How many non-congruent triangles can you draw with the given properties? a. Sides measuring 7 inches, 8 inches, and 16 inches b. Sides measuring 4 inches, 4 inches, and 6 inches c. Angles measuring 30°, 60°, and 90° d. Three angles measuring 120° e. Two angles measuring 45° and one side length measuring 10 inches

Answers

Answer 1

Answer:

The answers are;

a. None

b. None

c. Infinite

d. None

e. None

Step-by-step explanation:

The number of non congruent triangles that can be drawn depends on the uniqueness of the triangle

The parameters of a unique triangle are;

Knowing the Side Side Side (SSS)

Knowing the Side Angle Side (SAS)

Knowing the Angle Side Angle (ASA)

Knowing the Angle Angle Side (AAS)

However, knowing only the Side Side Angle it is possible to draw two non-congruent triangles

Therefore, considering each of the triangles gives;

a. Sides 7 inches, 8 in., and 16 in. which is of the form SSS hence the triangle is well defined and it is not possible to draw two non-congruent triangle with the provided properties

b. Similarly, the given triangle parameters are 4 in., 4 in., and 6 in. which is of the form SSS hence the triangle is well defined and it is not possible to draw two non-congruent triangle with the provided information

c. The parameters of the triangle given here are angles 30°, 60°, and 90° which is of the form Angle Angle Angle, or AAA for which the sides can be scaled to form an infinite number of non-congruent triangles

d. The parameters given are three angles measuring 120° which does not form a triangle as the sum of triangles in a triangle = 180°

Hence the number of non-congruent triangles that can be drawn in this case = 0

e. The parameters given are two angles measuring 45° and one side length of 10 in., hence the parameter is of the forms AAS or ASA hence the triangle is unique and it is not possible to draw two non-congruent triangle with the provided properties.


Related Questions

The ratio of men to women is 5 to 8. If there are 286 employees total how many women work for the company ??
Please answer

Answers

Answer:

There are 176 women in the company.

Step-by-step explanation:

Let number of men are 5x and number of women are 8x.

Total number of employees in the company are 286.

But according to given condition, total no of employees are :

[tex]5x+8x = 286\\\\13x=286\\\\x=\dfrac{286}{13}\\\\x=22[/tex]

Total no of women are 8x. It means [tex]22\times 8=176[/tex]. Hence, there are 176 women in the company.

There are eight black socks six blue socks and 14 White Socks in a drawer if one sock is randomly chosen from the drawer than what is the probability that the sock Will not be blue?

Answers

Answer:

22/28 = 11/14

Step-by-step explanation:

no of socks other than blue = 22

total no of socks = 28

so probability= 22/28 = 11/14

Answer:

22

Step-by-step explanation:

8 black 6 blue and 14 white is equal to 28

and if 6 are blue the rest are not so 6-28=22

A recipe calls for 2 3/4 cups on milk. If the recipe is tripled, how much milk is needed?

Answers

8 1/4 should be the answer

Answer:

8 1/4

Step-by-step explanation:

33/4 simplified is 8 1/4

Your very helpful my dude

Answers

Answer:

Angle 1 or Angle 3

Step-by-step explanation:

They are the only two that are immediately next to angle 2

Answer:

angle 1

Step-by-step explanation:

This one and 1 more !!!

Answers

Answer: 30!

Step-by-step explanation: add carter’s, lucas’, davi’s, alice’s numbers. ( equaling 25).. add 5 since it turns to 30, 30 dived by 5 is 6.

The hypotenuse of a right triangle is 14 centimeters long. One of the legs of the triangle is 6 centimeters. What is the length of the triangle's other leg?


Answers

Answer: 12.65 cm

Step-by-step explanation:

Use the Pythagoras theorem,

a^2 + b^2= c^2

You are given the hypotenuse , which is c and another leg which is either a or b, does not particularly matter- rearrange to find the missing length

c^2 - b^2 = a^2

14^2 - 6^2 = 160

Square root 160 to find the missing length

12.65

Hope this helped :)

Find the volume of a right circular cone that has a height of 14.3 ft and a base with a diameter of 17.2 ft. Round your answer to the nearest tenth of a cubic foot.

Answers

Answer:

Volume of the given cone is 1107.6 cubic feet.

Step-by-step explanation:

Formula to get the volume of a right circular cone is,

V = [tex]\frac{1}{3}\pi r^{2}h[/tex]

Here r = radius of the circular base

h = height of the cone

Now we put the values in the given formula

Volume = [tex]\frac{1}{3}\pi (8.6)^2(14.3)[/tex]  [ radius = [tex]\frac{17.2}{2}=8.6[/tex] ]

             = [tex]\frac{1057.628\pi }{3}[/tex]

             = 1107.55

             ≈ 1107.6 cubic feet

Therefore, volume of the given cone is 1107.6 cubic feet.

