Jack is 2 times as old as Lacy. 5 years ago the sum of their ages was 20. How old are they now?

Solve the following problem. Choose the correct answer. Fairhaven Church buys four tires for its van. Each tire is priced at $43

morpeh [17]

Answer:

169.65

Step-by-step explanation:

43.95x4= 175.80 175.80x3.5=6.15 175.80-6.15=169.65

5 0

3 years ago

Please help with this one :/

Naddika [18.5K]

Answer:

6.3°

Step-by-step explanation:

$\because \: \pi^{c} = 180 \degree \\ \\ \therefore \: 1^{c} = \frac{180 \degree }{\pi} \\ \\ \therefore \: 0.11^{c} = \frac{180 \degree }{3.14} \times 0.11 \\ \\ \therefore \: 0.11^{c} = \frac{180 \degree }{314} \times 11 \\ \\ \therefore \: 0.11^{c} = \frac{1980 \degree }{314} \times 11 \\ \\ \therefore \: 0.11^{c} = 6.30573248\degree \\ \\ \huge \red{ \boxed{\therefore \: 0.11^{c} = 6.3\degree }} \\ \\$

8 0

4 years ago

Use De Moivre's theorem to write the complex number in trigonometric form: (cos(3pi/5) + i sin (3pi/5))^3

docker41 [41]

By De Moivre's theorem,

$\left(\cos\dfrac{3\pi}5+i\sin\dfrac{3\pi}5\right)^3=\boxed{\cos\dfrac{9\pi}5+i\sin\dfrac{9\pi}5}$

We can stop here ...

# # #

... but we can also express these trig ratios in terms of square roots. Let $x=\dfrac\pi5$ and let $c=\cos x$ . Then recall that

$\cos5x=c^5-10c^3\sin^2x+5c\sin^4x$

$\cos5x=c^5-10c^3(1-c^2)+5c(1-2c^2+c^4)$

$\cos5x=16c^5-20c^3+5c$

On the left, $5x=\pi$ so that

$16c^5-20c^3+5c+1=(c+1)(4c^2-2c-1)^2=0$

Since $c=\cos\dfrac\pi5\neq1$ , we're left with

$4c^2-2c-1=0\implies c=\dfrac{1+\sqrt5}4$

because we know to expect $\cos x>0$ . Then from the Pythagorean identity, and knowing to expect $\sin x>0$ , we get

$\sin x=\sqrt{1-c^2}=\sqrt{\dfrac58-\dfrac{\sqrt5}8}$

Both $\cos$ and $\sin$ are $2\pi$ -periodic, so that

$\cos\dfrac{9\pi}5=\cos\left(\dfrac{9\pi}5-2\pi\right)=\cos\left(-\dfrac\pi5\right)=\cos\dfrac\pi5$

and

$\sin\dfrac{9\pi}5=\sin\left(-\dfrac\pi5\right)=-\sin\dfrac\pi5$

so that the answer we left in trigonometric form above is equal to

$\cos\dfrac\pi5-i\sin\dfrac\pi5=\boxed{\dfrac{1+\sqrt5}4+i\sqrt{\dfrac58+\dfrac{\sqrt5}8}}$

7 0

3 years ago

Need help in these 2 last questions!!!

Alexandra [31]

Question 9

The point (30,15) means that x = 30 and y = 15 pair up together.

Similarly, (40,25) means we have x = 40 and y = 25 paired up.

Apply the slope formula to get

m = (y2-y1)/(x2-x1)

m = (25-15)/(40-30)

m = 10/10

m = 1

The slope is 1.

It tells us that each time y goes up by 1, x is also increasing by 1.

slope = rise/run = 1/1

rise = 1, run = 1

The rise is the change in y, the run is the change in x.

This means the plant's height (y) goes up by 1 cm each time the number of days (x) goes up by 1.

In short, the plant's height is increasing by 1 cm per day

<h3>Answer: Choice D</h3>

========================================================

Question 10

y varies directly with x, so y = kx for some constant k.

We're then told that x = -1 and y = -2 pair up together.

Let's find k based on those items

y = kx

y/x = k

k = y/x

k = -2/(-1)

k = 2

So y = kx becomes y = 2x

Then we're asked to find x when y = -4

y = 2x

y/2 = x

x = y/2

x = -4/2

x = -2

<h3>Answer: Choice D</h3>

6 0

3 years ago

Solve the following expression for p.

xxTIMURxx [149]

Answer:

9 that what p stands for hope it help

Step-by-step explanation:

7 0

3 years ago