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qwelly [4]
3 years ago
13

A triangle has side lengths measuring 20 cm, 5 cm, and n cm. Which describes the possible values of n? 5 < n < 15 5 < n

< 20 15 < n < 20 15 < n < 25 How far would Pete walk if he went from A to B to C? yards The direct distance from A to C is more than yards. The inequality w < represents the distance, w, that Pete might save by taking the direct path.
Mathematics
1 answer:
Nata [24]3 years ago
8 0

Answer:

15 < n < 25

Step-by-step explanation:

Given

Side\ 1 = 20cm

Side\ 2 = 5cm

Side\ 3 = n

Required

Determine n using inequality

The three sides of the triangle must satisfy two of  the following conditions

Side\ 1 + Side\ 2 > Side\ 3

Side\ 1 + Side\ 3 > Side\ 2

Side\ 2 + Side\ 3 > Side\ 1

Substitute values in the above inequalities;

20 + 5 > n

20 + n > 5

5 + n > 20

Solve each of the inequalities

20 + 5 > n

25 > n

n < 25

20 + n > 5

n > 5 - 20

n > -15

5 + n > 20

n > 20 -5

n>15

Since, the second inequality has negative, we simply ignore it

So, we combine the first and the third:

n>15 and n < 25

15 < n and n < 25

Combine both

15 < n < 25

<em>The second question is not clear and it is unanswerable</em>

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The difference of a number and 8 is the same as 34 less the number. find the number.
Dovator [93]
Let the number be x.

8 - x = x -34

2x = 8 + 34

2x = 42

x = 21

Answer: The number is 21.
4 0
3 years ago
The length of the hypotenuse of the right triangle is 25 cm, the length of one of the legs is 10 cm. What is the length of the s
Anna007 [38]

Answer:

  21 cm

Step-by-step explanation:

Call the triangle ABC, with the right angle at B, the hypotenuse AC=25, and the given leg AB=10. The altitude to the hypotenuse can be BD. Since the "other leg" is BC, we believe the question is asking for the length of DC.

The right triangles formed by the altitude are all similar to the original. That means ...

  AD/AB = AB/AC . . . . . . ratio of short side to hypotenuse is a constant

Multiplying by AB and substituting the given numbers, we get ...

  AD = AB²/AC = 10²/25

  AD = 4

Then the segment DC is ...

  DC = AC -AD = 25 -4

  DC = 21 . . . . . centimeters

6 0
3 years ago
Triangle ABC below is reflected across the y-axis and then translated 1 unit right and 2 units down.
hodyreva [135]
Any point with coordinates (x, y) reflected across the y-axis is going to have the opposite x value that it did before.
You should be able to find the coordinates yourself for part a. (you didn't provide the original ones so I can't help you there)
Here is the "rule" for a reflection across the y-axis:
(x,\ y)\rightarrow(-x,\ y)
And when we go 1 unit to the right and 2 down, that's the same as
(x,\ y)\rightarrow(x+1,\ y-2)

Combining those into one rule is pretty simple, Use our result for the first in the second and we would get (-x+1,\ y-2), so the rule is
\boxed{(x,\ y)\rightarrow(-x+1,\ y-2).
Part A is asking for the coordinates after the reflection (x, y) ⇒ (-x, y).
Part C is asking for the coordinates after the full translation ⇒ (-x+1, y-2)
8 0
4 years ago
Help help help help help help help help
netineya [11]

Answer:

5 cartons  of eggs

3 packages  of steaks

Total cost=$55

Step-by-step explanation:

Hi, to answer this question we have to find the least common multiple of  

6 (number of eggs in a carton) and 10 (number of ham steaks in each package)

LCM = 30

6 12 18 24 30

10 20 30 40 50

Since each carton of eggs (x) has 6 eggs, that expression must be equal to 30(eggs) to find the number of cartons.

6 (x ) = 30

Solving for x

x = 30/6

x = 5 cartons

Same process for the steak, where y= number of packages .  

10 y = 30

y = 30/10

y=3 packages

Since each carton costs $2 and each package of steaks cost $15:

Total Cost =x 2+y 15  

Replacing with the values of x and y calculated

Total cost = (5)2 + (3)15 = 10+45 =$55

Feel free to ask for more if needed or if you did not understand something.

6 0
3 years ago
What are the converse, inverse, and contrapositive of the following conditional statement? What are the truth values of each? If
IrinaK [193]
1. If tomorrow is Monday then, today is Sunday.
2. If today is not Sunday then tomorrow is not Monday.
3. If  tomorrow is not Monday then today is not Sunday
4 0
4 years ago
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