Answer:

146.6 ft3

Step-by-step explanation:

Derek is playing a prank on Grace and hid her pencil inside a tissue box that has a width of 4 inches, a length of 8 inches, and a height of 4 inches. The pencil fits perfectly from the upper left corner to the bottom right corner of the box. What is the length of Grace’s pencil to the nearest tenth of an inch?

Answers

Answer:

9.8 Inch

Step-by-step explanation:

The distance from the upper left corner to the bottom right corner of the box is the longest diagonal of the box.

For a rectangular prism:

Length of the Longest diagonal [tex]=\sqrt{ l^2+h^2+w^2}[/tex]

Therefore:

Length of the pencil[tex]=\sqrt{ 8^2+4^2+4^2}[/tex]

[tex]=\sqrt{96}\\=9.8$ inch(correct to the nearest tenth of an inch)[/tex]

Answer: length of pencil is 9.8 inches.

Step-by-step explanation:

The pencil fits perfectly from the upper left corner to the bottom right corner of the box. This is the diagonal of the box(not the diagonal of a face). To determine the length of the pencil, we would determine the length of the diagonal of the box. The formula formula is

d = √(l² + w² + h²)

Where

d = diagonal = length of pencil

w = width = 4 inches

h = height = 4 inches

l = length = 8 inches

Therefore,

d = √(4² + 4² + 8²) = √96

d = 9.8 inches

What is cumulative frequency

Answers

Explanation:

Cumulative frequency analysis is the analysis of the frequency of occurrence of values of a phenomenon less than a reference value. The phenomenon may be time- or space-dependent. Cumulative frequency is also called frequency of non-exceedance.

Cumulative frequency is defined as a running total of frequencies. The frequency of an element in a set refers to how many of that element there are in the set. Cumulative frequency can also defined as the sum of all previous frequencies up to the current point.

A contractor bought 44 boxes of nails at a price of $1 per box. Each box
contained contained 56 nails. If he distributed the nails to the 4 houses he
was building and made sure each house received the same number of
nails, how many nails would each house get?

Answers

Answer:

616 nails

Step-by-step explanation:

No. of nail box bought  = 44

No. of nail in each box = 56.

Total no of nail in 44 box = No. of nail box bought * No. of nail in each box

                                          = 44 * 56 = 2,464

These nails were distributed in 4 houses equally.

Let no. of nail distributed in 1 houses be x.

Thus, total nails  distributed in 4 houses equally = 4x.

These 4x nail should be equal to Total no of nail in 44 box

4x = 2464

=> x = 2464/4 = 616

Thus, each house would get 616 nails.

HELP PLEASEEEE!!!!!!
I put all my POINTS in

you pick a card from a deck containing 5 cards and roll a 6-sided die. How many
outcomes are possible?

Answers

Answer:

30

Step-by-step explanation:

Since there are 5 possible outcomes for the cards, and 6 possible outcomes for the die, there are a total of 5*6=30 outcomes possible. Hope this helps!

Eva is 29 years old and has 2 children, ages 3 and 5. She makes 48,500 a year. Eva decides to buy a 400,000 10-year term policy then renew the policy for another ten years afterwards. To renew the policy the insurance company charges an extra 40% to her premium rate.

Answers

Answer:

Eva would have been better off selecting the 20-year term policy.

Step-by-step explanation:

Base on the scenario been described in the question, Eva would have been better off selecting the 20-year term policy. This reason is because assuming Eva bought the 20-year term policy, she wont be paying the new charge of extra 40% to her premium rate, compared to when she bought the 10-year term policy then renew the policy for another ten years.

Eva's best option would be to buy on a 20-year policy. This is better because she is able to evade the additional, 40% to her premium rate.

Insurance Premium;

Premiums are percentages of the cost value charged by the insurance company for their services and benefits.

If she pays, 400,000 in ten years, this means she pays 40,000 each year.

Upon renewal, she'll have to 40% more and her new premium will be; 56,000.

Read more on insurance premium;

https://brainly.com/question/9696972

Please help!!

6a. Given two sides of 5 cm and 6 cm. To determine a triangle the MINIMUM whole number length of the third side would be _____ cm. *

6b. Given two sides of 5 cm and 6 cm. To determine a triangle the MAXIMUM whole number length of the third side would be _____ cm. *

7a. Given two sides of 3 cm and 7 cm. To determine a triangle the MINIMUM whole number length of the third side would be _____ cm. *

7b. Given two sides of 3 cm and 7 cm. To determine a triangle the MAXIMUM whole number length of the third side would be _____ cm. *

8a. Given two sides of 4 cm and 10 cm. To determine a triangle the MINIMUM whole number length of the third side would be _____ cm. *

8b. Given two sides of 4 cm and 10 cm. To determine a triangle the MAXIMUM whole number length of the third side would be _____ cm. *

9a. Given two sides of 1 cm and 12 cm. To determine a triangle, the MINIMUM whole number length of the third side would be _____ cm. *

9b. Given two sides of 1 cm and 12 cm. To determine a triangle, the MAXIMUM whole number length of the third side would be _____ cm. *

Answers

Answer:

6a) 1

6b) 11

7a) 4

7b) 10

8a) 6

8b) 14

9a) 11

9b) 13

Step-by-step explanation:

In order to make a triangle, we need to follow this property:

a <= b + c

(Known as "triangle inequality")

Where 'a' is the bigger side and 'b' and 'c' are the other two sides.

