Patrick uses scrap metal to build sculptures. He wants to build a sculpture with triangles. He finds metal rods that are 20 in., 27 in., 47 in., and 67 in. long. Which combinations of three of these lengths can Patrick use to form a triangle? Justify your answer.

Answers

Answer 1

Hello !

- for a triangle to be constructible, the longest side must be less than the sum of the other two sides. -

so :

67 smaller than 27+47 ?

67 ⟨ 74 it's the right answer.

I hope I helped you !!

Have a good evening !!!

Answer 2
Final answer:

Patrick can form a triangle using the rod lengths of 20 inches and 27 inches and 47 inches. The other combinations of rod lengths do not meet the conditions laid out by the triangle inequality theorem.

Explanation:

The subject of this question is Mathematics, specifically focusing on geometric properties of triangles. According to the triangle inequality theorem, a triangle can only form if the sum of the lengths of the two shorter sides is greater than the length of the longest side. In this context, Patrick uses scrap metal to build sculptures and wants to create triangles from metal rods which are 20 inches, 27 inches, 47 inches, and 67 inches long.                                                    Using the triangle inequality theorem, we can determine which combinations of rod lengths can form a triangle:

If he uses the rod lengths 20 inches, 27 inches, and 47 inches, it would satisfy the theorem since 20+27 = 47. Therefore, these lengths can form a triangle.For the rods with lengths of 20 inches, 47 inches, and 67 inches, the sum of the two shorter lengths (20+47 = 67) is not greater than the length of the longest rod (67). Hence, these lengths cannot form a triangle.Similarly, for rods measuring 20 inches, 27 inches, and 67 inches, the sum of the two shorter rods (20+27 = 47) is less than the length of the longest rod (67). Therefore, this combination can't form a triangle either.

Learn more about Triangle Inequality Theorem


Related Questions

HELP HELP HELP PLSSSS

HELP HELP HELP PLSSSS

Answers

Answer:

blue increased is addition

Step-by-step explanation:

I believe it’s 20 + y

Please help me with this question .

Please help me with this question .

Answers

Answer:

B

Step-by-step explanation:

hope it helps

The second one
have a good day

Maya used 7/8 can of white paint. She used 1/4 can of blue paint. How many more cans of white paint than blue paint did Maya use?

6/32 can
5/8 can
8/12 can
1 1/8 cans

Answers

Answer:

3/8

Step-by-step explanation:

The answer would be 5/8 can

2, 3, 5, 9, 17, 22, 31, 39

Regina kept track of the points she scored during her team’s first eight basketball games. What is Regina’s mean score?
Responses
A 3939
B 1616
C 3737
D 1313
E 17

Answers

Answer:

Mean = 16

Step-by-step explanation:

MEAN can be find bg the sum of all score divided by the amount of the score.

Mean = total amount / number of amount

Total amount = 2 + 3 + 5 + 9 + 17+ 22 + 31 + 39

= 128

number of amount = 2, 3, 5, 9, 17, 22, 31, 39

= 8

Then we can calculate mean as

Mean = 128/8

Mean = 16

16
2+3+5+9+17+22+31+39=128
128/8=16

Can I get some help?

Can I get some help?

Answers

Answer:

A

Step-by-step explanation:

8x (the babysitter gets paid 8 dollars an hour, and x represents number of hours)

3 (this is the additional tip the babysitter gets; it's not dependent on the number of hours she/he works)

The babysitter will get paid the same despite babysitting two kids- no variable here is dependent on the amount of kids the babysitter babysits.

Answer:

A) 8x + 3

Step-by-step explanation:

The babysitter gets 8 dollars per hours, and x is the hours, so 8x, 8 dollars per hour. She also gets 3 dollars if she gets the children to sleep on time, so add 3. The equation is 8x + 3.

You can use place value to think about the expression 9×6,128
9
×
6
,
128
.

Fill in the blanks to show a way to represent 9×6,128
9
×
6
,
128
with an area model.

Answers

Sorry not good at math

Choose the model for the problem 1/4 divided by 5 .
5/8
3/40
1/20
1/4

Answers

Hey there!

