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tensa zangetsu [6.8K]
3 years ago
9

The perimeter of an isosceles triangle is 7.5m, and the length of a leg is 2m. Find the length of the base.

Mathematics
1 answer:
seraphim [82]3 years ago
5 0
The legs of an isosceles triangle are congruent; they have the same length, so if one leg measures 2 m, the other leg also measures 2 m.

2m + 2m + b = 7.5 m

b + 4 m = 7.5 m

b = 3.5 m

The length of the base is 3.5 m.
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2 years ago
A ball is thrown straight out at 80 feet per second from an upstairs window that's 15 feet off the ground. Find the ball's horiz
Alex73 [517]

Answer:

Step-by-step explanation:

In order to find the horizontal distance the ball travels, we need to know first how long it took to hit the ground. We will find that time in the y-dimension, and then use that time in the x-dimension, which is the dimension in question when we talk about horizontal distance. Here's what we know in the y-dimension:

a = -32 ft/s/s

v₀ = 0 (since the ball is being thrown straight out the window, the angle is 0 degrees, which translates to no upwards velocity at all)

Δx = -15 feet (negative because the ball lands 15 feet below the point from which it drops)

t = ?? sec.

The equation we will use is the one for displacement:

Δx = v_0t+\frac{1}{2}at^2 and filling in:

-15=(0)t+\frac{1}{2}(-32)t^2 which simplifies down to

-15=-16t^2 so

t=\sqrt{\frac{-15}{-16} } so

t = .968 sec (That is not the correct number of sig fig's but if I use the correct number, the answer doesn't come out to be one of the choices given. So I deviate from the rules a bit here out of necessity.)

Now we use that time in the x-dimension. Here's what we know in that dimension specifically:

a = 0 (acceleration in this dimension is always 0)

v₀ = 80 ft/sec

t = .968 sec

Δx = ?? feet

We use the equation for displacement again, and filling in what we know in this dimension:

Δx = (80)(.968) +(0)(.968)^2 and of course the portion of that after the plus sign goes to 0, leaving us with simply:

Δx = (80)(.968)

Δx = 77.46 feet

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3 years ago
An investment analyst has tracked a certain bluechip stock for the past six months and found that on any given day, it either go
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Answer:

0.2109 or 21.09%

Step-by-step explanation:

In order to maintain the same price after two days, the stock must go up (U) on two days and go down (D) on two days, the sample space for this event is:

S={UUDD, UDUD, UDDU, DDUU, DUDU, DUUD}

There are 6 equally likely possible outcomes. The probability that the price of the stock will be the same as it is today is:

P =6* (0.25*0.25*0.75*0.75)\\P=0.2109=21.09\%

The probability is 0.2109 or 21.09%.

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\bf 12^x\times 12^4=12^8\implies \stackrel{\textit{if the base is the same, so are the exponents}}{12^{x+4}=12^8} \\\\\\ x+4=8\implies x=4

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3 years ago
Find the slope and y-intercept of y=8x-7
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\bf \begin{array}{|c|ll}\cline{1-1}\textit{slope-intercept form}\\\cline{1-1}\\y=\stackrel{slope}{m}x+\stackrel{y-intercept}{b}\\\\\cline{1-1}\end{array}~\hspace{2em} y=\stackrel{slope}{8}x\stackrel{y-intercept}{-7}~~\begin{cases}m=8\\y-intercept = (0, -7)\end{cases}

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