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MAXImum [283]
2 years ago
5

9. Find the value of b so that the slope of the line passing through the points A(5, - 8) and B(- 1, b) is -2

Mathematics
1 answer:
gtnhenbr [62]2 years ago
4 0

Answer:

The value of b is 4.

Step-by-step explanation:

First, find the y-intercept.

y = mx + b

-8 = -2(5) + b

-8 = -10 + b

2 = b

So now our equation is y = -2x + 2. Now plug in the values.

y = -2(-1) + 2

y = 4  

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What is the 11th term of the geometric sequence with this explicit formula?<br> an = 5.(-2)(n-1)
erastova [34]

Answer:

5,120

Step-by-step explanation:

an = 5.(-2)^(n-1)

a11 = 5.(-2)^(11-1)

= 5.(-2)^10

= 5.(1,024)

= 5,120

7 0
2 years ago
5. Write the slope-intercept form of the equation that passes through the point (-1, 2) and is perpendicular to the line y = 3/2
kap26 [50]

Answer:

D.  y = -2/3 x + 4/3

Step-by-step explanation:

When you have a perpendicular line, everything except the y-intercept becomes opposite. So 3/2x + 6 will become -2/3x.

To find the slope, you have to plug the coordinates into the equation so far which is y = -2/3x + b

y = -2/3x + b

2 = -2/3(-1) + b

2 = 2/3 + b

4/3 = b

So the equation is y = -2/3 x + 4/3.

6 0
3 years ago
13. Write an equation for the given function given the amplitude, period, phase shift, and vertical shift.
Paul [167]

Answer:

y=4sin(\frac{2\pi(t+\frac{4}{3}\pi ) }{4\pi } )-2

Step-by-step explanation:

Let's start with the original function.

y=a sin\frac{2\pi t}{T}

We can immediately fill in the amplitude 'a' and period 'T' , as the question defines these for us, and provides values for 'a' and 'T', 4 and 4\pi respectively.

y=4sin(\frac{2\pi t}{4\pi } )

Now we only have phase shift and vertical shift to do. Vertical shift is very easy, you can just add it to the end of the right side of the expression. A positive value will shift the graph up, while a negative value will move shift the graph down. We have '-2' as our value for vertical shift, so we can add that on as so:

y=4sin(\frac{2\pit }{4\pi } )-2

Now phase shift the most complicated of the transformations. Basically, it is just movement left or right. A negative phase shift moves the graph right, a positive phase shift moves the graph left (I know, confusing!). Phase shift applies directly to the x variable, or in this case the t variable. To achieve a -4/3 pi phase shift, we need to input +4/3 pi into the function, because of the aforementioned negative positive rule. Here is what the function looks like with the correct phase shift:

y=4sin(\frac{2\pi(t+\frac{4}{3}\pi ) }{4\pi } )-2

This function has vertical shift -2, phase shift -4/3 \pi, amplitude 4, and period 4\pi.

Desmos.com/calculator is a great tool for learning about how various parts of an equation affect the graph of the function, If you want you can input each step of this problem into desmos and watch the graph change to match the criteria.

8 0
3 years ago
MATH: EXPONENTIAL WORK PROBLEM 1. HELP PLEASE! 13 pts
Strike441 [17]

The amount of the radioactive substance is 374.6 g

<h3>How to determine the amount of radioactive substance?</h3>

The given parameters are:

  • Initial, a = 424 mg
  • Rate, r = 6%
  • Time, t = 2 hours

The amount of the radioactive substance is calculated as:

A(t) = a(1 - r)^t

This gives

A(t) = 424 * (1 - 6%)^t

At 2 hours, we have:

A(2) = 424 * (1 - 6%)^2

Evaluate

A(2) = 374.6

Hence, the amount of the radioactive substance is 374.6 g

Read more about exponential functions at:

brainly.com/question/2456547

#SPJ1

4 0
2 years ago
Find the missing measurement for each figure.
earnstyle [38]

To find h, divide the area by the base:

h = 2442 / 12 = 203.5 km.

6 0
3 years ago
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