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3 years ago

Find the slope of the line and that passes through (7, 2) and (-7, 48)

Mathematics

1 answer:

Vedmedyk [2.9K]3 years ago

7 0

Answer:

-23/7

Step-by-step explanation:

y2 - y1 / x2 - x1

48 - 2 / -7 - 7

46 / -14

= -23/7

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Consider the first four terms of the sequence below. -3, -12, -48, -192, . . . What is the 8th term of this sequence? A. -49,152

kolbaska11 [484]

Answer:

Step-by-step explanation:

there is a common ratio between consecutive terms , that is

- 12 ÷ - 3 = - 48 ÷ - 12 = - 192 ÷ - 48 = 4

this indicates the sequence is geometric with nth term

$a_{n}$ = a₁ $r^{n-1}$

where a₁ is the first term and r the common ratio

here a₁ = - 3 and r = 4 , then

a₈ = - 3 × $4^{7}$ = - 3 × 16,384 = - 49,152

7 0

1 year ago

The blue string is 0.98 meters long. The

Yuliya22 [10]

Answer:

22 centimeters

Step-by-step explanation:

1. See how many centimeters are in a meter:

There is 100 centimeters in one meter

2. Multiply each number by 100 to convert the meters to centimeters 

0.98 x 100= 98

0.76 x 100 = 76

3. Subtract to find the difference

98 - 76 = 22

Hence, the blue string is 22 centimeters longer than the yellow string.

have great night! :D

4 0

2 years ago

General solutions of sin(x-90)+cos(x+270)=-1 {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

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