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3 years ago

Thrice the difference between X and 4 is less than 9

1 answer:

4 0

Thrice means three, so 3 times the difference of x and 4.

3(x - 4) < 9
multiply 3 by all in parentheses
(3*x) + (3*-4) < 9
3x - 12 < 9
add 12 to both sides
3x < 21
divide both sides by 3
x < 7

ANSWER: x < 7

Hope this helps! :)

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Pip and Sara win some money and share it in ratio 5:4 pip gets £50 how much did they get all together

N76 [4]

Answer: £90

Step-by-step explanation:

Pip and Sara get some money. They share it in the ratio 5 : 4.

Pip gets £50 so what did Sara get:

Use direct proportion:

5 : 4

50 : x

5x = 200

x = 200/5

x = £40

Pip got £50 and Sara got £40.

Together they got:

= 50 + 40

= £90

4 0

2 years ago

General solutions of sin(x-90)+cos(x+270)=-1<br> {both 90 and 270 are in degrees}

mixer [17]

Answer:

$\left[\begin{array}{l}x=2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{2}+2\pi k,\ k\in Z\end{array}\right.$

Step-by-step explanation:

Given:

$\sin (x-90^{\circ})+\cos(x+270^{\circ})=-1$

First, note that

$\sin (x-90^{\circ})=-\cos x\\ \\\cos(x+270^{\circ})=\sin x$

So, the equation is

$-\cos x+\sin x= -1$

Multiply this equation by $\frac{\sqrt{2}}{2}:$

$-\dfrac{\sqrt{2}}{2}\cos x+\dfrac{\sqrt{2}}{2}\sin x= -\dfrac{\sqrt{2}}{2}\\ \\\dfrac{\sqrt{2}}{2}\cos x-\dfrac{\sqrt{2}}{2}\sin x=\dfrac{\sqrt{2}}{2}\\ \\\cos 45^{\circ}\cos x-\sin 45^{\circ}\sin x=\dfrac{\sqrt{2}}{2}\\ \\\cos (x+45^{\circ})=\dfrac{\sqrt{2}}{2}$

The general solution is

$x+45^{\circ}=\pm \arccos \left(\dfrac{\sqrt{2}}{2}\right)+2\pi k,\ \ k\in Z\\ \\x+\dfrac{\pi }{4}=\pm \dfrac{\pi }{4}+2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{4}\pm \dfrac{\pi }{4}+2\pi k,\ \ k\in Z\\ \\\left[\begin{array}{l}x=2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{2}+2\pi k,\ k\in Z\end{array}\right.$

4 0

3 years ago

One liter is approximately 34 ounces. A 2-liter soda bottle can hold how many 12-ounce

Zielflug [23.3K]

64 oz / 12 oz = between 5 and 6 cans

4 0

2 years ago

2x+3y= -1<br> 3x+4y = -4

Mariana [72]

Answer:

Point Form- (-8,5)

Equation Form- x= -8, y= 5

Add the equations in order to solve for the first variable. Plug this value into the other equation in order to solve for the remaining variables.

3 0

3 years ago

Some the equation 4y-6x=12 for y.

antoniya [11.8K]

Answer:

y = 3 + 1.5x

Step-by-step explanation:

4y = 12 + 6x

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Divide each side by '4'.

y = 3 + 1.5x

Simplifying

y = 3 + 1.5x

7 0

3 years ago