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Katyanochek1 [597]
2 years ago
10

A​ triangular-shaped deck has one side that is 4 feet longer than the shortest side and a third side that is 4 feet shorter than

twice the length of the shortest side. If the perimeter of the deck is 80 ​feet, what are the lengths of the three​ sides?
Mathematics
1 answer:
Inessa05 [86]2 years ago
8 0

Answer:

The shortest side is 20 feet, the second side is 24 feet and the third side is 36 feet.

Step-by-step explanation:

Assuming that the shortest side of this triangle has a length of "x" feet, then one side is "x + 4" feet and the third is "2*x - 4" feet. Since the perimeter of the deck is 80 feet, then the sum of the length of these sides should be equal to that.

x + x + 4 + 2*x - 4 = 80\\4*x = 80\\x = \frac{80}{4} = 20 \text{ feet}\\

The shortest side is 20 feet, the second side is 24 feet and the third side is 36 feet.

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The triangle shown below has an area of 121212 units^2 <br> 2<br> squared.<br> Find xxx.
dalvyx [7]

Answer:

4

Step-by-step explanation:

Let's set up an equation using the formula for the area of a triangle.

Hint #22 / 3

\begin{aligned} \text{Area of a triangle} &= \dfrac12 \cdot \text{base} \cdot \text{height}\\\\ 12&= \dfrac12 \cdot 6 \cdot x \\\\ 12&= 3x \\\\ \dfrac{12}{\blueD{3}}&= \dfrac{3x}{\blueD{3}} ~~~~~~~\text{divide both sides by } {\blueD{ 3}}\\\\ \dfrac{12}{\blueD{3}}&= \dfrac{\cancel{3}x}{\blueD{\cancel{3}}}\\\\ x &=\dfrac{12}{\blueD{3}}\\\\ x &=4\end{aligned}  

Area of a triangle

12

12

3

12

​  

 

3

12

​  

 

x

x

​  

 

=  

2

1

​  

⋅base⋅height

=  

2

1

​  

⋅6⋅x

=3x

=  

3

3x

​  

       divide both sides by 3

=  

3

​  

 

3

​  

x

​  

 

=  

3

12

​  

 

=4

​  

5 0
2 years ago
Cynthia rounds a number, x,to one decimal place. the result is 6.3.
gladu [14]

The answer is: 6.25\leq6.3

The explanation is shown below:

1. Cynthia rounds the number, which is identified as x, to one decimal place and the result is 6.3.

2. Based on this, we know that x could have been between 6.25 and 6.35. Therefore, the error interval for x is given by:

 6.25\leq6.3

Where \leq indicates that the value 6.25 is included and indicates that the value 6.35 is not included (Because if x had been exactly 6.35, Cynthia would round up to 6.4).

7 0
2 years ago
Below is a scale drawing of the town swimming pool in the drawing the longest side of the pool has length of 10 inches Paco crea
quester [9]

Answer:

2:1 that is 2 inches in real life is equal to 1 inch in the drawing.

Step-by-step explanation:

We are given the following in the question:

Longest side of the pool = 10 inches

Longest side of the pool in drawing = 5 inches

Scale:

We find the ratio of the real length of pool and the measurement of the length of the pool in the drawing.

\text{Scale} = \dfrac{10\text{ inches}}{5\text{ inches}} = 2:1

Thus, we can say Paco's new drawing follows a scale of 2:1 that is 2 inches in real life is equal to 1 inch in the drawing.

6 0
2 years ago
Read 2 more answers
A prisoner is trapped in a cell containing three doors. The first door leads to a tunnel that returns him to his cell after two
Greeley [361]

Answer:

The expected number of days until the prisoner reaches freedom is 2.8.

Step-by-step explanation:

Door 1: 0.3 probability of being selected. Leads to his cell after two days' travel.

Door 2: 0.5 probability of being selected. Leads to his cell after four days' travel.

Door 3: 0.2 probability of being selected. Leads to his cell after one day of travel.

What is the expected number of days until the prisoner reaches freedom?

We multiply the probability of each door being used by the time that it leads to the cell. So

E = 0.3*2 + 0.5*4 + 0.2*1 = 2.8

The expected number of days until the prisoner reaches freedom is 2.8.

4 0
2 years ago
What are the coordinates of the image of vertex R -3,4 after a reflection across the y-axis? (–4, 3) (4, –3) (–3, –4) (3, 4)
Feliz [49]
The coordinate of the image after being reflected is R(3,4).

When dealing with reflection of a line or shape or a figure in the coordinate plane, especially if it is reflected across the y- axis, you just have to give the opposite of the given (original) x- coordinate in order to give a symmetric figure.
7 0
2 years ago
Read 2 more answers
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