1) a normal distribution has a mean of 101 and a standard deviation of 4.2. what is the z-score of 105?

Answers

Step-by-step explanation:

z = (specific score - mean) / standard deviation

in our case

z = (105 - 101)/4.2 = 4/4.2 = 0.952380952... ≈ 0.95

as z-tables usually round the z-scores to hundredths.

The z-score of the normal distribution is 0.95.

What is normal distribution?

A probability distribution which is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution.

It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution shows as a "bell curve" on a graph.

Z-score: A Z-score is just a metric that quantifies how closely a value relates to a mean of a set of values. Standard deviations from of the mean are used to measure Z-score.

A Z-score of zero means the data point is actually score is the same as the mean score.

The formula for z-score is-

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

Z = standard score

x  is observed value = 105

[tex]\mu[/tex] is mean of the sample 101.

[tex]\sigma[/tex] is standard deviation of the sample 4.2.

Substitute all the values in the z-score formula;

z = ( 105 - 101)/4.2

z = 0.9523..

z  = 0.95

Therefore, the z-score the given normal distribution is  0.95.

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Find the fifth term of the sequence.

Answers

a) Substituting in n = 2,

[tex]\frac{3(2)^{2}}{2}=6[/tex]

b) Substituting in n = 5,

[tex]\frac{3(5)^{2}}{2}=\frac{75}{2}[/tex]

c) Setting the nth term to be greater than 50,

[tex]\frac{3n^{2}}{2}>50 \\ \\ n^{2} >\frac{100}{3} \\ \\ n>\frac{10}{\sqrt{3}} \\ \\ \lceil n \rceil = 6[/tex]

Given the sequence 4, 8, 16, 32, 64, ..., find the explicit formula.

Answers

Answer:

[tex]\sf 2^{(n+1)}[/tex]

Step-by-step explanation:

Explicit formula is used to represent all the terms of the geometric sequence using a single formula.

  [tex]\sf \boxed{\bf t_n=ar^{(n-1)}}[/tex]

Here, a is the first term.

r is the common ratio.

r = second term ÷ first term

4, 8,16,32,64,.....

    a = 4

    r = 8 ÷4 = 2

[tex]\sf t_n =4*2^{(n-1)}[/tex]

    [tex]\sf = 4*2^n * 2^{(-1)}\\\\ = 4*2^n*\dfrac{1}{2}\\\\ = 2*2^n[/tex]

   [tex]\sf = 2^{(n+1)}[/tex]

Find the indicated term of the geometric sequence.
10th term of 0.6, 0.06, 0.006,...

Answers

Answer:

0.0000000006

Step-by-step explanation:

0.6 * (0.1)^9 = 0.0000000006

Brainliest for answer
A quadratic equation is graphed to the left. Which of the following equations could be paired with the graphed equation to create a system of equations whose solution set is comprised of the points (2,-4)and (-4,2)?

Answers

The linear function that goes through the points (2,-4) and (-4,2) is:

y = -x + 2.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

A linear function going through the points (2,-4) and (-4,2) would intersect the parabola at these points, hence these points would be the solution for the system of equations.

The slope of the line is:

m = (-4 - 2)/(2 - (-4)) = -1.

The line goes through point (2,-4), that is, when x = 2, y = -4, which we use to find the y-intercept b.

y = -x + b

-4 = -2 + b

b = -2.

Hence the equation is:

y = -x + 2.

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NEED HELP ASAP
Factor the trinomial: x² +22x + 72. Explain your steps.

Answers

I got you, bro

Answer:

(x+4)(x+18)

Explanation

Let's factor x2+22x+72

x2+22x+72

The middle number is 22 and the last number is 72.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get 22

Multiply together to get 72

Can you think of the two numbers?

Try 4 and 18:

4+18 = 22

4*18 = 72

Fill in the blanks in

(x+_)(x+_)

with 4 and 18 to get...