So, using this property, we can solve the following problems:

6a) Maximum side will be 6:

6 <= 5 + c

c = 1

6b) Minimum sides will be 5 and 6:

a <= 5 + 6

a = 11

7a) Maximum side will be 7:

7 <= 3 + c

c = 4

7b) Minimum sides will be 3 and 7:

a <= 3 + 7

a = 10

8a) Maximum side will be 10:

10 <= 4 + c

c = 6

8b) Minimum sides will be 4 and 10:

a <= 4 + 10

a = 14

9a) Maximum side will be 12:

12 <= 1 + c

c = 11

9b) Minimum sides will be 1 and 12:

a <= 1 + 12

a = 13

Un laboratorio comercializa perfume en frascos que tienen una capacidad de 3/20 de litros ¿ cuantos litros de perfume se han de fabricar para llenar 1.000 frascos?

Answers

Answer:

Se debe fabricar 150 litros para llenar 1.000 frascos

Step-by-step explanation:

Segun los datos en el ejercicio un laboratorio comercializa perfume en frascos que tienen una capacidad de 3/20 de litros.

Para saber cuantos litros de perfume se han de fabricar para llenar 1.000 frascos hay que multiplicar la capacidad de los frascos por el número de frascos con el siguiente calculo:

litros de perfume se han de fabricar para llenar 1.000 frascos=(1,000/20) x 3

litros de perfume=50 x3

litros de perfume=150

Se debe fabricar 150 litros para llenar 1.000 frascos

Read the word problem below. Jill had $90. She bought a skirt that normally costs $42 but was on sale for half price. She also bought a T-shirt that was $8 off its regular price. Before sales tax, the total cost of the clothes was $31. What was the regular price of the T-shirt? What question is being asked in this word problem? What is the regular price of the skirt? How much money does Jill have left? How much does the T-shirt normally cost? What is the amount Jill pays in sales tax?

Answers

Answer:

What was the regular price of the T-shirt?

$18

What question is being asked in this word problem?

what is the regular cost of the t-shirt purchased by Jill.

What is the regular price of the skirt?

$42

How much money does Jill have left?

without considering sales tax, Jill has $90 - $31 = $59 left.If I use the sales tax from where I live, the sales tax = $1.86, so the money that Jill will have left = $59 - $1.86 = $57.14

How much does the T-shirt normally cost?

$18 (same as question 1)

What is the amount Jill pays in sales tax?

since you do not include the sales tax % in the question, I will simply use the sales tax from where I live = $31 x 6% = $1.86

Step-by-step explanation:

skirt $21

t-shirt = p - $8

before sales tax, total cost was $31

$21 + p - $8 = $31

p = $18


Which statements are true regarding the prism? Check
all that apply.
The prism has no vertices.
The prism has 9 edges.
The bases of the prism are triangles.
The bases of the prism are rectangles.
The prism has 5 faces.​

Answers

Answer:

The prism has 9 edges, The bases of the prism are triangles, and the prism has 5 faces.

Would really appreciate a brainliest! Hope this helped! =)

Answer: B, C, E

Step-by-step explanation: dude trust me c'mon

easy geometric shapes question #4 help please!

Answers

Answer:

254.469 inches^3

Step-by-step explanation:

v=(pi)(r)^2(h)

pi(3)^2(9)

pi(9)(9)

pi(81)

254.469

How many 5 card hands are possible with four black cards and one red card?

Answers

Answer:

1 i believe

Step-by-step explanation:

Use the data set below to answer question
91, 76, 83, 100, 76
What is the mode? What is the median?
What is the mean?"

Answers

Answer:

the mode is 76, the median is 83, and the mean is 85.2

Step-by-step explanation:

Mode is the number which appears most often in a set of numbers.

To find the Median, place the numbers in value order and find the middle number.