1/4 ÷ 5

=> 4/1 × 5/1

=> 20/1

Therefore, 20/1 is the answer

Answer:

\(\frac{1}{20}\)

Step-by-step explanation:

\(\frac{1}{4}\div 5\\\\ \frac{1}{4}*\frac{1}{5}\\\\\frac{1}{20}\)<== final answer

Hope this helps!

There are 5 blue socks in Josh’s drawer. After he removes 3 non-blue socks, the probability to pick a blue sock at random becomes . How 1/7 many non-blue socks were in Josh’s drawer originally?

Answers

Answer: There is 5 non blue sock in Josh's drawer

Step-by-step explanation:

The denominator shows the total of nonblue and blue socks. So there are 7 non-blue and blue socks in the drawer after he removes 3 non blue socks.To find how many non-blue where in the drawer originally you need to find how many non blue are in the draw after removing the three. So you subtract 7 from 5 which gives you 2. So there are 2 non-blue socks in the drawer after removing the three. Now you need to find how many non-blue were there before he removed the three. So add the 3 non blue socks that he removed to the two that were there after which gives you five.

there are 5 non blue socks

A function with an input of 1 has and output of 3. Which of the following could NOT be the function equation?
1. y= 3x
2. y= x+2
3. y= 4x-3
4. y= 4x-1

Answers

Answer:

The answer is 3

y=4x-3

Step-by-step explanation:

1)y=3x=3(1)=3✅

2)y=x+2=1+2=3✅

3)y=4x-3=4-3=1❌

4)y=4x-1=4-1=3✅

the answer would be 3!

What are multiples for 5 and 2

Answers

10, 20, 30, 40, 50...
These are multiples of five 5,10,15,20,25,30,35,40
These are multiples of twos
2,4,6,8,10,12,14,16,18,19,20

If the bill is $47.96 and you leave a 15% tip, what is the tip amount?​

Answers

Answer:

7.19 is the tip

Step-by-step explanation:

Take the amount of the bill and multiply by the tip percentage

47.96 * 15%

Change to decimal form

47.96 * .15

7.194

Round to 2 decimal places

7.19

Answer: $7.19

Step-by-step explanation:

15/100 = 0.15

We only want the tip, not the total cost:

Do 0.15 * $47.96 to get about $7.19

How many different possible outcomes are in the sample space?

How many different possible outcomes are in the sample space?

Answers

Answer:  18

Work Shown:

3 choices for the 1st column2 choices for each subsection in the next column3 choices for each subsection after that

3*2*3 = 18 different outcomes possible in the sample space. This is the number of possible pathways in the tree diagram.

Help. I'll mark as brainlist.

Help. I'll mark as brainlist.

Answers

Answer: okay, I think the answer would be <NQP and <PQN if the answer is asking for a different way to identify it other than <Q

Angle NQP and angle PQN

Which scenario can be modeled by the linear function
y = -15x + 500?

A. The temperature on Jupiter is
15℉ and increases by 500℉ every day.

B. There is a population of 500 giraffes in Western Africa that decreases by 15 giraffes each year.

C. A carpet cleaning service charges $500 plus an additional $15 for every hour.

D. A membership fee for a movie streaming service is free, but each rental costs $15.

Answers

I think the answer is C
The answer is a because it is able to be modeled unlike the rest

hhelpppp! plz show me how to do it

hhelpppp! plz show me how to do it

Answers

Answer:

0.625

Step-by-step explanation:

Divide the top number by the bottom; 5 divided by 8.

Answer:

0.625

Step-by-step explanation:

Long division:

\(\left[\begin{array}{cccccc}&0&.&6&2&5\\&-&-&_{5} \ -}&_{2} \ -&_{4} \ -\\8 |&5&.&0&0&0&\end{array}\right]\)

You write the denominator first, which is the number beneath and the number being divided by;

You can then put a vertical line to the right of this;

Then the numerator goes after the vertical line, i.e. the number above and the number being divided;

As you can see above, this looks like:
8 | 5

Now, quite simply ask how many 8s go into 5;

The answer is 0;

8 × 1 = 8, which is greater than 5;

The 5 is shifted to the next number;

This would be 0 after the decimal point;

The number becomes 50;

Once again, how many 8s go into 50;

8 × 6 = 48

So, we write 6 above the 0;

There is a remainder of 2, since 50 - 48 = 2;

The 2 is shifted to the next number;

This would also be 0;

The number becomes 20;

How many 8s go into 20;

8 × 2 = 16

So, 2 goes above this 0;

The remainder is 4, 20 - 16 = 4;

This 4 is shifted to the next number:

This too is a 0;

The number is 40;

Once again, how many 8s go into 40;

8 × 5 = 40

So, 5 goes above this 0;

There is no remainder so the division is completed;

The answer is the number above:

0.625

This method applies to any division and is very useful and yet simple.

