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3 years ago

Rearranging literal equations ASAP NEED HELP

Mathematics

1 answer:

Tju [1.3M]3 years ago

5 0

When we look at this thing for the first time, it looks like it's going to be a dog of a bear to solve, because 'q' is buried inside a squared term and a cubed term.

But this is why it's so important to learn that in math, you DON't immediately ignite your hair and go running around in circles as soon as you see the problem. The first thing you have to do every time is sit still, look at the problem, breathe air, and switch your brain into the 'ON' position.

Look at that big ugly fraction in the equation. Can it be simplified ? You betcha it can ! The quantity (q+r) is a factor of the numerator and denominator, so we can do some canceling.

Divide the top and the bottom of the fraction by (q+r)², and then the problem says . . .

p = (q+r)/12 + 4r

which is MUCH easier to unravel and solve for 'q' . Let's do this !

p = (q+r)/12 + 4r

Subtract (q+r)/12 from each side . . . p - (q+r)/12 = 4r

Subtract 'p' from each side . . . -(q+r)/12 = 4r - p

Multiply each side by -1 . . . (q+r)/12 = p - 4r

Multiply each side by 12 . . . (q+r) = 12p - 48r

Subtract 'r' from each side . . . q = 12p - 49r

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Three times a number plus twice another is 10, while their sum is 10, Find the numbers

Aleks [24]

$3a+2b=10 \\\\ a+b=10 \\\\ \boxed{a=10-b} \\\\ 3(10-b)+2b=10 \\\\ 30-3b+b=10 \\\\ -b=10-30 \\\\ -b=-20 \\\\ \boxed{b=20} \\\\ a=10-20 \\\\ \boxed{a=-10}$

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3 years ago

500th term of 24,31,38,45,52

tensa zangetsu [6.8K]

This looks like a simple arithmetic series. Each term is 7 greater than the previous term.

Therefore, the Nth term is 17 + 7N.

For example, the first term is 17 + 7*1 = 17 + 7 = 24.

The second term is 17 + 7*2 = 17 + 14 = 31

etc...

And the 500th term is 17 + 7 * 500 = 17 + 3500 = 3517

3 0

3 years ago

What two numbers multiply to -20 then add to -8?

VARVARA [1.3K]

Answer:

-10 and 2

Step-by-step explanation:

1. Think about what numbers multiply to -20: -10 and 2, 10 and -2, -20 and 1, 20 and -1, 4 and -5, -4 and 5

2. Then, think about which of the above adds to -8. This leaves you with -10 and 2

7 0

2 years ago

Read 2 more answers

Graph ARST with vertices R(6, 6), S(3, -6), and T(0, 3) and its image after a

padilas [110]

Answer:

The answer is the second figure and the vertices of Δ R'S'T' are:

R' = (-6 , 6) , S' = (-3 , -6) , T' = (0 , 3)

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) reflected across the x-axis

∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

∴ Its image is (-y , -x)

- Now we can solve the problem

∵ R = (6 , 6) , S = (3 , -6) , T = (0 , 3), they are the vertices of ΔRST

- The triangle RST is reflected over the y-axis

- According to the rule above the signs of x-coordinates will change

∵ R = (6 , 6)

∴ Its image is (-6 , 6)

∵ S = (3 , -6)

∴ Its image is (-3 , -6)

∵ T = (0 , 3)

∴ Its image is (0 , 3)

* Now lets look to the figure to find the correct answers

- The image of Δ RST is ΔR'S'T'

∵ The vertices of the image of ΔRST are:

R' = (-6 , 6) , S' = (-3 , -6) , T' = (0 , 3)

* The answer is the second figure

7 0

3 years ago

How do I find the arc length with given radius & central angel?

ella [17]

The length of an arc subtended by a central angle is proportional to the circle's circumference. If the given central angle has measure $\theta$ and the circle has radius $r$ , then the arc has length $\ell$ such that

$\dfrac{\ell}\theta=\dfrac{2\pi r}{2\pi}=r$

where $\theta$ is given in radians. Then

$\ell=r\theta$

If $\theta$ is given in degrees, then

$\dfrac{\ell}\theta=\dfrac{2\pi r}{360}\implies\ell=\dfrac{\theta\pi r}{180}$

8 0

3 years ago