(x+4)(x+18)

Answer:

(x+4)(x+18)

Answer:

(x+4)(x+18)

Step-by-step explanation:

Using the factorisation method :

We need 2 numbers that multiply to give +72 and add to give +22 :

To find these numbers we write out all the factors of 72 :

1, 72

2 , 36

3 , 24

4 , 18    ----> These must be the numbers as 4+18 = 22

Now we split +22x into +4x and +18x :

x² + 4x + 18x + 72

Factor the first 2 terms together and the last two terms :

x(x+4) + 18(x+4)

Keep 1 bracket and terms outside the brackets collect them into one:

(x+4)(x+18)

This is our final answer

Hope this helped and have a good day

Find the interest on 16,100 for 4 years and 6months at 10% compounded quarterly.

Answers

25,110.51 is the total amount accrued over the course of 4.5 years, principle plus interest, on a principal of 16,100.00.

Compound interest calculation

We may employ the compound interest future value formula provided by:

[tex]A=P(1+r/n)^{nt}[/tex]

Where A is the final amount, P stands for the current value,

r=interest rate, n represents how many times interest is compounded annually, and t represents the number of years.

In this case,

P= 16100

r = 10%

t = 4 years and 6 months=4.5 years

n=4

So, A=[tex]16100(1+0.1/4)^{4*4.5}[/tex]

A= [tex]16100(1+0.025)^{18}[/tex]

A= 25110.51

So, 25,110.51 is the total amount accrued over the course of 4.5 years, principle plus interest, on a principal of 16,100.00 at a rate of 10 percent per year compounded four times each year.

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Mary won $200,000 in a state lottery. she first paid income tax of 30% on the winnings. she invested some of the rest at 1.5% and some at 4%, earning $4,350 interest per year. how much did she invest at each rate?

Answers

Marry rate of investment is 4%.

Lets solve it through simple steps,

30% 0f $200,000 = $60,000

$200,000-$60,000 = $140,000

Rate 1.5%

Rate 4% = (140,000-x)

Interest earned = $4,350

1.5x+4(150,000-x)=4350*100

1.5x+600,000-4x=435,000

1.5x-4x=435,000-600,000

-2.5x=-165,000 /-2.5

x=66000

$ 66,000  1.5%

Balance = $74,000 at  4%

Hence the rate is 4%

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Can someone help? ASAP

Answers

Answer:

11.  [tex]\frac{\sqrt{2} }{2}[/tex]

12. [tex]\sqrt{3}[/tex]

13. [tex]\frac{\sqrt{3} }{2}[/tex]

14. [tex]\frac{\sqrt{3} }{3}[/tex]

15. [tex]\sqrt{2}[/tex]

16. [tex]\frac{2\sqrt{3} }{3}[/tex]  

Step-by-step explanation:

Hope this helps

a nickel has 5 grams what is the mass of a nickel in milligrams

Answers

The mass of the same nickel which is 5 grams in milligrams is 5,000 milligram.

Weight

1 gram = 1000 milligram

Weight of a nickel = 5 gram

Weight of same nickel in milligram = 5 grams × 1000

= 5,000 milligram

Therefore, the mass of the same nickel is 5,000 milligram

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N=
Help me please thanks :))

Answers

The measure of n of the sector with the given area is: 100°

What is the Area of a Sector?

The area of a sector of a circle = ∅/360 × πr².

We are given that:

Area of the sector = 40π

Radius (r) = 12 units

∅ = n°

Plug in the values and solve for n

40π = n/360 × π(12²)

40π = n/360 × π144

Divide both sides by 144π

40π/144π = n/360 × 144π/144π

40/144 = n/360

40(360) = n(144)

14,400/144 = n

n = 100°

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How do plants and animals survive in this harsh climate?Both plants and animals have adaptationseither behaviors or parts of their bodiesthat help them to live in the desert. For example, fennec foxes have large ears that allow heat to leave their bodies more easily. Camels store fat in their humps, which their bodies break down into food and water when those provisions are unavailable. Many small desert animals stay out of the hot sun during the day and come out to eat at night. How is Jacksons purpose different from Abaras purpose? Jackson provides information about desert climate, while Abara explains how animals can live in the desert. Jackson gives details about the areas of the world where deserts are found, while Abara explains what a desert is. Jackson explains how much precipitation falls in a desert, while Abara relates what animals need to survive.Jackson describes winter desert temperatures, while Abara explains how daytime and nighttime temperatures differ. 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