(Angles) Use the diagram at the right

(Angles) Use the diagram at the right

Answers

Answer:

10.

Angle NSR, angle QSM, and angle PSM

11.

Angle QSR and angle QSM

12.

Angle MSR

13.

Angle NSM, angle PSR, and angle OSR

Step-by-step explanation:

10. Obtuse angles are greater than a 90 degree angle

11. Right angles make like a half square shape

12. Straight angles are like straight lines

13. Acute angles are less than 90 degrees 

Also, sorry I could do the ones with a protractor, I did not have one on hand lol

.........help...............

.........help...............

Answers

Answer:

1. X axis, 8, 3

2. Y axis, 4,-9

Step-by-step explanation:

The rule of reflections that the place opposite of the axis is negative so:

The rule for x-axis reflection is (x,-y)

The rule for y-axis is (-x,y)

For the first one, x has remained the same, so that means it’s a x-axis reflection.

So change -3 to 3

Same for the next one.

-9 is not changed so that means it’s a y-axis reflection.

And the point is 4,-9

Answer:

1) x axis, (8, 3)

2) y axis, (4, -9)

show that the (5,5),(5,0),and (0,0) are the vertices of an isosceles triangle.

Answers

An isosceles triangle has 2 sides that are equal.

I plotted these points. See attached screenshot.

The first side's distance is 5. You can just count those units along the x axis. (0,0) and (5,0) share the same y coordinate, so the difference in x coordinates is 5-0 = 5.

The next sides's distance is also 5. You can count that distance on the coordinate plane. (5,5) and (5,0) share the same x coordinate, so the difference in y coordinates is 5-0 = 5.

These two sides make a right triangle and are equal length. This is an isosceles right triangle.

show that the (5,5),(5,0),and (0,0) are the vertices of an isosceles triangle.

20pts! A toy pyramid has the dimensions shown below. The base of the pyramid is an equilateral triangle. What is the surface area of this pyramid?



48 cm 2
129 cm 2
102 cm 2
81 cm 2

20pts! A toy pyramid has the dimensions shown below. The base of the pyramid is an equilateral triangle.

Answers

(9 x 6)/2 x 3 = 81
(6 x 7)/2 + 81 = 102

Answer:
102cm 2
102 cm 2 because of the length

Use the Midpoint Rule with \(n=5\) to estimate the volume obtained by rotating about the y-axis the region under the curve \(y=\sqrt{1+x^3}\), \(0\leq x\leq 1\).

Answers

To estimate the volume using the Midpoint Rule with \(\displaystyle n=5\), we need to divide the interval \(\displaystyle 0\leq x\leq 1\) into \(\displaystyle n\) subintervals of equal width. Since \(\displaystyle n=5\), each subinterval will have a width of \(\displaystyle \Delta x=\frac{1-0}{5}=\frac{1}{5}\).

Now, let's calculate the volume using the Midpoint Rule. The formula for the volume obtained by rotating about the y-axis is:

\(\displaystyle V\approx 2\pi \sum _{i=1}^{n}y_{i}\Delta x\)

where \(\displaystyle y_{i}\) represents the value of the function \(\displaystyle y=\sqrt{1+x^{3}}\) evaluated at the midpoint of each subinterval.

