The rate at which Mr. Story's Twitch subscribers increased per year after 2020 is

Joan is 5 years older than ellen, and 3 years ago the sum of their ages was 17 years. in how many years will joan be 21 years ol

Anna11 [10]

For this case, the first thing we must do is define variables.
We have then:
x: number of years of Joan y: number of years of ellen We now write the system of equations:
$y = x + 5

 (x-3) + (y-3) = 17$
Solving the system we have:
$x = 9

 y = 14$
So that Joan is 21 years old then:
$j + 9 = 21

 j = 21 - 9

 j = 12$
Answer:
joan will be 21 years old in 12 years

7 0

4 years ago

Read 2 more answers

A rectangular prism measure 8 inches by 6 inches by 12 inches.

Serjik [45]

Answer:

576

Step-by-step explanation:

4 0

3 years ago

Help needed ASAP! Please

Marina CMI [18]

It is infinitely many solutions I hope this helps

4 0

3 years ago

Read 2 more answers

Find the values of the six trigonometric functions of an angle in standard position if the point with coordinates (84, 13) lies

tia_tia [17]

Answer:

$\sin \theta = 0.153$ , $\cos \theta = 0.988$ , $\tan \theta = 0.155$ , $\cot \theta = 6.462$ , $\sec \theta = 1.012$ , $\csc \theta = 6.538$

Step-by-step explanation:

Let be the point $(x,y)$ , the six trigonometric functions of the angle are represented by following formulas:

$\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}$ (1)

$\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}$ (2)

$\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{y}{x}$ (3)

$\cot \theta = \frac{1}{\tan \theta} = \frac{x}{y}$ (4)

$\sec \theta = \frac{1}{\cos \theta} = \frac{\sqrt{x^{2}+y^{2}}}{x}$ (5)

$\csc \theta = \frac{1}{\sin \theta} = \frac{\sqrt{x^{2}+y^{2}}}{y}$ (6)

If we know that $x = 84$ and $y = 13$ , then the values of the six trigonometric functions is:

$\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}$

$\sin \theta = 0.153$

$\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}$

$\cos \theta = 0.988$

$\tan \theta = \frac{y}{x}$

$\tan \theta = 0.155$

$\cot \theta = \frac{x}{y}$

$\cot \theta = 6.462$

$\sec \theta = \frac{\sqrt{x^{2}+y^{2}}}{x}$

$\sec \theta = 1.012$

$\csc \theta = \frac{\sqrt{x^{2}+y^{2}}}{y}$

$\csc \theta = 6.538$

4 0

3 years ago

jim and lisa had a total of $300. After jim boughy a jacket with 2/3 if her money,she had $90 less than lisa. find the cost of t

Yuri [45]

Answer:

$84

Firstly, what we must do, is establish a system of equations:

$\frac{2}{3}J = L -90$

$J + L = 300$

Due the circumstances, it is decided we will use the method of substitution:

$\frac{2}{3}J = L - 90$

$\frac{2}{3}J + 90 = L$

↓

$J + \frac{2}{3}J + 90 = 300$

Now, we solve the 2-variable equation above:

$J + \frac{2}{3}J + 90 = 300$

$J + \frac{2}{3}J = 300 - 90$

$J + \frac{2}{3}J = 210$

$J(3) + (\frac{2}{3}J)(3) = 210(3)$

$3J + 2J = 630$

$5J = 630$

$J = \frac{630}{5}$

$\bf~J = 126$

Now, we must see how much money each one of them had & the price of the jacket:

Now we know that Jim had $126. In other words, $126 is $\frac{3}{3}$ of his money (total money).

So, if Jim has $126, which corresponds to $\frac{3}{3}$ of his money, $\frac{2}{3}$ of his money is:

$\frac{126}{3} = 42$

$126 * \frac{2}{3} = 42 + 42$

$\bf~126 * \frac{2}{3} = 84$

Hope it helped,

BiologiaMagister

3 0

3 years ago