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3 years ago

-18,-13,-8,-3,.... Find the above sequential formula

Mathematics

1 answer:

zhuklara [117]3 years ago

5 0

The first term (a) is - 18

You add 5 to get to the next term. Or you can solve it by taking any 2 consecutive terms and find their difference.

Formula

d = t4- t3

Givens

t4 = - 3

t3 = - 8

Solution 1

d = t4 - t3 Substitute

d = -3 - ( - 8) Remove the brackets

d = -3 + 8 Combine

d = 5 Difference

Remark

Find the general formula

tn = - a + (n - 1)d Substitute

So term 20 = Example

t20 = -18 + (20 - 1)*5 Combine the inside of the brackets. Remove the brackets

t20 = - 18 + 19*5 Combine 19 and 5

t20 = -18 + 95 "Subtract"

t20 = 77 Answer

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3 years ago

Solve by graphing u=v and 6u=2v-24

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Answer:

$u=-6 \\ \\ v=-6$

Step-by-step explanation:

In this exercise, we have two equations, namely:

$u=v \ and \ 6u=2v-24$

And we are asked to solve this problem by graphing. In this way, we can write a system of linear equations in two variables, but first of all, let's rewrite:

$u=y \\ \\ v=x$

Then:

$\left\{ \begin{array}{c}y=x\\6y=2x-24\end{array}\right.$

So here we have two lines.

The first one is:

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This line passes through the origin and has a slope $m=1$

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This line has a slope $m=\frac{1}{3}$ and cuts the y-axis at $b=-4$

By using graph tools, we get the graph shown below, then:

$x=-6 \\ \\ y=-6 \\ \\ \\ Since \ u=y \ and \ v=x, then: \\ \\ u=-6 \\ \\ v=-6$

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3 years ago

A boutique prices merchandise by adding 80% to its cost. It later decreases by 25% the price of items that do not sell quickly

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A. Write a function f(x) to represent the price after the 80% markup.
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c. Use a composition function to find the price of an item after both price adjustments that originally costs the boutique $150. 
d. Does the order in which the adjustments are applied make a difference? Explain.

answers

a) f(x) = 1.8x

b) f(x) = 0.75(1.8x)

c) f(150) = 0.75(1.8(150) = $202.50

d) No, it doesn't matter. The result is the same.

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