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3 years ago

Find the missing side of each triangle. Leave your answer in simplest radical form.

Mathematics

1 answer:

xenn [34]3 years ago

4 0

Answer:

x= $\sqrt{220}$

Step-by-step explanation:

Since this is a right angle triangle, and we have two lengths already found, we can use pythagoras to find x.

We know that

a²+b²=c²

Where a, and b are the smaller lengths (the adjacent and opposite), and C is always the longest one (the hypotenuse).

In this case,

x=a

b=6

c=16

So to plug these into the equation, we get:

x²+6²=16²

To isolate x,

we get:

x²=16²-6²

x= $\sqrt{16^2-6^2}$

$x=\sqrt[]{220}$

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Anyone good with this problem! pls help , due in 16.

nikitadnepr [17]

Its the second one yeah im pretty sure

4 0

3 years ago

A plane is flying from Albuquerque new Mexico to Austin Texas so far it has flown 161 miles or 23% of the total distance of the

Karo-lina-s [1.5K]

Answer: 700 miles.

Step-by-step explanation:

1. You know that 23% of the total distance of the flight from Albuquerque New Mexico to Austin Texas is 161 miles.

2. Then, keeping that information on mind, you can calculate the total distance of the flight (which you call $x$ ) as following:

$\frac{161miles}{23\%}=\frac{x}{100\%}$

Solve for $x$ . Then, you obtain that the result is:

$x=\frac{161miles*100\%}{23\%}\\x=700miles$

3 0

4 years ago

Find an ordered pair (x,y) that is a solution to the equation.<br> 6x-y=1

natita [175]

Answer:
(1, 3 )
Step-by-step explanation:
To find a solution to the equation.
Rearrange making y the subject by subtracting 6x from both sides
Given
6x + y = 9, then
y = 9 - 6x
Substitute any value of x into the equation and solve for y to obtain a solution
x = 1 → y = 9 - 6(1) = 9 - 6 = 3
Thus (1, 3) is a solution to the equation

3 0

3 years ago

Read 2 more answers

2x^3y + 18xy - 10x^2y - 90y part b: rewrite the expression completely factored.

pogonyaev

Answer:

Part A: Factor out the GCF. In this case, the GCF is 2y. So it looks like

2 x^3 * y+18xy-10 x^2 * y-90y=2y (x^3 - 5 x^2 + 9x-45)

Part B: The result from above will need to be factored by grouping.

Part C: If you switch the terms, the factoring will work out differently, but at the end, the factorization will be the same.

Step-by-step explanation:

8 0

3 years ago

A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimi

mestny [16]

Answer:

Base Length of 84cm
Height of 42 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume, $V=x^2h=296352$

$h=\dfrac{296352}{x^2}$

Surface Area of the box = Base Area + Area of 4 sides

$A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}$

Step 2: Find the derivative of A(x)

$If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}$

Step 3: Set A'(x)=0 and solve for x

$A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84$

Step 4: Verify that x=84 is a minimum value

We use the second derivative test

$A''(x)=\dfrac{2x^3+2370816}{x^3}\\$When x=84$\\A''(x)=6$

Since the second derivative is positive at x=84, then it is a minimum point.

Recall:

$h=\dfrac{296352}{x^2}=\dfrac{296352}{84^2}=42$

Therefore, the dimensions that minimizes the box surface area are:

Base Length of 84cm
Height of 42 cm.

5 0

3 years ago