First, let's find the midpoints of the subintervals. Since the width of each subinterval is \(\displaystyle \Delta x=\frac{1}{5}\), the midpoint of the \(\displaystyle i\)-th subinterval is given by:

\(\displaystyle x_{i}=\frac{\Delta x}{2}+\left( i-\frac{1}{2}\right) \Delta x=\frac{1}{10}+\left( i-\frac{1}{2}\right) \frac{1}{5}\)

Substituting \(\displaystyle x_{i}\) into the function \(\displaystyle y=\sqrt{1+x^{3}}\), we obtain:

\(\displaystyle y_{i}=\sqrt{1+\left( \frac{1}{10}+\left( i-\frac{1}{2}\right) \frac{1}{5}\right) ^{3}}\)

Now, we can calculate the approximate volume using the Midpoint Rule:

\(\displaystyle V\approx 2\pi \sum _{i=1}^{5}y_{i}\Delta x\)

Substituting the values of \(\displaystyle y_{i}\) and \(\displaystyle \Delta x\) into the formula, we can evaluate the sum and compute the estimated volume.

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The answer your looking for is right above my

A rectangle in a coordinate plane has vertices L (−3, 9) , M (4, −2) , N (−3, −2) , and O (4, 9) . What is the distance between point L and point N, in units?

Answers

Answer:

Step-by-step explanation:well 1+1 equals 2 so figure it out yourself

Well 9 + -2 is 11 so the answer is 11

Write the following in algabraic expression: the sum of the number a and three times the square of the number b

Answers

Answer:

a+3b^2

Step-by-step explanation:

a+3b^2 is the correct answer

Alyson is restocking her pantry. She buys 4 kinds of canned soup: tomato (T), mushroom (M), vegetable (V), and chicken noodle (N). She also buys garlic croutons (G) and cheese croutons (C) to pair with the soups. Which TWO statements are TRUE for this situation?

A.{ T, M, V, N, G, C} is the sample space.
B.{TG, TC, MG, MC, VG, VC, NG, NC} is the sample space.
C.There are 8 serving combinations.
D.{T, M, V, N} is the sample space.
E.There are 6 serving combinations.

Answers

Answer:

A and D would be your 2 sample spaces

Step-by-step explanation: because we can see its clearly not C or E so that leaves us with A , B, and D. I belive that B isnt a asnswer choice so that leaves A, and D

mark me brainless please it helps me

hope this helps

I would say A and D

There is no way that E and C are the answer. B is a no because TG…? What does TG mean? Some of the letters in choice B doesn’t make sense to me.

NEED HELP ASAP Triangle JKL was dilated with the origin as the center of dilation to create triangle J'K'L'. The triangle was dilated using a scale factor of 1/2 Which rule represents the dilation applied to triangle J K L to create its image, triangle J′ K′ L′ ?

NEED HELP ASAP Triangle JKL was dilated with the origin as the center of dilation to create triangle

Answers

Answer:

Step-by-step explanation:

C

C hope this helps you

a store bought a vacuum cleaner for $120. the overhead is 5% of the cost. the store wants to make a profit of 10% over the cost plus overhead. find the selling price of the cleaner.

Answers

Answer:

The selling price of the cleaner is:

$138.6

Step-by-step explanation:

First, we have the base of the value that is $120, now we know that the overhead is 5%, so we must calculate this value in dollars, the 5% of $120 is:

$120 * 5% = $6

This value you must add to the base ($120), so the cost with the overhead is $126. How the store wants to make a profit of 10%, you must calculate this 10% of the total cost obtained ($126):

$126 * 10% = $12.6

And you must add this value to obtain the final price in the store:

$126 + $12.6 = $138.6

What is the elevation of 7 feet below sea level?

Answers

Answer:

-7

Step-by-step explanation:

it would be -7 because the more you go under the number becomes a negative but if you go above sea level the number becomes a positive!

Answer:7 feet below sea level is a lower elevation than 4 1/2 feet above sea level

Step-by-step explanation:

Explain the cosine rule and sine rule while also saying how to use it and provide examples (keep it in simple terms)

Answers

Answer:

Sure, I'll explain the cosine rule and sine rule in simple terms:

The cosine rule (also known as the law of cosines) is used to find the length of a side or the measure of an angle in a triangle given the lengths of the other sides and the angle between those sides. It states that c^2 = a^2 + b^2 - 2ab cos(C), where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.

Here's an example of how to use the cosine

Suppose we have a triangle with sides a=6, b=8, and an angle between them c=45 degrees. We want to find the length of the remaining side of the triangle, side a.

