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bekas [8.4K]
2 years ago
11

Find the area of the given triangles.

Mathematics
1 answer:
liubo4ka [24]2 years ago
3 0

Answer:

40 ft squared

Step-by-step explanation:

to find the area of a triangle, you do base x height divided by 2

5 x 16 = 80

80 divided by 2 is 40

You might be interested in
How to know if a function is periodic without graphing it ?
zhenek [66]
A function f(t) is periodic if there is some constant k such that f(t+k)=f(k) for all t in the domain of f(t). Then k is the "period" of f(t).

Example:

If f(x)=\sin x, then we have \sin(x+2\pi)=\sin x\cos2\pi+\cos x\sin2\pi=\sin x, and so \sin x is periodic with period 2\pi.

It gets a bit more complicated for a function like yours. We're looking for k such that

\pi\sin\left(\dfrac\pi2(t+k)\right)+1.8\cos\left(\dfrac{7\pi}5(t+k)\right)=\pi\sin\dfrac{\pi t}2+1.8\cos\dfrac{7\pi t}5

Expanding on the left, you have

\pi\sin\dfrac{\pi t}2\cos\dfrac{k\pi}2+\pi\cos\dfrac{\pi t}2\sin\dfrac{k\pi}2

and

1.8\cos\dfrac{7\pi t}5\cos\dfrac{7k\pi}5-1.8\sin\dfrac{7\pi t}5\sin\dfrac{7k\pi}5

It follows that the following must be satisfied:

\begin{cases}\cos\dfrac{k\pi}2=1\\\\\sin\dfrac{k\pi}2=0\\\\\cos\dfrac{7k\pi}5=1\\\\\sin\dfrac{7k\pi}5=0\end{cases}

The first two equations are satisfied whenever k\in\{0,\pm4,\pm8,\ldots\}, or more generally, when k=4n and n\in\mathbb Z (i.e. any multiple of 4).

The second two are satisfied whenever k\in\left\{0,\pm\dfrac{10}7,\pm\dfrac{20}7,\ldots\right\}, and more generally when k=\dfrac{10n}7 with n\in\mathbb Z (any multiple of 10/7).

It then follows that all four equations will be satisfied whenever the two sets above intersect. This happens when k is any common multiple of 4 and 10/7. The least positive one would be 20, which means the period for your function is 20.

Let's verify:

\sin\left(\dfrac\pi2(t+20)\right)=\sin\dfrac{\pi t}2\underbrace{\cos10\pi}_1+\cos\dfrac{\pi t}2\underbrace{\sin10\pi}_0=\sin\dfrac{\pi t}2

\cos\left(\dfrac{7\pi}5(t+20)\right)=\cos\dfrac{7\pi t}5\underbrace{\cos28\pi}_1-\sin\dfrac{7\pi t}5\underbrace{\sin28\pi}_0=\cos\dfrac{7\pi t}5

More generally, it can be shown that

f(t)=\displaystyle\sum_{i=1}^n(a_i\sin(b_it)+c_i\cos(d_it))

is periodic with period \mbox{lcm}(b_1,\ldots,b_n,d_1,\ldots,d_n).
4 0
3 years ago
You are selling lemonade for $1.50, a bag of kettle corn for $3, and a hot dog for $2.50 at a fair. Write and simplify an expres
kozerog [31]

Answer:

1.5p + 3p + 2.5p

Step-by-step explanation:

This expression, 1.5p + 3p + 2.5p, will represent the amount of money received when p people buy one of each food item.

Since the price of each is the coefficient for p, this will represent how much money will be gained from each food item. All 3 terms will be added together to represent the total amount of money gained from selling all 3 items.

4 0
3 years ago
- Isabella makes $14.35 an hour at her company. Skyler, who works at the same company,
olga55 [171]

Answer:

It would be 8 years ago.

Step-by-step explanation:

-First, subtract $14.35 from $16.35, which gives you 2.

-Next, remember that $0.25 is a quarter, so how many quarters make $2?

-0.25x4 gives you a dollar, so 0.25x8 gives you 2 dollars.

Hope it helps!

7 0
2 years ago
Help w this plsss,!,!,, 20pointsss
Kay [80]

Answer:

Area = Length × width

16 = (3x +2 ) × ( x)

16 = 3x² +2x

3x² +2x -16=0

( 3x+8 ) ( x -2 ) =0

3x +8=0 —> 3x = – 8 —> x = – 8/3 —> x = – 2.6

x-2=0 —> x = 2

I hope I helped you^_^

5 0
2 years ago
SOMEONE HELP I NEED IT BAD!!!<br> solve for x
Mrac [35]
R=1 s=1 x=4 or you can basically double it and be like rs=2 x=8 i dont know your options or i could help better
7 0
3 years ago
Read 2 more answers
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