All categories

3 years ago

Tell whether it is possible to draw a triangle with the given side lengths.

Mathematics

1 answer:

expeople1 [14]3 years ago

4 0

Answer:

Step-by-step explanation:

Since the 2 shorter sides are greater than the longest side when added, it meet the triangle inequality thoerem. Triangle Inequality Theorom: The longest side of a triangle is less then the 2 shorter sides added.

You might be interested in

Given:

lys-0071 [83]

Answer:

$PS=13\text{ units}$

Step-by-step explanation:

So, we know that PR is 20, SR is 11, and QS is 5.

We also know that PQ is perpendicular to QR, forming the right angle at ∠Q.

We know all the side lengths except for PQ and PS (the one we want to find). Notice that if we find PQ first, we can then use the Pythagorean Theorem to find PS since we already know QS.

So, let's find PQ.

We can see that we can also use the Pythagorean Theorem on PQ. PQ, QR, and PR (the hypotenuse) will be our sides. So:

$(PQ)^2+(QR)^2=(PR)^2$

We know that PR is 20.

QR is the combined length of QS+SR, so QR is 5+11 or 16.

So, substitute:

$(PQ)^2+(16)^2=(20)^2$

Solve for PQ. Square:

$(PQ)^2+256=400$

Subtract 256 from both sides:

$(PQ)^2=144$

Take the square root of both sides:

$PQ=12$

So, the side length of PQ is 12.

Now, we can use the Pythagorean Theorem again to find PS. Notice that PQ, QS, and PS also form a right triangle, with PS being the hypotenuse. So:

$(PQ)^2+(QS)^2=(PS)^2$

We already know that QS is 5. We also just determined that PQ is 12. Substitute:

$(12)^2+(5)^2=(PS)^2$

Square:

$144+25=(PS)^2$

Add:

$169=(PS)^2$

Take the square root of both sides:

$PS=13$

Therefore, the length of PS is 13 units.

And we're done!

7 0

3 years ago

Calcula el valor de la serie:<br> S = 12 + 22 + 32 +42 + ... 172

Doss [256]

Answer:

S = 1564

Step-by-step explanation:

S = 12 + 22 + 32 + .. + 172

= 12 + (12+10) + (12+20) + .. + (12+160)

= 10(1 + 2 + .. + 16) + 12×17

= 10×16×17/2 + 12×17

= 1360 + 204

= 1564

6 0

3 years ago

Janie receives an allowance of $3 per week. In addition, she can earn $2 for each chore she does. This week, she wants to earn e

tangare [24]

5c+3=13

Hope I helped!

7 0

3 years ago

The table shows the mean monthly temperatures in Alcudia for the last 2 years in degrees Celsius. °C Jan Feb Mar Apr May Jun Jul

KonstantinChe [14]

To find:
1. Range of temperature between two years
2. Modal temperature last year
3. Median temperature 2 years ago.
Solution:
1. Range is difference between the highest and lowest value.
Range of last year = highest value-lowest value
= 27-6 = 23
Range 2 years ago = highest value - lowest value
= 25-17 = 18
So, difference in range of temperature between two years = 23-18 = 5
2. Modal temperature last year = 11Â°C
(number that appears most frequently in the series arranged in numerical
order from smallest to largest)
3. Median temperature 2 years ago,
Median = middle number of the series.
Arrange numbers from lowest to highest. As this series contains even
numbers of entries, so median is average of middle numbers. So, (13+17)/2 = 15

5 0

3 years ago

What is the image point of (0,1)after a translation right 5 units and up 5 units?

yaroslaw [1]

Answer:

6,5

Step-by-step explanation:

(x,y)

X: 0 + 5 right = 5,*

Y: 1 + 5 up = *,6

6,5

5 0

2 years ago