To find mean add up all the numbers, then divide by how many numbers there are

solve the inequality -6(1+2 x)> 6(2x-1)+2x

Answers

Answer:

x <0

Step-by-step explanation:

hello :

-6(1+2 x)> 6(2x-1)+2x

1) divide by 6 : -(1+2 x)> (2x-1)+(1/3)x

2) multiply by 3 : -3(1+2x) >3(2x-1)+x

calculate : -3-6x  > 6x-3+x

now add 3 : -6x  > 6x+x

-6x  > 6x+x

add 6x :   0>12x+x    means : 13x <0

x <0/13    but 0/13 =0

conclusion : x <0

A cow can give 5 gallons of milk if it eats 2 pounds of grass. Express x in terms of y, where y is the number of gallons of milk the cow gives, and x is the number of pounds of grass it eats.

Answers

Answer:

x = 2.5y

Step-by-step explanation:

If a cow can give 5 gallons of milk after eating 2 pounds of grass.

Let's consider 'x' is the number of pounds of grass it eats and 'y' is the number of gallons of milk the cow gives.

Hence,

5y = 2x

We will simplify it to get what x equal to y by dividing 2 on both side we find,

x = 2.5y

x is equal to 2.5 y

By eating 1 pound of grass cow can give 2.5 gallons of milk.

Answer:

26xy

Step-by-step explanation:

#THANKMELATER

The data show the bug chirps per minute at different temperatures. Find the regression​ equation, letting the first variable be the independent​ (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of 0.05. What is wrong with this predicted​ value?

Answers

Answer:

This predicted value is that it is unrealistically high

Step-by-step explanation:

According to the data given in order to calculate the predicted value we would have to make the following calculation of the predicted value and then conclude.

predicted value=26.693 + 0.055*3000

predicted value=191.693

By having the result of the predicted value we can conclude that what is wrong about this predicted value is that it is unrealistically high.

ASAP
In the expression 3x + 5, the value of 3 is the best described as:
A. The constant
B. The operation
C. The variable
D. The coefficient

Answers

Answer:

D) The coefficient

Explanation:

The coefficient is the number placed before the variable in the expression.

In 3x x is the variable and 3 is the number placed before it making it the coefficient.

Twelve-year-olds have heights that are normally distributed with a mean of heights of 57 inches and a standard deviation of 4.6 inches. what percent of 12-year-old boys will have heights less than 55 inches?
A) 33%
B) 37%
C) 42%
D) 49%

Answers

Answer:

A

Step-by-step explanation:

To calculate this, the first thing we need to do is to calculate the z-score

Mathematically,

z-score =( x - mean )/SD

according to the question, X = 55 inches, mean = 57 inches and SD = 4.6 inches

we plug these values into the equation

z-score =( 55-57)/4.6 = -2/4.6 = -0.4348

The required probability we are trying to calculate is;

P( z < -0.4348) or simply P(x<55)

To calculate this probability we use the standard score table

From the standard score table,

P( z < -0.4348) = 0.33186

In percentage this is 33.186%

To the nearest percentage, this is 33%

Please help, I’m so desperate for this answer. I’ve been here for two hours and no one wants to help :/ (find x)

Answers

Answer

i can't see the image can you post it again.

Step-by-step explanation:

Answer:

29 + 64 =x which is 93 for question 2

Step-by-step explanation:

function f whose zeros are -3 and -4 f(x) please I need help right now

Answers

Answer:

f(x) = x² + 7x + 12

Step-by-step explanation:

Given that the zeros are x = - 3 and x = - 4, then the factors are

(x - (- 3)) and (x - (- 4)), that is (x + 3) and (x + 4)

f(x) is the product of the factors, that is

f(x) = (x + 3)(x + 4) ← expand using FOIL

f(x) = x² + 7x + 12

You spin the spinner below once. What is the probability that the arrow will land on 3

Answers

Answer:

how many numbers are there and if there is more of the same number then that will be ur probability

Step-by-step explanation:

What is (2x^2+2x-6) times (x-4)?

Answers

Answer:

2x^3-6x^2-14x+24

Step-by-step explanation:

What is the probability of Red and yellow?

What is the probability of NOT BROWN?

What is the probability of Purple?

Answers

Answer:

3/8 for red and yellow

1 for not brown

0 for purple

Step-by-step explanation:

Answer:

probability of red and yellow: [tex]\frac{3}{8}[/tex]

probability of not brown: [tex]\frac{8}{8}[/tex]

probability of purple: [tex]\frac{0}{8}[/tex]

Step-by-step explanation:

The denominator will always be 8 because that is the total number of things that could be spun. The numerator will change based on the question.

Find the equation of the line parallel to 2y-3x= 4 and passing through the point (6,7)

Answers

Answer:

We have equation of a line:

2y - 3x = 4 => y = (3/2)x + 4

The equation of the line that is parallel to above line and passes through the point (6, 7) would have form y = ax + b, and

a = 3/2

6a + b = 7

=> b = 7 - 6a = 7 - 6 x 3/2 = 7 - 9 = -2

=> The equation of that line: y = (3/2)x - 2

Hope this helps!

:)

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