Using the cosine rule:

a^2 = b^2 + c^2 - 2bc * cosA

where A is the angle opposite side a, we can plug in our values and solve for a:

a^2 = 8^2 + 6^2 - 2(8)(6) * cos(45)

a^2 = 64 + 36 - 96 * 0.707

a^2 = 10.56

a = sqrt(10.56)

a = 3.25 (rounded to two decimal places)

Therefore, the length of side a is approximately 3.25 units.

Answer:

Step-by-step explanation:

Coach Gonzalez asked a group of her swim team members to record the number of miles they swam this month. The students' responses are in the chart below.

Number of Miles Swam This Month. Swim Team. Member Name. Miles Swam This Month. Tiara. 6.8 miles. Anthony. 8. 1 over 4 miles. Alejandra. 7. 3 over 4 miles. David. 9.1 miles.

If Coach Gonzalez's goal was for this group to swim 50 miles this month, what is the best estimate of how many more miles they will need to swim to reach this goal?

Answers

Organizing info you gave me =)

Number of Miles Swam This Month.

Swim Team.

Member Name.

Miles Swam This Month.

Tiara. 6.8 miles.

Anthony. 8.1/4

Alejandra. 7.3/4

David. 9.1 miles.

so, 40-(7.3/4+6.8+9.1+8.1/4)=20.25

Describe how the data is dispersed in a box plot with the following data set: 25, 36, 21, 30, 20, 32, 38, 19, 36, 31, 26, 33, 27, 18, 24.

AND PLEASE ACTUALLY EXPLAIN/DESCRIBE!

Answers

In a box plot, also known as a box-and-whisker plot, the data is dispersed and represented visually to provide a summary of the distribution and key characteristics of the dataset. Let's describe how the data is dispersed in the box plot for the given data set: 25, 36, 21, 30, 20, 32, 38, 19, 36, 31, 26, 33, 27, 18, 24.

1. Median (Q2): The median represents the middle value of the dataset when arranged in ascending order. In this case, the median is around 27 or 28, as it lies between the values 27 and 30.

2. Lower Quartile (Q1): The lower quartile marks the boundary between the lower 25% of the data and the upper 75%. It is located approximately around 22 or 23, as it falls between the values 21 and 24.

3. Upper Quartile (Q3): The upper quartile marks the boundary between the lower 75% of the data and the upper 25%. It is located around 34 or 35, as it lies between the values 33 and 36.

4. Interquartile Range (IQR): The IQR is the range between the upper and lower quartiles (Q3 - Q1). In this case, the IQR is approximately 12 (35 - 23).

5. Whiskers: The whiskers represent the range of the data excluding any outliers. They extend from the lower quartile (Q1) to the minimum value and from the upper quartile (Q3) to the maximum value. However, in some cases, the whiskers can also be defined based on certain criteria, such as 1.5 times the IQR. Outliers, if present, are depicted as individual data points beyond the whiskers.

6. Outliers: Outliers are data points that significantly deviate from the rest of the dataset. In this case, there are no clear outliers based on the data provided.

7. Box: The box in the box plot spans from the lower quartile (Q1) to the upper quartile (Q3) and represents the middle 50% of the data. In this case, the box spans approximately from 23 to 35.

By observing the box plot, we can see that the data is moderately dispersed, with the majority of values concentrated around the median. The range of the data is approximately 20 to 38, with some variability within the dataset.

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

To create a box plot for this data set, we need to find the minimum value, maximum value, median, and quartiles.

Minimum value: 18
First quartile (Q1): 22
Median: 29
Third quartile (Q3): 36
Maximum value: 38

The box plot is created using these values. A box is drawn from Q1 to Q3 with a line inside the box at the median. Whiskers are drawn from the box to the minimum and maximum values. Any data points beyond the whiskers are plotted as individual points.

In this box plot, the data is dispersed fairly evenly, with no outliers beyond the whiskers. The box is centered around the median, indicating that the data is roughly symmetric. The lower half of the data is slightly more spread out than the upper half, as indicated by the longer whisker on the left side of the box. Overall, the box plot shows that the data is relatively consistent, with no extreme values.

Due in 5 min pls help

Due in 5 min pls help

Answers

Answer:

Step-by-step explanation:

12 or 3

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